https://en.xen.wiki/api.php?action=feedcontributions&feedformat=atom&user=Keenan+Pepper Xenharmonic Wiki - User contributions [en] 2026-06-04T16:57:38Z User contributions MediaWiki 1.43.6 https://en.xen.wiki/index.php?title=Lumatone_mapping_for_Amity&diff=188642 Lumatone mapping for Amity 2025-03-28T21:35:07Z <p>Keenan Pepper: Keenan Pepper moved page Lumatone mapping for Amity to Lumatone mapping for amity: consistency</p> <hr /> <div>#REDIRECT [[Lumatone mapping for amity]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Lumatone_mapping_for_amity&diff=188641 Lumatone mapping for amity 2025-03-28T21:35:07Z <p>Keenan Pepper: Keenan Pepper moved page Lumatone mapping for Amity to Lumatone mapping for amity: consistency</p> <hr /> <div>This is a keyboard mapping which is useful for [[Amity_family#Hitchcock|hitchcock]] temperament and other members of the [[Amity family]].<br /> <br /> {{Lumatone mapping|<br /> <br /> {{Lumatone key|x=4|y=1|label=−14}}<br /> {{Lumatone key|x=5|y=1|label=−17}}<br /> <br /> {{Lumatone key|x=4|y=2|label=−7}}<br /> {{Lumatone key|x=5|y=2|label=−10}}<br /> {{Lumatone key|x=6|y=2|label=−13}}<br /> {{Lumatone key|x=7|y=2|label=−16}}<br /> {{Lumatone key|x=8|y=2|label=−19}}<br /> <br /> {{Lumatone key|x=4|y=3|label=0}}<br /> {{Lumatone key|x=5|y=3|label=−3}}<br /> {{Lumatone key|x=6|y=3|label=−6}}<br /> {{Lumatone key|x=7|y=3|label=−9}}<br /> {{Lumatone key|x=8|y=3|label=−12}}<br /> {{Lumatone key|x=9|y=3|label=−15}}<br /> {{Lumatone key|x=10|y=3|label=−18}}<br /> <br /> {{Lumatone key|x=5|y=4|label=+4}}<br /> {{Lumatone key|x=6|y=4|label=+1}}<br /> {{Lumatone key|x=7|y=4|label=−2}}<br /> {{Lumatone key|x=8|y=4|label=−5}}<br /> {{Lumatone key|x=9|y=4|label=−8}}<br /> {{Lumatone key|x=10|y=4|label=−11}}<br /> <br /> {{Lumatone key|x=5|y=5|label=+11}}<br /> {{Lumatone key|x=6|y=5|label=+8}}<br /> {{Lumatone key|x=7|y=5|label=+5}}<br /> {{Lumatone key|x=8|y=5|label=+2}}<br /> {{Lumatone key|x=9|y=5|label=−1}}<br /> {{Lumatone key|x=10|y=5|label=−4}}<br /> <br /> {{Lumatone key|x=5|y=6|label=+18}}<br /> {{Lumatone key|x=6|y=6|label=+15}}<br /> {{Lumatone key|x=7|y=6|label=+12}}<br /> {{Lumatone key|x=8|y=6|label=+9}}<br /> {{Lumatone key|x=9|y=6|label=+6}}<br /> {{Lumatone key|x=10|y=6|label=+3}}<br /> <br /> {{Lumatone key|x=7|y=7|label=+19}}<br /> {{Lumatone key|x=8|y=7|label=+16}}<br /> {{Lumatone key|x=9|y=7|label=+13}}<br /> {{Lumatone key|x=10|y=7|label=+10}}<br /> {{Lumatone key|x=11|y=7|label=+7}}<br /> <br /> {{Lumatone key|x=10|y=8|label=+17}}<br /> {{Lumatone key|x=11|y=8|label=+14}}<br /> <br /> {{Lumatone key|x=11|y=4|label=−14}}<br /> {{Lumatone key|x=12|y=4|label=−17}}<br /> <br /> {{Lumatone key|x=11|y=5|label=−7}}<br /> {{Lumatone key|x=12|y=5|label=−10}}<br /> {{Lumatone key|x=13|y=5|label=−13}}<br /> {{Lumatone key|x=14|y=5|label=−16}}<br /> {{Lumatone key|x=15|y=5|label=−19}}<br /> <br /> {{Lumatone key|x=11|y=6|label=0}}<br /> {{Lumatone key|x=12|y=6|label=−3}}<br /> {{Lumatone key|x=13|y=6|label=−6}}<br /> {{Lumatone key|x=14|y=6|label=−9}}<br /> {{Lumatone key|x=15|y=6|label=−12}}<br /> {{Lumatone key|x=16|y=6|label=−15}}<br /> {{Lumatone key|x=17|y=6|label=−18}}<br /> <br /> {{Lumatone key|x=12|y=7|label=+4}}<br /> {{Lumatone key|x=13|y=7|label=+1}}<br /> {{Lumatone key|x=14|y=7|label=−2}}<br /> {{Lumatone key|x=15|y=7|label=−5}}<br /> {{Lumatone key|x=16|y=7|label=−8}}<br /> {{Lumatone key|x=17|y=7|label=−11}}<br /> <br /> {{Lumatone key|x=12|y=8|label=+11}}<br /> {{Lumatone key|x=13|y=8|label=+8}}<br /> {{Lumatone key|x=14|y=8|label=+5}}<br /> {{Lumatone key|x=15|y=8|label=+2}}<br /> {{Lumatone key|x=16|y=8|label=−1}}<br /> {{Lumatone key|x=17|y=8|label=−4}}<br /> <br /> {{Lumatone key|x=12|y=9|label=+18}}<br /> {{Lumatone key|x=13|y=9|label=+15}}<br /> {{Lumatone key|x=14|y=9|label=+12}}<br /> {{Lumatone key|x=15|y=9|label=+9}}<br /> {{Lumatone key|x=16|y=9|label=+6}}<br /> {{Lumatone key|x=17|y=9|label=+3}}<br /> <br /> {{Lumatone key|x=14|y=10|label=+19}}<br /> {{Lumatone key|x=15|y=10|label=+16}}<br /> {{Lumatone key|x=16|y=10|label=+13}}<br /> {{Lumatone key|x=17|y=10|label=+10}}<br /> {{Lumatone key|x=18|y=10|label=+7}}<br /> <br /> {{Lumatone key|x=17|y=11|label=+17}}<br /> {{Lumatone key|x=18|y=11|label=+14}}<br /> <br /> {{Lumatone key|x=18|y=7|label=−14}}<br /> {{Lumatone key|x=19|y=7|label=−17}}<br /> <br /> {{Lumatone key|x=18|y=8|label=−7}}<br /> {{Lumatone key|x=19|y=8|label=−10}}<br /> {{Lumatone key|x=20|y=8|label=−13}}<br /> {{Lumatone key|x=21|y=8|label=−16}}<br /> {{Lumatone key|x=22|y=8|label=−19}}<br /> <br /> {{Lumatone key|x=18|y=9|label=0}}<br /> {{Lumatone key|x=19|y=9|label=−3}}<br /> {{Lumatone key|x=20|y=9|label=−6}}<br /> {{Lumatone key|x=21|y=9|label=−9}}<br /> {{Lumatone key|x=22|y=9|label=−12}}<br /> {{Lumatone key|x=23|y=9|label=−15}}<br /> {{Lumatone key|x=24|y=9|label=−18}}<br /> <br /> {{Lumatone key|x=19|y=10|label=+4}}<br /> {{Lumatone key|x=20|y=10|label=+1}}<br /> {{Lumatone key|x=21|y=10|label=−2}}<br /> {{Lumatone key|x=22|y=10|label=−5}}<br /> {{Lumatone key|x=23|y=10|label=−8}}<br /> {{Lumatone key|x=24|y=10|label=−11}}<br /> <br /> {{Lumatone key|x=19|y=11|label=+11}}<br /> {{Lumatone key|x=20|y=11|label=+8}}<br /> {{Lumatone key|x=21|y=11|label=+5}}<br /> {{Lumatone key|x=22|y=11|label=+2}}<br /> {{Lumatone key|x=23|y=11|label=−1}}<br /> {{Lumatone key|x=24|y=11|label=−4}}<br /> <br /> {{Lumatone key|x=19|y=12|label=+18}}<br /> {{Lumatone key|x=20|y=12|label=+15}}<br /> {{Lumatone key|x=21|y=12|label=+12}}<br /> {{Lumatone key|x=22|y=12|label=+9}}<br /> {{Lumatone key|x=23|y=12|label=+6}}<br /> {{Lumatone key|x=24|y=12|label=+3}}<br /> <br /> {{Lumatone key|x=21|y=13|label=+19}}<br /> {{Lumatone key|x=22|y=13|label=+16}}<br /> {{Lumatone key|x=23|y=13|label=+13}}<br /> {{Lumatone key|x=24|y=13|label=+10}}<br /> {{Lumatone key|x=25|y=13|label=+7}}<br /> <br /> {{Lumatone key|x=24|y=14|label=+17}}<br /> {{Lumatone key|x=25|y=14|label=+14}}<br /> <br /> {{Lumatone key|x=25|y=12|label=0}}<br /> }}<br /> <br /> [[Category:Lumatone mappings]]<br /> [[Category:Hitchcock]]<br /> [[Category:Amity family]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Middle_Path_table_of_11-limit_rank-2_temperaments&diff=145303 Middle Path table of 11-limit rank-2 temperaments 2024-05-29T21:24:07Z <p>Keenan Pepper: we changed &quot;cassandra&quot; to &quot;andromeda&quot; but this instance didn&#039;t get updated</p> <hr /> <div>This table is supposed to be the best guess at what would have appeared in [[:File:MiddlePath2015.pdf|A Middle Path]] Part 2, had [[Paul_Erlich|Paul Erlich]] finished it. It is similar to the [[Middle_Path_table_of_five-limit_rank_two_temperaments|Middle Path table of five-limit rank two temperaments]] and [[Middle_Path_table_of_seven-limit_rank_two_temperaments|Middle Path table of seven-limit rank two temperaments]] from Part 1. It is intended to comprise all possible 11-limit 2D cases where complexity/7.65 + damage/10 &amp;lt; 1.<br /> <br /> {| class=&quot;wikitable&quot;<br /> |-<br /> | | Commas<br /> | | Name<br /> | | TOP<br /> <br /> period<br /> | | TOP<br /> <br /> generator<br /> | | Mapping<br /> | | Cmplx<br /> | | TOP<br /> <br /> Dmg<br /> | | ETs<br /> |-<br /> | | 36/35, 50/49, 64/63, 81/80, 126/125...<br /> | | [[Duodecim|Duodecim]]<br /> | | 99.59<br /> | | 31.48<br /> | | [&amp;lt;12 19 28 34 42|, &amp;lt;0 0 0 0 -1|]<br /> | | 2.59<br /> | | 6.14<br /> | | [[24edo|24d]], [[36edo|36d]], 48cdde, (48cdd)...<br /> |-<br /> | | 45/44, 56/55, 81/80, 100/99, 125/121...<br /> | | [[Meanenneadecal|Meanenneadecal]]<br /> | | 1198.56<br /> | | 503.60<br /> | | [&amp;lt;1 2 4 7 6|, &amp;lt;0 -1 -4 -10 -6|]<br /> | | 3.06<br /> | | 5.32<br /> | | [[31edo|31e]], [[50edo|50ee]], (62eee), 69dee, 81eee...<br /> |-<br /> | | 36/35, 56/55, 64/63, 81/80, 99/98...<br /> | | [[dominant|Dominant]]<br /> | | 1195.04<br /> | | 495.58<br /> | | [&amp;lt;1 2 4 2 1|, &amp;lt;0 -1 -4 2 6|]<br /> | | 3.08<br /> | | 4.96<br /> | | [[29edo|29cde]], 41cdee, 53cddeee...<br /> |-<br /> | | 49/48, 56/55, 77/75, 121/120, 176/175...<br /> | | [[Triforce|Triforce]]<br /> | | 399.80<br /> | | 155.57<br /> | | [&amp;lt;3 4 7 8 10|, &amp;lt;0 2 0 1 1|]<br /> | | 3.22<br /> | | 5.29<br /> | | [[39edo|39]], 54cd, 69bcd, (78cd), 93bccdd...<br /> |-<br /> | | 45/44, 50/49, 81/80, 99/98, 100/99...<br /> | | [[Injera|Injera]]<br /> | | 601.24<br /> | | 92.99<br /> | | [&amp;lt;2 3 4 5 6|, &amp;lt;0 1 4 4 6|]<br /> | | 3.38<br /> | | 4.06<br /> | | [[26edo|26]], [[38edo|38e]], 50dee, (52c), 64ce, 66bcc...<br /> |-<br /> | | 33/32, 49/48, 77/75, 99/98, 176/175...<br /> | | [[Negric|Negric]]<br /> | | 1205.30<br /> | | 129.26<br /> | | [&amp;lt;1 2 2 3 3|, &amp;lt;0 -4 3 -2 4|]<br /> | | 3.52<br /> | | 5.30<br /> | | [[28edo|28de]], (56bddeee), (84bbdddeeeee)...<br /> |-<br /> | | 56/55, 64/63, 100/99, 126/125, 176/175...<br /> | | [[Augene|Augene]]<br /> | | 398.88<br /> | | 87.10<br /> | | [&amp;lt;3 5 7 8 10|, &amp;lt;0 -1 0 2 2|]<br /> | | 3.66<br /> | | 3.37<br /> | | [[27edo|27e]], [[39edo|39dee]], 42e, (54cee), 57bce...<br /> |-<br /> | | 45/44, 49/48, 81/80, 100/99, 125/121...<br /> | | [[Godzilla|Godzilla]]<br /> | | 1204.09<br /> | | 254.92<br /> | | [&amp;lt;1 2 4 3 6|, &amp;lt;0 -2 -8 -1 -12|]<br /> | | 3.71<br /> | | 4.09<br /> | | [[33edo|33cd]], 52cd, (66bccdd), 71bcdd...<br /> |-<br /> | | 50/49, 55/54, 99/98, 100/99, 121/120...<br /> | | [[Hedgehog|Hedgehog]]<br /> | | 599.09<br /> | | 163.15<br /> | | [&amp;lt;2 4 6 7 8|, &amp;lt;0 -3 -5 -5 -4|]<br /> | | 3.75<br /> | | 3.23<br /> | | [[22edo|22]], 36ce, (44), 52bdd, 58ce, (66d)...<br /> |-<br /> | | 49/48, 55/54, 77/75, 126/125, 176/175...<br /> | | [[Darjeeling|Darjeeling]]<br /> | | 1202.79<br /> | | 318.16<br /> | | [&amp;lt;1 0 1 2 0|, &amp;lt;0 6 5 3 13|]<br /> | | 3.81<br /> | | 4.41<br /> | | [[34edo|34e]], 53dee, (68dee), 83ddee...<br /> |-<br /> | | 56/55, 64/63, 77/75, 121/120, 392/375...<br /> | | [[Progress|Progress]]<br /> | | 1195.64<br /> | | 559.36<br /> | | [&amp;lt;1 3 0 0 3|, &amp;lt;0 -3 5 6 1|]<br /> | | 3.81<br /> | | 4.51<br /> | | [[47edo|47bc]], 62bcce, (94bbccce)...<br /> |-<br /> | | 55/54, 64/63, 100/99, 121/120, 176/175...<br /> | | [[Porcupine|Porcupine]]<br /> | | 1198.23<br /> | | 163.15<br /> | | [&amp;lt;1 2 3 2 4|, &amp;lt;0 -3 -5 6 -4|]<br /> | | 3.90<br /> | | 3.18<br /> | | [[22edo|22]], [[37edo|37]], (44), 52b, 59, (66d), 67b...<br /> |-<br /> | | 49/48, 56/55, 100/99, 126/125, 343/330...<br /> | | [[Keemun|Keemun]]<br /> | | 1200.82<br /> | | 318.18<br /> | | [&amp;lt;1 0 1 2 4|, &amp;lt;0 6 5 3 -2|]<br /> | | 4.05<br /> | | 4.50<br /> | | [[83edo|83dde]], 117bddee, 151bdddeee...<br /> |-<br /> | | 49/48, 81/80, 126/125, 225/224, 245/243...<br /> | | [[Undevigintone|Undevigintone]]<br /> | | 63.36<br /> | | 30.42<br /> | | [&amp;lt;19 30 44 53 66|, &amp;lt;0 0 0 0 -1|]<br /> | | 4.07<br /> | | 3.83<br /> | | [[38edo|38d]], 57dd, 57ddee, 76dd, (76dde)...<br /> |-<br /> | | 50/49, 64/63, 99/98, 100/99, 176/175...<br /> | | [[pajara|Pajara]]<br /> | | 598.45<br /> | | 106.57<br /> | | [&amp;lt;2 3 5 6 8|, &amp;lt;0 1 -2 -2 -6|]<br /> | | 4.17<br /> | | 3.11<br /> | | [[22edo|22]], [[34edo|34d]], (44), 46de, 56d, 58ddee...<br /> |-<br /> | | 49/48, 55/54, 100/99, 121/120, 250/243...<br /> | | [[Nautilus|Nautilus]]<br /> | | 1202.66<br /> | | 82.97<br /> | | [&amp;lt;1 2 3 3 4|, &amp;lt;0 -6 -10 -3 -8|]<br /> | | 4.21<br /> | | 3.48<br /> | | [[29edo|29]], (58cde), 72ccddee, 73cde...<br /> |-<br /> | | 45/44, 81/80, 100/99, 125/121, 385/384...<br /> | | [[Flattone|Flattone]]<br /> | | 1203.00<br /> | | 508.77<br /> | | [&amp;lt;1 2 4 -1 6|, &amp;lt;0 -1 -4 9 -6|]<br /> | | 4.30<br /> | | 4.06<br /> | | [[26edo|26]], [[45edo|45]], (52c), 64cde, 71bc, (78bcc)...<br /> |-<br /> | | 50/49, 55/54, 64/63, 225/224, 385/384...<br /> | | [[Pajarous|Pajarous]]<br /> | | 599.29<br /> | | 108.86<br /> | | [&amp;lt;2 3 5 6 6|, &amp;lt;0 1 -2 -2 5|]<br /> | | 4.44<br /> | | 3.27<br /> | | [[22edo|22]], (44), (66d), (88bd), 98bcd...<br /> |-<br /> | | 56/55, 81/80, 128/125, 176/175, 245/242...<br /> | | [[Catnip|Catnip]]<br /> | | 99.81<br /> | | 31.73<br /> | | [&amp;lt;12 19 28 34 42|, &amp;lt;0 0 0 -1 -1|]<br /> | | 4.48<br /> | | 3.56<br /> | | [[36edo|36]], [[48edo|48ce]], (72ce), 84cee, (96cceee)...<br /> |-<br /> | | 55/54, 99/98, 176/175, 225/224, 245/243...<br /> | | [[Telepathy|Telepathy]]<br /> | | 1199.00<br /> | | 381.39<br /> | | [&amp;lt;1 0 2 -1 -1|, &amp;lt;0 5 1 12 14|]<br /> | | 4.52<br /> | | 3.15<br /> | | [[22edo|22]], [[41edo|41e]], (44), 63e, (66d), (82eee)...<br /> |-<br /> | | 55/54, 100/99, 121/120, 225/224, 250/243...<br /> | | [[Porky|Porky]]<br /> | | 1198.78<br /> | | 163.50<br /> | | [&amp;lt;1 2 3 5 4|, &amp;lt;0 -3 -5 -16 -4|]<br /> | | 4.61<br /> | | 3.22<br /> | | [[22edo|22]], [[29edo|29]], (44), 51, (58cde), (66d)...<br /> |-<br /> | | 56/55, 100/99, 126/125, 245/243, 540/539...<br /> | | [[Sensis|Sensis]]<br /> | | 1196.58<br /> | | 442.49<br /> | | [&amp;lt;1 -1 -1 -2 2|, &amp;lt;0 7 9 13 4|]<br /> | | 4.68<br /> | | 3.42<br /> | | [[27edo|27e]], (54cee), 73ee, (81bcdeee)...<br /> |-<br /> | | 55/54, 64/63, 99/98, 245/243, 352/343...<br /> | | [[Suprapyth|Suprapyth]]<br /> | | 1198.59<br /> | | 490.29<br /> | | [&amp;lt;1 2 6 2 1|, &amp;lt;0 -1 -9 2 6|]<br /> | | 4.68<br /> | | 3.18<br /> | | [[22edo|22]], (44), (66d), (88bd), 93bde...<br /> |-<br /> | | 50/49, 64/63, 225/224, 245/243, 250/243...<br /> | | [[Vigintiduo|Vigintiduo]]<br /> | | 54.48<br /> | | 10.51<br /> | | [&amp;lt;22 35 51 62 76|, &amp;lt;0 0 0 0 1|]<br /> | | 4.74<br /> | | 3.28<br /> | | [[66edo|66de]], 88bde, 110bdd, 110bddee...<br /> |-<br /> | | 81/80, 99/98, 126/125, 176/175, 225/224...<br /> | | [[Meantone|Meantone]]<br /> | | 1201.61<br /> | | 504.02<br /> | | [&amp;lt;1 2 4 7 11|, &amp;lt;0 -1 -4 -10 -18|]<br /> | | 4.96<br /> | | 1.74<br /> | | [[31edo|31]], [[43edo|43]], [[50edo|50e]], 55de, (62), 74, 81ee...<br /> |-<br /> | | 50/49, 55/54, 176/175, 352/343, 540/539...<br /> | | [[Fleetwood|Fleetwood]]<br /> | | 599.28<br /> | | 272.31<br /> | | [&amp;lt;2 5 6 7 11|, &amp;lt;0 -4 -3 -3 -9|]<br /> | | 4.96<br /> | | 3.27<br /> | | [[22edo|22]], (44), (66d), (88bd), (110bdde)...<br /> |-<br /> | | 50/49, 121/120, 176/175, 352/343, 385/384...<br /> | | [[Astrology|Astrology]]<br /> | | 599.32<br /> | | 217.89<br /> | | [&amp;lt;2 5 5 6 8|, &amp;lt;0 -5 -1 -1 -3|]<br /> | | 5.07<br /> | | 3.28<br /> | | [[22edo|22]], (44), (66d), (88bd), (110bdde)...<br /> |-<br /> | | 49/48, 55/54, 225/224, 441/440, 525/512...<br /> | | [[Negroni|Negroni]]<br /> | | 1203.19<br /> | | 124.84<br /> | | [&amp;lt;1 2 2 3 5|, &amp;lt;0 -4 3 -2 -15|]<br /> | | 5.11<br /> | | 3.19<br /> | | [[77edo|77cddee]], 106ccdddeee...<br /> |-<br /> | | 64/63, 99/98, 121/120, 352/343, 540/539...<br /> | | [[Quasisupra|Quasisupra]]<br /> | | 1197.34<br /> | | 490.80<br /> | | [&amp;lt;1 2 -3 2 1|, &amp;lt;0 -1 13 2 6|]<br /> | | 5.29<br /> | | 2.66<br /> | | [[39edo|39d]], 61d, (78cdd), 83d, 100bcdd...<br /> |-<br /> | | 99/98, 121/120, 176/175, 225/224, 385/384...<br /> | | [[Orwell|Orwell]]<br /> | | 1201.25<br /> | | 271.43<br /> | | [&amp;lt;1 0 3 1 3|, &amp;lt;0 7 -3 8 2|]<br /> | | 5.30<br /> | | 1.36<br /> | | [[31edo|31]], [[53edo|53]], (62), 75, 84e, (93e), 97de...<br /> |-<br /> | | 81/80, 99/98, 121/120, 441/440, 540/539...<br /> | | [[Squares|Squares]]<br /> | | 1201.70<br /> | | 426.46<br /> | | [&amp;lt;1 3 8 6 7|, &amp;lt;0 -4 -16 -9 -10|]<br /> | | 5.37<br /> | | 1.70<br /> | | [[31edo|31]], 45e, (62), 76e, 79c, 90bcdee...<br /> |-<br /> | | 64/63, 100/99, 176/175, 245/243, 540/539...<br /> | | [[Superpyth|Superpyth]]<br /> | | 1197.60<br /> | | 489.43<br /> | | [&amp;lt;1 2 6 2 10|, &amp;lt;0 -1 -9 2 -16|]<br /> | | 5.42<br /> | | 2.40<br /> | | [[49edo|49]], 71d, 76bcdee, 93bd, (98bde)...<br /> |-<br /> | | 121/120, 126/125, 176/175, 385/384, 441/440...<br /> | | [[Valentine|Valentine]]<br /> | | 1200.87<br /> | | 77.63<br /> | | [&amp;lt;1 1 2 3 3|, &amp;lt;0 9 5 -3 7|]<br /> | | 5.82<br /> | | 1.54<br /> | | [[31edo|31]], [[46edo|46]], (62), 77, (92), (93e), 107c...<br /> |-<br /> | | 81/80, 121/120, 176/175, 243/242, 385/384...<br /> | | [[Mohajira|Mohajira]]<br /> | | 1201.70<br /> | | 348.78<br /> | | [&amp;lt;1 1 0 6 2|, &amp;lt;0 2 8 -11 5|]<br /> | | 6.01<br /> | | 1.70<br /> | | [[31edo|31]], (62), (93e), (124be), 148be...<br /> |-<br /> | | 100/99, 225/224, 245/243, 385/384, 540/539...<br /> | | [[Magic|Magic]]<br /> | | 1200.75<br /> | | 380.92<br /> | | [&amp;lt;1 0 2 -1 6|, &amp;lt;0 5 1 12 -8|]<br /> | | 6.07<br /> | | 1.68<br /> | | [[41edo|41]], [[63edo|63]], (82), 104, (123c), (126c)...<br /> |-<br /> | | 81/80, 126/125, 225/224, 385/384, 540/539...<br /> | | [[Meanpop|Meanpop]]<br /> | | 1201.70<br /> | | 504.13<br /> | | [&amp;lt;1 2 4 7 -2|, &amp;lt;0 -1 -4 -10 13|]<br /> | | 6.08<br /> | | 1.70<br /> | | [[31edo|31]], [[50edo|50]], (62), 81, (93e), (100d), 112b...<br /> |-<br /> | | 81/80, 121/120, 126/125, 225/224, 243/242...<br /> | | [[Migration|Migration]]<br /> | | 1201.70<br /> | | 348.78<br /> | | [&amp;lt;1 1 0 -3 2|, &amp;lt;0 2 8 20 5|]<br /> | | 6.10<br /> | | 1.70<br /> | | [[31edo|31]], (62), (93e), 100de, (124be)...<br /> |-<br /> | | 99/98, 121/120, 126/125, 540/539, 891/875...<br /> | | [[Nusecond|Nusecond]]<br /> | | 1200.46<br /> | | 154.74<br /> | | [&amp;lt;1 3 4 5 5|, &amp;lt;0 -11 -13 -17 -12|]<br /> | | 6.13<br /> | | 1.70<br /> | | [[31edo|31]], (62), (93e), 101, (124be), 132ce...<br /> |-<br /> | | 100/99, 225/224, 245/242, 441/440, 625/616...<br /> | | [[Schismatic family#Andromeda|Andromeda]]<br /> | | 1201.36<br /> | | 497.94<br /> | | [&amp;lt;1 2 -1 -3 -4|, &amp;lt;0 -1 8 14 18|]<br /> | | 6.19<br /> | | 1.79<br /> | | [[152edo|152cd]], 193ccd, 234ccd, 263cccdd...<br /> |-<br /> | | 225/224, 243/242, 385/384, 441/440, 540/539...<br /> | | [[Miracle|Miracle]]<br /> | | 1200.63<br /> | | 116.72<br /> | | [&amp;lt;1 1 3 3 2|, &amp;lt;0 6 -7 -2 15|]<br /> | | 7.14<br /> | | 0.63<br /> | | [[72edo|72]], (144), (216c), (288cd), (360bcd)...<br /> |-<br /> | colspan=&quot;7&quot; | A BONUS TEMPERAMENT:<br /> | | <br /> |-<br /> | | 2401/2400, 3025/3024, 4375/4374, 9801/9800...<br /> | | [[Hemiennealimmal|Hemiennealimmal]]<br /> | | 66.67<br /> | | 17.64<br /> | | [&amp;lt;18 28 41 50 62|, &amp;lt;0 2 3 2 1|]<br /> | | 23.81<br /> | | 0.05<br /> | | <br /> |}<br /> <br /> ==Comparisons of closely related temperaments==<br /> <br /> {| class=&quot;wikitable&quot;<br /> |-<br /> | | 36/35, 50/49, 64/63, 81/80, 126/125...<br /> | | [[Duodecim|Duodecim]]<br /> | | 99.59<br /> | | 31.48<br /> | | [&amp;lt;12 19 28 34 42|, &amp;lt;0 0 0 0 -1|]<br /> | | 2.59<br /> | | 6.14<br /> | | [[24edo|24d]], [[36edo|36d]], 48cdde, (48cdd)...<br /> |-<br /> | | 56/55, 81/80, 128/125, 176/175, 245/242...<br /> | | [[Catnip|Catnip]]<br /> | | 99.81<br /> | | 31.73<br /> | | [&amp;lt;12 19 28 34 42|, &amp;lt;0 0 0 -1 -1|]<br /> | | 4.48<br /> | | 3.56<br /> | | [[36edo|36]], [[48edo|48ce]], (72ce), 84cee, (96cceee)...<br /> |}<br /> Since the TOP tunings of duodecim and catnip are so similar, there is little practical use for duodecim temperament. If notes so altered from 12edo are available, there is no reason not to use them for ratios of 7 as well as ratios of 11.<br /> <br /> {| class=&quot;wikitable&quot;<br /> |-<br /> | | 45/44, 56/55, 81/80, 100/99, 125/121...<br /> | | [[Meanenneadecal|Meanenneadecal]]<br /> | | 1198.56<br /> | | 503.60<br /> | | [&amp;lt;1 2 4 7 6|, &amp;lt;0 -1 -4 -10 -6|]<br /> | | 3.06<br /> | | 5.32<br /> | | [[31edo|31e]], [[50edo|50ee]], (62eee), 69dee, 81eee...<br /> |-<br /> | | 36/35, 56/55, 64/63, 81/80, 99/98...<br /> | | [[dominant|Dominant]]<br /> | | 1195.04<br /> | | 495.58<br /> | | [&amp;lt;1 2 4 2 1|, &amp;lt;0 -1 -4 2 6|]<br /> | | 3.08<br /> | | 4.96<br /> | | [[29edo|29cde]], 41cdee, 53cddeee...<br /> |-<br /> | | 45/44, 81/80, 100/99, 125/121, 385/384...<br /> | | [[Flattone|Flattone]]<br /> | | 1203.00<br /> | | 508.77<br /> | | [&amp;lt;1 2 4 -1 6|, &amp;lt;0 -1 -4 9 -6|]<br /> | | 4.30<br /> | | 4.06<br /> | | [[26edo|26]], [[45edo|45]], (52c), 64cde, 71bc, (78bcc)...<br /> |-<br /> | | 81/80, 99/98, 126/125, 176/175, 225/224...<br /> | | [[Meantone|Meantone]]<br /> | | 1201.61<br /> | | 504.02<br /> | | [&amp;lt;1 2 4 7 11|, &amp;lt;0 -1 -4 -10 -18|]<br /> | | 4.96<br /> | | 1.74<br /> | | [[31edo|31]], [[43edo|43]], [[50edo|50e]], 55de, (62), 74, 81ee...<br /> |-<br /> | | 81/80, 126/125, 225/224, 385/384, 540/539...<br /> | | [[Meanpop|Meanpop]]<br /> | | 1201.70<br /> | | 504.13<br /> | | [&amp;lt;1 2 4 7 -2|, &amp;lt;0 -1 -4 -10 13|]<br /> | | 6.08<br /> | | 1.70<br /> | | [[31edo|31]], [[50edo|50]], (62), 81, (93e), (100d), 112b...<br /> |}<br /> These temperaments all temper out 81/80, making them extensions of 5-limit meantone. The differences are in the mappings of 7 and 11.<br /> <br /> {| class=&quot;wikitable&quot;<br /> |-<br /> | | 36/35, 56/55, 64/63, 81/80, 99/98...<br /> | | [[dominant|Dominant]]<br /> | | 1195.04<br /> | | 495.58<br /> | | [&amp;lt;1 2 4 2 1|, &amp;lt;0 -1 -4 2 6|]<br /> | | 3.08<br /> | | 4.96<br /> | | [[29edo|29cde]], 41cdee, 53cddeee...<br /> |-<br /> | | 55/54, 64/63, 99/98, 245/243, 352/343...<br /> | | [[Suprapyth|Suprapyth]]<br /> | | 1198.59<br /> | | 490.29<br /> | | [&amp;lt;1 2 6 2 1|, &amp;lt;0 -1 -9 2 6|]<br /> | | 4.68<br /> | | 3.18<br /> | | [[22edo|22]], (44), (66d), (88bd), 93bde...<br /> |-<br /> | | 64/63, 99/98, 121/120, 352/343, 540/539...<br /> | | [[Quasisupra|Quasisupra]]<br /> | | 1197.34<br /> | | 490.80<br /> | | [&amp;lt;1 2 -3 2 1|, &amp;lt;0 -1 13 2 6|]<br /> | | 5.29<br /> | | 2.66<br /> | | [[39edo|39d]], 61d, (78cdd), 83d, 100bcdd...<br /> |-<br /> | | 64/63, 100/99, 176/175, 245/243, 540/539...<br /> | | [[Superpyth|Superpyth]]<br /> | | 1197.60<br /> | | 489.43<br /> | | [&amp;lt;1 2 6 2 10|, &amp;lt;0 -1 -9 2 -16|]<br /> | | 5.42<br /> | | 2.40<br /> | | [[49edo|49]], 71d, 76bcdee, 93bd, (98bde)...<br /> |}<br /> In contrast, these temperaments all temper out 64/63, making them extensions of [[Archy|archy]] temperament. The differences are in the mappings of 5 and 11. Temperaments in both this and the above list comprise the dominant family, which has only one representative here. Note that andromeda is in neither of the two families, because it preserves both 64/63 and 81/80 as non-vanishing intervals (and makes them both equal to the Pythagorean comma).<br /> <br /> {| class=&quot;wikitable&quot;<br /> |-<br /> | | 33/32, 49/48, 77/75, 99/98, 176/175...<br /> | | [[Negric|Negric]]<br /> | | 1205.30<br /> | | 129.26<br /> | | [&amp;lt;1 2 2 3 3|, &amp;lt;0 -4 3 -2 4|]<br /> | | 3.52<br /> | | 5.30<br /> | | [[28edo|28de]], (56bddeee), (84bbdddeeeee)...<br /> |-<br /> | | 49/48, 55/54, 225/224, 441/440, 525/512...<br /> | | [[Negroni|Negroni]]<br /> | | 1203.19<br /> | | 124.84<br /> | | [&amp;lt;1 2 2 3 5|, &amp;lt;0 -4 3 -2 -15|]<br /> | | 5.11<br /> | | 3.19<br /> | | [[77edo|77cddee]], 106ccdddeee...<br /> |}<br /> The difference is only in the mapping of 11. The two temperaments intersect in [[19edo|19edo]] (using the 19e val tempering out 33/32), which is a fine tuning for negric (despite that it doesn't show up in the list), but sub-optimal for negroni (which does not temper out 33/32).<br /> <br /> {| class=&quot;wikitable&quot;<br /> |-<br /> | | 50/49, 64/63, 99/98, 100/99, 176/175...<br /> | | [[pajara|Pajara]]<br /> | | 598.45<br /> | | 106.57<br /> | | [&amp;lt;2 3 5 6 8|, &amp;lt;0 1 -2 -2 -6|]<br /> | | 4.17<br /> | | 3.11<br /> | | [[22edo|22]], [[34edo|34d]], (44), 46de, 56d, 58ddee...<br /> |-<br /> | | 50/49, 55/54, 64/63, 225/224, 385/384...<br /> | | [[Pajarous|Pajarous]]<br /> | | 599.29<br /> | | 108.86<br /> | | [&amp;lt;2 3 5 6 6|, &amp;lt;0 1 -2 -2 5|]<br /> | | 4.44<br /> | | 3.27<br /> | | [[22edo|22]], (44), (66d), (88bd), 98bcd...<br /> |}<br /> The difference is only in the mapping of 11. The two temperaments intersect in [[22edo|22edo]], a fine tuning for both.<br /> <br /> {| class=&quot;wikitable&quot;<br /> |-<br /> | | 49/48, 55/54, 77/75, 126/125, 176/175...<br /> | | [[Darjeeling|Darjeeling]]<br /> | | 1202.79<br /> | | 318.16<br /> | | [&amp;lt;1 0 1 2 0|, &amp;lt;0 6 5 3 13|]<br /> | | 3.81<br /> | | 4.41<br /> | | [[34edo|34e]], 53dee, (68dee), 83ddee...<br /> |-<br /> | | 49/48, 56/55, 100/99, 126/125, 343/330...<br /> | | [[Keemun|Keemun]]<br /> | | 1200.82<br /> | | 318.18<br /> | | [&amp;lt;1 0 1 2 4|, &amp;lt;0 6 5 3 -2|]<br /> | | 4.05<br /> | | 4.50<br /> | | [[83edo|83dde]], 117bddee, 151bdddeee...<br /> |}<br /> The difference is only in the mapping of 11. The two intersect in [[15edo|15edo]], which is, however, not a great tuning for either. In 19edo, darjeeling uses the 19e val, which tempers out 33/32, whereas keemun uses the patent val.<br /> <br /> {| class=&quot;wikitable&quot;<br /> |-<br /> | | 55/54, 64/63, 100/99, 121/120, 176/175...<br /> | | [[Porcupine|Porcupine]]<br /> | | 1198.23<br /> | | 163.15<br /> | | [&amp;lt;1 2 3 2 4|, &amp;lt;0 -3 -5 6 -4|]<br /> | | 3.90<br /> | | 3.18<br /> | | [[22edo|22]], [[37edo|37]], (44), 52b, 59, (66d), 67b...<br /> |-<br /> | | 55/54, 100/99, 121/120, 225/224, 250/243...<br /> | | [[Porky|Porky]]<br /> | | 1198.78<br /> | | 163.50<br /> | | [&amp;lt;1 2 3 5 4|, &amp;lt;0 -3 -5 -16 -4|]<br /> | | 4.61<br /> | | 3.22<br /> | | [[22edo|22]], [[29edo|29]], (44), 51, (58cde), (66d)...<br /> |}<br /> The difference is only in the mapping of 7. The two intersect in [[22edo|22edo]], which is probably the only reasonable incarnation of porky temperament.<br /> <br /> {| class=&quot;wikitable&quot;<br /> |-<br /> | | 55/54, 99/98, 176/175, 225/224, 245/243...<br /> | | [[Telepathy|Telepathy]]<br /> | | 1199.00<br /> | | 381.39<br /> | | [&amp;lt;1 0 2 -1 -1|, &amp;lt;0 5 1 12 14|]<br /> | | 4.52<br /> | | 3.15<br /> | | [[22edo|22]], [[41edo|41e]], (44), 63e, (66d), (82eee)...<br /> |-<br /> | | 100/99, 225/224, 245/243, 385/384, 540/539...<br /> | | [[Magic|Magic]]<br /> | | 1200.75<br /> | | 380.92<br /> | | [&amp;lt;1 0 2 -1 6|, &amp;lt;0 5 1 12 -8|]<br /> | | 6.07<br /> | | 1.68<br /> | | [[41edo|41]], [[63edo|63]], (82), 104, (123c), (126c)...<br /> |}<br /> The difference is only in the mapping of 11. The two intersect in [[22edo|22edo]], which is a fine telepathy tuning but slightly sub-optimal for magic. Since telepathy is significantly higher in error, it can be regarded as an alternate version of magic that exists in 22edo.<br /> <br /> {| class=&quot;wikitable&quot;<br /> |-<br /> | | 81/80, 121/120, 176/175, 243/242, 385/384...<br /> | | [[Mohajira|Mohajira]]<br /> | | 1201.70<br /> | | 348.78<br /> | | [&amp;lt;1 1 0 6 2|, &amp;lt;0 2 8 -11 5|]<br /> | | 6.01<br /> | | 1.70<br /> | | [[31edo|31]], (62), (93e), (124be), 148be...<br /> |-<br /> | | 81/80, 121/120, 126/125, 225/224, 243/242...<br /> | | [[Migration|Migration]]<br /> | | 1201.70<br /> | | 348.78<br /> | | [&amp;lt;1 1 0 -3 2|, &amp;lt;0 2 8 20 5|]<br /> | | 6.10<br /> | | 1.70<br /> | | [[31edo|31]], (62), (93e), 100de, (124be)...<br /> |}<br /> The TOP tunings of mohajira and migration are not merely close, but exactly equal, because the prime 7 does not affect the TOP tuning. The two temperaments intersect in [[31edo|31edo]], which is also near-optimal for both.<br /> <br /> {| class=&quot;wikitable&quot;<br /> |-<br /> | | ET<br /> | | TOP damage<br /> | | TOP octave<br /> | | Rank-2 temperaments supported<br /> |-<br /> | | 22<br /> | | <br /> | | <br /> | | hedgehog, porcupine, pajara, pajarous, telepathy, porky, suprapyth, fleetwood, astrology<br /> |-<br /> | | 24d<br /> | | <br /> | | <br /> | | duodecim<br /> |-<br /> | | 26<br /> | | <br /> | | <br /> | | injera, flattone<br /> |-<br /> | | 27e<br /> | | <br /> | | <br /> | | augene, sensis<br /> |-<br /> | | 28de<br /> | | <br /> | | <br /> | | negric<br /> |-<br /> | | 29<br /> | | <br /> | | <br /> | | nautilus, porky<br /> |-<br /> | | 29cde<br /> | | <br /> | | <br /> | | dominant<br /> |-<br /> | | 31<br /> | | <br /> | | <br /> | | meantone, orwell, squares, valentine, mohajira, meanpop, migration, nusecond<br /> |-<br /> | | 31e<br /> | | <br /> | | <br /> | | meanenneadecal<br /> |-<br /> | | 33cd<br /> | | <br /> | | <br /> | | godzilla<br /> |-<br /> | | 34d<br /> | | <br /> | | <br /> | | pajara<br /> |-<br /> | | 34e<br /> | | <br /> | | <br /> | | darjeeling<br /> |-<br /> | | 36<br /> | | <br /> | | <br /> | | catnip<br /> |-<br /> | | 36ce<br /> | | <br /> | | <br /> | | hedgehog<br /> |-<br /> | | 36d<br /> | | <br /> | | <br /> | | duodecim<br /> |-<br /> | | 37<br /> | | <br /> | | <br /> | | porcupine<br /> |-<br /> | | 38d<br /> | | <br /> | | <br /> | | undevigintone<br /> |-<br /> | | 38e<br /> | | <br /> | | <br /> | | injera<br /> |-<br /> | | 39<br /> | | <br /> | | <br /> | | triforce<br /> |-<br /> | | 39d<br /> | | <br /> | | <br /> | | quasisupra<br /> |-<br /> | | 39dee<br /> | | <br /> | | <br /> | | augene<br /> |-<br /> | | 41<br /> | | <br /> | | <br /> | | magic<br /> |-<br /> | | 41cdee<br /> | | <br /> | | <br /> | | dominant<br /> |-<br /> | | 41e<br /> | | <br /> | | <br /> | | telepathy<br /> |-<br /> | | 42e<br /> | | <br /> | | <br /> | | augene<br /> |-<br /> | | 43<br /> | | <br /> | | <br /> | | meantone<br /> |-<br /> | | 44*<br /> | | <br /> | | <br /> | | hedgehog, porcupine, pajara, pajarous, telepathy, porky, suprapyth, fleetwood, astrology<br /> |-<br /> | | 45<br /> | | <br /> | | <br /> | | flattone<br /> |-<br /> | | 45e<br /> | | <br /> | | <br /> | | squares<br /> |-<br /> | | 46<br /> | | <br /> | | <br /> | | valentine<br /> |-<br /> | | 46de<br /> | | <br /> | | <br /> | | pajara<br /> |-<br /> | | 47bc<br /> | | <br /> | | <br /> | | progress<br /> |-<br /> | | 48cdd*<br /> | | <br /> | | <br /> | | duodecim<br /> |-<br /> | | 48cdde<br /> | | <br /> | | <br /> | | duodecim<br /> |-<br /> | | 48ce<br /> | | <br /> | | <br /> | | catnip<br /> |-<br /> | | 49<br /> | | <br /> | | <br /> | | superpyth<br /> |-<br /> | | 50<br /> | | <br /> | | <br /> | | meanpop<br /> |-<br /> | | 50dee<br /> | | <br /> | | <br /> | | injera<br /> |-<br /> | | 50e<br /> | | <br /> | | <br /> | | meantone<br /> |-<br /> | | 50ee<br /> | | <br /> | | <br /> | | meanenneadecal<br /> |-<br /> | | 51<br /> | | <br /> | | <br /> | | porky<br /> |-<br /> | | 52b<br /> | | <br /> | | <br /> | | porcupine<br /> |-<br /> | | 52bdd<br /> | | <br /> | | <br /> | | hedgehog<br /> |-<br /> | | 52c*<br /> | | <br /> | | <br /> | | injera, flattone<br /> |-<br /> | | 52cd<br /> | | <br /> | | <br /> | | godzilla<br /> |-<br /> | | 53<br /> | | <br /> | | <br /> | | orwell<br /> |-<br /> | | 53cddeee<br /> | | <br /> | | <br /> | | dominant<br /> |-<br /> | | 53dee<br /> | | <br /> | | <br /> | | darjeeling<br /> |-<br /> | | 54cd<br /> | | <br /> | | <br /> | | triforce<br /> |-<br /> | | 54cee*<br /> | | <br /> | | <br /> | | augene, sensis<br /> |-<br /> | | 55de<br /> | | <br /> | | <br /> | | meantone<br /> |-<br /> | | 56bddeee*<br /> | | <br /> | | <br /> | | negric<br /> |-<br /> | | 56d<br /> | | <br /> | | <br /> | | pajara<br /> |-<br /> | | 57bce<br /> | | <br /> | | <br /> | | augene<br /> |-<br /> | | 57dd<br /> | | <br /> | | <br /> | | undevigintone<br /> |-<br /> | | 57ddee<br /> | | <br /> | | <br /> | | undevigintone<br /> |-<br /> | | 58cde*<br /> | | <br /> | | <br /> | | nautilus, porky<br /> |-<br /> | | 58ce<br /> | | <br /> | | <br /> | | hedgehog<br /> |-<br /> | | 58ccddee*<br /> | | <br /> | | <br /> | | dominant<br /> |-<br /> | | 58ddee<br /> | | <br /> | | <br /> | | pajara<br /> |-<br /> | | 59<br /> | | <br /> | | <br /> | | porcupine<br /> |-<br /> | | 60cddd<br /> | | <br /> | | <br /> | | duodecim<br /> |-<br /> | | 60cdddee<br /> | | <br /> | | <br /> | | duodecim<br /> |-<br /> | | 61d<br /> | | <br /> | | <br /> | | quasisupra<br /> |-<br /> | | 62*<br /> | | <br /> | | <br /> | | meantone, orwell, squares, valentine, mohajira, meanpop, migration, nusecond<br /> |-<br /> | | 62bcce<br /> | | <br /> | | <br /> | | progress<br /> |-<br /> | | 62eee*<br /> | | <br /> | | <br /> | | meanenneadecal<br /> |-<br /> | | 63<br /> | | <br /> | | <br /> | | magic<br /> |-<br /> | | 63e<br /> | | <br /> | | <br /> | | telepathy<br /> |-<br /> | | 64cd<br /> | | <br /> | | <br /> | | injera<br /> |-<br /> | | 64cde<br /> | | <br /> | | <br /> | | flattone<br /> |-<br /> | | 65ccdddeeee<br /> | | <br /> | | <br /> | | dominant<br /> |-<br /> | | 66bcc<br /> | | <br /> | | <br /> | | injera<br /> |-<br /> | | 66bccdd*<br /> | | <br /> | | <br /> | | godzilla<br /> |-<br /> | | 66d*<br /> | | <br /> | | <br /> | | hedgehog, porcupine, pajara, pajarous, telepathy, porky, suprapyth, fleetwood, astrology<br /> |-<br /> | | 66de<br /> | | <br /> | | <br /> | | vigintiduo<br /> |-<br /> | | 67b<br /> | | <br /> | | <br /> | | porcupine<br /> |-<br /> | | 68dde*<br /> | | <br /> | | <br /> | | pajara<br /> |-<br /> | | 68dee*<br /> | | <br /> | | <br /> | | darjeeling<br /> |-<br /> | | 69bcd<br /> | | <br /> | | <br /> | | triforce<br /> |-<br /> | | 69bcee<br /> | | <br /> | | <br /> | | augene<br /> |-<br /> | | 69dee<br /> | | <br /> | | <br /> | | meanenneadecal<br /> |-<br /> | | 70ccddeee<br /> | | <br /> | | <br /> | | dominant<br /> |-<br /> | | 70ddeee<br /> | | <br /> | | <br /> | | pajara<br /> |-<br /> | | 71bc<br /> | | <br /> | | <br /> | | flattone<br /> |-<br /> | | 71bcdd<br /> | | <br /> | | <br /> | | godzilla<br /> |-<br /> | | 71d<br /> | | <br /> | | <br /> | | superpyth<br /> |-<br /> | | 72<br /> | | <br /> | | <br /> | | miracle<br /> |-<br /> | | 72bce<br /> | | <br /> | | <br /> | | augene<br /> |-<br /> | | 72ccddee<br /> | | <br /> | | <br /> | | nautilus<br /> |-<br /> | | 72ccee*<br /> | | <br /> | | <br /> | | hedgehog<br /> |-<br /> | | 72cddd*<br /> | | <br /> | | <br /> | | duodecim<br /> |-<br /> | | 72cddde*<br /> | | <br /> | | <br /> | | duodecim<br /> |-<br /> | | 72cdddeee<br /> | | <br /> | | <br /> | | duodecim<br /> |-<br /> | | 72ce*<br /> | | <br /> | | <br /> | | catnip<br /> |}<br /> [[Category:Lists of temperaments]]<br /> [[Category:11-limit]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Starling_temperaments&diff=141520 Starling temperaments 2024-04-20T22:28:40Z <p>Keenan Pepper: /* Valentine */ mosses -&gt; MOSes</p> <hr /> <div>This page discusses miscellaneous rank-2 temperaments tempering out [[126/125]], the starling comma or septimal semicomma. <br /> <br /> Temperaments discussed in families and clans are:<br /> * ''[[Pater]]'' (+16/15) → [[Father family #Pater|Father family]]<br /> * ''[[Flat]]'' (+21/20) → [[Dicot family #Flat|Dicot family]]<br /> * ''[[Opossum]]'' (+28/27) → [[Trienstonic clan #Opossum|Trienstonic clan]]<br /> * ''[[Diminished]]'' (+36/35) → [[Dimipent family #Diminished|Dimipent family]] / [[Jubilismic clan #Diminished|jubilismic clan]]<br /> * [[Keemun]] (+49/48) → [[Kleismic family #Keemun|Kleismic family]]<br /> * ''[[Augene]]'' (+64/63) → [[Augmented family #Augene|Augmented family]]<br /> * [[Meantone]] (+81/80) → [[Meantone family #Septimal meantone|Meantone family]]<br /> * [[Mavila]] (+135/128) → [[Pelogic family #Mavila|Pelogic family]]<br /> * [[Sensi]] (+245/243), [[Sensipent family #Sensi|Sensipent family]] / [[Sensamagic clan #Sensi|sensamagic clan]]<br /> * ''[[Gilead]]'' (+343/324) → [[Shibboleth family #Gilead|Shibboleth family]]<br /> * [[Muggles]] (+525/512) → [[Magic family #Muggles|Magic family]]<br /> * ''[[Diaschismic]]'' (+2048/2025)} → [[Diaschismic family #Diaschismic|Diaschismic family]]<br /> * ''[[Wollemia]]'' (+2240/2187) → [[Tetracot family #Wollemia|Tetracot family]]<br /> * ''[[Unicorn]]'' (+10976/10935) → [[Unicorn family #Unicorn|Unicorn family]]<br /> * ''[[Coblack]]'' (+16807/16384) → [[Trisedodge family #Coblack|Trisedodge family]] / [[Cloudy clan #Coblack|cloudy clan]]<br /> * ''[[Grackle]]'' (+32805/32768) → [[Schismatic family #Grackle|Schismatic family]]<br /> * ''[[Worschmidt]]'' (+33075/32768) → [[Würschmidt family #Worschmidt|Würschmidt family]]<br /> * ''[[Passionate]]'' (+131072/127575) → [[Passion family #Passionate|Passion family]]<br /> * ''[[Vishnean]]'' (+540225/524288) → [[Vishnuzmic family #Vishnean|Vishnuzmic family]]<br /> * ''[[Ditonic]]'' (+8751645/8388608) → [[Ditonmic family #Ditonic|Ditonmic family]]<br /> * ''[[Muscogee]]'' (+33756345/33554432) → [[Mabila family #Muscogee|Mabila family]]<br /> <br /> Since (6/5)&lt;sup&gt;3&lt;/sup&gt; = 126/125 × 12/7, these temperaments tend to have a relatively small complexity for 6/5. They also possess the [[starling tetrad]], the 6/5-6/5-6/5-7/6 versions of the diminished seventh chord. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before [[12edo]] established itself as the standard tuning, it is arguably more authentic to tune it as three stacked minor thirds and an augmented second, which is what it is in meantone, than as the modern version of four stacked very flat minor thirds. <br /> <br /> == Myna ==<br /> : ''For the 5-limit version of this temperament, see [[High badness temperaments #Mynic]].''<br /> {{Main| Myna }}<br /> <br /> In addition to 126/125, myna tempers out [[1728/1715]], the orwell comma, and [[2401/2400]], the breedsma. It can also be described as the 27 &amp;amp; 31 temperament. It has 6/5 as a generator, and [[58edo]] can be used as a tuning, with [[89edo]] being a better one, and fans of round amounts in cents may like [[120edo]]. It is also possible to tune myna with pure fifths by taking 6&lt;sup&gt;1/10&lt;/sup&gt; as the generator. Myna extends naturally but with much increased complexity to the 11 and 13 limits.<br /> <br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 126/125, 1728/1715<br /> <br /> {{Mapping|legend=1| 1 9 9 8 | 0 -10 -9 -7 }}<br /> <br /> : mapping generators: ~2, ~5/3<br /> <br /> {{Multival|legend=1| 10 9 7 -9 -17 -9 }}<br /> <br /> [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 310.146<br /> <br /> [[Minimax tuning]]: <br /> * 7- and [[9-odd-limit]]: ~6/5 = {{monzo| 1/10 1/10 0 0}}<br /> : {{monzo list| 1 0 0 0 | 0 1 0 0 | 9/10 9/10 0 0 | 17/10 7/10 0 0 }}<br /> : [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.3<br /> <br /> {{Optimal ET sequence|legend=1| 27, 31, 58, 89 }}<br /> <br /> [[Badness]]: 0.027044<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 126/125, 176/175, 243/242<br /> <br /> Mapping: {{mapping| 1 9 9 8 22 | 0 -10 -9 -7 -25 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 310.144<br /> <br /> {{Optimal ET sequence|legend=1| 27e, 31, 58, 89 }}<br /> <br /> Badness: 0.016842<br /> <br /> ==== 13-limit ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 126/125, 144/143, 176/175, 196/195<br /> <br /> Mapping: {{mapping| 1 9 9 8 22 0 | 0 -10 -9 -7 -25 5 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 310.276<br /> <br /> {{Optimal ET sequence|legend=1| 27e, 31, 58 }}<br /> <br /> Badness: 0.017125<br /> <br /> ==== Minah ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 78/77, 91/90, 126/125, 176/175<br /> <br /> Mapping: {{mapping| 1 9 9 8 22 20 | 0 -10 -9 -7 -25 -22 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 310.381<br /> <br /> {{Optimal ET sequence|legend=1| 27e, 31f, 58f }}<br /> <br /> Badness: 0.027568<br /> <br /> ==== Maneh ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 66/65, 105/104, 126/125, 540/539<br /> <br /> Mapping: {{mapping| 1 9 9 8 22 23 | 0 -10 -9 -7 -25 -26 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 309.804<br /> <br /> {{Optimal ET sequence|legend=1| 27eff, 31 }}<br /> <br /> Badness: 0.029868<br /> <br /> === Myno ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 99/98, 126/125, 385/384<br /> <br /> Mapping: {{mapping| 1 9 9 8 -1 | 0 -10 -9 -7 6 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 309.737<br /> <br /> {{Optimal ET sequence|legend=1| 27, 31 }}<br /> <br /> Badness: 0.033434<br /> <br /> === Coleto ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 56/55, 100/99, 1728/1715<br /> <br /> Mapping: {{mapping| 1 9 9 8 2 | 0 -10 -9 -7 2 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 310.853<br /> <br /> {{Optimal ET sequence|legend=1| 4, 23bc, 27e }}<br /> <br /> Badness: 0.048687<br /> <br /> == Valentine ==<br /> {{Main| Valentine }}<br /> <br /> Valentine tempers out [[1029/1024]] and [[6144/6125]] as well as 126/125, so it also fits under the heading of the gamelismic clan. It has a generator of 21/20, which can be stripped of its 2 and taken as 3×7/5. In this respect it resembles miracle, with a generator of 3×5/7, and casablanca, with a generator of 5×7/3. These three generators are the simplest in terms of the relationship of tetrads in the [[The Seven Limit Symmetrical Lattices|lattice of 7-limit tetrads]]. Valentine can also be described as the 31 &amp;amp; 46 temperament, and [[77edo]], [[108edo]] or [[185edo]] make for excellent tunings, which also happen to be excellent tunings for starling temperament, the 126/125 planar temperament. Hence 7-limit valentine can be used whenever starling is wanted, with the extra tempering out of 1029/1024 having no discernible effect on tuning accuracy. Another tuning for valentine uses (3/2)&lt;sup&gt;1/9&lt;/sup&gt; as a generator, giving pure 3/2 fifths. Valentine extends naturally to the 11-limit as {{multival| 9 5 -3 7 … }}, tempering out 121/120 and 441/440; 46edo has a valentine generator 3\46 which is only 0.0117 cents sharp of the minimax generator, (11/7)&lt;sup&gt;1/10&lt;/sup&gt;.<br /> <br /> Valentine is very closely related to [[Carlos Alpha]], the rank-1 non-octave temperament of Wendy Carlos, as the generator chain of valentine is the same thing as Carlos Alpha. Indeed, the way Carlos uses Alpha in ''Beauty in the Beast'' suggests that she really intended Alpha to be the same thing as valentine, and that it is misdescribed as a rank-1 temperament. Carlos tells us that &quot;[t]he melodic motions of Alpha are amazingly exotic and fresh, like you've never heard before&quot;, and since Alpha lives inside valentine this comment carries over and applies to it if you stick close melodically to generator steps, which is almost impossible not to do since the generator step is so small. MOSes of 15, 16, 31 and 46 notes are available to explore these exotic and fresh melodies, or the less exotic ones you might cook up otherwise.<br /> <br /> [[Subgroup]]: 2.3.5<br /> <br /> [[Comma list]]: 1990656/1953125<br /> <br /> {{Mapping|legend=1| 1 1 2 | 0 9 5 }}<br /> <br /> [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~25/24 = 78.039<br /> <br /> {{Optimal ET sequence|legend=1| 15, 31, 46, 77, 123 }}<br /> <br /> [[Badness]]: 0.122765<br /> <br /> === 7-limit ===<br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 126/125, 1029/1024<br /> <br /> {{Mapping|legend=1| 1 1 2 3 | 0 9 5 -3 }}<br /> <br /> : mapping generators: ~2, ~21/20<br /> <br /> [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~21/20 = 77.864<br /> <br /> [[Minimax tuning]]:<br /> * [[7-odd-limit]]: ~21/20 = {{monzo| 1/6 1/12 0 -1/12 }}<br /> : [{{monzo| 1 0 0 0 }}, {{monzo| 5/2 3/4 0 -3/4 }}, {{monzo| 17/6 5/12 0 -5/12 }}, {{monzo| 5/2 -1/4 0 1/4 }}]<br /> : [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7/3<br /> * [[9-odd-limit]]: ~21/20 = {{monzo| 1/21 2/21 0 -1/21}}<br /> : [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 47/21 10/21 0 -5/21 }}, {{monzo| 20/7 -2/7 0 1/7 }}]<br /> : [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/7<br /> <br /> [[Algebraic generator]]: smaller root of ''x''&lt;sup&gt;2&lt;/sup&gt; - 89''x'' + 92, or (89 - sqrt (7553))/2, at 77.8616 cents. <br /> <br /> {{Optimal ET sequence|legend=1| 15, 31, 46, 77, 185, 262cd }}<br /> <br /> [[Badness]]: 0.031056<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 121/120, 126/125, 176/175<br /> <br /> Mapping: {{mapping| 1 1 2 3 3 | 0 9 5 -3 7 }}<br /> <br /> : mapping generators: ~2, ~21/20<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 77.881<br /> <br /> Minimax tuning:<br /> * [[11-odd-limit]]: ~21/20 = {{monzo| 0 0 0 -1/10 1/10 }}<br /> : [{{monzo| 1 0 0 0 0 }}, {{monzo| 1 0 0 -9/10 9/10 }}, {{monzo| 2 0 0 -1/2 1/2 }}, {{monzo| 3 0 0 3/10 -3/10 }}, {{monzo| 3 0 0 -7/10 7/10 }}]<br /> : eigenmonzo (unchanged-interval) basis: 2.11/7<br /> <br /> Algebraic generator: positive root of 4''x''&lt;sup&gt;3&lt;/sup&gt; + 15''x''&lt;sup&gt;2&lt;/sup&gt; - 21, or else Gontrand2, the smallest positive root of 4''x''&lt;sup&gt;7&lt;/sup&gt; - 8''x''&lt;sup&gt;6&lt;/sup&gt; + 5.<br /> <br /> {{Optimal ET sequence|legend=1| 15, 31, 46, 77, 262cdee, 339cdeee }}<br /> <br /> Badness: 0.016687<br /> <br /> ==== Dwynwen ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 91/90, 121/120, 126/125, 176/175<br /> <br /> Mapping: {{mapping| 1 1 2 3 3 2 | 0 9 5 -3 7 26 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 78.219<br /> <br /> {{Optimal ET sequence|legend=1| 15, 31f, 46 }}<br /> <br /> Badness: 0.023461<br /> <br /> ==== Lupercalia ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 66/65, 105/104, 121/120, 126/125<br /> <br /> Mapping: {{mapping| 1 1 2 3 3 3 | 0 9 5 -3 7 11 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 77.709<br /> <br /> {{Optimal ET sequence|legend=1| 15, 31, 77ff, 108eff, 139efff }}<br /> <br /> Badness: 0.021328<br /> <br /> ==== Valentino ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 121/120, 126/125, 176/175, 196/195<br /> <br /> Mapping: {{mapping| 1 1 2 3 3 5 | 0 9 5 -3 7 -20 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 77.958<br /> <br /> {{Optimal ET sequence|legend=1| 15f, 31, 46, 77 }}<br /> <br /> Badness: 0.020665<br /> <br /> ===== 17-limit =====<br /> Subgroup: 2.3.5.7.11.13.17<br /> <br /> Comma list: 121/120, 126/125, 154/153, 176/175, 196/195<br /> <br /> Mapping: {{mapping| 1 1 2 3 3 5 5 | 0 9 5 -3 7 -20 -14 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 78.003<br /> <br /> {{Optimal ET sequence|legend=1| 15f, 31, 46, 77, 123e, 200ceg }}<br /> <br /> Badness: 0.016768<br /> <br /> ==== Semivalentine ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 121/120, 126/125, 169/168, 176/175<br /> <br /> Mapping: {{mapping| 2 2 4 6 6 7 | 0 9 5 -3 7 3 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 77.839<br /> <br /> {{Optimal ET sequence|legend=1| 16, 30, 46, 62, 108ef }}<br /> <br /> Badness: 0.032749<br /> <br /> ==== Hemivalentine ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 121/120, 126/125, 176/175, 343/338<br /> <br /> Mapping: {{mapping| 1 1 2 3 3 4 | 0 18 10 -6 14 -9 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~40/39 = 39.044<br /> <br /> {{Optimal ET sequence|legend=1| 30, 31, 61, 92f, 123f }}<br /> <br /> Badness: 0.047059<br /> <br /> === Hemivalentino ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 126/125, 243/242, 1029/1024<br /> <br /> Mapping: {{mapping| 1 1 2 3 2 | 0 18 10 -6 45 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~45/44 = 38.921<br /> <br /> {{Optimal ET sequence|legend=1| 31, 92e, 123, 154, 185 }}<br /> <br /> Badness: 0.061275<br /> <br /> ==== 13-limit ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 126/125, 196/195, 243/242, 1029/1024<br /> <br /> Mapping: {{mapping| 1 1 2 3 2 5 | 0 18 10 -6 45 -40 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~45/44 = 38.948<br /> <br /> {{Optimal ET sequence|legend=1| 31, 92e, 123, 154 }}<br /> <br /> Badness: 0.057919<br /> <br /> ==== Hemivalentoid ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 126/125, 144/143, 243/242, 343/338<br /> <br /> Mapping: {{mapping| 1 1 2 3 2 4 | 0 18 10 -6 45 -9 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~40/39 = 38.993<br /> <br /> {{Optimal ET sequence|legend=1| 31, 92ef, 123f }}<br /> <br /> Badness: 0.057931<br /> <br /> == Nusecond ==<br /> : ''For the 5-limit version of this temperament, see [[High badness temperaments #Nusecond]].''<br /> <br /> Nusecond tempers out 2430/2401 and 16875/16807 in addition to 126/125, and may be described as 31 &amp;amp; 70. It has a neutral second generator of 49/45, two of which make up a 6/5 minor third since 2430/2401 is tempered out. [[31edo]] can be used as a tuning, or [[132edo]] with a val which is the sum of the [[patent val]]s for 31 and 101. Because 49/45 is flat of 12/11 by only 540/539, nusecond is more naturally thought of as an 11-limit temperament with a combined 12/11 and 11/10 as a generator, tempering out 99/98, 121/120 and 540/539. Because of all the neutral seconds, an exotic Middle Eastern sound comes naturally to nusecond. Mosses of 15, 23, or 31 notes are enough to give fuller effect to the harmony, but the 8-note mos might also be considered from the melodic point of view.<br /> <br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 126/125, 2430/2401<br /> <br /> {{Mapping|legend=1| 1 3 4 5 | 0 -11 -13 -17 }}<br /> <br /> : mapping generators: ~2, ~49/45<br /> <br /> {{Multival|legend=1| 11 13 17 -5 -4 3 }}<br /> <br /> [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/45 = 154.579<br /> <br /> [[Minimax tuning]]: <br /> * [[7-odd-limit]]: ~49/45 = {{monzo| 4/13 0 -1/13 }}<br /> : {{monzo list| 1 0 0 0 | -5/13 0 11/13 0 | 0 0 1 0 | -3/13 0 17/13 0 }}<br /> : [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5<br /> * [[9-odd-limit]]: ~49/45 = {{monzo| 3/11 -1/11 }}<br /> : {{monzo list| 1 0 0 0 | 0 1 0 0 | 5/11 13/11 0 0 | 4/11 17/11 0 0 }}<br /> : [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.3<br /> <br /> {{Optimal ET sequence|legend=1| 8d, 23d, 31, 101, 132c, 163c }}<br /> <br /> [[Badness]]: 0.050389<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 99/98, 121/120, 126/125<br /> <br /> Mapping: {{mapping| 1 3 4 5 5 | 0 -11 -13 -17 -12 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 154.645<br /> <br /> Minimax tuning: <br /> * [[11-odd-limit]]: ~11/10 = {{monzo| 1/10 -1/5 0 0 1/10 }}<br /> : [{{monzo| 1 0 0 0 0 }}, {{monzo| 19/10 11/5 0 0 -11/10 }}, {{monzo| 27/10 13/5 0 0 -13/10 }}, {{monzo| 33/10 17/5 0 0 -17/10 }}, {{monzo| 19/5 12/5 0 0 -6/5 }}]<br /> : eigenmonzo (unchanged-interval) basis: 2.11/9<br /> <br /> Algebraic generator: positive root of 15''x''&lt;sup&gt;2&lt;/sup&gt; - 10''x'' - 7, or (5 + sqrt (130))/15, at 154.6652 cents. The recurrence converges very quickly.<br /> <br /> {{Optimal ET sequence|legend=1| 8d, 23de, 31, 101, 132ce, 163ce, 194cee }}<br /> <br /> Badness: 0.025621<br /> <br /> === 13-limit ===<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 66/65, 99/98, 121/120, 126/125<br /> <br /> Mapping: {{mapping| 1 3 4 5 5 5 | 0 -11 -13 -17 -12 -10 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 154.478<br /> <br /> {{Optimal ET sequence|legend=1| 8d, 23de, 31, 70f, 101ff }}<br /> <br /> Badness: 0.023323<br /> <br /> == Oolong ==<br /> {{Main| Oolong }}<br /> : ''For the 5-limit version of this temperament, see [[High badness temperaments #Oolong]].''<br /> <br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 126/125, 117649/116640<br /> <br /> {{Mapping|legend=1| 1 6 7 8 | 0 -17 -18 -20 }}<br /> <br /> {{Multival|legend=1| 17 18 20 -11 -16 -4 }}<br /> <br /> [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~6/5 = 311.679<br /> <br /> {{Optimal ET sequence|legend=1| 27, 50, 77 }}<br /> <br /> [[Badness]]: 0.073509<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 126/125, 176/175, 26411/26244<br /> <br /> Mapping: {{mapping| 1 6 7 8 18 | 0 -17 -18 -20 -56 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 311.587<br /> <br /> {{Optimal ET sequence|legend=1| 27e, 77, 104c, 181c }}<br /> <br /> Badness: 0.056915<br /> <br /> === 13-limit ===<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 126/125, 176/175, 196/195, 13013/12960<br /> <br /> Mapping: {{mapping| 1 6 7 8 18 5 | 0 -17 -18 -20 -56 -5 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~6/5 = 311.591<br /> <br /> {{Optimal ET sequence|legend=1| 27e, 77, 104c, 181c }}<br /> <br /> Badness: 0.035582<br /> <br /> == Vines ==<br /> : ''For the 5-limit version of this temperament, see [[High badness temperaments #Vines]].''<br /> <br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 126/125, 84035/82944<br /> <br /> {{Mapping|legend=1| 2 7 8 8 | 0 -8 -7 -5 }}<br /> <br /> [[Optimal tuning]] ([[POTE]]): 1\2, ~6/5 = 312.602<br /> <br /> {{Optimal ET sequence|legend=1| 42, 46, 96d, 142d, 238dd }}<br /> <br /> [[Badness]]: 0.078049<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 126/125, 385/384, 2401/2376<br /> <br /> Mapping: {{mapping| 2 7 8 8 5 | 0 -8 -7 -5 4 }}<br /> <br /> Optimal tuning (POTE): 1\2, ~6/5 = 312.601<br /> <br /> {{Optimal ET sequence|legend=1| 42, 46, 96d, 142d, 238dd }}<br /> <br /> Badness: 0.044499<br /> <br /> === 13-limit ===<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 126/125, 196/195, 364/363, 385/384<br /> <br /> Mapping: {{mapping| 2 7 8 8 5 5 | 0 -8 -7 -5 4 5 }}<br /> <br /> Optimal tuning (POTE): 1\2, ~6/5 = 312.564<br /> <br /> {{Optimal ET sequence|legend=1| 42, 46, 96d, 238ddf }}<br /> <br /> Badness: 0.029693<br /> <br /> == Kumonga ==<br /> : ''For the 5-limit version of this temperament, see [[High badness temperaments #Kumonga]].''<br /> <br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 126/125, 12288/12005<br /> <br /> {{Mapping|legend=1| 1 4 4 3 | 0 -13 -9 -1 }}<br /> <br /> {{Multival|legend=1| 13 9 1 -16 -35 -23 }}<br /> <br /> [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8/7 = 222.797<br /> <br /> {{Optimal ET sequence|legend=1| 16, 27, 43, 70, 167ccdd }}<br /> <br /> [[Badness]]: 0.087500<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 126/125, 176/175, 864/847<br /> <br /> Mapping: {{mapping| 1 4 4 3 7 | 0 -13 -9 -1 -19 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 222.898<br /> <br /> {{Optimal ET sequence|legend=1| 16, 27e, 43, 70e }}<br /> <br /> Badness: 0.043336<br /> <br /> === 13-limit ===<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 78/77, 126/125, 144/143, 176/175<br /> <br /> Mapping: {{mapping| 1 4 4 3 7 5 | 0 -13 -9 -1 -19 -7 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 222.961<br /> <br /> {{Optimal ET sequence|legend=1| 16, 27e, 43, 70e, 113cdee }}<br /> <br /> Badness: 0.028920<br /> <br /> == Thuja ==<br /> : ''For the 5-limit version of this temperament, see [[High badness temperaments #Thuja]].''<br /> <br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 126/125, 65536/64827<br /> <br /> {{Mapping|legend=1| 1 -4 0 7 | 0 12 5 -9 }}<br /> <br /> {{Multival|legend=1| 12 5 -9 -20 -48 -35 }}<br /> <br /> [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~175/128 = 558.605<br /> <br /> {{Optimal ET sequence|legend=1| 15, 43, 58 }}<br /> <br /> [[Badness]]: 0.088441<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 126/125, 176/175, 1344/1331<br /> <br /> Mapping: {{mapping| 1 -4 0 7 3 | 0 12 5 -9 1 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 558.620<br /> <br /> {{Optimal ET sequence|legend=1| 15, 43, 58 }}<br /> <br /> Badness: 0.033078<br /> <br /> === 13-limit ===<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 126/125, 144/143, 176/175, 364/363<br /> <br /> Mapping: {{mapping| 1 -4 0 7 3 -7 | 0 12 5 -9 1 23 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 558.589<br /> <br /> {{Optimal ET sequence|legend=1| 15, 43, 58 }}<br /> <br /> Badness: 0.022838<br /> <br /> === 17-limit ===<br /> Subgroup: 2.3.5.7.11.13.17<br /> <br /> Comma list: 126/125, 144/143, 176/175, 221/220, 256/255<br /> <br /> Mapping: {{mapping| 1 -4 0 7 3 -7 12 | 0 12 5 -9 1 23 -17 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 558.509<br /> <br /> {{Optimal ET sequence|legend=1| 15, 43, 58 }}<br /> <br /> Badness: 0.022293<br /> <br /> === 19-limit ===<br /> Subgroup: 2.3.5.7.11.13.17.19<br /> <br /> Comma list: 96/95, 126/125, 144/143, 153/152, 176/175, 221/220<br /> <br /> Mapping: {{mapping| 1 -4 0 7 3 -7 12 1 | 0 12 5 -9 1 23 -17 7 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 558.504<br /> <br /> {{Optimal ET sequence|legend=1| 15, 43, 58h }}<br /> <br /> Badness: 0.018938<br /> <br /> === 23-limit ===<br /> Subgroup: 2.3.5.7.11.13.17.19.23<br /> <br /> Comma list: 96/95, 126/125, 144/143, 153/152, 176/175, 221/220, 231/230<br /> <br /> Mapping: {{mapping| 1 -4 0 7 3 -7 12 1 5 | 0 12 5 -9 1 23 -17 7 -1 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 558.522<br /> <br /> {{Optimal ET sequence|legend=1| 15, 43, 58hi }}<br /> <br /> Badness: 0.016581<br /> <br /> === 29-limit ===<br /> The ''raison d'etre'' of this entry is the simple and accurate approximation of factor twenty-nine, the 2.5.11.21.29 subgroup being of especially good accuracy and simplicity.<br /> <br /> Subgroup: 2.3.5.7.11.13.17.19.23.29<br /> <br /> Comma list: 96/95, 116/115, 126/125, 144/143, 153/152, 176/175, 221/220, 231/230<br /> <br /> Mapping: {{mapping| 1 -4 0 7 3 -7 12 1 5 3 | 0 12 5 -9 1 23 -17 7 -1 4 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 558.520<br /> <br /> {{Optimal ET sequence|legend=1| 15, 43, 58hi }}<br /> <br /> Badness: 0.013762<br /> <br /> == Cypress ==<br /> : ''For the 5-limit version of this temperament, see [[High badness temperaments #Cypress]].''<br /> <br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 126/125, 19683/19208<br /> <br /> {{Mapping|legend=1| 1 7 10 15 | 0 -12 -17 -27 }}<br /> <br /> {{Multival|legend=1| 12 17 27 -1 9 15 }}<br /> <br /> [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~135/98 = 541.828<br /> <br /> {{Optimal ET sequence|legend=1| 11cd, 20cd, 31, 206bcd, 237bcd, 268bcd, 299bcd, 330bbcd }}<br /> <br /> [[Badness]]: 0.099801<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 99/98, 126/125, 243/242<br /> <br /> Mapping: {{mapping| 1 7 10 15 17 | 0 -12 -17 -27 -30 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 541.772<br /> <br /> {{Optimal ET sequence|legend=1| 11cdee, 20cde, 31, 144cd, 175cd, 206bcde, 237bcde }}<br /> <br /> Badness: 0.042719<br /> <br /> === 13-limit ===<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 66/65, 99/98, 126/125, 243/242<br /> <br /> Mapping: {{mapping| 1 7 10 15 17 15 | 0 -12 -17 -27 -30 -25 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 541.778<br /> <br /> {{Optimal ET sequence|legend=1| 11cdeef, 20cdef, 31 }}<br /> <br /> Badness: 0.037849<br /> <br /> == Bisemidim ==<br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 126/125, 118098/117649<br /> <br /> {{Mapping|legend=1| 2 1 2 2 | 0 9 11 15 }}<br /> <br /> {{Multival|legend=1| 18 22 30 -7 -3 8 }}<br /> <br /> [[Optimal tuning]] ([[POTE]]): ~343/243 = 1\2, ~35/27 = 455.445<br /> <br /> {{Optimal ET sequence|legend=1| 50, 58, 108, 166c, 408ccc }}<br /> <br /> [[Badness]]: 0.097786<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 126/125, 540/539, 1344/1331<br /> <br /> Mapping: {{mapping| 2 1 2 2 5 | 0 9 11 15 8 }}<br /> <br /> Optimal tuning (POTE): ~99/70 = 1\2, ~35/27 = 455.373<br /> <br /> {{Optimal ET sequence|legend=1| 50, 58, 108, 166ce, 224cee }}<br /> <br /> Badness: 0.041190<br /> <br /> === 13-limit ===<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 126/125, 144/143, 196/195, 364/363<br /> <br /> Mapping: {{mapping| 2 1 2 2 5 5 | 0 9 11 15 8 10 }}<br /> <br /> Optimal tuning (POTE): ~55/39 = 1\2, ~13/10 = 455.347<br /> <br /> {{Optimal ET sequence|legend=1| 50, 58, 166cef, 224ceeff }}<br /> <br /> Badness: 0.023877<br /> <br /> == Casablanca ==<br /> : ''For the 5-limit version of this temperament, see [[High badness temperaments #Casablanca]].''<br /> <br /> Aside from 126/125, casablanca tempers out the no-threes comma 823543/819200 and also 589824/588245, and may also be described as 31 &amp;amp; 73. 74\135 or 91\166 supply good tunings for the generator, and 20- and 31-note mosses are available.<br /> <br /> It may not seem like casablanca has much to offer, but peering under the hood a bit harder suggests otherwise. For one thing, the ~35/24 generator is particularly interesting; like 15/14 and 21/20, it represents an interval between one vertex of a [[hexany]] and the opposite vertex, which makes it particularly simple with regard to the cubic lattice of tetrads. For another, if we add 385/384 to the list of commas, 35/24 is identified with 16/11, and casablanca is revealed as an 11-limit temperament with a very low complexity for 11 and not too high a one for 7; we might compare 1, 4, 14, 19, the generator steps to 11, 7, 5 and 3 respectively, with 1, 4, 10, 18, the steps to 3, 5, 7 and 11 in 11-limit meantone.<br /> <br /> Marrakesh, named by [[Herman Miller]] in 2011&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_19166.html#19186 Yahoo! Tuning Group | ''A rose by any other name . . .'']&lt;/ref&gt;, is a more accurate 11-limit extension where the generator is identified with 22/15 as opposed to 16/11 in casablanca. <br /> <br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 126/125, 589824/588245<br /> <br /> {{Mapping|legend=1| 1 12 10 5 | 0 -19 -14 -4 }}<br /> <br /> {{Multival|legend=1| 19 14 4 -22 -47 -30 }}<br /> <br /> [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~35/24 = 657.818<br /> <br /> {{Optimal ET sequence|legend=1| 11b, 20b, 31, 104c, 135c, 166c }}<br /> <br /> [[Badness]]: 0.101191<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 126/125, 385/384, 2420/2401<br /> <br /> Mapping: {{mapping| 1 12 10 5 4 | 0 -19 -14 -4 -1 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~16/11 = 657.923<br /> <br /> {{Optimal ET sequence|legend=1| 11b, 20b, 31 }}<br /> <br /> Badness: 0.067291<br /> <br /> ==== 13-limit ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 126/125, 196/195, 385/384, 2420/2401<br /> <br /> Mapping: {{mapping| 1 12 10 5 4 7 | 0 -19 -14 -4 -1 -6 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~16/11 = 657.854<br /> <br /> {{Optimal ET sequence|legend=1| 11b, 20b, 31 }}<br /> <br /> === Marrakesh ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 126/125, 176/175, 14641/14580<br /> <br /> Mapping: {{mapping| 1 12 10 5 21 | 0 -19 -14 -4 -32 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~22/15 = 657.791<br /> <br /> {{Optimal ET sequence|legend=1| 31, 73, 104c, 135c }}<br /> <br /> Badness: 0.040539<br /> <br /> ==== 13-limit ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 126/125, 176/175, 196/195, 14641/14580<br /> <br /> Mapping: {{mapping| 1 12 10 5 21 -10 | 0 -19 -14 -4 -32 25 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~22/15 = 657.756<br /> <br /> {{Optimal ET sequence|legend=1| 31, 73, 104c, 135c, 239ccf }}<br /> <br /> Badness: 0.040774<br /> <br /> ==== Murakuc ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 126/125, 144/143, 176/175, 1540/1521<br /> <br /> Mapping: {{mapping| 1 12 10 5 21 7 | 0 -19 -14 -4 -32 -6 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~22/15 = 657.700<br /> <br /> {{Optimal ET sequence|legend=1| 31, 104cff, 135cff }}<br /> <br /> Badness: 0.041395<br /> <br /> == Amigo ==<br /> {{See also| High badness temperaments #Magus }}<br /> <br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 126/125, 2097152/2083725<br /> <br /> {{Mapping|legend=1| 1 -2 2 9 | 0 11 1 -19 }}<br /> <br /> {{Multival|legend=1| 11 1 -19 -24 -61 -47 }}<br /> <br /> [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~5/4 = 391.094<br /> <br /> {{Optimal ET sequence|legend=1| 43, 46, 89, 135c, 359cc }}<br /> <br /> [[Badness]]: 0.110873<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 126/125, 176/175, 16384/16335<br /> <br /> Mapping: {{mapping| 1 -2 2 9 9 | 0 11 1 -19 -17 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 391.075<br /> <br /> {{Optimal ET sequence|legend=1| 43, 46, 89, 135c, 224c }}<br /> <br /> Badness: 0.043438<br /> <br /> === 13-limit ===<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 126/125, 169/168, 176/175, 364/363<br /> <br /> Mapping: {{mapping| 1 -2 2 9 9 5 | 0 11 1 -19 -17 -4 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 391.073<br /> <br /> {{Optimal ET sequence|legend=1| 43, 46, 89, 135cf, 224cf }}<br /> <br /> Badness: 0.030666<br /> <br /> == Supersensi ==<br /> Supersensi (8d &amp;amp; 43) has supermajor third as a generator like [[sensi]], but the no-fives comma 17496/16807 rather than 245/243 tempered out.<br /> <br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 126/125, 17496/16807<br /> <br /> {{Mapping|legend=1| 1 -4 -4 -5 | 0 15 17 21 }}<br /> <br /> {{Multival|legend=1| 15 17 21 -8 -9 1 }}<br /> <br /> [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~343/270 = 446.568<br /> <br /> {{Optimal ET sequence|legend=1| 8d, 35, 43 }}<br /> <br /> [[Badness]]: 0.148531<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 99/98, 126/125, 864/847<br /> <br /> Mapping: {{mapping| 1 -4 -4 -5 -1 | 0 15 17 21 12 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~72/55 = 446.616<br /> <br /> {{Optimal ET sequence|legend=1| 8d, 35, 43 }}<br /> <br /> Badness: 0.059449<br /> <br /> === 13-limit ===<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 78/77, 99/98, 126/125, 144/143<br /> <br /> Mapping: {{mapping| 1 -4 -4 -5 -1 -3 | 0 15 17 21 12 18 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~13/10 = 446.598<br /> <br /> {{Optimal ET sequence|legend=1| 8d, 35f, 43 }}<br /> <br /> Badness: 0.035258<br /> <br /> === 17-limit ===<br /> Subgroup: 2.3.5.7.11.13.17<br /> <br /> Comma list: 78/77, 99/98, 120/119, 126/125, 144/143<br /> <br /> Mapping: {{mapping| 1 -4 -4 -5 -1 -3 0 | 0 15 17 21 12 18 11 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~13/10 = 446.631<br /> <br /> {{Optimal ET sequence|legend=1| 8d, 35f, 43 }}<br /> <br /> Badness: 0.025907<br /> <br /> == Cobalt ==<br /> The name of the cobalt temperament comes from the 27th element.<br /> <br /> Cobalt (27 &amp;amp; 81) has a period of 1/27 octave and tempers out 126/125 and 540/539, as well as the [[Starling family #Aplonis|aplonis temperament]]. <br /> <br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 126/125, 40353607/40310784<br /> <br /> {{Mapping|legend=1| 27 43 63 76 | 0 -1 -1 -1 }}<br /> <br /> [[Optimal tuning]] ([[POTE]]): 1\27, ~3/2 = 701.244<br /> <br /> {{Optimal ET sequence|legend=1| 27, 81, 108, 135c, 243c }}<br /> <br /> [[Badness]]: 0.173308<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 126/125, 540/539, 21609/21296<br /> <br /> Mapping: {{mapping| 27 43 63 76 94 | 0 -1 -1 -1 -2 }}<br /> <br /> Optimal tuning (POTE): 1\27, ~3/2 = 700.001<br /> <br /> {{Optimal ET sequence|legend=1| 27e, 81, 108 }}<br /> <br /> Badness: 0.078060<br /> <br /> ==== 13-limit ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 126/125, 144/143, 196/195, 21609/21296<br /> <br /> Mapping: {{mapping| 27 43 63 76 94 100 | 0 -1 -1 -1 -2 0 }}<br /> <br /> Optimal tuning (POTE): 1\27, ~3/2 = 700.867<br /> <br /> {{Optimal ET sequence|legend=1| 27e, 81, 108, 243ceef }}<br /> <br /> Badness: 0.057145<br /> <br /> ===== Cobaltous =====<br /> Subgroup: 2.3.5.7.11.13.17<br /> <br /> Comma list: 126/125, 144/143, 189/187, 196/195, 1452/1445<br /> <br /> Mapping: {{mapping| 27 43 63 76 94 100 111 | 0 -1 -1 -1 -2 0 -2 }}<br /> <br /> Optimal tuning (POTE): 1\27, ~3/2 = 700.397<br /> <br /> {{Optimal ET sequence|legend=1| 27eg, 81, 108g }}<br /> <br /> Badness: 0.042106<br /> <br /> ====== 19-limit ======<br /> Subgroup: 2.3.5.7.11.13.17.19<br /> <br /> Comma list: 126/125, 144/143, 171/170, 189/187, 196/195, 969/968<br /> <br /> Mapping: {{mapping| 27 43 63 76 94 100 111 115 | 0 -1 -1 -1 -2 0 -2 -1 }}<br /> <br /> Optimal tuning (POTE): 1\27, ~3/2 = 700.429<br /> <br /> {{Optimal ET sequence|legend=1| 27eg, 81, 108g }}<br /> <br /> Badness: 0.030415<br /> <br /> ===== Cobaltic =====<br /> Subgroup: 2.3.5.7.11.13.17<br /> <br /> Comma list: 126/125, 144/143, 196/195, 221/220, 12005/11968<br /> <br /> Mapping: {{mapping| 27 43 63 76 94 100 111 | 0 -1 -1 -1 -2 0 -3 }}<br /> <br /> Optimal tuning (POTE): 1\27, ~3/2 = 701.595<br /> <br /> {{Optimal ET sequence|legend=1| 27eg, 81gg, 108, 135ce }}<br /> <br /> Badness: 0.047163<br /> <br /> ====== 19-limit ======<br /> Subgroup: 2.3.5.7.11.13.17.19<br /> <br /> Comma list: 126/125, 144/143, 196/195, 210/209, 221/220, 1088/1083<br /> <br /> Mapping: {{mapping| 27 43 63 76 94 100 111 115 | 0 -1 -1 -1 -2 0 -3 -1 }}<br /> <br /> Optimal tuning (POTE): 1\27, ~3/2 = 701.673<br /> <br /> {{Optimal ET sequence|legend=1| 27eg, 81gg, 108, 135ceh }}<br /> <br /> Badness: 0.034176<br /> <br /> ==== Cobaltite ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 126/125, 169/168, 540/539, 975/968<br /> <br /> Mapping: {{mapping| 27 43 63 76 94 100 | 0 -1 -1 -1 -2 -1 }}<br /> <br /> Optimal tuning (POTE): 1\27, ~3/2 = 699.179<br /> <br /> {{Optimal ET sequence|legend=1| 27e, 54bdef, 81f, 108f }}<br /> <br /> Badness: 0.052732<br /> <br /> [[Category:Temperament collections]]<br /> [[Category:Starling temperaments| ]] &lt;!-- main article --&gt;<br /> [[Category:Myna]]<br /> [[Category:Rank 2]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Cluster_MOS&diff=141518 Cluster MOS 2024-04-20T22:26:49Z <p>Keenan Pepper: use table header rows</p> <hr /> <div>A '''cluster MOS''' or '''cluster scale''' is a very particular kind of [[MOS]]-based system (i.e. a system based on stacks of [[period]]s and [[generator]]s) whose generator is quite near a rational fraction of an octave. Therefore some MOS generated by the generator is quasi-equal (which should be reasonably sized for it to be a good cluster MOS, usually between 5 and 10 notes per octave). But not only that; in a cluster temperament, the different versions of each interval, differing by a chroma (&quot;diminished&quot;, &quot;minor&quot;, &quot;major&quot;, &quot;augmented&quot;...) include many nearby interval colors that are individually recognizable, yet conceptually grouped into the same category (or &quot;cluster&quot;) because they're so close.<br /> <br /> A '''cluster temperament''' (named by [[Keenan Pepper]]) is a rank-2 [[regular temperament]] interpretation of a cluster MOS. This means that in a cluster temperament, many different versions of each interval, differing by a chroma, these colors ''represent nearby JI intervals'' specifically (because a temperament is a JI interpretation of MOS generator chains separated by the period).<br /> <br /> An example of something that is '''not''' a cluster temperament is [[amity]], because although the amity generator is within 4 cents of 2\7, making amity[7] near equal, amity is too complex of a temperament and most of the intervals differing by a chroma do not represent simple JI intervals at all. For example, the list of amity &quot;thirds&quot; includes ...6/5 (339.5) (363.2) 5/4... where the intervals given in cents are not representable as simple JI intervals (243/200 and 100/81 are about as simple as you can get).<br /> <br /> Another way to describe this property is that the chroma of the near-equal MOS is a kind of &quot;super-comma&quot;, a set of many useful commas that are tempered to become the same, non-vanishing, interval. It should be obvious that &quot;cluster temperament&quot; is a vague, qualitative phrase and not mathematically well-defined.<br /> <br /> Rather than simply denoting one of a list of rank-2 temperaments, the phrase &quot;cluster scale&quot; is also associated with a compositional philosophy. It is often said that temperaments such as slendric are melodically &quot;bad&quot; or have &quot;bad MOS structure&quot;, because some MOS (in this case slendric[5]) is &quot;too equal&quot; and the next higher MOSes are &quot;too unequal&quot;. But this can be thought of as a feature rather than a bug. Rather than forcing them into the MOS framework, one can think of cluster scales as having two hierarchical levels of melodic structure: the &quot;step&quot; (a step of the quasi-equal MOS), and the &quot;chroma&quot;, and a chroma is so much smaller than a step that the steps seldom go out of order no matter how many chromas are involved.<br /> <br /> == Examples of cluster MOSes ==<br /> [[4L 3s #Parasoft|Parasoft smitonic]] is a cluster MOS.<br /> == Examples of cluster temperaments ==<br /> <br /> === Slendric ===<br /> Main article: [[Slendric]]<br /> <br /> Chroma: 49/48 ~ 64/63<br /> <br /> {| class=&quot;wikitable&quot;<br /> |-<br /> ! | Steps<br /> ! | &quot;Diminished&quot;<br /> ! | &quot;Minor&quot;<br /> ! | &quot;Major&quot;<br /> ! | &quot;Augmented&quot;<br /> |-<br /> | | 1<br /> | | 9/8<br /> | | 8/7<br /> | | 7/6<br /> | | 32/27<br /> |-<br /> | | 2<br /> | | 9/7<br /> | | 21/16<br /> | | 4/3<br /> | | <br /> |-<br /> | | 3<br /> | | <br /> | | 3/2<br /> | | 32/21<br /> | | 14/9<br /> |-<br /> | | 4<br /> | | 27/16<br /> | | 12/7<br /> | | 7/4<br /> | | 16/9<br /> |}<br /> * [http://sevish.com/scaleworkshop/index.htm?name=36edo%20slendric&amp;data=33.333333333333336%0A66.66666666666667%0A100.%0A133.33333333333334%0A166.66666666666669%0A200.%0A233.33333333333334%0A266.6666666666667%0A300.%0A333.33333333333337%0A366.6666666666667%0A400.%0A433.33333333333337%0A466.6666666666667%0A500.00000000000006%0A533.3333333333334%0A566.6666666666667%0A600.%0A633.3333333333334%0A666.6666666666667%0A700.%0A733.3333333333334%0A766.6666666666667%0A800.%0A833.3333333333334%0A866.6666666666667%0A900.0000000000001%0A933.3333333333334%0A966.6666666666667%0A1000.0000000000001%0A1033.3333333333335%0A1066.6666666666667%0A1100.%0A1133.3333333333335%0A1166.6666666666667%0A1200.&amp;vert=-6&amp;horiz=7&amp;midi=12 Play Slendric in 36edo]<br /> Slendric has two quite different extensions that are both also cluster scales:<br /> <br /> ==== Mothra ====<br /> Main article: [[Mothra]]<br /> <br /> Chroma: 33/32 ~ 36/35 ~ 49/48 ~ 55/54 ~ 56/55 ~ 64/63<br /> <br /> {| class=&quot;wikitable&quot;<br /> |-<br /> ! | Steps<br /> ! | <br /> ! | &quot;Diminished&quot;<br /> ! | &quot;Minor&quot;<br /> ! | &quot;Major&quot;<br /> ! | &quot;Augmented&quot;<br /> ! | <br /> |-<br /> | | 1<br /> | | 12/11<br /> | | 10/9~9/8<br /> | | 8/7<br /> | | 7/6<br /> | | 6/5<br /> | | 11/9<br /> |-<br /> | | 2<br /> | | 5/4<br /> | | 14/11~9/7<br /> | | 21/16<br /> | | 4/3<br /> | | 11/8<br /> | | 7/5<br /> |-<br /> | | 3<br /> | | 10/7<br /> | | 16/11<br /> | | 3/2<br /> | | 32/21<br /> | | 14/9~11/7<br /> | | 8/5<br /> |-<br /> | | 4<br /> | | 18/11<br /> | | 5/3<br /> | | 12/7<br /> | | 7/4<br /> | | 16/9~9/5<br /> | | 11/6<br /> |}<br /> * [http://sevish.com/scaleworkshop/index.htm?name=31edo%20mothra&amp;data=38.70967741935484%0A77.41935483870968%0A116.12903225806451%0A154.83870967741936%0A193.5483870967742%0A232.25806451612902%0A270.9677419354839%0A309.6774193548387%0A348.38709677419354%0A387.0967741935484%0A425.80645161290323%0A464.51612903225805%0A503.2258064516129%0A541.9354838709678%0A580.6451612903226%0A619.3548387096774%0A658.0645161290323%0A696.7741935483871%0A735.483870967742%0A774.1935483870968%0A812.9032258064516%0A851.6129032258065%0A890.3225806451613%0A929.0322580645161%0A967.741935483871%0A1006.4516129032259%0A1045.1612903225807%0A1083.8709677419356%0A1122.5806451612902%0A1161.2903225806451%0A1200.&amp;vert=-5&amp;horiz=6&amp;midi=16 Play Mothra in 31edo]<br /> <br /> ==== Rodan ====<br /> Main article: [[Rodan]]<br /> <br /> Chroma: 49/48 ~ 55/54 ~ 56/55 ~ 64/63 ~ 81/80 ~ 99/98<br /> <br /> {| class=&quot;wikitable&quot;<br /> |-<br /> ! | Steps<br /> ! | <br /> ! | <br /> ! | &quot;Diminished&quot;<br /> ! | &quot;Minor&quot;<br /> ! | &quot;Major&quot;<br /> ! | &quot;Augmented&quot;<br /> ! | <br /> ! | <br /> |-<br /> | | 1<br /> | | 12/11<br /> | | 10/9<br /> | | 9/8<br /> | | 8/7<br /> | | 7/6<br /> | | 32/27<br /> | | 6/5<br /> | | 11/9<br /> |-<br /> | | 2<br /> | | 5/4<br /> | | 14/11<br /> | | 9/7<br /> | | 21/16<br /> | | 4/3<br /> | | 27/20<br /> | | 11/8<br /> | | 7/5<br /> |-<br /> | | 3<br /> | | 10/7<br /> | | 16/11<br /> | | 40/27<br /> | | 3/2<br /> | | 32/21<br /> | | 14/9<br /> | | 11/7<br /> | | 8/5<br /> |-<br /> | | 4<br /> | | 18/11<br /> | | 5/3<br /> | | 27/16<br /> | | 12/7<br /> | | 7/4<br /> | | 16/9<br /> | | 9/5<br /> | | 11/6<br /> |} <br /> <br /> === Modus (of the tetracot family) ===<br /> Main article: [[Tetracot]] and [[Modus]]<br /> <br /> Chroma: 40/39 ~ 45/44 ~ 55/54 ~ 65/64 ~ 66/65 ~ 81/80 ~ 121/120<br /> <br /> {| class=&quot;wikitable&quot;<br /> |-<br /> ! | Steps<br /> ! | &quot;Diminished&quot;<br /> ! | &quot;Minor&quot;<br /> ! | &quot;Major&quot;<br /> ! | &quot;Augmented&quot;<br /> |-<br /> | | 1<br /> | | 16/15<br /> | | 13/12~12/11<br /> | | 11/10~10/9<br /> | | 9/8<br /> |-<br /> | | 2<br /> | | 13/11~32/27<br /> | | 6/5<br /> | | 11/9~16/13<br /> | | 5/4<br /> |-<br /> | | 3<br /> | | 13/10<br /> | | 4/3<br /> | | 27/20~15/11<br /> | | 11/8~18/13<br /> |-<br /> | | 4<br /> | | 13/9~16/11<br /> | | 22/15~40/27<br /> | | 3/2<br /> | | 20/13<br /> |-<br /> | | 5<br /> | | 8/5<br /> | | 13/8~18/11<br /> | | 5/3<br /> | | 27/16~22/13<br /> |-<br /> | | 6<br /> | | 16/9<br /> | | 9/5~20/11<br /> | | 11/6~24/13<br /> | | 15/8<br /> |}<br /> * [http://sevish.com/scaleworkshop/index.htm?name=34edo%20modus&amp;data=35.294117647058826%0A70.58823529411765%0A105.88235294117648%0A141.1764705882353%0A176.47058823529414%0A211.76470588235296%0A247.05882352941177%0A282.3529411764706%0A317.64705882352945%0A352.9411764705883%0A388.2352941176471%0A423.5294117647059%0A458.82352941176475%0A494.11764705882354%0A529.4117647058824%0A564.7058823529412%0A600.%0A635.2941176470589%0A670.5882352941177%0A705.8823529411766%0A741.1764705882354%0A776.4705882352941%0A811.764705882353%0A847.0588235294118%0A882.3529411764706%0A917.6470588235295%0A952.9411764705883%0A988.2352941176471%0A1023.529411764706%0A1058.8235294117649%0A1094.1176470588236%0A1129.4117647058824%0A1164.7058823529412%0A1200.&amp;vert=-4&amp;horiz=5 Play Modus in 34edo]<br /> <br /> === Miracle ===<br /> Main article: [[Miracle]]<br /> <br /> Chroma: 45/44 ~ 49/48 ~ 50/49 ~ 55/54 ~ 56/55 ~ 64/63<br /> <br /> {| class=&quot;wikitable&quot;<br /> |-<br /> ! | Steps<br /> ! | <br /> ! | &quot;Diminished&quot;<br /> ! | &quot;Minor&quot;<br /> ! | &quot;Major&quot;<br /> ! | &quot;Augmented&quot;<br /> ! | <br /> |-<br /> | | 1<br /> | | <br /> | | 22/21~21/20<br /> | | 16/15~15/14<br /> | | 12/11<br /> | | 10/9<br /> | | <br /> |-<br /> | | 2<br /> | | 11/10<br /> | | 9/8<br /> | | 8/7<br /> | | 7/6<br /> | | 32/27<br /> | | <br /> |-<br /> | | 3<br /> | | <br /> | | 6/5<br /> | | 11/9<br /> | | 5/4<br /> | | 14/11<br /> | | <br /> |-<br /> | | 4<br /> | | <br /> | | 9/7<br /> | | 21/16<br /> | | 4/3<br /> | | <br /> | | <br /> |-<br /> | | 5<br /> | | <br /> | | 11/8<br /> | | 7/5<br /> | | 10/7<br /> | | 16/11<br /> | | <br /> |-<br /> | | 6<br /> | | <br /> | | <br /> | | 3/2<br /> | | 32/21<br /> | | 14/9<br /> | | <br /> |-<br /> | | 7<br /> | | <br /> | | 11/7<br /> | | 8/5<br /> | | 18/11<br /> | | 5/3<br /> | | <br /> |-<br /> | | 8<br /> | | <br /> | | 27/16<br /> | | 12/7<br /> | | 7/4<br /> | | 16/9<br /> | | 20/11<br /> |-<br /> | | 9<br /> | | <br /> | | 9/5<br /> | | 11/6<br /> | | 15/8<br /> | | 21/11<br /> | | <br /> |}<br /> <br /> === Porcupine ===<br /> Main article: [[Porcupine]]<br /> <br /> Chroma: 22/21 ~ 25/24 ~ 26/25&lt;sup&gt;*&lt;/sup&gt; ~ 33/32 ~ 36/35 ~ 45/44 ~ 81/80<br /> <br /> {| class=&quot;wikitable&quot;<br /> |-<br /> ! | Steps<br /> ! | &quot;Diminished&quot;<br /> ! | &quot;Minor&quot;<br /> ! | &quot;Major&quot;<br /> ! | &quot;Augmented&quot;<br /> |-<br /> | | 1<br /> | | 21/20~16/15<br /> | | 12/11~11/10~10/9<br /> | | 9/8~8/7<br /> | | 13/11&lt;sup&gt;*&lt;/sup&gt;<br /> |-<br /> | | 2<br /> | | 7/6<br /> | | 6/5~11/9<br /> | | 5/4<br /> | | 9/7~13/10&lt;sup&gt;*&lt;/sup&gt;<br /> |-<br /> | | 3<br /> | | 14/11<br /> | | 4/3<br /> | | 11/8<br /> | | 10/7~13/9&lt;sup&gt;*&lt;/sup&gt;<br /> |-<br /> | | 4<br /> | | 7/5~18/13&lt;sup&gt;*&lt;/sup&gt;<br /> | | 16/11<br /> | | 3/2<br /> | | 11/7<br /> |-<br /> | | 5<br /> | | 14/9~20/13&lt;sup&gt;*&lt;/sup&gt;<br /> | | 8/5<br /> | | 5/3~18/11<br /> | | 12/7<br /> |-<br /> | | 6<br /> | | 22/13&lt;sup&gt;*&lt;/sup&gt;<br /> | | 7/4~16/9<br /> | | 9/5~11/6<br /> | | 40/21~15/8<br /> |}<br /> : &lt;sup&gt;*&lt;/sup&gt; 13-limit porcupinefish interpretation<br /> <br /> === Valentino ===<br /> Chroma: 49/48 ~ 51/50 ~ 52/51 ~ 55/54 ~ 56/55 ~ 64/63 ~ 65/64 ~ 77/75 ~ 85/84 ~ 119/117 ~ 128/125 ~ 143/140<br /> <br /> {| class=&quot;wikitable&quot;<br /> |-<br /> ! | Steps<br /> ! | <br /> ! | &quot;Diminished&quot;<br /> ! | &quot;Minor&quot;<br /> ! | &quot;Major&quot;<br /> ! | &quot;Augmented&quot;<br /> ! | <br /> |-<br /> | | 1<br /> | | <br /> | | 36/35<br /> | | 21/20~25/24<br /> | | 17/16~16/15<br /> | | 13/12<br /> | | <br /> |-<br /> | | 2<br /> | | <br /> | | 14/13<br /> | | 12/11~11/10<br /> | | 10/9<br /> | | 17/15<br /> | | 20/17<br /> |-<br /> | | 3<br /> | | <br /> | | 9/8<br /> | | 8/7<br /> | | 7/6<br /> | | 32/27<br /> | | <br /> |-<br /> | | 4<br /> | | <br /> | | 13/11<br /> | | 6/5<br /> | | 11/9~17/14<br /> | | <br /> | | <br /> |-<br /> | | 5<br /> | | <br /> | | 16/13~21/17<br /> | | 5/4<br /> | | 14/11<br /> | | 13/10<br /> | | 27/20<br /> |-<br /> | | 6<br /> | | <br /> | | 9/7<br /> | | 21/16~17/13<br /> | | 4/3<br /> | | 34/25<br /> | | <br /> |-<br /> | | 7<br /> | | <br /> | | 27/20<br /> | | 11/8~15/11<br /> | | 7/5<br /> | | 17/12<br /> | | <br /> |-<br /> | | 8<br /> | | <br /> | | 24/17<br /> | | 10/7<br /> | | 16/11~22/15<br /> | | 40/27<br /> | | <br /> |-<br /> | | 9<br /> | | <br /> | | 25/17<br /> | | 3/2<br /> | | 26/17~32/21<br /> | | 14/9<br /> | | <br /> |-<br /> | | 10<br /> | | 40/27<br /> | | 20/13<br /> | | 11/7<br /> | | 8/5<br /> | | 13/8~34/21<br /> | | <br /> |-<br /> | | 11<br /> | | <br /> | | <br /> | | 18/11~28/17<br /> | | 5/3<br /> | | 22/13<br /> | | <br /> |-<br /> | | 12<br /> | | <br /> | | 27/16<br /> | | 12/7<br /> | | 7/4<br /> | | 16/9<br /> | | <br /> |-<br /> | | 13<br /> | | 17/10<br /> | | 30/14<br /> | | 9/5<br /> | | 11/6~20/11<br /> | | 13/7<br /> | | <br /> |-<br /> | | 14<br /> | | <br /> | | 24/13<br /> | | 15/8<br /> | | 40/21~48/25<br /> | | 35/18<br /> | | <br /> |}<br /> <br /> === 2.3.5.11.13 hitchcock ===<br /> Unlike amity itself, this 2.3.5.11.13 amity extension is a cluster temperament because the intervals between 6/5 and 5/4 are mapped to 11/9 and 16/13.<br /> <br /> {| class=&quot;wikitable&quot;<br /> |-<br /> ! | Steps<br /> ! | <br /> ! | &quot;Diminished&quot;<br /> ! | &quot;Minor&quot;<br /> ! | &quot;Major&quot;<br /> ! | &quot;Augmented&quot;<br /> ! | <br /> |-<br /> | | 1<br /> | | <br /> | | 13/12<br /> | | 12/11~11/10<br /> | | 10/9<br /> | | 9/8<br /> | | <br /> |-<br /> | | 2<br /> | | 13/11<br /> | | 6/5<br /> | | 11/9<br /> | | 16/13<br /> | | 5/4<br /> | | <br /> |-<br /> | | 3<br /> | | 13/10<br /> | | <br /> | | 4/3<br /> | | 27/20<br /> | | 11/8<br /> | | 18/13<br /> |-<br /> | | 4<br /> | | 13/9<br /> | | 16/11<br /> | | 40/27<br /> | | 3/2<br /> | | <br /> | | 20/13<br /> |-<br /> | | 5<br /> | | <br /> | | 8/5<br /> | | 13/8<br /> | | 18/11<br /> | | 5/3<br /> | | 22/13<br /> |-<br /> | | 6<br /> | | <br /> | | 16/9<br /> | | 9/5<br /> | | 11/6<br /> | | 24/13<br /> | | <br /> |}<br /> <br /> [[Category:Rank 2]]<br /> [[Category:MOS scales]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Cluster_scale&diff=141516 Cluster scale 2024-04-20T22:21:03Z <p>Keenan Pepper: #redirect Cluster MOS</p> <hr /> <div>#redirect [[Cluster MOS]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Lumatone_mapping_for_58edo&diff=141515 Lumatone mapping for 58edo 2024-04-20T22:17:13Z <p>Keenan Pepper: (as in Lumatone mapping for harry)</p> <hr /> <div>There are many conceivable ways to map [[58edo]] onto the [[Lumatone]] keyboard. Unfortunately, as it has multiple rings of 5ths, the [[Standard Lumatone mapping for Pythagorean]] is not one of them, and due to it's size, would not cover the whole gamut even if it was. Instead, the [[2L 8s]] [[diaschismic]] mapping is probably the most intuitive way of providing access to all intervals while putting well-tuned ones close together.<br /> {{Lumatone EDO mapping|n=58|start=19|xstep=5|ystep=4}}<br /> <br /> However, this results in a range barely over 3 octaves. <br /> <br /> <br /> The [[6L 2s]] [[Echidna]] mapping has fewer repeated notes while still providing the full gamut, giving you a range almost as large as the standard mapping. (This mapping, like many others, is [https://www.facebook.com/groups/lumatone.keyboard/permalink/5624482024327650 available from the Lumatone Facebook group].)<br /> {{Lumatone EDO mapping|n=58|start=54|xstep=8|ystep=-3}}<br /> <br /> Other good options include [[7L 3s]] [[Hemififths]]<br /> {{Lumatone EDO mapping|n=58|start=2|xstep=7|ystep=-4}}<br /> <br /> Or if you don't mind the smaller range and want to more easily exploit narrow intervals, [[2L 12s]] [[Harry]] (as in [[Lumatone mapping for harry]])<br /> {{Lumatone EDO mapping|n=58|start=40|xstep=4|ystep=1}}<br /> <br /> [[Category:Lumatone mappings]] [[Category:58edo]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Lumatone_mapping_for_59edo&diff=141514 Lumatone mapping for 59edo 2024-04-20T22:05:07Z <p>Keenan Pepper: &quot;technically correct&quot; is a bizarre way to say patent val I think</p> <hr /> <div>There are many conceivable ways to map [[59edo]] onto the [[Lumatone]] keyboard. However, as both it's 5ths are about as far away from just as possible, neither the sharp or the flat versions of the [[Standard Lumatone mapping for Pythagorean]] work particularly well, although the sharp one is slightly closer making it the [[patent val]]. In addition, neither covers the full gamut of every octave, with multiple skipped notes.<br /> {{Lumatone EDO mapping|n=59|start=14|xstep=11|ystep=-9}}<br /> {{Lumatone EDO mapping|n=59|start=49|xstep=9|ystep=-2}}<br /> Instead, as it is it's optimal patent val, using the expanded mapping of [[porcupine]] is probably the best way of organising the intervals of 59edo while being able to access them all, although the range is slightly smaller than the pythagorean mapping. <br /> {{Lumatone EDO mapping|n=59|start=6|xstep=8|ystep=-5}}<br /> <br /> [[Category:Lumatone mappings]] [[Category:59edo]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Lumatone_mapping_for_47edo&diff=141513 Lumatone mapping for 47edo 2024-04-20T22:04:49Z <p>Keenan Pepper: &quot;technically correct&quot; is a bizarre way to say patent val I think</p> <hr /> <div>There are many conceivable ways to map [[47edo]] onto the [[Lumatone]] keyboard. However, as both it's 5ths are about as far away from just as possible, neither the sharp or the flat versions of the [[Standard Lumatone mapping for Pythagorean]] work particularly well, although the flat one is slightly closer making it the [[patent val]].<br /> {{Lumatone EDO mapping|n=47|start=37|xstep=7|ystep=-1}}<br /> {{Lumatone EDO mapping|n=47|start=14|xstep=9|ystep=-8}}<br /> Instead, it is probably better to treat it as a no-3's subgroup temperament, which the [[baldy]] mapping does quite effectively.<br /> {{Lumatone EDO mapping|n=47|start=29|xstep=8|ystep=-1}}<br /> <br /> [[Category:Lumatone mappings]] [[Category:47edo]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Lumatone_mapping_for_55edo&diff=141512 Lumatone mapping for 55edo 2024-04-20T22:02:24Z <p>Keenan Pepper: no underscore</p> <hr /> <div>There are many conceivable ways to map [[55edo]] onto the [[Lumatone]] keyboard. Only one, however, agrees with the [[Standard Lumatone mapping for Pythagorean]].<br /> {{Lumatone EDO mapping|n=55|start=53|xstep=9|ystep=-4}}<br /> <br /> The [[6L 1s]] mapping also provides a heptatonic scale that gives you access to all the notes in the gamut in an intuitive way without any backtracking. <br /> {{Lumatone EDO mapping|n=55|start=37|xstep=8|ystep=-1}}<br /> <br /> [[Category:Lumatone mappings]] [[Category:55edo]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Template:Sharpness-sharp5-extended&diff=141505 Template:Sharpness-sharp5-extended 2024-04-20T21:38:52Z <p>Keenan Pepper: &lt;noinclude&gt;</p> <hr /> <div>{| class=&quot;wikitable center-all&quot;<br /> ! Step Offset<br /> | '''0'''<br /> | 1<br /> | 2<br /> | 3<br /> | 4<br /> | '''5'''<br /> | 6<br /> | 7<br /> | 8<br /> | 9<br /> | '''10'''<br /> | 11<br /> | 12<br /> | 13<br /> |-<br /> ! rowspan=&quot;2&quot; | Sharp Symbol<br /> | rowspan=&quot;4&quot; | [[File:Heji18.svg|15px|center]]<br /> | rowspan=&quot;2&quot; | [[File:Heji19.svg|18px|center]]<br /> | [[File:Heji20.svg|18px|center]]<br /> | [[File:Heji21.svg|17px|center]]<br /> | rowspan=&quot;2&quot; | [[File:Heji24.svg|17px|center]]<br /> | rowspan=&quot;2&quot; | [[File:Heji25.svg|17px|center]]<br /> | rowspan=&quot;2&quot; | [[File:Heji26.svg|18px|center]]<br /> | [[File:Heji27.svg|18px|center]]<br /> | [[File:Heji28.svg|18px|center]]<br /> | rowspan=&quot;2&quot; | [[File:Heji31.svg|18px|center]]<br /> | rowspan=&quot;2&quot; | [[File:Heji32.svg|18px|center]]<br /> | rowspan=&quot;2&quot; | [[File:Heji33.svg|18px|center]]<br /> | rowspan=&quot;2&quot; | [[File:Heji34.svg|18px|center]]<br /> | rowspan=&quot;2&quot; | [[File:Heji35.svg|18px|center]]<br /> |-<br /> | [[File:Heji22.svg|17px|center]]<br /> | [[File:Heji23.svg|17px|center]]<br /> | [[File:Heji29.svg|18px|center]]<br /> | [[File:Heji30.svg|18px|center]]<br /> |-<br /> ! rowspan=&quot;2&quot; | Flat Symbol<br /> | rowspan=&quot;2&quot; | [[File:Heji17.svg|15px|center]]<br /> | [[File:Heji16.svg|15px|center]]<br /> | [[File:Heji15.svg|15px|center]]<br /> | rowspan=&quot;2&quot; | [[File:Heji12.svg|18px|center]]<br /> | rowspan=&quot;2&quot; | [[File:Heji11.svg|15px|center]]<br /> | rowspan=&quot;2&quot; | [[File:Heji10.svg|19px|center]]<br /> | [[File:Heji9.svg|19px|center]]<br /> | [[File:Heji8.svg|19px|center]]<br /> | rowspan=&quot;2&quot; | [[File:Heji5.svg|27px|center]]<br /> | rowspan=&quot;2&quot; | [[File:Heji4.svg|24px|center]]<br /> | rowspan=&quot;2&quot; | [[File:Heji3.svg|24px|center]]<br /> | rowspan=&quot;2&quot; | [[File:Heji2.svg|24px|center]]<br /> | rowspan=&quot;2&quot; | [[File:Heji1.svg|24px|center]]<br /> |-<br /> | [[File:Heji14.svg|18px|center]]<br /> | [[File:Heji13.svg|18px|center]]<br /> | [[File:Heji7.svg|27px|center]]<br /> | [[File:Heji6.svg|27px|center]]<br /> |}&lt;noinclude&gt;<br /> <br /> [[Category:Templates]]<br /> {{Todo|add documentation}}<br /> &lt;/noinclude&gt;</div> Keenan Pepper https://en.xen.wiki/index.php?title=Template:Sharpness-sharp3-extended&diff=141504 Template:Sharpness-sharp3-extended 2024-04-20T21:38:06Z <p>Keenan Pepper: &lt;noinclude&gt;</p> <hr /> <div>{| class=&quot;wikitable center-all&quot;<br /> ! Steps<br /> | '''0'''<br /> | 1<br /> | 2<br /> | '''3'''<br /> | 4<br /> | 5<br /> | '''6'''<br /> | 7<br /> | 8<br /> |-<br /> ! rowspan=&quot;2&quot; | Sharp Symbol<br /> | rowspan=&quot;4&quot; | [[File:Heji18.svg|15px|center]]<br /> | [[File:Heji19.svg|18px|center]]<br /> | [[File:Heji20.svg|18px|center]]<br /> | rowspan=&quot;2&quot; | [[File:Heji25.svg|17px|center]]<br /> | [[File:Heji26.svg|18px|center]]<br /> | [[File:Heji27.svg|18px|center]]<br /> | rowspan=&quot;2&quot; | [[File:Heji32.svg|18px|center]]<br /> | rowspan=&quot;2&quot; | [[File:Heji33.svg|18px|center]]<br /> | rowspan=&quot;2&quot; | [[File:Heji34.svg|18px|center]]<br /> |-<br /> | [[File:Heji23.svg|17px|center]]<br /> | [[File:Heji24.svg|17px|center]]<br /> | [[File:Heji30.svg|18px|center]]<br /> | [[File:Heji31.svg|18px|center]]<br /> |-<br /> ! rowspan=&quot;2&quot; | Flat Symbol<br /> | [[File:Heji17.svg|15px|center]]<br /> | [[File:Heji16.svg|15px|center]]<br /> | rowspan=&quot;2&quot; | [[File:Heji11.svg|15px|center]]<br /> | [[File:Heji10.svg|19px|center]]<br /> | [[File:Heji9.svg|19px|center]]<br /> | rowspan=&quot;2&quot; | [[File:Heji4.svg|24px|center]]<br /> | rowspan=&quot;2&quot; | [[File:Heji3.svg|24px|center]]<br /> | rowspan=&quot;2&quot; | [[File:Heji2.svg|24px|center]]<br /> |-<br /> | [[File:Heji13.svg|18px|center]]<br /> | [[File:Heji12.svg|18px|center]]<br /> | [[File:Heji6.svg|27px|center]]<br /> | [[File:Heji5.svg|27px|center]]<br /> |}&lt;noinclude&gt;<br /> <br /> [[Category:Templates]]<br /> {{Todo|add documentation}}<br /> &lt;/noinclude&gt;</div> Keenan Pepper https://en.xen.wiki/index.php?title=Template:Sharpness-sharp4&diff=141503 Template:Sharpness-sharp4 2024-04-20T21:37:22Z <p>Keenan Pepper: &lt;noinclude&gt;</p> <hr /> <div>{| class=&quot;wikitable center-all&quot;<br /> ! Step Offset<br /> | '''0'''<br /> | 1<br /> | 2<br /> | 3<br /> | '''4'''<br /> | 5<br /> | 6<br /> | 7<br /> | '''8'''<br /> | 9<br /> |-<br /> ! Sharp Symbol<br /> | rowspan=&quot;2&quot; | [[File:Heji18.svg|15px|center]]<br /> | [[File:Heji19.svg|18px|center]]<br /> | [[File:HeQu1.svg|14px|center]]<br /> | [[File:Heji24.svg|17px|center]]<br /> | [[File:Heji25.svg|17px|center]]<br /> | [[File:Heji26.svg|18px|center]]<br /> | [[File:HeQu3.svg|20px|center]]<br /> | [[File:Heji31.svg|18px|center]]<br /> | [[File:Heji32.svg|18px|center]]<br /> | [[File:Heji33.svg|18px|center]]<br /> |-<br /> ! Flat Symbol<br /> | [[File:Heji17.svg|15px|center]]<br /> | [[File:HeQd1.svg|15px|center]]<br /> | [[File:Heji12.svg|18px|center]]<br /> | [[File:Heji11.svg|15px|center]]<br /> | [[File:Heji10.svg|19px|center]]<br /> | [[File:HeQd3.svg|24px|center]]<br /> | [[File:Heji5.svg|27px|center]]<br /> | [[File:Heji4.svg|24px|center]]<br /> | [[File:Heji3.svg|24px|center]]<br /> |}&lt;noinclude&gt;<br /> <br /> [[Category:Templates]]<br /> {{Todo|add documentation}}<br /> &lt;/noinclude&gt;</div> Keenan Pepper https://en.xen.wiki/index.php?title=Ennealimmal&diff=106050 Ennealimmal 2023-03-22T19:46:15Z <p>Keenan Pepper: add little table of EDO mapping components, mostly for my own reference</p> <hr /> <div>'''Ennealimmal temperament''' has a period of 1/9 octave and tempers out [[2401/2400]] and [[4375/4374]]. EDOs that support ennealimmal include EDOs {{EDOs| 27, 45, 72, 99, 171, 270, 441, and 612 }}.<br /> <br /> See [[Ragismic microtemperaments #Ennealimmal]] for more technical data.<br /> <br /> Ennealimmal scales are built from a ''period'' (which is exactly 1/9 of an octave), and a ''generator'' (which is approximately 49 cents and represents several small intervals including 36/35). Depending on the size of the generator and the period in steps, the above listed EDOs make sense:<br /> <br /> {| class=&quot;wikitable<br /> ! Period (steps) !! Generator (steps) !! Generator (cents) &lt;br/&gt; (pure octave) !! EDO<br /> |-<br /> | 3 || 1 || 44.444 || 27<br /> |-<br /> | 11 || 4 || 48.485 || 99<br /> |-<br /> | 30 || 11 || 48.889 || 270<br /> |-<br /> | 19 || 7 || 49.123 || 171<br /> |-<br /> | 8 || 3 || 50.000 || 72<br /> |-<br /> | 5 || 2 || 53.333 || 45<br /> |}<br /> <br /> == Interval chain ==<br /> {| class=&quot;wikitable&quot;<br /> |+Generator based off 11-limit ennealimmal<br /> !Generator<br /> !Period 1<br /> !Period 2<br /> !Period 3<br /> !Period 4<br /> !Period 5<br /> !Period 6<br /> !Period 7<br /> !Period 8<br /> !Period 9 (0)<br /> |-<br /> !0<br /> |133.333<br /> |266.666<br /> |400.000<br /> |533.333<br /> |666.666<br /> |800.000<br /> |933.333<br /> |1066.666<br /> |1200.000<br /> |-<br /> !-1<br /> |84.430<br /> |217.764<br /> |351.097<br /> |484.430<br /> |617.764<br /> |751.097<br /> |884.430<br /> |1017.764<br /> |1151.097<br /> |-<br /> !-2<br /> |35.527<br /> |168.861<br /> |302.194<br /> |435.527<br /> |568.861<br /> |702.194<br /> |835.527<br /> |968.861<br /> |1102.194<br /> |-<br /> !-3<br /> |1186.624<br /> |119.958<br /> |253.291<br /> |386.624<br /> |519.958<br /> |653.291<br /> |786.624<br /> |919.958<br /> |1053.291<br /> |-<br /> !-4<br /> |1137.721<br /> |71.055<br /> |204.388<br /> |337.721<br /> |471.055<br /> |604.388<br /> |737.721<br /> |871.055<br /> |1004.388<br /> |-<br /> !-5<br /> |1088.818<br /> |22.152<br /> |155.485<br /> |288.818<br /> |422.152<br /> |555.485<br /> |688.818<br /> |822.152<br /> |955.485<br /> |-<br /> !-6<br /> |1039.915<br /> |1173.249<br /> |106.582<br /> |239.915<br /> |373.249<br /> |506.582<br /> |639.915<br /> |773.249<br /> |906.582<br /> |-<br /> !-7<br /> |991.012<br /> |1124.346<br /> |57.679<br /> |191.012<br /> |324.346<br /> |457.679<br /> |591.012<br /> |724.346<br /> |857.679<br /> |-<br /> !-8<br /> |942.109<br /> |1075.443<br /> |8.776<br /> |142.109<br /> |275.443<br /> |408.776<br /> |542.109<br /> |675.443<br /> |808.776<br /> |-<br /> !-9<br /> |893.206<br /> |1026.540<br /> |1159.873<br /> |93.206<br /> |226.540<br /> |359.873<br /> |493.206<br /> |626.540<br /> |759.873<br /> |-<br /> !-10<br /> |844.303<br /> |977.637<br /> |1110.970<br /> |44.303<br /> |177.637<br /> |310.970<br /> |444.303<br /> |577.637<br /> |710.970<br /> |-<br /> !-11<br /> |795.400<br /> |928.734<br /> |1062.067<br /> |1195.400<br /> |128.734<br /> |262.067<br /> |395.400<br /> |528.734<br /> |662.067<br /> |-<br /> !-12<br /> |746.497<br /> |879.831<br /> |1013.164<br /> |1146.497<br /> |79.831<br /> |213.164<br /> |346.497<br /> |479.831<br /> |613.164<br /> |-<br /> !-13<br /> |697.594<br /> |830.928<br /> |964.261<br /> |1097.594<br /> |30.928<br /> |164.261<br /> |297.594<br /> |430.928<br /> |564.261<br /> |-<br /> !-14<br /> |648.691<br /> |782.025<br /> |915.358<br /> |1048.691<br /> |1182.025<br /> |115.358<br /> |248.691<br /> |382.025<br /> |515.358<br /> |-<br /> !-15<br /> |599.788<br /> |733.122<br /> |866.455<br /> |999.788<br /> |1133.122<br /> |66.455<br /> |199.788<br /> |333.122<br /> |466.455<br /> |-<br /> !-16<br /> |550.885<br /> |684.219<br /> |817.552<br /> |950.885<br /> |1084.219<br /> |17.552<br /> |150.885<br /> |284.219<br /> |417.552<br /> |-<br /> !-17<br /> |501.982<br /> |635.316<br /> |768.649<br /> |901.982<br /> |1035.316<br /> |1168.649<br /> |101.982<br /> |235.316<br /> |368.649<br /> |}<br /> <br /> == Ennealimmal extensions ==<br /> Ennealimmal temperament has various extensions to the 11-limit. These are all members of the ennealimmal family, but in addition they are linear temperaments:<br /> * Ennealimmal (99e &amp;amp; 270) - tempering out 2401/2400, 4375/4374, 5632/5625<br /> * Ennealimmia (171 &amp;amp; 270) - tempering out 2401/2400, 4375/4374, 131072/130977<br /> * Ennealimnic (72 &amp;amp; 99e) - tempering out 243/242, 441/440, 4375/4356<br /> * Ennealiminal (72 &amp;amp; 171e) - tempering out 385/384, 1375/1372, 4375/4374<br /> <br /> == Scales ==<br /> * [[Ennealimmal27]] - proper [[18L 9s]]. Ninth-octave analog of haplotonic scale<br /> * [[Ennealimmal45]] - improper [[27L 18s]]. Ninth-octave analog of mega-haplotonic scale<br /> ** [[Ennealimmal45trans]] - symmetric 5-limit transversal version<br /> * [[Ennealimmal72]] - proper [[27L 45s]]. Ninth-octave analog of albitonic scale<br /> * [[Ennealimmal99]] - proper [[72L 27s]]. Ninth-octave analog of chromatic scale<br /> * [[Ennealimmal171]] - [[99L 72s]] scale. The boundary of propriety is [[270edo|270EDO]].<br /> <br /> [[Category:Ragismic microtemperaments]]<br /> [[Category:Temperaments]]<br /> [[Category:Ennealimmal| ]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Hardware_Synths&diff=84174 Hardware Synths 2022-01-17T23:28:08Z <p>Keenan Pepper: /* Eurorack */ rm / from end of link</p> <hr /> <div>This is a list of hardware electronic instruments that have support for microtonal tuning.<br /> <br /> == Keyboards ==<br /> * [https://www.ashunsoundmachines.com/ Ashun Sound Machines] (ASM) Hydrasynth Keyboard (firmware 1.5 and later) - supports MIDI Tuning Standard<br /> * [https://hpi.zentral.zone/tonalplexus Hπ Tonal Plexus]<br /> * Korg monologue<br /> * [http://www.modormusic.com/os13.html Modor NF-1] - Built-in quarter tones, Just Intonation, Harmonic series, many EDOs and a number of hexanies/dekanies + scales via Midi Tuning Standard.<br /> * Roli Seaboard<br /> * Starr Labs Microzone U-648<br /> * [https://www.striso.org/ Striso board] - Generalized keyboard which supports [[fifthspan]] and [[7-limit]] JI tunings<br /> <br /> == Sound modules ==<br /> * Ashun Sound Machines (ASM) Hydrasynth Desktop (firmware 1.5 and later) - supports MIDI Tuning Standard<br /> * Yamaha TX81Z<br /> <br /> <br /> == Eurorack ==<br /> * [https://ornament-and-cri.me/ ornament &amp; crime] - CV generator<br /> * [https://tubbutec.de/%C2%B5tune/ Tubbutec μTune] - two-channel microtonal quantizer/mapper<br /> * [https://www.expert-sleepers.co.uk/fh2.html Expert Sleepers FH-2 'Factotum'] - MPE and .scl/kmb MIDI to CV<br /> <br /> == Other ==<br /> * [https://hpi.zentral.zone/tbx2b Hπ TBX2b] - tuning unit that retunes GM (multichannel) synths, monophonic synths, MTS synths, and proprietary sysex synths.<br /> * Theremin<br /> [[Category:hardware]]<br /> [[Category:synths]]<br /> [[Category:todo:expand]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Lumatone_mapping_for_34edo&diff=83976 Lumatone mapping for 34edo 2022-01-14T18:41:50Z <p>Keenan Pepper: add into and another mapping</p> <hr /> <div>34edo is an interesting case for [[Lumatone]] mappings, since ([[Lumatone mapping for 24edo|like 24edo]]), it is not generated by fifths and octaves, so the [[Standard Lumatone mapping for Pythagorean]] cannot be used.<br /> <br /> A [[5L 3s]]-based mapping for [[34edo]]:<br /> {{Lumatone EDO mapping|n=34|start=-2|xstep=5|ystep=-2}}<br /> <br /> A [[6L 1s]]-based mapping:<br /> {{Lumatone EDO mapping|n=34|start=16|xstep=5|ystep=-1}}<br /> <br /> [[Category:Lumatone mappings]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Lumatone_mapping_for_31edo&diff=83602 Lumatone mapping for 31edo 2022-01-10T00:04:49Z <p>Keenan Pepper: more mappings</p> <hr /> <div>There are many conceivable ways to map [[31edo]] onto the [[Lumatone]] keyboard.<br /> <br /> ==Standard Bosanquet-Wilson==<br /> <br /> This agrees with the [[Standard Lumatone mapping for Pythagorean]]. This is also &quot;Preset 8 — 31-ET Bosanquet&quot; in the official Lumatone manual.<br /> {{Lumatone EDO mapping|n=31|start=-2|xstep=5|ystep=-2}}<br /> <br /> ==Double-Bosanquet==<br /> <br /> As in [[Lumatone mapping for neutral thirds scales]], this cuts the chromatic semitones in the &quot;vertical&quot; direction in half, so neutral intervals appear in between minor and major intervals. Octaves are no longer at a perfect horizontal separation but instead all over the place.<br /> {{Lumatone EDO mapping|n=31|start=-6|xstep=5|ystep=-1}}<br /> <br /> ==Anti-Double-Bosanquet==<br /> <br /> This is a flipped version of Double-Bosanquet which results in octaves being closer to horizontal. The step shape normally mapped to major seconds is here mapped to neutral seconds.<br /> {{Lumatone EDO mapping|n=31|start=-5|xstep=4|ystep=1}}<br /> <br /> [[Category:Lumatone mappings]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Lumatone_mapping_for_lemba&diff=83601 Lumatone mapping for lemba 2022-01-09T23:25:00Z <p>Keenan Pepper: add tonality diamond</p> <hr /> <div>Here is one possible keyboard arrangement for the basic 10-note MOS of [[lemba]] temperament, arbitrarily labeled with the letters A-J. Using Sagittal notation, a lemba scale centered on D can be notated like this:<br /> <br /> {| class=&quot;wikitable&quot;<br /> |A<br /> |B<br /> |C<br /> |D<br /> |E<br /> |F<br /> |G<br /> |H<br /> |I<br /> |J<br /> |-<br /> |&lt;nowiki&gt;+0, -1&lt;/nowiki&gt;<br /> |&lt;nowiki&gt;-1, +2&lt;/nowiki&gt;<br /> |&lt;nowiki&gt;+0, +0&lt;/nowiki&gt;<br /> |&lt;nowiki&gt;+1, -2&lt;/nowiki&gt;<br /> |&lt;nowiki&gt;+0, +1&lt;/nowiki&gt;<br /> |&lt;nowiki&gt;+1, -1&lt;/nowiki&gt;<br /> |&lt;nowiki&gt;+0, +2&lt;/nowiki&gt;<br /> |&lt;nowiki&gt;+1, +0&lt;/nowiki&gt;<br /> |&lt;nowiki&gt;+2, -2&lt;/nowiki&gt;<br /> |&lt;nowiki&gt;+1, +1&lt;/nowiki&gt;<br /> |-<br /> |C!)<br /> |&lt;nowiki&gt;C/|)&lt;/nowiki&gt;<br /> |D<br /> |E\!)<br /> |&lt;nowiki&gt;E|)&lt;/nowiki&gt;<br /> |&lt;nowiki&gt;F/|)&lt;/nowiki&gt;<br /> |G!)<br /> |&lt;nowiki&gt;G|||(&lt;/nowiki&gt;<br /> |&lt;nowiki&gt;A)||(&lt;/nowiki&gt;<br /> |B\!)<br /> |}<br /> {{Lumatone mapping|<br /> <br /> {{Lumatone key|x=2|y=4|label=A}}<br /> {{Lumatone key|x=2|y=3|label=B}}<br /> {{Lumatone key|x=3|y=4|label=C}}<br /> {{Lumatone key|x=4|y=5|label=D}}<br /> {{Lumatone key|x=4|y=4|label=E}}<br /> {{Lumatone key|x=5|y=5|label=F}}<br /> {{Lumatone key|x=5|y=4|label=G}}<br /> {{Lumatone key|x=6|y=5|label=H}}<br /> {{Lumatone key|x=7|y=6|label=I}}<br /> {{Lumatone key|x=7|y=5|label=J}}<br /> <br /> {{Lumatone key|x=8|y=6|label=A}}<br /> {{Lumatone key|x=8|y=5|label=B}}<br /> {{Lumatone key|x=9|y=6|label=C}}<br /> {{Lumatone key|x=10|y=7|label=D}}<br /> {{Lumatone key|x=10|y=6|label=E}}<br /> {{Lumatone key|x=11|y=7|label=F}}<br /> {{Lumatone key|x=11|y=6|label=G}}<br /> {{Lumatone key|x=12|y=7|label=H}}<br /> {{Lumatone key|x=13|y=8|label=I}}<br /> {{Lumatone key|x=13|y=7|label=J}}<br /> <br /> {{Lumatone key|x=14|y=8|label=A}}<br /> {{Lumatone key|x=14|y=7|label=B}}<br /> {{Lumatone key|x=15|y=8|label=C}}<br /> {{Lumatone key|x=16|y=9|label=D}}<br /> {{Lumatone key|x=16|y=8|label=E}}<br /> {{Lumatone key|x=17|y=9|label=F}}<br /> {{Lumatone key|x=17|y=8|label=G}}<br /> {{Lumatone key|x=18|y=9|label=H}}<br /> {{Lumatone key|x=19|y=10|label=I}}<br /> {{Lumatone key|x=19|y=9|label=J}}<br /> <br /> {{Lumatone key|x=20|y=10|label=A}}<br /> {{Lumatone key|x=20|y=9|label=B}}<br /> {{Lumatone key|x=21|y=10|label=C}}<br /> {{Lumatone key|x=22|y=11|label=D}}<br /> {{Lumatone key|x=22|y=10|label=E}}<br /> {{Lumatone key|x=23|y=11|label=F}}<br /> {{Lumatone key|x=23|y=10|label=G}}<br /> {{Lumatone key|x=24|y=11|label=H}}<br /> {{Lumatone key|x=25|y=12|label=I}}<br /> {{Lumatone key|x=25|y=11|label=J}}<br /> <br /> {{Lumatone key|x=26|y=12|label=A}}<br /> {{Lumatone key|x=26|y=11|label=B}}<br /> {{Lumatone key|x=27|y=12|label=C}}<br /> {{Lumatone key|x=28|y=13|label=D}}<br /> {{Lumatone key|x=28|y=12|label=E}}<br /> {{Lumatone key|x=29|y=13|label=F}}<br /> {{Lumatone key|x=29|y=12|label=G}}<br /> {{Lumatone key|x=30|y=13|label=H}}<br /> {{Lumatone key|x=31|y=14|label=I}}<br /> {{Lumatone key|x=31|y=13|label=J}}<br /> <br /> {{Lumatone key|x=32|y=14|label=A}}<br /> {{Lumatone key|x=32|y=13|label=B}}<br /> {{Lumatone key|x=33|y=14|label=C}}<br /> {{Lumatone key|x=34|y=15|label=D}}<br /> {{Lumatone key|x=34|y=14|label=E}}<br /> {{Lumatone key|x=35|y=15|label=F}}<br /> {{Lumatone key|x=35|y=14|label=G}}<br /> {{Lumatone key|x=36|y=15|label=H}}<br /> {{Lumatone key|x=37|y=16|label=I}}<br /> {{Lumatone key|x=37|y=15|label=J}}<br /> <br /> }}<br /> <br /> Here is one 7-limit tonality diamond, to show the shapes of simple intervals. Note that 50/49 is tempered out so 10/7~7/5.<br /> {{Lumatone mapping|<br /> <br /> {{Lumatone key|x=17|y=7|label=6/5}}<br /> <br /> {{Lumatone key|x=16|y=8|label=1/1}}<br /> {{Lumatone key|x=17|y=8|label=8/7}}<br /> {{Lumatone key|x=18|y=8|label=21/16|size=10px}}<br /> {{Lumatone key|x=19|y=8|label=3/2}}<br /> {{Lumatone key|x=20|y=8|label=12/7|size=12px}}<br /> <br /> {{Lumatone key|x=18|y=9|label=5/4}}<br /> {{Lumatone key|x=19|y=9|label=7/5}}<br /> {{Lumatone key|x=20|y=9|label=8/5}}<br /> <br /> {{Lumatone key|x=18|y=10|label=7/6}}<br /> {{Lumatone key|x=19|y=10|label=4/3}}<br /> {{Lumatone key|x=20|y=10|label=32/21|size=10px}}<br /> {{Lumatone key|x=21|y=10|label=7/4}}<br /> {{Lumatone key|x=22|y=10|label=1/1}}<br /> <br /> {{Lumatone key|x=21|y=11|label=5/3}}<br /> <br /> }}<br /> <br /> [[Category:Lumatone mappings]]<br /> [[Category:Lemba]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Trivial_temperament&diff=83600 Trivial temperament 2022-01-09T22:54:23Z <p>Keenan Pepper: change OM to Om</p> <hr /> <div>A '''trivial temperament''' is something that fits the mathematical definition of &quot;regular temperament&quot;, but is a unique, extreme case that people might be uncomfortable calling a &quot;[[temperament]]&quot;. There are two kinds of trivial temperaments - [[JI]], in which nothing is tempered, and '''Om''' temperament, in which everything is tempered.<br /> <br /> Just intonation is a codimension-0 &quot;temperament&quot;, which means nothing is tempered. The set of commas that are tempered out is the set {1/1}, but that's still a set, so JI is still a regular temperament. There is an infinite family of these &quot;temperaments&quot;, one for each subgroup of JI. The [[2-limit]] version is the equal temperament [[1edo]]. The [[3-limit]] version is the rank-2 temperament [[pythagorean]], which has all the properties of any other rank-2 temperament except that it tempers no commas. The [[5-limit]] version is rank-3, and so on. The mapping for this temperament is an nxn identity matrix, with wedgies of &amp;lt;1|, &amp;lt;&amp;lt;1||, &amp;lt;&amp;lt;&amp;lt;1|||... .<br /> <br /> '''Om''' temperament is the rank-0 temperament, in which every interval is a comma. Thus all notes are represented by the same note. This is different from 1edo because not even octaves exist; it could be described as [[0edo]]. The mapping for this is the 0-val, &amp;lt;0 0 ... 0|.<br /> <br /> [[Category:Temperament]]<br /> [[Category:Theory]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Lumatone_mapping_for_orwell&diff=83599 Lumatone mapping for orwell 2022-01-09T22:45:53Z <p>Keenan Pepper: </p> <hr /> <div>Note the following equivalences in [[orwell]], meaning that a key labeled with one of the ratios actually represents both:<br /> * 16/15 ~ 15/14<br /> * 12/11 ~ 11/10<br /> * 14/11 ~ 9/7<br /> * 14/9 ~ 11/7<br /> * 20/11 ~ 11/6<br /> * 28/15 ~ 15/8<br /> <br /> ==Compressed==<br /> <br /> This mapping covers 6 complete octaves. The orwell[9] MOS has a zigzag pattern with 60 degree angles.<br /> {{Lumatone mapping|<br /> <br /> {{Lumatone key|x=1|y=2|label=9/5}}<br /> <br /> {{Lumatone key|x=3|y=3|label=9/8}}<br /> {{Lumatone key|x=4|y=3|label=}}<br /> {{Lumatone key|x=5|y=3|label=}}<br /> {{Lumatone key|x=6|y=3|label=9/5}}<br /> <br /> {{Lumatone key|x=2|y=4|label=7/4}}<br /> {{Lumatone key|x=3|y=4|label=}}<br /> {{Lumatone key|x=4|y=4|label=6/5}}<br /> {{Lumatone key|x=5|y=4|label=7/5}}<br /> {{Lumatone key|x=6|y=4|label=}}<br /> {{Lumatone key|x=7|y=4|label=}}<br /> {{Lumatone key|x=8|y=4|label=9/8}}<br /> {{Lumatone key|x=9|y=4|label=}}<br /> {{Lumatone key|x=10|y=4|label=}}<br /> {{Lumatone key|x=11|y=4|label=9/5}}<br /> <br /> {{Lumatone key|x=3|y=5|label=15/8|size=12px}}<br /> {{Lumatone key|x=4|y=5|label=11/10|size=10px}}<br /> {{Lumatone key|x=5|y=5|label=9/7}}<br /> {{Lumatone key|x=6|y=5|label=3/2}}<br /> {{Lumatone key|x=7|y=5|label=7/4}}<br /> {{Lumatone key|x=8|y=5|label=}}<br /> {{Lumatone key|x=9|y=5|label=6/5}}<br /> {{Lumatone key|x=10|y=5|label=7/5}}<br /> {{Lumatone key|x=11|y=5|label=}}<br /> {{Lumatone key|x=12|y=5|label=}}<br /> {{Lumatone key|x=13|y=5|label=9/8}}<br /> {{Lumatone key|x=14|y=5|label=}}<br /> {{Lumatone key|x=15|y=5|label=}}<br /> {{Lumatone key|x=16|y=5|label=9/5}}<br /> <br /> {{Lumatone key|x=3|y=6|label=12/7|size=12px}}<br /> {{Lumatone key|x=4|y=6|label=1/1}}<br /> {{Lumatone key|x=5|y=6|label=7/6}}<br /> {{Lumatone key|x=6|y=6|label=11/8|size=12px}}<br /> {{Lumatone key|x=7|y=6|label=8/5}}<br /> {{Lumatone key|x=8|y=6|label=15/8|size=12px}}<br /> {{Lumatone key|x=9|y=6|label=11/10|size=10px}}<br /> {{Lumatone key|x=10|y=6|label=9/7}}<br /> {{Lumatone key|x=11|y=6|label=3/2}}<br /> {{Lumatone key|x=12|y=6|label=7/4}}<br /> {{Lumatone key|x=13|y=6|label=}}<br /> {{Lumatone key|x=14|y=6|label=6/5}}<br /> {{Lumatone key|x=15|y=6|label=7/5}}<br /> {{Lumatone key|x=16|y=6|label=}}<br /> {{Lumatone key|x=17|y=6|label=}}<br /> {{Lumatone key|x=18|y=6|label=9/8}}<br /> {{Lumatone key|x=19|y=6|label=}}<br /> {{Lumatone key|x=20|y=6|label=}}<br /> {{Lumatone key|x=21|y=6|label=9/5}}<br /> <br /> {{Lumatone key|x=4|y=7|label=11/6|size=12px}}<br /> {{Lumatone key|x=5|y=7|label=15/14|size=10px}}<br /> {{Lumatone key|x=6|y=7|label=5/4}}<br /> {{Lumatone key|x=7|y=7|label=16/11|size=10px}}<br /> {{Lumatone key|x=8|y=7|label=12/7|size=12px}}<br /> {{Lumatone key|x=9|y=7|label=1/1}}<br /> {{Lumatone key|x=10|y=7|label=7/6}}<br /> {{Lumatone key|x=11|y=7|label=11/8|size=12px}}<br /> {{Lumatone key|x=12|y=7|label=8/5}}<br /> {{Lumatone key|x=13|y=7|label=15/8|size=12px}}<br /> {{Lumatone key|x=14|y=7|label=11/10|size=10px}}<br /> {{Lumatone key|x=15|y=7|label=9/7}}<br /> {{Lumatone key|x=16|y=7|label=3/2}}<br /> {{Lumatone key|x=17|y=7|label=7/4}}<br /> {{Lumatone key|x=18|y=7|label=}}<br /> {{Lumatone key|x=19|y=7|label=6/5}}<br /> {{Lumatone key|x=20|y=7|label=7/5}}<br /> {{Lumatone key|x=21|y=7|label=}}<br /> {{Lumatone key|x=22|y=7|label=}}<br /> {{Lumatone key|x=23|y=7|label=9/8}}<br /> {{Lumatone key|x=24|y=7|label=}}<br /> {{Lumatone key|x=25|y=7|label=}}<br /> {{Lumatone key|x=26|y=7|label=9/5}}<br /> <br /> {{Lumatone key|x=4|y=8|label=5/3}}<br /> {{Lumatone key|x=5|y=8|label=}}<br /> {{Lumatone key|x=6|y=8|label=8/7}}<br /> {{Lumatone key|x=7|y=8|label=4/3}}<br /> {{Lumatone key|x=8|y=8|label=11/7|size=12px}}<br /> {{Lumatone key|x=9|y=8|label=11/6|size=12px}}<br /> {{Lumatone key|x=10|y=8|label=15/14|size=10px}}<br /> {{Lumatone key|x=11|y=8|label=5/4}}<br /> {{Lumatone key|x=12|y=8|label=16/11|size=10px}}<br /> {{Lumatone key|x=13|y=8|label=12/7|size=12px}}<br /> {{Lumatone key|x=14|y=8|label=1/1}}<br /> {{Lumatone key|x=15|y=8|label=7/6}}<br /> {{Lumatone key|x=16|y=8|label=11/8|size=12px}}<br /> {{Lumatone key|x=17|y=8|label=8/5}}<br /> {{Lumatone key|x=18|y=8|label=15/8|size=12px}}<br /> {{Lumatone key|x=19|y=8|label=11/10|size=10px}}<br /> {{Lumatone key|x=20|y=8|label=9/7}}<br /> {{Lumatone key|x=21|y=8|label=3/2}}<br /> {{Lumatone key|x=22|y=8|label=7/4}}<br /> {{Lumatone key|x=23|y=8|label=}}<br /> {{Lumatone key|x=24|y=8|label=6/5}}<br /> {{Lumatone key|x=25|y=8|label=7/5}}<br /> {{Lumatone key|x=26|y=8|label=}}<br /> {{Lumatone key|x=27|y=8|label=}}<br /> {{Lumatone key|x=28|y=8|label=9/8}}<br /> {{Lumatone key|x=29|y=8|label=}}<br /> {{Lumatone key|x=30|y=8|label=}}<br /> <br /> {{Lumatone key|x=6|y=9|label=}}<br /> {{Lumatone key|x=7|y=9|label=}}<br /> {{Lumatone key|x=8|y=9|label=10/7|size=12px}}<br /> {{Lumatone key|x=9|y=9|label=5/3}}<br /> {{Lumatone key|x=10|y=9|label=}}<br /> {{Lumatone key|x=11|y=9|label=8/7}}<br /> {{Lumatone key|x=12|y=9|label=4/3}}<br /> {{Lumatone key|x=13|y=9|label=11/7|size=12px}}<br /> {{Lumatone key|x=14|y=9|label=11/6|size=12px}}<br /> {{Lumatone key|x=15|y=9|label=15/14|size=10px}}<br /> {{Lumatone key|x=16|y=9|label=5/4}}<br /> {{Lumatone key|x=17|y=9|label=16/11|size=10px}}<br /> {{Lumatone key|x=18|y=9|label=12/7|size=12px}}<br /> {{Lumatone key|x=19|y=9|label=1/1}}<br /> {{Lumatone key|x=20|y=9|label=7/6}}<br /> {{Lumatone key|x=21|y=9|label=11/8|size=12px}}<br /> {{Lumatone key|x=22|y=9|label=8/5}}<br /> {{Lumatone key|x=23|y=9|label=15/8|size=12px}}<br /> {{Lumatone key|x=24|y=9|label=11/10|size=10px}}<br /> {{Lumatone key|x=25|y=9|label=9/7}}<br /> {{Lumatone key|x=26|y=9|label=3/2}}<br /> {{Lumatone key|x=27|y=9|label=7/4}}<br /> {{Lumatone key|x=28|y=9|label=}}<br /> {{Lumatone key|x=29|y=9|label=6/5}}<br /> {{Lumatone key|x=30|y=9|label=7/5}}<br /> {{Lumatone key|x=31|y=9|label=}}<br /> {{Lumatone key|x=32|y=9|label=}}<br /> {{Lumatone key|x=33|y=9|label=9/8}}<br /> <br /> {{Lumatone key|x=9|y=10|label=}}<br /> {{Lumatone key|x=10|y=10|label=16/9|size=12px}}<br /> {{Lumatone key|x=11|y=10|label=}}<br /> {{Lumatone key|x=12|y=10|label=}}<br /> {{Lumatone key|x=13|y=10|label=10/7|size=12px}}<br /> {{Lumatone key|x=14|y=10|label=5/3}}<br /> {{Lumatone key|x=15|y=10|label=}}<br /> {{Lumatone key|x=16|y=10|label=8/7}}<br /> {{Lumatone key|x=17|y=10|label=4/3}}<br /> {{Lumatone key|x=18|y=10|label=11/7|size=12px}}<br /> {{Lumatone key|x=19|y=10|label=11/6|size=12px}}<br /> {{Lumatone key|x=20|y=10|label=15/14|size=10px}}<br /> {{Lumatone key|x=21|y=10|label=5/4}}<br /> {{Lumatone key|x=22|y=10|label=16/11|size=10px}}<br /> {{Lumatone key|x=23|y=10|label=12/7|size=12px}}<br /> {{Lumatone key|x=24|y=10|label=1/1}}<br /> {{Lumatone key|x=25|y=10|label=7/6}}<br /> {{Lumatone key|x=26|y=10|label=11/8|size=12px}}<br /> {{Lumatone key|x=27|y=10|label=8/5}}<br /> {{Lumatone key|x=28|y=10|label=15/8|size=12px}}<br /> {{Lumatone key|x=29|y=10|label=11/10|size=10px}}<br /> {{Lumatone key|x=30|y=10|label=9/7}}<br /> {{Lumatone key|x=31|y=10|label=3/2}}<br /> {{Lumatone key|x=32|y=10|label=7/4}}<br /> {{Lumatone key|x=33|y=10|label=}}<br /> {{Lumatone key|x=34|y=10|label=6/5}}<br /> <br /> {{Lumatone key|x=13|y=11|label=}}<br /> {{Lumatone key|x=14|y=11|label=}}<br /> {{Lumatone key|x=15|y=11|label=16/9|size=12px}}<br /> {{Lumatone key|x=16|y=11|label=}}<br /> {{Lumatone key|x=17|y=11|label=}}<br /> {{Lumatone key|x=18|y=11|label=10/7|size=12px}}<br /> {{Lumatone key|x=19|y=11|label=5/3}}<br /> {{Lumatone key|x=20|y=11|label=}}<br /> {{Lumatone key|x=21|y=11|label=8/7}}<br /> {{Lumatone key|x=22|y=11|label=4/3}}<br /> {{Lumatone key|x=23|y=11|label=11/7|size=12px}}<br /> {{Lumatone key|x=24|y=11|label=11/6|size=12px}}<br /> {{Lumatone key|x=25|y=11|label=15/14|size=10px}}<br /> {{Lumatone key|x=26|y=11|label=5/4}}<br /> {{Lumatone key|x=27|y=11|label=16/11|size=10px}}<br /> {{Lumatone key|x=28|y=11|label=12/7|size=12px}}<br /> {{Lumatone key|x=29|y=11|label=1/1}}<br /> {{Lumatone key|x=30|y=11|label=7/6}}<br /> {{Lumatone key|x=31|y=11|label=11/8|size=12px}}<br /> {{Lumatone key|x=32|y=11|label=8/5}}<br /> {{Lumatone key|x=33|y=11|label=15/8|size=12px}}<br /> {{Lumatone key|x=34|y=11|label=11/10|size=10px}}<br /> {{Lumatone key|x=35|y=11|label=9/7}}<br /> <br /> {{Lumatone key|x=16|y=12|label=}}<br /> {{Lumatone key|x=17|y=12|label=10/9|size=12px}}<br /> {{Lumatone key|x=18|y=12|label=}}<br /> {{Lumatone key|x=19|y=12|label=}}<br /> {{Lumatone key|x=20|y=12|label=16/9|size=12px}}<br /> {{Lumatone key|x=21|y=12|label=}}<br /> {{Lumatone key|x=22|y=12|label=}}<br /> {{Lumatone key|x=23|y=12|label=10/7|size=12px}}<br /> {{Lumatone key|x=24|y=12|label=5/3}}<br /> {{Lumatone key|x=25|y=12|label=}}<br /> {{Lumatone key|x=26|y=12|label=8/7}}<br /> {{Lumatone key|x=27|y=12|label=4/3}}<br /> {{Lumatone key|x=28|y=12|label=11/7|size=12px}}<br /> {{Lumatone key|x=29|y=12|label=11/6|size=12px}}<br /> {{Lumatone key|x=30|y=12|label=15/14|size=10px}}<br /> {{Lumatone key|x=31|y=12|label=5/4}}<br /> {{Lumatone key|x=32|y=12|label=16/11|size=10px}}<br /> {{Lumatone key|x=33|y=12|label=12/7|size=12px}}<br /> {{Lumatone key|x=34|y=12|label=1/1}}<br /> {{Lumatone key|x=35|y=12|label=7/6}}<br /> <br /> {{Lumatone key|x=22|y=13|label=10/9|size=12px}}<br /> {{Lumatone key|x=23|y=13|label=}}<br /> {{Lumatone key|x=24|y=13|label=}}<br /> {{Lumatone key|x=25|y=13|label=16/9|size=12px}}<br /> {{Lumatone key|x=26|y=13|label=}}<br /> {{Lumatone key|x=27|y=13|label=}}<br /> {{Lumatone key|x=28|y=13|label=10/7|size=12px}}<br /> {{Lumatone key|x=29|y=13|label=5/3}}<br /> {{Lumatone key|x=30|y=13|label=}}<br /> {{Lumatone key|x=31|y=13|label=8/7}}<br /> {{Lumatone key|x=32|y=13|label=4/3}}<br /> {{Lumatone key|x=33|y=13|label=11/7|size=12px}}<br /> {{Lumatone key|x=34|y=13|label=11/6|size=12px}}<br /> {{Lumatone key|x=35|y=13|label=15/14|size=10px}}<br /> {{Lumatone key|x=36|y=13|label=5/4}}<br /> <br /> {{Lumatone key|x=27|y=14|label=10/9|size=12px}}<br /> {{Lumatone key|x=28|y=14|label=}}<br /> {{Lumatone key|x=29|y=14|label=}}<br /> {{Lumatone key|x=30|y=14|label=16/9|size=12px}}<br /> {{Lumatone key|x=31|y=14|label=}}<br /> {{Lumatone key|x=32|y=14|label=}}<br /> {{Lumatone key|x=33|y=14|label=10/7|size=12px}}<br /> {{Lumatone key|x=34|y=14|label=5/3}}<br /> {{Lumatone key|x=35|y=14|label=}}<br /> {{Lumatone key|x=36|y=14|label=8/7}}<br /> <br /> {{Lumatone key|x=32|y=15|label=10/9|size=12px}}<br /> {{Lumatone key|x=33|y=15|label=}}<br /> {{Lumatone key|x=34|y=15|label=}}<br /> {{Lumatone key|x=35|y=15|label=16/9|size=12px}}<br /> <br /> {{Lumatone key|x=37|y=16|label=10/9|size=12px}}<br /> <br /> }}<br /> <br /> ==Expanded==<br /> <br /> There are only 4 complete octaves. The orwell[9] MOS has a straighter zigzag with 120 degree angles. The direction of the chroma is also reversed.<br /> {{Lumatone mapping|<br /> <br /> {{Lumatone key|x=1|y=1|label=1/1}}<br /> {{Lumatone key|x=2|y=1|label=15/14|size=10px}}<br /> {{Lumatone key|x=3|y=1|label=8/7}}<br /> <br /> {{Lumatone key|x=2|y=2|label=11/10|size=10px}}<br /> {{Lumatone key|x=3|y=2|label=7/6}}<br /> {{Lumatone key|x=4|y=2|label=5/4}}<br /> {{Lumatone key|x=5|y=2|label=4/3}}<br /> {{Lumatone key|x=6|y=2|label=10/7|size=12px}}<br /> <br /> {{Lumatone key|x=2|y=3|label=9/8}}<br /> {{Lumatone key|x=3|y=3|label=6/5}}<br /> {{Lumatone key|x=4|y=3|label=9/7}}<br /> {{Lumatone key|x=5|y=3|label=11/8|size=12px}}<br /> {{Lumatone key|x=6|y=3|label=16/11|size=10px}}<br /> {{Lumatone key|x=7|y=3|label=11/7|size=12px}}<br /> {{Lumatone key|x=8|y=3|label=5/3}}<br /> {{Lumatone key|x=9|y=3|label=16/9|size=12px}}<br /> <br /> {{Lumatone key|x=5|y=4|label=7/5}}<br /> {{Lumatone key|x=6|y=4|label=3/2}}<br /> {{Lumatone key|x=7|y=4|label=8/5}}<br /> {{Lumatone key|x=8|y=4|label=12/7|size=12px}}<br /> {{Lumatone key|x=9|y=4|label=11/6|size=12px}}<br /> {{Lumatone key|x=10|y=4|label=}}<br /> {{Lumatone key|x=11|y=4|label=}}<br /> {{Lumatone key|x=12|y=4|label=10/9|size=12px}}<br /> <br /> {{Lumatone key|x=8|y=5|label=7/4}}<br /> {{Lumatone key|x=9|y=5|label=15/8|size=12px}}<br /> {{Lumatone key|x=10|y=5|label=1/1}}<br /> {{Lumatone key|x=11|y=5|label=15/14|size=10px}}<br /> {{Lumatone key|x=12|y=5|label=8/7}}<br /> <br /> {{Lumatone key|x=8|y=6|label=9/5}}<br /> {{Lumatone key|x=9|y=6|label=}}<br /> {{Lumatone key|x=10|y=6|label=}}<br /> {{Lumatone key|x=11|y=6|label=11/10|size=10px}}<br /> {{Lumatone key|x=12|y=6|label=7/6}}<br /> {{Lumatone key|x=13|y=6|label=5/4}}<br /> {{Lumatone key|x=14|y=6|label=4/3}}<br /> {{Lumatone key|x=15|y=6|label=10/7|size=12px}}<br /> <br /> {{Lumatone key|x=11|y=7|label=9/8}}<br /> {{Lumatone key|x=12|y=7|label=6/5}}<br /> {{Lumatone key|x=13|y=7|label=9/7}}<br /> {{Lumatone key|x=14|y=7|label=11/8|size=12px}}<br /> {{Lumatone key|x=15|y=7|label=16/11|size=10px}}<br /> {{Lumatone key|x=16|y=7|label=11/7|size=12px}}<br /> {{Lumatone key|x=17|y=7|label=5/3}}<br /> {{Lumatone key|x=18|y=7|label=16/9|size=12px}}<br /> <br /> {{Lumatone key|x=14|y=8|label=7/5}}<br /> {{Lumatone key|x=15|y=8|label=3/2}}<br /> {{Lumatone key|x=16|y=8|label=8/5}}<br /> {{Lumatone key|x=17|y=8|label=12/7|size=12px}}<br /> {{Lumatone key|x=18|y=8|label=11/6|size=12px}}<br /> {{Lumatone key|x=19|y=8|label=}}<br /> {{Lumatone key|x=20|y=8|label=}}<br /> {{Lumatone key|x=21|y=8|label=10/9|size=12px}}<br /> <br /> {{Lumatone key|x=17|y=9|label=7/4}}<br /> {{Lumatone key|x=18|y=9|label=15/8|size=12px}}<br /> {{Lumatone key|x=19|y=9|label=1/1}}<br /> {{Lumatone key|x=20|y=9|label=15/14|size=10px}}<br /> {{Lumatone key|x=21|y=9|label=8/7}}<br /> <br /> {{Lumatone key|x=17|y=10|label=9/5}}<br /> {{Lumatone key|x=18|y=10|label=}}<br /> {{Lumatone key|x=19|y=10|label=}}<br /> {{Lumatone key|x=20|y=10|label=11/10|size=10px}}<br /> {{Lumatone key|x=21|y=10|label=7/6}}<br /> {{Lumatone key|x=22|y=10|label=5/4}}<br /> {{Lumatone key|x=23|y=10|label=4/3}}<br /> {{Lumatone key|x=24|y=10|label=10/7|size=12px}}<br /> <br /> {{Lumatone key|x=20|y=11|label=9/8}}<br /> {{Lumatone key|x=21|y=11|label=6/5}}<br /> {{Lumatone key|x=22|y=11|label=9/7}}<br /> {{Lumatone key|x=23|y=11|label=11/8|size=12px}}<br /> {{Lumatone key|x=24|y=11|label=16/11|size=10px}}<br /> {{Lumatone key|x=25|y=11|label=11/7|size=12px}}<br /> {{Lumatone key|x=26|y=11|label=5/3}}<br /> {{Lumatone key|x=27|y=11|label=16/9|size=12px}}<br /> <br /> {{Lumatone key|x=23|y=12|label=7/5}}<br /> {{Lumatone key|x=24|y=12|label=3/2}}<br /> {{Lumatone key|x=25|y=12|label=8/5}}<br /> {{Lumatone key|x=26|y=12|label=12/7|size=12px}}<br /> {{Lumatone key|x=27|y=12|label=11/6|size=12px}}<br /> {{Lumatone key|x=28|y=12|label=}}<br /> {{Lumatone key|x=29|y=12|label=}}<br /> {{Lumatone key|x=30|y=12|label=10/9|size=12px}}<br /> <br /> {{Lumatone key|x=26|y=13|label=7/4}}<br /> {{Lumatone key|x=27|y=13|label=15/8|size=12px}}<br /> {{Lumatone key|x=28|y=13|label=1/1}}<br /> {{Lumatone key|x=29|y=13|label=15/14|size=10px}}<br /> {{Lumatone key|x=30|y=13|label=8/7}}<br /> <br /> {{Lumatone key|x=26|y=14|label=9/5}}<br /> {{Lumatone key|x=27|y=14|label=}}<br /> {{Lumatone key|x=28|y=14|label=}}<br /> {{Lumatone key|x=29|y=14|label=11/10|size=10px}}<br /> {{Lumatone key|x=30|y=14|label=7/6}}<br /> {{Lumatone key|x=31|y=14|label=5/4}}<br /> {{Lumatone key|x=32|y=14|label=4/3}}<br /> {{Lumatone key|x=33|y=14|label=10/7|size=12px}}<br /> <br /> {{Lumatone key|x=29|y=15|label=9/8}}<br /> {{Lumatone key|x=30|y=15|label=6/5}}<br /> {{Lumatone key|x=31|y=15|label=9/7}}<br /> {{Lumatone key|x=32|y=15|label=11/8|size=12px}}<br /> {{Lumatone key|x=33|y=15|label=16/11|size=10px}}<br /> {{Lumatone key|x=34|y=15|label=11/7|size=12px}}<br /> {{Lumatone key|x=35|y=15|label=5/3}}<br /> {{Lumatone key|x=36|y=15|label=16/9|size=12px}}<br /> <br /> {{Lumatone key|x=32|y=16|label=7/5}}<br /> {{Lumatone key|x=33|y=16|label=3/2}}<br /> {{Lumatone key|x=34|y=16|label=8/5}}<br /> {{Lumatone key|x=35|y=16|label=12/7|size=12px}}<br /> {{Lumatone key|x=36|y=16|label=11/6|size=12px}}<br /> <br /> {{Lumatone key|x=35|y=17|label=7/4}}<br /> {{Lumatone key|x=36|y=17|label=15/8|size=12px}}<br /> {{Lumatone key|x=37|y=17|label=1/1}}<br /> {{Lumatone key|x=38|y=17|label=15/14|size=10px}}<br /> <br /> {{Lumatone key|x=38|y=18|label=11/10|size=10px}}<br /> <br /> }}<br /> <br /> ==External links==<br /> * [https://www.youtube.com/watch?v=PU4B5NLaw-0 Orwell temperament on the Lumatone keyboard] by [[Herman Miller]]<br /> <br /> [[Category:Lumatone mappings]]<br /> [[Category:Orwell]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Lumatone_mapping_for_orwell&diff=83595 Lumatone mapping for orwell 2022-01-09T21:40:05Z <p>Keenan Pepper: Created page with &quot;Note the following equivalences in orwell, meaning that a key labeled with one of the ratios actually represents both: * 16/15 ~ 15/14 * 12/11 ~ 11/10 * 14/11 ~ 9/7 * 14/9...&quot;</p> <hr /> <div>Note the following equivalences in [[orwell]], meaning that a key labeled with one of the ratios actually represents both:<br /> * 16/15 ~ 15/14<br /> * 12/11 ~ 11/10<br /> * 14/11 ~ 9/7<br /> * 14/9 ~ 11/7<br /> * 20/11 ~ 11/6<br /> * 28/15 ~ 15/8<br /> <br /> ==Compressed==<br /> <br /> This mapping covers 6 complete octaves. The orwell[9] MOS has a zigzag pattern with 60 degree angles.<br /> <br /> {{Lumatone mapping|<br /> <br /> {{Lumatone key|x=1|y=2|label=9/5}}<br /> <br /> {{Lumatone key|x=3|y=3|label=9/8}}<br /> {{Lumatone key|x=4|y=3|label=}}<br /> {{Lumatone key|x=5|y=3|label=}}<br /> {{Lumatone key|x=6|y=3|label=9/5}}<br /> <br /> {{Lumatone key|x=2|y=4|label=7/4}}<br /> {{Lumatone key|x=3|y=4|label=}}<br /> {{Lumatone key|x=4|y=4|label=6/5}}<br /> {{Lumatone key|x=5|y=4|label=7/5}}<br /> {{Lumatone key|x=6|y=4|label=}}<br /> {{Lumatone key|x=7|y=4|label=}}<br /> {{Lumatone key|x=8|y=4|label=9/8}}<br /> {{Lumatone key|x=9|y=4|label=}}<br /> {{Lumatone key|x=10|y=4|label=}}<br /> {{Lumatone key|x=11|y=4|label=9/5}}<br /> <br /> {{Lumatone key|x=3|y=5|label=15/8|size=12px}}<br /> {{Lumatone key|x=4|y=5|label=11/10|size=10px}}<br /> {{Lumatone key|x=5|y=5|label=9/7}}<br /> {{Lumatone key|x=6|y=5|label=3/2}}<br /> {{Lumatone key|x=7|y=5|label=7/4}}<br /> {{Lumatone key|x=8|y=5|label=}}<br /> {{Lumatone key|x=9|y=5|label=6/5}}<br /> {{Lumatone key|x=10|y=5|label=7/5}}<br /> {{Lumatone key|x=11|y=5|label=}}<br /> {{Lumatone key|x=12|y=5|label=}}<br /> {{Lumatone key|x=13|y=5|label=9/8}}<br /> {{Lumatone key|x=14|y=5|label=}}<br /> {{Lumatone key|x=15|y=5|label=}}<br /> {{Lumatone key|x=16|y=5|label=9/5}}<br /> <br /> {{Lumatone key|x=3|y=6|label=12/7|size=12px}}<br /> {{Lumatone key|x=4|y=6|label=1/1}}<br /> {{Lumatone key|x=5|y=6|label=7/6}}<br /> {{Lumatone key|x=6|y=6|label=11/8|size=12px}}<br /> {{Lumatone key|x=7|y=6|label=8/5}}<br /> {{Lumatone key|x=8|y=6|label=15/8|size=12px}}<br /> {{Lumatone key|x=9|y=6|label=11/10|size=10px}}<br /> {{Lumatone key|x=10|y=6|label=9/7}}<br /> {{Lumatone key|x=11|y=6|label=3/2}}<br /> {{Lumatone key|x=12|y=6|label=7/4}}<br /> {{Lumatone key|x=13|y=6|label=}}<br /> {{Lumatone key|x=14|y=6|label=6/5}}<br /> {{Lumatone key|x=15|y=6|label=7/5}}<br /> {{Lumatone key|x=16|y=6|label=}}<br /> {{Lumatone key|x=17|y=6|label=}}<br /> {{Lumatone key|x=18|y=6|label=9/8}}<br /> {{Lumatone key|x=19|y=6|label=}}<br /> {{Lumatone key|x=20|y=6|label=}}<br /> {{Lumatone key|x=21|y=6|label=9/5}}<br /> <br /> {{Lumatone key|x=4|y=7|label=11/6|size=12px}}<br /> {{Lumatone key|x=5|y=7|label=15/14|size=10px}}<br /> {{Lumatone key|x=6|y=7|label=5/4}}<br /> {{Lumatone key|x=7|y=7|label=16/11|size=10px}}<br /> {{Lumatone key|x=8|y=7|label=12/7|size=12px}}<br /> {{Lumatone key|x=9|y=7|label=1/1}}<br /> {{Lumatone key|x=10|y=7|label=7/6}}<br /> {{Lumatone key|x=11|y=7|label=11/8|size=12px}}<br /> {{Lumatone key|x=12|y=7|label=8/5}}<br /> {{Lumatone key|x=13|y=7|label=15/8|size=12px}}<br /> {{Lumatone key|x=14|y=7|label=11/10|size=10px}}<br /> {{Lumatone key|x=15|y=7|label=9/7}}<br /> {{Lumatone key|x=16|y=7|label=3/2}}<br /> {{Lumatone key|x=17|y=7|label=7/4}}<br /> {{Lumatone key|x=18|y=7|label=}}<br /> {{Lumatone key|x=19|y=7|label=6/5}}<br /> {{Lumatone key|x=20|y=7|label=7/5}}<br /> {{Lumatone key|x=21|y=7|label=}}<br /> {{Lumatone key|x=22|y=7|label=}}<br /> {{Lumatone key|x=23|y=7|label=9/8}}<br /> {{Lumatone key|x=24|y=7|label=}}<br /> {{Lumatone key|x=25|y=7|label=}}<br /> {{Lumatone key|x=26|y=7|label=9/5}}<br /> <br /> {{Lumatone key|x=4|y=8|label=5/3}}<br /> {{Lumatone key|x=5|y=8|label=}}<br /> {{Lumatone key|x=6|y=8|label=8/7}}<br /> {{Lumatone key|x=7|y=8|label=4/3}}<br /> {{Lumatone key|x=8|y=8|label=11/7|size=12px}}<br /> {{Lumatone key|x=9|y=8|label=11/6|size=12px}}<br /> {{Lumatone key|x=10|y=8|label=15/14|size=10px}}<br /> {{Lumatone key|x=11|y=8|label=5/4}}<br /> {{Lumatone key|x=12|y=8|label=16/11|size=10px}}<br /> {{Lumatone key|x=13|y=8|label=12/7|size=12px}}<br /> {{Lumatone key|x=14|y=8|label=1/1}}<br /> {{Lumatone key|x=15|y=8|label=7/6}}<br /> {{Lumatone key|x=16|y=8|label=11/8|size=12px}}<br /> {{Lumatone key|x=17|y=8|label=8/5}}<br /> {{Lumatone key|x=18|y=8|label=15/8|size=12px}}<br /> {{Lumatone key|x=19|y=8|label=11/10|size=10px}}<br /> {{Lumatone key|x=20|y=8|label=9/7}}<br /> {{Lumatone key|x=21|y=8|label=3/2}}<br /> {{Lumatone key|x=22|y=8|label=7/4}}<br /> {{Lumatone key|x=23|y=8|label=}}<br /> {{Lumatone key|x=24|y=8|label=6/5}}<br /> {{Lumatone key|x=25|y=8|label=7/5}}<br /> {{Lumatone key|x=26|y=8|label=}}<br /> {{Lumatone key|x=27|y=8|label=}}<br /> {{Lumatone key|x=28|y=8|label=9/8}}<br /> {{Lumatone key|x=29|y=8|label=}}<br /> {{Lumatone key|x=30|y=8|label=}}<br /> <br /> {{Lumatone key|x=6|y=9|label=}}<br /> {{Lumatone key|x=7|y=9|label=}}<br /> {{Lumatone key|x=8|y=9|label=10/7|size=12px}}<br /> {{Lumatone key|x=9|y=9|label=5/3}}<br /> {{Lumatone key|x=10|y=9|label=}}<br /> {{Lumatone key|x=11|y=9|label=8/7}}<br /> {{Lumatone key|x=12|y=9|label=4/3}}<br /> {{Lumatone key|x=13|y=9|label=11/7|size=12px}}<br /> {{Lumatone key|x=14|y=9|label=11/6|size=12px}}<br /> {{Lumatone key|x=15|y=9|label=15/14|size=10px}}<br /> {{Lumatone key|x=16|y=9|label=5/4}}<br /> {{Lumatone key|x=17|y=9|label=16/11|size=10px}}<br /> {{Lumatone key|x=18|y=9|label=12/7|size=12px}}<br /> {{Lumatone key|x=19|y=9|label=1/1}}<br /> {{Lumatone key|x=20|y=9|label=7/6}}<br /> {{Lumatone key|x=21|y=9|label=11/8|size=12px}}<br /> {{Lumatone key|x=22|y=9|label=8/5}}<br /> {{Lumatone key|x=23|y=9|label=15/8|size=12px}}<br /> {{Lumatone key|x=24|y=9|label=11/10|size=10px}}<br /> {{Lumatone key|x=25|y=9|label=9/7}}<br /> {{Lumatone key|x=26|y=9|label=3/2}}<br /> {{Lumatone key|x=27|y=9|label=7/4}}<br /> {{Lumatone key|x=28|y=9|label=}}<br /> {{Lumatone key|x=29|y=9|label=6/5}}<br /> {{Lumatone key|x=30|y=9|label=7/5}}<br /> {{Lumatone key|x=31|y=9|label=}}<br /> {{Lumatone key|x=32|y=9|label=}}<br /> {{Lumatone key|x=33|y=9|label=9/8}}<br /> <br /> {{Lumatone key|x=9|y=10|label=}}<br /> {{Lumatone key|x=10|y=10|label=16/9|size=12px}}<br /> {{Lumatone key|x=11|y=10|label=}}<br /> {{Lumatone key|x=12|y=10|label=}}<br /> {{Lumatone key|x=13|y=10|label=10/7|size=12px}}<br /> {{Lumatone key|x=14|y=10|label=5/3}}<br /> {{Lumatone key|x=15|y=10|label=}}<br /> {{Lumatone key|x=16|y=10|label=8/7}}<br /> {{Lumatone key|x=17|y=10|label=4/3}}<br /> {{Lumatone key|x=18|y=10|label=11/7|size=12px}}<br /> {{Lumatone key|x=19|y=10|label=11/6|size=12px}}<br /> {{Lumatone key|x=20|y=10|label=15/14|size=10px}}<br /> {{Lumatone key|x=21|y=10|label=5/4}}<br /> {{Lumatone key|x=22|y=10|label=16/11|size=10px}}<br /> {{Lumatone key|x=23|y=10|label=12/7|size=12px}}<br /> {{Lumatone key|x=24|y=10|label=1/1}}<br /> {{Lumatone key|x=25|y=10|label=7/6}}<br /> {{Lumatone key|x=26|y=10|label=11/8|size=12px}}<br /> {{Lumatone key|x=27|y=10|label=8/5}}<br /> {{Lumatone key|x=28|y=10|label=15/8|size=12px}}<br /> {{Lumatone key|x=29|y=10|label=11/10|size=10px}}<br /> {{Lumatone key|x=30|y=10|label=9/7}}<br /> {{Lumatone key|x=31|y=10|label=3/2}}<br /> {{Lumatone key|x=32|y=10|label=7/4}}<br /> {{Lumatone key|x=33|y=10|label=}}<br /> {{Lumatone key|x=34|y=10|label=6/5}}<br /> <br /> {{Lumatone key|x=13|y=11|label=}}<br /> {{Lumatone key|x=14|y=11|label=}}<br /> {{Lumatone key|x=15|y=11|label=16/9|size=12px}}<br /> {{Lumatone key|x=16|y=11|label=}}<br /> {{Lumatone key|x=17|y=11|label=}}<br /> {{Lumatone key|x=18|y=11|label=10/7|size=12px}}<br /> {{Lumatone key|x=19|y=11|label=5/3}}<br /> {{Lumatone key|x=20|y=11|label=}}<br /> {{Lumatone key|x=21|y=11|label=8/7}}<br /> {{Lumatone key|x=22|y=11|label=4/3}}<br /> {{Lumatone key|x=23|y=11|label=11/7|size=12px}}<br /> {{Lumatone key|x=24|y=11|label=11/6|size=12px}}<br /> {{Lumatone key|x=25|y=11|label=15/14|size=10px}}<br /> {{Lumatone key|x=26|y=11|label=5/4}}<br /> {{Lumatone key|x=27|y=11|label=16/11|size=10px}}<br /> {{Lumatone key|x=28|y=11|label=12/7|size=12px}}<br /> {{Lumatone key|x=29|y=11|label=1/1}}<br /> {{Lumatone key|x=30|y=11|label=7/6}}<br /> {{Lumatone key|x=31|y=11|label=11/8|size=12px}}<br /> {{Lumatone key|x=32|y=11|label=8/5}}<br /> {{Lumatone key|x=33|y=11|label=15/8|size=12px}}<br /> {{Lumatone key|x=34|y=11|label=11/10|size=10px}}<br /> {{Lumatone key|x=35|y=11|label=9/7}}<br /> <br /> {{Lumatone key|x=16|y=12|label=}}<br /> {{Lumatone key|x=17|y=12|label=10/9|size=12px}}<br /> {{Lumatone key|x=18|y=12|label=}}<br /> {{Lumatone key|x=19|y=12|label=}}<br /> {{Lumatone key|x=20|y=12|label=16/9|size=12px}}<br /> {{Lumatone key|x=21|y=12|label=}}<br /> {{Lumatone key|x=22|y=12|label=}}<br /> {{Lumatone key|x=23|y=12|label=10/7|size=12px}}<br /> {{Lumatone key|x=24|y=12|label=5/3}}<br /> {{Lumatone key|x=25|y=12|label=}}<br /> {{Lumatone key|x=26|y=12|label=8/7}}<br /> {{Lumatone key|x=27|y=12|label=4/3}}<br /> {{Lumatone key|x=28|y=12|label=11/7|size=12px}}<br /> {{Lumatone key|x=29|y=12|label=11/6|size=12px}}<br /> {{Lumatone key|x=30|y=12|label=15/14|size=10px}}<br /> {{Lumatone key|x=31|y=12|label=5/4}}<br /> {{Lumatone key|x=32|y=12|label=16/11|size=10px}}<br /> {{Lumatone key|x=33|y=12|label=12/7|size=12px}}<br /> {{Lumatone key|x=34|y=12|label=1/1}}<br /> {{Lumatone key|x=35|y=12|label=7/6}}<br /> <br /> {{Lumatone key|x=23|y=13|label=10/9|size=12px}}<br /> {{Lumatone key|x=23|y=13|label=}}<br /> {{Lumatone key|x=24|y=13|label=}}<br /> {{Lumatone key|x=25|y=13|label=16/9|size=12px}}<br /> {{Lumatone key|x=26|y=13|label=}}<br /> {{Lumatone key|x=27|y=13|label=}}<br /> {{Lumatone key|x=28|y=13|label=10/7|size=12px}}<br /> {{Lumatone key|x=29|y=13|label=5/3}}<br /> {{Lumatone key|x=30|y=13|label=}}<br /> {{Lumatone key|x=31|y=13|label=8/7}}<br /> {{Lumatone key|x=32|y=13|label=4/3}}<br /> {{Lumatone key|x=33|y=13|label=11/7|size=12px}}<br /> {{Lumatone key|x=34|y=13|label=11/6|size=12px}}<br /> {{Lumatone key|x=35|y=13|label=15/14|size=10px}}<br /> {{Lumatone key|x=36|y=13|label=5/4}}<br /> <br /> {{Lumatone key|x=27|y=14|label=10/9|size=12px}}<br /> {{Lumatone key|x=28|y=14|label=}}<br /> {{Lumatone key|x=29|y=14|label=}}<br /> {{Lumatone key|x=30|y=14|label=16/9|size=12px}}<br /> {{Lumatone key|x=31|y=14|label=}}<br /> {{Lumatone key|x=32|y=14|label=}}<br /> {{Lumatone key|x=33|y=14|label=10/7|size=12px}}<br /> {{Lumatone key|x=34|y=14|label=5/3}}<br /> {{Lumatone key|x=35|y=14|label=}}<br /> {{Lumatone key|x=36|y=14|label=8/7}}<br /> <br /> {{Lumatone key|x=32|y=15|label=10/9|size=12px}}<br /> {{Lumatone key|x=33|y=15|label=}}<br /> {{Lumatone key|x=34|y=15|label=}}<br /> {{Lumatone key|x=35|y=15|label=16/9|size=12px}}<br /> <br /> {{Lumatone key|x=37|y=16|label=10/9|size=12px}}<br /> <br /> }}<br /> <br /> [[Category:Lumatone mappings]]<br /> [[Category:Orwell]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Lumatone_mapping_for_harry&diff=83593 Lumatone mapping for harry 2022-01-09T20:41:41Z <p>Keenan Pepper: Created page with &quot;Harry mapping with only 11-limit tonality diamond shown: {{Lumatone mapping| {{Lumatone key|x=7|y=6|label=12/11|size=10px}} {{Lumatone key|x=8|y=6|label=8/7}} {{Lumat...&quot;</p> <hr /> <div>[[Harry]] mapping with only 11-limit [[tonality diamond]] shown:<br /> {{Lumatone mapping|<br /> <br /> {{Lumatone key|x=7|y=6|label=12/11|size=10px}}<br /> {{Lumatone key|x=8|y=6|label=8/7}}<br /> {{Lumatone key|x=9|y=6|label=6/5}}<br /> {{Lumatone key|x=13|y=6|label=16/11|size=10px}}<br /> {{Lumatone key|x=15|y=6|label=8/5}}<br /> <br /> {{Lumatone key|x=5|y=7|label=1/1}}<br /> {{Lumatone key|x=7|y=7|label=11/10|size=10px}}<br /> {{Lumatone key|x=10|y=7|label=14/11|size=10px}}<br /> {{Lumatone key|x=11|y=7|label=4/3}}<br /> {{Lumatone key|x=12|y=7|label=7/5}}<br /> {{Lumatone key|x=17|y=7|label=16/9|size=12px}}<br /> <br /> {{Lumatone key|x=7|y=8|label=10/9|size=12px}}<br /> {{Lumatone key|x=8|y=8|label=7/6}}<br /> {{Lumatone key|x=9|y=8|label=11/9|size=12px}}<br /> {{Lumatone key|x=10|y=8|label=9/7}}<br /> {{Lumatone key|x=14|y=8|label=14/9|size=12px}}<br /> {{Lumatone key|x=15|y=8|label=18/11|size=10px}}<br /> {{Lumatone key|x=16|y=8|label=12/7|size=12px}}<br /> {{Lumatone key|x=17|y=8|label=9/5}}<br /> <br /> {{Lumatone key|x=7|y=9|label=9/8}}<br /> {{Lumatone key|x=12|y=9|label=10/7|size=12px}}<br /> {{Lumatone key|x=13|y=9|label=3/2}}<br /> {{Lumatone key|x=14|y=9|label=11/7|size=12px}}<br /> {{Lumatone key|x=17|y=9|label=20/11|size=10px}}<br /> {{Lumatone key|x=19|y=9|label=1/1}}<br /> <br /> {{Lumatone key|x=9|y=10|label=5/4}}<br /> {{Lumatone key|x=11|y=10|label=11/8|size=12px}}<br /> {{Lumatone key|x=15|y=10|label=5/3}}<br /> {{Lumatone key|x=16|y=10|label=7/4}}<br /> {{Lumatone key|x=17|y=10|label=11/6|size=12px}}<br /> <br /> {{Lumatone key|x=33|y=11|label=1/1}}<br /> <br /> }}<br /> <br /> [[Category:Lumatone mappings]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Lumatone_mapping_for_Tetracot&diff=83582 Lumatone mapping for Tetracot 2022-01-09T19:18:25Z <p>Keenan Pepper: Keenan Pepper moved page Lumatone mapping for Tetracot to Lumatone mapping for tetracot: let&#039;s lowercase all the temperament names</p> <hr /> <div>#REDIRECT [[Lumatone mapping for tetracot]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Lumatone_mapping_for_tetracot&diff=83581 Lumatone mapping for tetracot 2022-01-09T19:18:24Z <p>Keenan Pepper: Keenan Pepper moved page Lumatone mapping for Tetracot to Lumatone mapping for tetracot: let&#039;s lowercase all the temperament names</p> <hr /> <div>This [[Lumatone]] keyboard mapping is for temperaments shaped like [[tetracot family|tetracot]], which divides 3/2 into four equal parts resulting in a [[6L 1s]] scale. The notation used here is that A-G is Tetracot[7], where G-A is the unique small step. In other words, every pair of consecutive letters of the alphabet (so not G-A) is a tetracot generator.<br /> <br /> This mapping has the same overall shape as the [[Lumatone mapping for Porcupine#Compressed|&quot;compressed&quot; mapping for porcupine]], but because the chroma goes in the other direction, this is already optimal and there is no reason to go to a more &quot;expanded&quot; mapping.<br /> {{Lumatone mapping|<br /> <br /> {{Lumatone key|x=3|y=5|label=F^}}<br /> {{Lumatone key|x=4|y=5|label=G^}}<br /> <br /> {{Lumatone key|x=3|y=6|label=F}}<br /> {{Lumatone key|x=4|y=6|label=G}}<br /> {{Lumatone key|x=5|y=6|label=A^}}<br /> {{Lumatone key|x=6|y=6|label=B^}}<br /> {{Lumatone key|x=7|y=6|label=C^}}<br /> {{Lumatone key|x=8|y=6|label=D^}}<br /> {{Lumatone key|x=9|y=6|label=E^}}<br /> {{Lumatone key|x=10|y=6|label=F^}}<br /> {{Lumatone key|x=11|y=6|label=G^}}<br /> <br /> {{Lumatone key|x=4|y=7|label=Gv}}<br /> {{Lumatone key|x=5|y=7|label=A}}<br /> {{Lumatone key|x=6|y=7|label=B}}<br /> {{Lumatone key|x=7|y=7|label=C}}<br /> {{Lumatone key|x=8|y=7|label=D}}<br /> {{Lumatone key|x=9|y=7|label=E}}<br /> {{Lumatone key|x=10|y=7|label=F}}<br /> {{Lumatone key|x=11|y=7|label=G}}<br /> {{Lumatone key|x=12|y=7|label=A^}}<br /> {{Lumatone key|x=13|y=7|label=B^}}<br /> {{Lumatone key|x=14|y=7|label=C^}}<br /> {{Lumatone key|x=15|y=7|label=D^}}<br /> {{Lumatone key|x=16|y=7|label=E^}}<br /> {{Lumatone key|x=17|y=7|label=F^}}<br /> {{Lumatone key|x=18|y=7|label=G^}}<br /> <br /> {{Lumatone key|x=5|y=8|label=Av}}<br /> {{Lumatone key|x=6|y=8|label=Bv}}<br /> {{Lumatone key|x=7|y=8|label=Cv}}<br /> {{Lumatone key|x=8|y=8|label=Dv}}<br /> {{Lumatone key|x=9|y=8|label=Ev}}<br /> {{Lumatone key|x=10|y=8|label=Fv}}<br /> {{Lumatone key|x=11|y=8|label=Gv}}<br /> {{Lumatone key|x=12|y=8|label=A}}<br /> {{Lumatone key|x=13|y=8|label=B}}<br /> {{Lumatone key|x=14|y=8|label=C}}<br /> {{Lumatone key|x=15|y=8|label=D}}<br /> {{Lumatone key|x=16|y=8|label=E}}<br /> {{Lumatone key|x=17|y=8|label=F}}<br /> {{Lumatone key|x=18|y=8|label=G}}<br /> {{Lumatone key|x=19|y=8|label=A^}}<br /> {{Lumatone key|x=20|y=8|label=B^}}<br /> {{Lumatone key|x=21|y=8|label=C^}}<br /> {{Lumatone key|x=22|y=8|label=D^}}<br /> {{Lumatone key|x=23|y=8|label=E^}}<br /> {{Lumatone key|x=24|y=8|label=F^}}<br /> {{Lumatone key|x=25|y=8|label=G^}}<br /> <br /> {{Lumatone key|x=12|y=9|label=Av}}<br /> {{Lumatone key|x=13|y=9|label=Bv}}<br /> {{Lumatone key|x=14|y=9|label=Cv}}<br /> {{Lumatone key|x=15|y=9|label=Dv}}<br /> {{Lumatone key|x=16|y=9|label=Ev}}<br /> {{Lumatone key|x=17|y=9|label=Fv}}<br /> {{Lumatone key|x=18|y=9|label=Gv}}<br /> {{Lumatone key|x=19|y=9|label=A}}<br /> {{Lumatone key|x=20|y=9|label=B}}<br /> {{Lumatone key|x=21|y=9|label=C}}<br /> {{Lumatone key|x=22|y=9|label=D}}<br /> {{Lumatone key|x=23|y=9|label=E}}<br /> {{Lumatone key|x=24|y=9|label=F}}<br /> {{Lumatone key|x=25|y=9|label=G}}<br /> {{Lumatone key|x=26|y=9|label=A^}}<br /> {{Lumatone key|x=27|y=9|label=B^}}<br /> {{Lumatone key|x=28|y=9|label=C^}}<br /> {{Lumatone key|x=29|y=9|label=D^}}<br /> {{Lumatone key|x=30|y=9|label=E^}}<br /> {{Lumatone key|x=31|y=9|label=F^}}<br /> {{Lumatone key|x=32|y=9|label=G^}}<br /> <br /> {{Lumatone key|x=19|y=10|label=Av}}<br /> {{Lumatone key|x=20|y=10|label=Bv}}<br /> {{Lumatone key|x=21|y=10|label=Cv}}<br /> {{Lumatone key|x=22|y=10|label=Dv}}<br /> {{Lumatone key|x=23|y=10|label=Ev}}<br /> {{Lumatone key|x=24|y=10|label=Fv}}<br /> {{Lumatone key|x=25|y=10|label=Gv}}<br /> {{Lumatone key|x=26|y=10|label=A}}<br /> {{Lumatone key|x=27|y=10|label=B}}<br /> {{Lumatone key|x=28|y=10|label=C}}<br /> {{Lumatone key|x=29|y=10|label=D}}<br /> {{Lumatone key|x=30|y=10|label=E}}<br /> {{Lumatone key|x=31|y=10|label=F}}<br /> {{Lumatone key|x=32|y=10|label=G}}<br /> {{Lumatone key|x=33|y=10|label=A^}}<br /> {{Lumatone key|x=34|y=10|label=B^}}<br /> <br /> {{Lumatone key|x=26|y=11|label=Av}}<br /> {{Lumatone key|x=27|y=11|label=Bv}}<br /> {{Lumatone key|x=28|y=11|label=Cv}}<br /> {{Lumatone key|x=29|y=11|label=Dv}}<br /> {{Lumatone key|x=30|y=11|label=Ev}}<br /> {{Lumatone key|x=31|y=11|label=Fv}}<br /> {{Lumatone key|x=32|y=11|label=Gv}}<br /> {{Lumatone key|x=33|y=11|label=A}}<br /> {{Lumatone key|x=34|y=11|label=B}}<br /> {{Lumatone key|x=35|y=11|label=C}}<br /> <br /> {{Lumatone key|x=33|y=12|label=Av}}<br /> {{Lumatone key|x=34|y=12|label=Bv}}<br /> {{Lumatone key|x=35|y=12|label=Cv}}<br /> <br /> }}<br /> <br /> ==Locations of harmonics in Monkey mapping==<br /> <br /> The specific temperament mapping used here is 13-limit [[Tetracot family#Monkey|monkey]].<br /> {{Lumatone mapping|<br /> <br /> {{Lumatone key|x=6|y=6|label=9/8}}<br /> {{Lumatone key|x=7|y=6|label=5/4}}<br /> {{Lumatone key|x=8|y=6|label=11/8}}<br /> {{Lumatone key|x=11|y=6|label=15/8}}<br /> <br /> {{Lumatone key|x=5|y=7|label=1/1}}<br /> {{Lumatone key|x=9|y=7|label=3/2}}<br /> {{Lumatone key|x=13|y=7|label=9/8}}<br /> {{Lumatone key|x=14|y=7|label=5/4}}<br /> {{Lumatone key|x=15|y=7|label=11/8}}<br /> {{Lumatone key|x=18|y=7|label=15/8}}<br /> <br /> {{Lumatone key|x=10|y=8|label=13/8}}<br /> {{Lumatone key|x=12|y=8|label=1/1}}<br /> {{Lumatone key|x=16|y=8|label=3/2}}<br /> {{Lumatone key|x=20|y=8|label=9/8}}<br /> {{Lumatone key|x=21|y=8|label=5/4}}<br /> {{Lumatone key|x=22|y=8|label=11/8}}<br /> {{Lumatone key|x=25|y=8|label=15/8}}<br /> <br /> {{Lumatone key|x=17|y=9|label=13/8}}<br /> {{Lumatone key|x=19|y=9|label=1/1}}<br /> {{Lumatone key|x=23|y=9|label=3/2}}<br /> {{Lumatone key|x=27|y=9|label=9/8}}<br /> {{Lumatone key|x=28|y=9|label=5/4}}<br /> {{Lumatone key|x=29|y=9|label=11/8}}<br /> {{Lumatone key|x=32|y=9|label=15/8}}<br /> <br /> {{Lumatone key|x=11|y=10|label=7/4}}<br /> {{Lumatone key|x=24|y=10|label=13/8}}<br /> {{Lumatone key|x=26|y=10|label=1/1}}<br /> {{Lumatone key|x=30|y=10|label=3/2}}<br /> {{Lumatone key|x=34|y=10|label=9/8}}<br /> <br /> {{Lumatone key|x=18|y=11|label=7/4}}<br /> {{Lumatone key|x=31|y=11|label=13/8}}<br /> {{Lumatone key|x=33|y=11|label=1/1}}<br /> <br /> {{Lumatone key|x=25|y=12|label=7/4}}<br /> <br /> {{Lumatone key|x=32|y=13|label=7/4}}<br /> <br /> }}<br /> <br /> ==External links==<br /> * [https://www.youtube.com/watch?v=SueBUSvkTEg The monkey puzzle] by Herman Miller<br /> <br /> [[Category:Lumatone mappings]]<br /> [[Category:Tetracot family]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Lumatone_mapping_for_Slendric&diff=83580 Lumatone mapping for Slendric 2022-01-09T19:18:11Z <p>Keenan Pepper: Keenan Pepper moved page Lumatone mapping for Slendric to Lumatone mapping for slendric: let&#039;s lowercase all the temperament names</p> <hr /> <div>#REDIRECT [[Lumatone mapping for slendric]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Lumatone_mapping_for_slendric&diff=83579 Lumatone mapping for slendric 2022-01-09T19:18:11Z <p>Keenan Pepper: Keenan Pepper moved page Lumatone mapping for Slendric to Lumatone mapping for slendric: let&#039;s lowercase all the temperament names</p> <hr /> <div>This is one proposed mapping of [[slendric]] temperament to the [[Lumatone]] keyboard. 6 complete octaves are available, and modulation to distant keys is possible.<br /> <br /> The keys marked &quot;c&quot; are one chroma up from 1/1, representing both 64/63 and 49/48. They keys marked &quot;-c&quot; are one chroma down from 1/1 (so 63/32 and 96/49).<br /> <br /> The same mapping could be used for any extension of slendric that has the same period and generator, including [[Cynder]], [[Rodan]], and [[Guiron]].<br /> <br /> {{Lumatone mapping|<br /> <br /> {{Lumatone key|x=3|y=4|label=27/16|size=10px}}<br /> {{Lumatone key|x=4|y=4|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=3|y=5|label=12/7}}<br /> {{Lumatone key|x=4|y=5|label=-c}}<br /> {{Lumatone key|x=5|y=5|label=9/8}}<br /> {{Lumatone key|x=6|y=5|label=9/7}}<br /> {{Lumatone key|x=7|y=5|label=}}<br /> {{Lumatone key|x=8|y=5|label=27/16|size=10px}}<br /> {{Lumatone key|x=9|y=5|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=3|y=6|label=7/4}}<br /> {{Lumatone key|x=4|y=6|label=1/1}}<br /> {{Lumatone key|x=5|y=6|label=8/7}}<br /> {{Lumatone key|x=6|y=6|label=21/16|size=10px}}<br /> {{Lumatone key|x=7|y=6|label=3/2}}<br /> {{Lumatone key|x=8|y=6|label=12/7}}<br /> {{Lumatone key|x=9|y=6|label=-c}}<br /> {{Lumatone key|x=10|y=6|label=9/8}}<br /> {{Lumatone key|x=11|y=6|label=9/7}}<br /> {{Lumatone key|x=12|y=6|label=}}<br /> {{Lumatone key|x=13|y=6|label=27/16|size=10px}}<br /> {{Lumatone key|x=14|y=6|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=21|y=6|label=Y}}<br /> <br /> {{Lumatone key|x=4|y=7|label=c}}<br /> {{Lumatone key|x=5|y=7|label=7/6}}<br /> {{Lumatone key|x=6|y=7|label=4/3}}<br /> {{Lumatone key|x=7|y=7|label=32/21|size=10px}}<br /> {{Lumatone key|x=8|y=7|label=7/4}}<br /> {{Lumatone key|x=9|y=7|label=1/1}}<br /> {{Lumatone key|x=10|y=7|label=8/7}}<br /> {{Lumatone key|x=11|y=7|label=21/16|size=10px}}<br /> {{Lumatone key|x=12|y=7|label=3/2}}<br /> {{Lumatone key|x=13|y=7|label=12/7}}<br /> {{Lumatone key|x=14|y=7|label=-c}}<br /> {{Lumatone key|x=15|y=7|label=9/8}}<br /> {{Lumatone key|x=16|y=7|label=9/7}}<br /> {{Lumatone key|x=17|y=7|label=}}<br /> {{Lumatone key|x=18|y=7|label=27/16|size=10px}}<br /> {{Lumatone key|x=19|y=7|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=21|y=7|label=X}}<br /> <br /> {{Lumatone key|x=4|y=8|label=28/27|size=10px}}<br /> {{Lumatone key|x=5|y=8|label=32/27|size=10px}}<br /> {{Lumatone key|x=6|y=8|label=}}<br /> {{Lumatone key|x=7|y=8|label=14/9}}<br /> {{Lumatone key|x=8|y=8|label=16/9}}<br /> {{Lumatone key|x=9|y=8|label=c}}<br /> {{Lumatone key|x=10|y=8|label=7/6}}<br /> {{Lumatone key|x=11|y=8|label=4/3}}<br /> {{Lumatone key|x=12|y=8|label=32/21|size=10px}}<br /> {{Lumatone key|x=13|y=8|label=7/4}}<br /> {{Lumatone key|x=14|y=8|label=1/1}}<br /> {{Lumatone key|x=15|y=8|label=8/7}}<br /> {{Lumatone key|x=16|y=8|label=21/16|size=10px}}<br /> {{Lumatone key|x=17|y=8|label=3/2}}<br /> {{Lumatone key|x=18|y=8|label=12/7}}<br /> {{Lumatone key|x=19|y=8|label=-c}}<br /> {{Lumatone key|x=20|y=8|label=9/8}}<br /> {{Lumatone key|x=21|y=8|label=9/7}}<br /> {{Lumatone key|x=22|y=8|label=}}<br /> {{Lumatone key|x=23|y=8|label=27/16|size=10px}}<br /> {{Lumatone key|x=24|y=8|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=9|y=9|label=28/27|size=10px}}<br /> {{Lumatone key|x=10|y=9|label=32/27|size=10px}}<br /> {{Lumatone key|x=11|y=9|label=}}<br /> {{Lumatone key|x=12|y=9|label=14/9}}<br /> {{Lumatone key|x=13|y=9|label=16/9}}<br /> {{Lumatone key|x=14|y=9|label=c}}<br /> {{Lumatone key|x=15|y=9|label=7/6}}<br /> {{Lumatone key|x=16|y=9|label=4/3}}<br /> {{Lumatone key|x=17|y=9|label=32/21|size=10px}}<br /> {{Lumatone key|x=18|y=9|label=7/4}}<br /> {{Lumatone key|x=19|y=9|label=1/1}}<br /> {{Lumatone key|x=20|y=9|label=8/7}}<br /> {{Lumatone key|x=21|y=9|label=21/16|size=10px}}<br /> {{Lumatone key|x=22|y=9|label=3/2}}<br /> {{Lumatone key|x=23|y=9|label=12/7}}<br /> {{Lumatone key|x=24|y=9|label=-c}}<br /> {{Lumatone key|x=25|y=9|label=9/8}}<br /> {{Lumatone key|x=26|y=9|label=9/7}}<br /> {{Lumatone key|x=27|y=9|label=}}<br /> {{Lumatone key|x=28|y=9|label=27/16|size=10px}}<br /> {{Lumatone key|x=29|y=9|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=14|y=10|label=28/27|size=10px}}<br /> {{Lumatone key|x=15|y=10|label=32/27|size=10px}}<br /> {{Lumatone key|x=16|y=10|label=}}<br /> {{Lumatone key|x=17|y=10|label=14/9}}<br /> {{Lumatone key|x=18|y=10|label=16/9}}<br /> {{Lumatone key|x=19|y=10|label=c}}<br /> {{Lumatone key|x=20|y=10|label=7/6}}<br /> {{Lumatone key|x=21|y=10|label=4/3}}<br /> {{Lumatone key|x=22|y=10|label=32/21|size=10px}}<br /> {{Lumatone key|x=23|y=10|label=7/4}}<br /> {{Lumatone key|x=24|y=10|label=1/1}}<br /> {{Lumatone key|x=25|y=10|label=8/7}}<br /> {{Lumatone key|x=26|y=10|label=21/16|size=10px}}<br /> {{Lumatone key|x=27|y=10|label=3/2}}<br /> {{Lumatone key|x=28|y=10|label=12/7}}<br /> {{Lumatone key|x=29|y=10|label=-c}}<br /> {{Lumatone key|x=30|y=10|label=9/8}}<br /> {{Lumatone key|x=31|y=10|label=9/7}}<br /> {{Lumatone key|x=32|y=10|label=}}<br /> {{Lumatone key|x=33|y=10|label=27/16|size=10px}}<br /> {{Lumatone key|x=34|y=10|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=19|y=11|label=28/27|size=10px}}<br /> {{Lumatone key|x=20|y=11|label=32/27|size=10px}}<br /> {{Lumatone key|x=21|y=11|label=}}<br /> {{Lumatone key|x=22|y=11|label=14/9}}<br /> {{Lumatone key|x=23|y=11|label=16/9}}<br /> {{Lumatone key|x=24|y=11|label=c}}<br /> {{Lumatone key|x=25|y=11|label=7/6}}<br /> {{Lumatone key|x=26|y=11|label=4/3}}<br /> {{Lumatone key|x=27|y=11|label=32/21|size=10px}}<br /> {{Lumatone key|x=28|y=11|label=7/4}}<br /> {{Lumatone key|x=29|y=11|label=1/1}}<br /> {{Lumatone key|x=30|y=11|label=8/7}}<br /> {{Lumatone key|x=31|y=11|label=21/16|size=10px}}<br /> {{Lumatone key|x=32|y=11|label=3/2}}<br /> {{Lumatone key|x=33|y=11|label=12/7}}<br /> {{Lumatone key|x=34|y=11|label=-c}}<br /> {{Lumatone key|x=35|y=11|label=9/8}}<br /> <br /> {{Lumatone key|x=24|y=12|label=28/27|size=10px}}<br /> {{Lumatone key|x=25|y=12|label=32/27|size=10px}}<br /> {{Lumatone key|x=26|y=12|label=}}<br /> {{Lumatone key|x=27|y=12|label=14/9}}<br /> {{Lumatone key|x=28|y=12|label=16/9}}<br /> {{Lumatone key|x=29|y=12|label=c}}<br /> {{Lumatone key|x=30|y=12|label=7/6}}<br /> {{Lumatone key|x=31|y=12|label=4/3}}<br /> {{Lumatone key|x=32|y=12|label=32/21|size=10px}}<br /> {{Lumatone key|x=33|y=12|label=7/4}}<br /> {{Lumatone key|x=34|y=12|label=1/1}}<br /> {{Lumatone key|x=35|y=12|label=8/7}}<br /> <br /> {{Lumatone key|x=29|y=13|label=28/27|size=10px}}<br /> {{Lumatone key|x=30|y=13|label=32/27|size=10px}}<br /> {{Lumatone key|x=31|y=13|label=}}<br /> {{Lumatone key|x=32|y=13|label=14/9}}<br /> {{Lumatone key|x=33|y=13|label=16/9}}<br /> {{Lumatone key|x=34|y=13|label=c}}<br /> {{Lumatone key|x=35|y=13|label=7/6}}<br /> {{Lumatone key|x=36|y=13|label=4/3}}<br /> <br /> {{Lumatone key|x=34|y=14|label=28/27|size=10px}}<br /> {{Lumatone key|x=35|y=14|label=32/27|size=10px}}<br /> <br /> {{Lumatone key|x=30|y=16|label=Z}}<br /> <br /> }}<br /> <br /> The differences between the extensions of slendric to the prime 5 can be visualized on this keyboard.<br /> * Cynder tempers out 81/80, so 9/8 above 9/8 is equivalent to 5/4 so 5/4 is mapped to the key marked &quot;X&quot;.<br /> * Rodan, on the other hand, makes 81/80 the same as the chroma c, so 5/4 is instead mapped to the key mapped &quot;Y&quot;, one chroma lower than &quot;X&quot;.<br /> * Guiron maps 5/4 to the key marked &quot;Z&quot;.<br /> <br /> Cynder and guiron intersect in 36edo, so in 36edo both &quot;X&quot; and &quot;Z&quot; represent 5/4. Rodan and guiron intersect in 41edo, so in 41edo both &quot;Y&quot; and &quot;Z&quot; represent 5/4.<br /> <br /> If the above layout is the &quot;compressed&quot; one then the below is an &quot;expanded&quot; one which has a range of only 5 octaves, but whose layout may make more intuitive sense:<br /> <br /> {{Lumatone mapping|<br /> <br /> {{Lumatone key|x=2|y=4|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=3|y=5|label=-c}}<br /> {{Lumatone key|x=4|y=5|label=9/8}}<br /> {{Lumatone key|x=5|y=5|label=9/7}}<br /> {{Lumatone key|x=6|y=5|label=}}<br /> {{Lumatone key|x=7|y=5|label=27/16|size=10px}}<br /> {{Lumatone key|x=8|y=5|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=3|y=6|label=7/4}}<br /> {{Lumatone key|x=4|y=6|label=1/1}}<br /> {{Lumatone key|x=5|y=6|label=8/7}}<br /> {{Lumatone key|x=6|y=6|label=21/16|size=10px}}<br /> {{Lumatone key|x=7|y=6|label=3/2}}<br /> {{Lumatone key|x=8|y=6|label=12/7}}<br /> {{Lumatone key|x=9|y=6|label=-c}}<br /> {{Lumatone key|x=10|y=6|label=9/8}}<br /> {{Lumatone key|x=11|y=6|label=9/7}}<br /> {{Lumatone key|x=12|y=6|label=}}<br /> {{Lumatone key|x=13|y=6|label=27/16|size=10px}}<br /> {{Lumatone key|x=14|y=6|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=21|y=6|label=Y}}<br /> <br /> {{Lumatone key|x=4|y=7|label=16/9}}<br /> {{Lumatone key|x=5|y=7|label=c}}<br /> {{Lumatone key|x=6|y=7|label=7/6}}<br /> {{Lumatone key|x=7|y=7|label=4/3}}<br /> {{Lumatone key|x=8|y=7|label=32/21|size=10px}}<br /> {{Lumatone key|x=9|y=7|label=7/4}}<br /> {{Lumatone key|x=10|y=7|label=1/1}}<br /> {{Lumatone key|x=11|y=7|label=8/7}}<br /> {{Lumatone key|x=12|y=7|label=21/16|size=10px}}<br /> {{Lumatone key|x=13|y=7|label=3/2}}<br /> {{Lumatone key|x=14|y=7|label=12/7}}<br /> {{Lumatone key|x=15|y=7|label=-c}}<br /> {{Lumatone key|x=16|y=7|label=9/8}}<br /> {{Lumatone key|x=17|y=7|label=9/7}}<br /> {{Lumatone key|x=18|y=7|label=}}<br /> {{Lumatone key|x=19|y=7|label=27/16|size=10px}}<br /> {{Lumatone key|x=20|y=7|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=22|y=7|label=X}}<br /> <br /> {{Lumatone key|x=6|y=8|label=28/27|size=10px}}<br /> {{Lumatone key|x=7|y=8|label=32/27|size=10px}}<br /> {{Lumatone key|x=8|y=8|label=}}<br /> {{Lumatone key|x=9|y=8|label=14/9}}<br /> {{Lumatone key|x=10|y=8|label=16/9}}<br /> {{Lumatone key|x=11|y=8|label=c}}<br /> {{Lumatone key|x=12|y=8|label=7/6}}<br /> {{Lumatone key|x=13|y=8|label=4/3}}<br /> {{Lumatone key|x=14|y=8|label=32/21|size=10px}}<br /> {{Lumatone key|x=15|y=8|label=7/4}}<br /> {{Lumatone key|x=16|y=8|label=1/1}}<br /> {{Lumatone key|x=17|y=8|label=8/7}}<br /> {{Lumatone key|x=18|y=8|label=21/16|size=10px}}<br /> {{Lumatone key|x=19|y=8|label=3/2}}<br /> {{Lumatone key|x=20|y=8|label=12/7}}<br /> {{Lumatone key|x=21|y=8|label=-c}}<br /> {{Lumatone key|x=22|y=8|label=9/8}}<br /> {{Lumatone key|x=23|y=8|label=9/7}}<br /> {{Lumatone key|x=24|y=8|label=}}<br /> {{Lumatone key|x=25|y=8|label=27/16|size=10px}}<br /> {{Lumatone key|x=26|y=8|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=12|y=9|label=28/27|size=10px}}<br /> {{Lumatone key|x=13|y=9|label=32/27|size=10px}}<br /> {{Lumatone key|x=14|y=9|label=}}<br /> {{Lumatone key|x=15|y=9|label=14/9}}<br /> {{Lumatone key|x=16|y=9|label=16/9}}<br /> {{Lumatone key|x=17|y=9|label=c}}<br /> {{Lumatone key|x=18|y=9|label=7/6}}<br /> {{Lumatone key|x=19|y=9|label=4/3}}<br /> {{Lumatone key|x=20|y=9|label=32/21|size=10px}}<br /> {{Lumatone key|x=21|y=9|label=7/4}}<br /> {{Lumatone key|x=22|y=9|label=1/1}}<br /> {{Lumatone key|x=23|y=9|label=8/7}}<br /> {{Lumatone key|x=24|y=9|label=21/16|size=10px}}<br /> {{Lumatone key|x=25|y=9|label=3/2}}<br /> {{Lumatone key|x=26|y=9|label=12/7}}<br /> {{Lumatone key|x=27|y=9|label=-c}}<br /> {{Lumatone key|x=28|y=9|label=9/8}}<br /> {{Lumatone key|x=29|y=9|label=9/7}}<br /> {{Lumatone key|x=30|y=9|label=}}<br /> {{Lumatone key|x=31|y=9|label=27/16|size=10px}}<br /> {{Lumatone key|x=32|y=9|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=18|y=10|label=28/27|size=10px}}<br /> {{Lumatone key|x=19|y=10|label=32/27|size=10px}}<br /> {{Lumatone key|x=20|y=10|label=}}<br /> {{Lumatone key|x=21|y=10|label=14/9}}<br /> {{Lumatone key|x=22|y=10|label=16/9}}<br /> {{Lumatone key|x=23|y=10|label=c}}<br /> {{Lumatone key|x=24|y=10|label=7/6}}<br /> {{Lumatone key|x=25|y=10|label=4/3}}<br /> {{Lumatone key|x=26|y=10|label=32/21|size=10px}}<br /> {{Lumatone key|x=27|y=10|label=7/4}}<br /> {{Lumatone key|x=28|y=10|label=1/1}}<br /> {{Lumatone key|x=29|y=10|label=8/7}}<br /> {{Lumatone key|x=30|y=10|label=21/16|size=10px}}<br /> {{Lumatone key|x=31|y=10|label=3/2}}<br /> {{Lumatone key|x=32|y=10|label=12/7}}<br /> {{Lumatone key|x=33|y=10|label=-c}}<br /> {{Lumatone key|x=34|y=10|label=9/8}}<br /> <br /> {{Lumatone key|x=24|y=11|label=28/27|size=10px}}<br /> {{Lumatone key|x=25|y=11|label=32/27|size=10px}}<br /> {{Lumatone key|x=26|y=11|label=}}<br /> {{Lumatone key|x=27|y=11|label=14/9}}<br /> {{Lumatone key|x=28|y=11|label=16/9}}<br /> {{Lumatone key|x=29|y=11|label=c}}<br /> {{Lumatone key|x=30|y=11|label=7/6}}<br /> {{Lumatone key|x=31|y=11|label=4/3}}<br /> {{Lumatone key|x=32|y=11|label=32/21|size=10px}}<br /> {{Lumatone key|x=33|y=11|label=7/4}}<br /> {{Lumatone key|x=34|y=11|label=1/1}}<br /> {{Lumatone key|x=35|y=11|label=8/7}}<br /> <br /> {{Lumatone key|x=30|y=12|label=28/27|size=10px}}<br /> {{Lumatone key|x=31|y=12|label=32/27|size=10px}}<br /> {{Lumatone key|x=32|y=12|label=}}<br /> {{Lumatone key|x=33|y=12|label=14/9}}<br /> {{Lumatone key|x=34|y=12|label=16/9}}<br /> {{Lumatone key|x=35|y=12|label=c}}<br /> <br /> {{Lumatone key|x=36|y=13|label=28/27|size=10px}}<br /> <br /> {{Lumatone key|x=34|y=15|label=Z}}<br /> <br /> }}<br /> <br /> [[Category:Lumatone mappings]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Lumatone_mapping_for_Porcupine&diff=83578 Lumatone mapping for Porcupine 2022-01-09T19:17:58Z <p>Keenan Pepper: Keenan Pepper moved page Lumatone mapping for Porcupine to Lumatone mapping for porcupine: let&#039;s lowercase all the temperament names</p> <hr /> <div>#REDIRECT [[Lumatone mapping for porcupine]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Lumatone_mapping_for_porcupine&diff=83577 Lumatone mapping for porcupine 2022-01-09T19:17:58Z <p>Keenan Pepper: Keenan Pepper moved page Lumatone mapping for Porcupine to Lumatone mapping for porcupine: let&#039;s lowercase all the temperament names</p> <hr /> <div>There are several ways to map [[porcupine]] temperament onto the [[Lumatone]] keyboard. This article uses the Porcupine[7] notation convention from [[Porcupine Notation]].<br /> <br /> The mappings pictured below are based on mapping consecutive porcupine generator steps (~160 cents) to adjacent keys going generally left-to-right across the keyboard.<br /> <br /> A completely different approach to playing porcupine music on the Lumatone would be to use a standard mapping for some porcupine EDO (e.g. the [[Lumatone mapping for 22edo]]) and learn the shapes of porcupine scales in that layout. For example in 22edo, porcupine steps go roughly vertically rather than roughly horizontally, thus requiring a lot of &quot;wrapping around&quot;. But if you just learn the shape of a &quot;porcupine tetrachord&quot; that could be a fruitful approach.<br /> <br /> ==Ultra-compressed==<br /> <br /> This has the largest range of any mapping shown here (5 complete octaves), but the sequence of nearby pitches can be confusing. In particular, notes separated by the Porcupine[7] chroma (denoted by ^/v here) are not mapped to adjacent keys.<br /> {{Lumatone mapping|<br /> <br /> {{Lumatone key|x=3|y=5|label=Ev}}<br /> {{Lumatone key|x=4|y=5|label=Fv}}<br /> {{Lumatone key|x=5|y=5|label=Gv}}<br /> <br /> {{Lumatone key|x=3|y=6|label=F}}<br /> {{Lumatone key|x=4|y=6|label=G}}<br /> {{Lumatone key|x=5|y=6|label=Av}}<br /> {{Lumatone key|x=6|y=6|label=Bv}}<br /> {{Lumatone key|x=7|y=6|label=Cv}}<br /> {{Lumatone key|x=8|y=6|label=Dv}}<br /> {{Lumatone key|x=9|y=6|label=Ev}}<br /> {{Lumatone key|x=10|y=6|label=Fv}}<br /> {{Lumatone key|x=11|y=6|label=Gv}}<br /> <br /> {{Lumatone key|x=4|y=7|label=A}}<br /> {{Lumatone key|x=5|y=7|label=B}}<br /> {{Lumatone key|x=6|y=7|label=C}}<br /> {{Lumatone key|x=7|y=7|label=D}}<br /> {{Lumatone key|x=8|y=7|label=E}}<br /> {{Lumatone key|x=9|y=7|label=F}}<br /> {{Lumatone key|x=10|y=7|label=G}}<br /> {{Lumatone key|x=11|y=7|label=Av}}<br /> {{Lumatone key|x=12|y=7|label=Bv}}<br /> {{Lumatone key|x=13|y=7|label=Cv}}<br /> {{Lumatone key|x=14|y=7|label=Dv}}<br /> {{Lumatone key|x=15|y=7|label=Ev}}<br /> {{Lumatone key|x=16|y=7|label=Fv}}<br /> {{Lumatone key|x=17|y=7|label=Gv}}<br /> <br /> {{Lumatone key|x=4|y=8|label=B^}}<br /> {{Lumatone key|x=5|y=8|label=C^}}<br /> {{Lumatone key|x=6|y=8|label=D^}}<br /> {{Lumatone key|x=7|y=8|label=E^}}<br /> {{Lumatone key|x=8|y=8|label=F^}}<br /> {{Lumatone key|x=9|y=8|label=G^}}<br /> {{Lumatone key|x=10|y=8|label=A}}<br /> {{Lumatone key|x=11|y=8|label=B}}<br /> {{Lumatone key|x=12|y=8|label=C}}<br /> {{Lumatone key|x=13|y=8|label=D}}<br /> {{Lumatone key|x=14|y=8|label=E}}<br /> {{Lumatone key|x=15|y=8|label=F}}<br /> {{Lumatone key|x=16|y=8|label=G}}<br /> {{Lumatone key|x=17|y=8|label=Av}}<br /> {{Lumatone key|x=18|y=8|label=Bv}}<br /> {{Lumatone key|x=19|y=8|label=Cv}}<br /> {{Lumatone key|x=20|y=8|label=Dv}}<br /> {{Lumatone key|x=21|y=8|label=Ev}}<br /> {{Lumatone key|x=22|y=8|label=Fv}}<br /> {{Lumatone key|x=23|y=8|label=Gv}}<br /> <br /> {{Lumatone key|x=9|y=9|label=A^}}<br /> {{Lumatone key|x=10|y=9|label=B^}}<br /> {{Lumatone key|x=11|y=9|label=C^}}<br /> {{Lumatone key|x=12|y=9|label=D^}}<br /> {{Lumatone key|x=13|y=9|label=E^}}<br /> {{Lumatone key|x=14|y=9|label=F^}}<br /> {{Lumatone key|x=15|y=9|label=G^}}<br /> {{Lumatone key|x=16|y=9|label=A}}<br /> {{Lumatone key|x=17|y=9|label=B}}<br /> {{Lumatone key|x=18|y=9|label=C}}<br /> {{Lumatone key|x=19|y=9|label=D}}<br /> {{Lumatone key|x=20|y=9|label=E}}<br /> {{Lumatone key|x=21|y=9|label=F}}<br /> {{Lumatone key|x=22|y=9|label=G}}<br /> {{Lumatone key|x=23|y=9|label=Av}}<br /> {{Lumatone key|x=24|y=9|label=Bv}}<br /> {{Lumatone key|x=25|y=9|label=Cv}}<br /> {{Lumatone key|x=26|y=9|label=Dv}}<br /> {{Lumatone key|x=27|y=9|label=Ev}}<br /> {{Lumatone key|x=28|y=9|label=Fv}}<br /> {{Lumatone key|x=29|y=9|label=Gv}}<br /> <br /> {{Lumatone key|x=15|y=10|label=A^}}<br /> {{Lumatone key|x=16|y=10|label=B^}}<br /> {{Lumatone key|x=17|y=10|label=C^}}<br /> {{Lumatone key|x=18|y=10|label=D^}}<br /> {{Lumatone key|x=19|y=10|label=E^}}<br /> {{Lumatone key|x=20|y=10|label=F^}}<br /> {{Lumatone key|x=21|y=10|label=G^}}<br /> {{Lumatone key|x=22|y=10|label=A}}<br /> {{Lumatone key|x=23|y=10|label=B}}<br /> {{Lumatone key|x=24|y=10|label=C}}<br /> {{Lumatone key|x=25|y=10|label=D}}<br /> {{Lumatone key|x=26|y=10|label=E}}<br /> {{Lumatone key|x=27|y=10|label=F}}<br /> {{Lumatone key|x=28|y=10|label=G}}<br /> {{Lumatone key|x=29|y=10|label=Av}}<br /> {{Lumatone key|x=30|y=10|label=Bv}}<br /> {{Lumatone key|x=31|y=10|label=Cv}}<br /> {{Lumatone key|x=32|y=10|label=Dv}}<br /> {{Lumatone key|x=33|y=10|label=Ev}}<br /> {{Lumatone key|x=34|y=10|label=Fv}}<br /> <br /> {{Lumatone key|x=21|y=11|label=A^}}<br /> {{Lumatone key|x=22|y=11|label=B^}}<br /> {{Lumatone key|x=23|y=11|label=C^}}<br /> {{Lumatone key|x=24|y=11|label=D^}}<br /> {{Lumatone key|x=25|y=11|label=E^}}<br /> {{Lumatone key|x=26|y=11|label=F^}}<br /> {{Lumatone key|x=27|y=11|label=G^}}<br /> {{Lumatone key|x=28|y=11|label=A}}<br /> {{Lumatone key|x=29|y=11|label=B}}<br /> {{Lumatone key|x=30|y=11|label=C}}<br /> {{Lumatone key|x=31|y=11|label=D}}<br /> {{Lumatone key|x=32|y=11|label=E}}<br /> {{Lumatone key|x=33|y=11|label=F}}<br /> {{Lumatone key|x=34|y=11|label=G}}<br /> {{Lumatone key|x=35|y=11|label=Av}}<br /> <br /> {{Lumatone key|x=27|y=12|label=A^}}<br /> {{Lumatone key|x=28|y=12|label=B^}}<br /> {{Lumatone key|x=29|y=12|label=C^}}<br /> {{Lumatone key|x=30|y=12|label=D^}}<br /> {{Lumatone key|x=31|y=12|label=E^}}<br /> {{Lumatone key|x=32|y=12|label=F^}}<br /> {{Lumatone key|x=33|y=12|label=G^}}<br /> {{Lumatone key|x=34|y=12|label=A}}<br /> {{Lumatone key|x=35|y=12|label=B}}<br /> <br /> {{Lumatone key|x=33|y=13|label=A^}}<br /> {{Lumatone key|x=34|y=13|label=B^}}<br /> {{Lumatone key|x=35|y=13|label=C^}}<br /> {{Lumatone key|x=36|y=13|label=D^}}<br /> <br /> }}<br /> <br /> ==Compressed==<br /> <br /> This is a compromise intermediate between the &quot;ultra-compressed&quot; and &quot;expanded&quot; mappings. It covers 4 complete octaves, and the Porcupine[7] chroma is now mapped to adjacent keys in the &quot;vertical&quot; direction. The sequence of pitches is still not completely intuitive, however: the Porcupine[15] chromatic scale still zigzags back and forth leaping over keys, rather than proceeding in mostly the same direction. This is because the Porcupine[8] chroma (denoted #/b on [[Porcupine Notation]] - for example the notes A and Bv are separated by this chroma) is still not mapped to adjacent keys.<br /> {{Lumatone mapping|<br /> <br /> {{Lumatone key|x=3|y=5|label=Fv}}<br /> {{Lumatone key|x=4|y=5|label=Gv}}<br /> <br /> {{Lumatone key|x=3|y=6|label=F}}<br /> {{Lumatone key|x=4|y=6|label=G}}<br /> {{Lumatone key|x=5|y=6|label=Av}}<br /> {{Lumatone key|x=6|y=6|label=Bv}}<br /> {{Lumatone key|x=7|y=6|label=Cv}}<br /> {{Lumatone key|x=8|y=6|label=Dv}}<br /> {{Lumatone key|x=9|y=6|label=Ev}}<br /> {{Lumatone key|x=10|y=6|label=Fv}}<br /> {{Lumatone key|x=11|y=6|label=Gv}}<br /> <br /> {{Lumatone key|x=4|y=7|label=G^}}<br /> {{Lumatone key|x=5|y=7|label=A}}<br /> {{Lumatone key|x=6|y=7|label=B}}<br /> {{Lumatone key|x=7|y=7|label=C}}<br /> {{Lumatone key|x=8|y=7|label=D}}<br /> {{Lumatone key|x=9|y=7|label=E}}<br /> {{Lumatone key|x=10|y=7|label=F}}<br /> {{Lumatone key|x=11|y=7|label=G}}<br /> {{Lumatone key|x=12|y=7|label=Av}}<br /> {{Lumatone key|x=13|y=7|label=Bv}}<br /> {{Lumatone key|x=14|y=7|label=Cv}}<br /> {{Lumatone key|x=15|y=7|label=Dv}}<br /> {{Lumatone key|x=16|y=7|label=Ev}}<br /> {{Lumatone key|x=17|y=7|label=Fv}}<br /> {{Lumatone key|x=18|y=7|label=Gv}}<br /> <br /> {{Lumatone key|x=5|y=8|label=A^}}<br /> {{Lumatone key|x=6|y=8|label=B^}}<br /> {{Lumatone key|x=7|y=8|label=C^}}<br /> {{Lumatone key|x=8|y=8|label=D^}}<br /> {{Lumatone key|x=9|y=8|label=E^}}<br /> {{Lumatone key|x=10|y=8|label=F^}}<br /> {{Lumatone key|x=11|y=8|label=G^}}<br /> {{Lumatone key|x=12|y=8|label=A}}<br /> {{Lumatone key|x=13|y=8|label=B}}<br /> {{Lumatone key|x=14|y=8|label=C}}<br /> {{Lumatone key|x=15|y=8|label=D}}<br /> {{Lumatone key|x=16|y=8|label=E}}<br /> {{Lumatone key|x=17|y=8|label=F}}<br /> {{Lumatone key|x=18|y=8|label=G}}<br /> {{Lumatone key|x=19|y=8|label=Av}}<br /> {{Lumatone key|x=20|y=8|label=Bv}}<br /> {{Lumatone key|x=21|y=8|label=Cv}}<br /> {{Lumatone key|x=22|y=8|label=Dv}}<br /> {{Lumatone key|x=23|y=8|label=Ev}}<br /> {{Lumatone key|x=24|y=8|label=Fv}}<br /> {{Lumatone key|x=25|y=8|label=Gv}}<br /> <br /> {{Lumatone key|x=12|y=9|label=A^}}<br /> {{Lumatone key|x=13|y=9|label=B^}}<br /> {{Lumatone key|x=14|y=9|label=C^}}<br /> {{Lumatone key|x=15|y=9|label=D^}}<br /> {{Lumatone key|x=16|y=9|label=E^}}<br /> {{Lumatone key|x=17|y=9|label=F^}}<br /> {{Lumatone key|x=18|y=9|label=G^}}<br /> {{Lumatone key|x=19|y=9|label=A}}<br /> {{Lumatone key|x=20|y=9|label=B}}<br /> {{Lumatone key|x=21|y=9|label=C}}<br /> {{Lumatone key|x=22|y=9|label=D}}<br /> {{Lumatone key|x=23|y=9|label=E}}<br /> {{Lumatone key|x=24|y=9|label=F}}<br /> {{Lumatone key|x=25|y=9|label=G}}<br /> {{Lumatone key|x=26|y=9|label=Av}}<br /> {{Lumatone key|x=27|y=9|label=Bv}}<br /> {{Lumatone key|x=28|y=9|label=Cv}}<br /> {{Lumatone key|x=29|y=9|label=Dv}}<br /> {{Lumatone key|x=30|y=9|label=Ev}}<br /> {{Lumatone key|x=31|y=9|label=Fv}}<br /> {{Lumatone key|x=32|y=9|label=Gv}}<br /> <br /> {{Lumatone key|x=19|y=10|label=A^}}<br /> {{Lumatone key|x=20|y=10|label=B^}}<br /> {{Lumatone key|x=21|y=10|label=C^}}<br /> {{Lumatone key|x=22|y=10|label=D^}}<br /> {{Lumatone key|x=23|y=10|label=E^}}<br /> {{Lumatone key|x=24|y=10|label=F^}}<br /> {{Lumatone key|x=25|y=10|label=G^}}<br /> {{Lumatone key|x=26|y=10|label=A}}<br /> {{Lumatone key|x=27|y=10|label=B}}<br /> {{Lumatone key|x=28|y=10|label=C}}<br /> {{Lumatone key|x=29|y=10|label=D}}<br /> {{Lumatone key|x=30|y=10|label=E}}<br /> {{Lumatone key|x=31|y=10|label=F}}<br /> {{Lumatone key|x=32|y=10|label=G}}<br /> {{Lumatone key|x=33|y=10|label=Av}}<br /> {{Lumatone key|x=34|y=10|label=Bv}}<br /> <br /> {{Lumatone key|x=26|y=11|label=A^}}<br /> {{Lumatone key|x=27|y=11|label=B^}}<br /> {{Lumatone key|x=28|y=11|label=C^}}<br /> {{Lumatone key|x=29|y=11|label=D^}}<br /> {{Lumatone key|x=30|y=11|label=E^}}<br /> {{Lumatone key|x=31|y=11|label=F^}}<br /> {{Lumatone key|x=32|y=11|label=G^}}<br /> {{Lumatone key|x=33|y=11|label=A}}<br /> {{Lumatone key|x=34|y=11|label=B}}<br /> {{Lumatone key|x=35|y=11|label=C}}<br /> <br /> {{Lumatone key|x=33|y=12|label=A^}}<br /> {{Lumatone key|x=34|y=12|label=B^}}<br /> {{Lumatone key|x=35|y=12|label=C^}}<br /> <br /> }}<br /> <br /> ==Expanded==<br /> <br /> This mapping has the smallest range of any presented here - less than 4 complete octaves - but its main advantage is mapping the Porcupine[15] scale to an intuitive zigzag pattern. In-between pitches always appear in-between on the keyboard, rather than off to the side.<br /> {{Lumatone mapping|<br /> <br /> {{Lumatone key|x=3|y=6|label=Gv}}<br /> <br /> {{Lumatone key|x=4|y=7|label=G}}<br /> {{Lumatone key|x=5|y=7|label=Av}}<br /> {{Lumatone key|x=6|y=7|label=Bv}}<br /> {{Lumatone key|x=7|y=7|label=Cv}}<br /> {{Lumatone key|x=8|y=7|label=Dv}}<br /> {{Lumatone key|x=9|y=7|label=Ev}}<br /> {{Lumatone key|x=10|y=7|label=Fv}}<br /> {{Lumatone key|x=11|y=7|label=Gv}}<br /> <br /> {{Lumatone key|x=4|y=8|label=F^}}<br /> {{Lumatone key|x=5|y=8|label=G^}}<br /> {{Lumatone key|x=6|y=8|label=A}}<br /> {{Lumatone key|x=7|y=8|label=B}}<br /> {{Lumatone key|x=8|y=8|label=C}}<br /> {{Lumatone key|x=9|y=8|label=D}}<br /> {{Lumatone key|x=10|y=8|label=E}}<br /> {{Lumatone key|x=11|y=8|label=F}}<br /> {{Lumatone key|x=12|y=8|label=G}}<br /> {{Lumatone key|x=13|y=8|label=Av}}<br /> {{Lumatone key|x=14|y=8|label=Bv}}<br /> {{Lumatone key|x=15|y=8|label=Cv}}<br /> {{Lumatone key|x=16|y=8|label=Dv}}<br /> {{Lumatone key|x=17|y=8|label=Ev}}<br /> {{Lumatone key|x=18|y=8|label=Fv}}<br /> {{Lumatone key|x=19|y=8|label=Gv}}<br /> <br /> {{Lumatone key|x=7|y=9|label=A^}}<br /> {{Lumatone key|x=8|y=9|label=B^}}<br /> {{Lumatone key|x=9|y=9|label=C^}}<br /> {{Lumatone key|x=10|y=9|label=D^}}<br /> {{Lumatone key|x=11|y=9|label=E^}}<br /> {{Lumatone key|x=12|y=9|label=F^}}<br /> {{Lumatone key|x=13|y=9|label=G^}}<br /> {{Lumatone key|x=14|y=9|label=A}}<br /> {{Lumatone key|x=15|y=9|label=B}}<br /> {{Lumatone key|x=16|y=9|label=C}}<br /> {{Lumatone key|x=17|y=9|label=D}}<br /> {{Lumatone key|x=18|y=9|label=E}}<br /> {{Lumatone key|x=19|y=9|label=F}}<br /> {{Lumatone key|x=20|y=9|label=G}}<br /> {{Lumatone key|x=21|y=9|label=Av}}<br /> {{Lumatone key|x=22|y=9|label=Bv}}<br /> {{Lumatone key|x=23|y=9|label=Cv}}<br /> {{Lumatone key|x=24|y=9|label=Dv}}<br /> {{Lumatone key|x=25|y=9|label=Ev}}<br /> {{Lumatone key|x=26|y=9|label=Fv}}<br /> {{Lumatone key|x=27|y=9|label=Gv}}<br /> <br /> {{Lumatone key|x=15|y=10|label=A^}}<br /> {{Lumatone key|x=16|y=10|label=B^}}<br /> {{Lumatone key|x=17|y=10|label=C^}}<br /> {{Lumatone key|x=18|y=10|label=D^}}<br /> {{Lumatone key|x=19|y=10|label=E^}}<br /> {{Lumatone key|x=20|y=10|label=F^}}<br /> {{Lumatone key|x=21|y=10|label=G^}}<br /> {{Lumatone key|x=22|y=10|label=A}}<br /> {{Lumatone key|x=23|y=10|label=B}}<br /> {{Lumatone key|x=24|y=10|label=C}}<br /> {{Lumatone key|x=25|y=10|label=D}}<br /> {{Lumatone key|x=26|y=10|label=E}}<br /> {{Lumatone key|x=27|y=10|label=F}}<br /> {{Lumatone key|x=28|y=10|label=G}}<br /> {{Lumatone key|x=29|y=10|label=Av}}<br /> {{Lumatone key|x=30|y=10|label=Bv}}<br /> {{Lumatone key|x=31|y=10|label=Cv}}<br /> {{Lumatone key|x=32|y=10|label=Dv}}<br /> {{Lumatone key|x=33|y=10|label=Ev}}<br /> {{Lumatone key|x=34|y=10|label=Fv}}<br /> <br /> {{Lumatone key|x=23|y=11|label=A^}}<br /> {{Lumatone key|x=24|y=11|label=B^}}<br /> {{Lumatone key|x=25|y=11|label=C^}}<br /> {{Lumatone key|x=26|y=11|label=D^}}<br /> {{Lumatone key|x=27|y=11|label=E^}}<br /> {{Lumatone key|x=28|y=11|label=F^}}<br /> {{Lumatone key|x=29|y=11|label=G^}}<br /> {{Lumatone key|x=30|y=11|label=A}}<br /> {{Lumatone key|x=31|y=11|label=B}}<br /> {{Lumatone key|x=32|y=11|label=C}}<br /> {{Lumatone key|x=33|y=11|label=D}}<br /> {{Lumatone key|x=34|y=11|label=E}}<br /> {{Lumatone key|x=35|y=11|label=F}}<br /> <br /> {{Lumatone key|x=31|y=12|label=A^}}<br /> {{Lumatone key|x=32|y=12|label=B^}}<br /> {{Lumatone key|x=33|y=12|label=C^}}<br /> {{Lumatone key|x=34|y=12|label=D^}}<br /> {{Lumatone key|x=35|y=12|label=E^}}<br /> <br /> }}<br /> <br /> [[Category:Lumatone mappings]]<br /> [[Category:Porcupine]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Lumatone_mapping_for_Miracle&diff=83576 Lumatone mapping for Miracle 2022-01-09T19:17:46Z <p>Keenan Pepper: Keenan Pepper moved page Lumatone mapping for Miracle to Lumatone mapping for miracle: let&#039;s lowercase all the temperament names</p> <hr /> <div>#REDIRECT [[Lumatone mapping for miracle]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Lumatone_mapping_for_miracle&diff=83575 Lumatone mapping for miracle 2022-01-09T19:17:46Z <p>Keenan Pepper: Keenan Pepper moved page Lumatone mapping for Miracle to Lumatone mapping for miracle: let&#039;s lowercase all the temperament names</p> <hr /> <div>This Lumatone mapping for [[miracle]] temperament spans 3 full octaves. The letter s refers to the secor (representing both 16/15 and 15/14). The letter c refers to the chroma (representing 45/44~49/48~50/49~55/54~56/55~64/63). The note labeled &quot;21/20&quot; also represents 22/21, and the note labeled &quot;21/11&quot; also represents 40/21.<br /> <br /> {{Lumatone mapping|<br /> <br /> {{Lumatone key|x=3|y=5|label=9/5}}<br /> {{Lumatone key|x=6|y=5|label=11/10|size=11px}}<br /> <br /> {{Lumatone key|x=3|y=6|label=11/6}}<br /> {{Lumatone key|x=4|y=6|label=-c}}<br /> {{Lumatone key|x=5|y=6|label=21/20|size=10px}}<br /> {{Lumatone key|x=6|y=6|label=9/8}}<br /> {{Lumatone key|x=7|y=6|label=6/5}}<br /> {{Lumatone key|x=8|y=6|label=9/7}}<br /> {{Lumatone key|x=9|y=6|label=11/8}}<br /> {{Lumatone key|x=10|y=6|label=22/15|size=11px}}<br /> {{Lumatone key|x=11|y=6|label=11/7}}<br /> {{Lumatone key|x=13|y=6|label=9/5}}<br /> {{Lumatone key|x=16|y=6|label=11/10|size=11px}}<br /> <br /> {{Lumatone key|x=4|y=7|label=1/1}}<br /> {{Lumatone key|x=5|y=7|label=s}}<br /> {{Lumatone key|x=6|y=7|label=8/7}}<br /> {{Lumatone key|x=7|y=7|label=11/9}}<br /> {{Lumatone key|x=8|y=7|label=21/16|size=10px}}<br /> {{Lumatone key|x=9|y=7|label=7/5}}<br /> {{Lumatone key|x=10|y=7|label=3/2}}<br /> {{Lumatone key|x=11|y=7|label=8/5}}<br /> {{Lumatone key|x=12|y=7|label=12/7}}<br /> {{Lumatone key|x=13|y=7|label=11/6}}<br /> {{Lumatone key|x=14|y=7|label=-c}}<br /> {{Lumatone key|x=15|y=7|label=21/20|size=10px}}<br /> {{Lumatone key|x=16|y=7|label=9/8}}<br /> {{Lumatone key|x=17|y=7|label=6/5}}<br /> {{Lumatone key|x=18|y=7|label=9/7}}<br /> {{Lumatone key|x=19|y=7|label=11/8}}<br /> {{Lumatone key|x=20|y=7|label=22/15|size=11px}}<br /> {{Lumatone key|x=21|y=7|label=11/7}}<br /> {{Lumatone key|x=23|y=7|label=9/5}}<br /> {{Lumatone key|x=26|y=7|label=11/10|size=11px}}<br /> <br /> {{Lumatone key|x=4|y=8|label=c}}<br /> {{Lumatone key|x=5|y=8|label=12/11|size=11px}}<br /> {{Lumatone key|x=6|y=8|label=7/6}}<br /> {{Lumatone key|x=7|y=8|label=5/4}}<br /> {{Lumatone key|x=8|y=8|label=4/3}}<br /> {{Lumatone key|x=9|y=8|label=10/7}}<br /> {{Lumatone key|x=10|y=8|label=32/21|size=10px}}<br /> {{Lumatone key|x=11|y=8|label=18/11|size=11px}}<br /> {{Lumatone key|x=12|y=8|label=7/4}}<br /> {{Lumatone key|x=13|y=8|label=-s}}<br /> {{Lumatone key|x=14|y=8|label=1/1}}<br /> {{Lumatone key|x=15|y=8|label=s}}<br /> {{Lumatone key|x=16|y=8|label=8/7}}<br /> {{Lumatone key|x=17|y=8|label=11/9}}<br /> {{Lumatone key|x=18|y=8|label=21/16|size=10px}}<br /> {{Lumatone key|x=19|y=8|label=7/5}}<br /> {{Lumatone key|x=20|y=8|label=3/2}}<br /> {{Lumatone key|x=21|y=8|label=8/5}}<br /> {{Lumatone key|x=22|y=8|label=12/7}}<br /> {{Lumatone key|x=23|y=8|label=11/6}}<br /> {{Lumatone key|x=24|y=8|label=-c}}<br /> {{Lumatone key|x=25|y=8|label=21/20|size=10px}}<br /> {{Lumatone key|x=26|y=8|label=9/8}}<br /> {{Lumatone key|x=27|y=8|label=6/5}}<br /> {{Lumatone key|x=28|y=8|label=9/7}}<br /> {{Lumatone key|x=29|y=8|label=11/8}}<br /> <br /> {{Lumatone key|x=7|y=9|label=14/11|size=11px}}<br /> {{Lumatone key|x=8|y=9|label=15/11|size=11px}}<br /> {{Lumatone key|x=9|y=9|label=16/11|size=11px}}<br /> {{Lumatone key|x=10|y=9|label=14/9}}<br /> {{Lumatone key|x=11|y=9|label=5/3}}<br /> {{Lumatone key|x=12|y=9|label=16/9}}<br /> {{Lumatone key|x=13|y=9|label=21/11|size=10px}}<br /> {{Lumatone key|x=14|y=9|label=c}}<br /> {{Lumatone key|x=15|y=9|label=12/11|size=11px}}<br /> {{Lumatone key|x=16|y=9|label=7/6}}<br /> {{Lumatone key|x=17|y=9|label=5/4}}<br /> {{Lumatone key|x=18|y=9|label=4/3}}<br /> {{Lumatone key|x=19|y=9|label=10/7}}<br /> {{Lumatone key|x=20|y=9|label=32/21|size=10px}}<br /> {{Lumatone key|x=21|y=9|label=18/11|size=11px}}<br /> {{Lumatone key|x=22|y=9|label=7/4}}<br /> {{Lumatone key|x=23|y=9|label=-s}}<br /> {{Lumatone key|x=24|y=9|label=1/1}}<br /> {{Lumatone key|x=25|y=9|label=s}}<br /> {{Lumatone key|x=26|y=9|label=8/7}}<br /> {{Lumatone key|x=27|y=9|label=11/9}}<br /> {{Lumatone key|x=28|y=9|label=21/16|size=10px}}<br /> {{Lumatone key|x=29|y=9|label=7/5}}<br /> {{Lumatone key|x=30|y=9|label=3/2}}<br /> {{Lumatone key|x=31|y=9|label=8/5}}<br /> {{Lumatone key|x=32|y=9|label=12/7}}<br /> {{Lumatone key|x=33|y=9|label=11/6}}<br /> <br /> {{Lumatone key|x=12|y=10|label=20/11|size=11px}}<br /> {{Lumatone key|x=15|y=10|label=10/9}}<br /> {{Lumatone key|x=17|y=10|label=14/11|size=11px}}<br /> {{Lumatone key|x=18|y=10|label=15/11|size=11px}}<br /> {{Lumatone key|x=19|y=10|label=16/11|size=11px}}<br /> {{Lumatone key|x=20|y=10|label=14/9}}<br /> {{Lumatone key|x=21|y=10|label=5/3}}<br /> {{Lumatone key|x=22|y=10|label=16/9}}<br /> {{Lumatone key|x=23|y=10|label=21/11|size=10px}}<br /> {{Lumatone key|x=24|y=10|label=c}}<br /> {{Lumatone key|x=25|y=10|label=12/11|size=11px}}<br /> {{Lumatone key|x=26|y=10|label=7/6}}<br /> {{Lumatone key|x=27|y=10|label=5/4}}<br /> {{Lumatone key|x=28|y=10|label=4/3}}<br /> {{Lumatone key|x=29|y=10|label=10/7}}<br /> {{Lumatone key|x=30|y=10|label=32/21|size=10px}}<br /> {{Lumatone key|x=31|y=10|label=18/11|size=11px}}<br /> {{Lumatone key|x=32|y=10|label=7/4}}<br /> {{Lumatone key|x=33|y=10|label=-s}}<br /> {{Lumatone key|x=34|y=10|label=1/1}}<br /> <br /> {{Lumatone key|x=22|y=11|label=20/11|size=11px}}<br /> {{Lumatone key|x=25|y=11|label=10/9}}<br /> {{Lumatone key|x=27|y=11|label=14/11|size=11px}}<br /> {{Lumatone key|x=28|y=11|label=15/11|size=11px}}<br /> {{Lumatone key|x=29|y=11|label=16/11|size=11px}}<br /> {{Lumatone key|x=30|y=11|label=14/9}}<br /> {{Lumatone key|x=31|y=11|label=5/3}}<br /> {{Lumatone key|x=32|y=11|label=16/9}}<br /> {{Lumatone key|x=33|y=11|label=21/11|size=10px}}<br /> {{Lumatone key|x=34|y=11|label=c}}<br /> {{Lumatone key|x=35|y=11|label=12/11|size=11px}}<br /> <br /> {{Lumatone key|x=32|y=12|label=20/11|size=11px}}<br /> {{Lumatone key|x=35|y=12|label=10/9}}<br /> <br /> }}<br /> <br /> [[Category:Lumatone mappings]]<br /> [[Category:Miracle]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Lumatone_mapping_for_Ennealimmal&diff=83574 Lumatone mapping for Ennealimmal 2022-01-09T19:17:28Z <p>Keenan Pepper: Keenan Pepper moved page Lumatone mapping for Ennealimmal to Lumatone mapping for ennealimmal: let&#039;s lowercase all the temperament names</p> <hr /> <div>#REDIRECT [[Lumatone mapping for ennealimmal]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Lumatone_mapping_for_ennealimmal&diff=83573 Lumatone mapping for ennealimmal 2022-01-09T19:17:28Z <p>Keenan Pepper: Keenan Pepper moved page Lumatone mapping for Ennealimmal to Lumatone mapping for ennealimmal: let&#039;s lowercase all the temperament names</p> <hr /> <div>This mapping for [[ennealimmal]] temperament contains 1/1 in 4 different octaves, and contains the complete 9-limit tonality diamond in the middle octave.<br /> <br /> (Note that JI ratios are used for labels, even tho ennealimmal is a temperament. Since ennealimmal is so remarkably accurate, this should not cause much confusion.)<br /> <br /> {{Lumatone mapping|<br /> {{Lumatone key|x=14|y=4|label=16/15|size=10px}}<br /> <br /> {{Lumatone key|x=12|y=5|label=16/9}}<br /> {{Lumatone key|x=13|y=5|label=48/25|size=10px}}<br /> {{Lumatone key|x=14|y=5|label=28/27|size=10px}}<br /> {{Lumatone key|x=15|y=5|label=28/25|size=10px}}<br /> {{Lumatone key|x=19|y=5|label=32/21|size=10px}}<br /> <br /> {{Lumatone key|x=19|y=6|label=40/27|size=10px}}<br /> {{Lumatone key|x=20|y=6|label=8/5}}<br /> {{Lumatone key|x=22|y=6|label=28/15|size=10px}}<br /> <br /> {{Lumatone key|x=16|y=7|label=8/7}}<br /> {{Lumatone key|x=18|y=7|label=4/3}}<br /> {{Lumatone key|x=19|y=7|label=36/25|size=10px}}<br /> {{Lumatone key|x=20|y=7|label=14/9}}<br /> {{Lumatone key|x=21|y=7|label=42/25|size=10px}}<br /> <br /> {{Lumatone key|x=14|y=8|label=40/21|size=10px}}<br /> {{Lumatone key|x=15|y=8|label=36/35|size=10px}}<br /> {{Lumatone key|x=16|y=8|label=10/9}}<br /> {{Lumatone key|x=17|y=8|label=6/5}}<br /> {{Lumatone key|x=19|y=8|label=7/5}}<br /> {{Lumatone key|x=23|y=8|label=40/21|size=10px}}<br /> {{Lumatone key|x=24|y=8|label=36/35|size=10px}}<br /> <br /> {{Lumatone key|x=6|y=9|label=1/1}}<br /> {{Lumatone key|x=14|y=9|label=50/27|size=10px}}<br /> {{Lumatone key|x=15|y=9|label=1/1}}<br /> {{Lumatone key|x=16|y=9|label=27/25|size=10px}}<br /> {{Lumatone key|x=17|y=9|label=7/6}}<br /> {{Lumatone key|x=18|y=9|label=(400)|size=10px}}<br /> {{Lumatone key|x=19|y=9|label=(533)|size=10px}}<br /> {{Lumatone key|x=20|y=9|label=(666)|size=10px}}<br /> {{Lumatone key|x=21|y=9|label=(800)|size=10px}}<br /> {{Lumatone key|x=22|y=9|label=12/7}}<br /> {{Lumatone key|x=23|y=9|label=50/27|size=10px}}<br /> {{Lumatone key|x=24|y=9|label=1/1}}<br /> {{Lumatone key|x=25|y=9|label=27/25|size=10px}}<br /> {{Lumatone key|x=33|y=9|label=1/1}}<br /> <br /> {{Lumatone key|x=15|y=10|label=35/18|size=10px}}<br /> {{Lumatone key|x=16|y=10|label=21/20|size=10px}}<br /> {{Lumatone key|x=20|y=10|label=10/7}}<br /> {{Lumatone key|x=22|y=10|label=5/3}}<br /> {{Lumatone key|x=23|y=10|label=9/5}}<br /> {{Lumatone key|x=24|y=10|label=35/18|size=10px}}<br /> {{Lumatone key|x=25|y=10|label=21/20|size=10px}}<br /> <br /> {{Lumatone key|x=16|y=11|label=49/48|size=10px}}<br /> {{Lumatone key|x=18|y=11|label=25/21|size=10px}}<br /> {{Lumatone key|x=19|y=11|label=9/7}}<br /> {{Lumatone key|x=20|y=11|label=25/18|size=10px}}<br /> {{Lumatone key|x=21|y=11|label=3/2}}<br /> {{Lumatone key|x=23|y=11|label=7/4}}<br /> {{Lumatone key|x=25|y=11|label=49/48|size=10px}}<br /> <br /> {{Lumatone key|x=17|y=12|label=15/14|size=10px}}<br /> {{Lumatone key|x=19|y=12|label=5/4}}<br /> {{Lumatone key|x=20|y=12|label=27/20|size=10px}}<br /> <br /> {{Lumatone key|x=20|y=13|label=21/16|size=10px}}<br /> {{Lumatone key|x=24|y=13|label=25/14|size=10px}}<br /> {{Lumatone key|x=25|y=13|label=27/14|size=10px}}<br /> {{Lumatone key|x=26|y=13|label=25/24|size=10px}}<br /> {{Lumatone key|x=27|y=13|label=9/8}}<br /> <br /> {{Lumatone key|x=25|y=14|label=15/8}}<br /> {{Lumatone key|x=26|y=14|label=81/80|size=10px}}<br /> }}<br /> <br /> [[Category:Lumatone mappings]]<br /> [[Category:Ennealimmal]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Harry&diff=83572 Harry 2022-01-09T19:16:21Z <p>Keenan Pepper: write intro and explain name</p> <hr /> <div>:''See also [[Gravity family #Harry]] or [[Breedsmic temperaments #Harry]].''<br /> <br /> '''Harry''' temperament has a period of half an octave and a generator somewhere between 22/21 and 21/20 (which are tempered together in harry), or around 83 cents. Alternatively it can be viewed as a [[cluster temperament]] with 14 clusters and a chroma that represents many important intervals including 81/80, 99/98, 100/99, and 121/120. In any case the first important [[MOS]] of harry has the shape [[2L 12s]].<br /> <br /> Harry was named after Harry Partch, which is ironic given that Harry Partch was adamantly opposed to the very idea of tempering. This is perhaps not so insulting to Harry when you consider that these mathematical structures can also be used to arrange JI intervals into patterns ([[constant structure]]s) and create JI [[detempering]]s of the temperament.<br /> <br /> This particular rank-2 temperament might be called &quot;harry&quot; because the lowest [[EDO]] in which [[Harry Partch's 43-tone scale]] is represented distinctly is [[58edo]], and harry is one of the best temperaments supported by 58edo (it is 58 &amp; 72). Alternatively, if you look at the tempered image of the 43-tone JI scale in this temperament, it is relatively compact and never &quot;backtracks&quot; from one of the 14 clusters to the previous one. In fact, the entire temperament can be derived from knowing that the fragment [12/11, 11/10, 10/9, 9/8] is supposed to be equidistant, and [14/11, 9/7] also has that same separation.<br /> <br /> (The steps of those scale fragments are 121/120, 100/99, 81/80, and 99/98. Tempering these together means that 4000/3993, 243/242, and 9801/9800 are all tempered out, and the unique 11-limit rank-2 temperament tempering those out is harry.)<br /> <br /> == Interval chain ==<br /> {| class=&quot;wikitable center-1 right-2 right-4&quot;<br /> ! rowspan=&quot;2&quot; | #<br /> ! colspan=&quot;2&quot; | Period 0<br /> ! colspan=&quot;2&quot; | Period 1<br /> |-<br /> ! Cents<br /> ! Approx. Ratios<br /> ! Cents<br /> ! Approx. Ratios<br /> |-<br /> | 0<br /> | 0.00<br /> | 1/1<br /> | 600.00<br /> | 99/70, 140/99<br /> |-<br /> | 1<br /> | 83.12<br /> | 21/20, 22/21<br /> | 683.12<br /> | 40/27<br /> |-<br /> | 2<br /> | 166.23<br /> | 11/10<br /> | 766.23<br /> | 14/9<br /> |-<br /> | 3<br /> | 249.35<br /> | 15/13<br /> | 849.35<br /> | 18/11, 44/27<br /> |-<br /> | 4<br /> | 332.46<br /> | 40/33<br /> | 932.46<br /> | 12/7<br /> |-<br /> | 5<br /> | 415.58<br /> | 14/11<br /> | 1015.58<br /> | 9/5<br /> |-<br /> | 6<br /> | 498.70<br /> | '''4/3'''<br /> | 1098.70<br /> | 66/35<br /> |-<br /> | 7<br /> | 581.81<br /> | 7/5<br /> | 1181.81<br /> | 160/81<br /> |-<br /> | 8<br /> | 664.92<br /> | 22/15<br /> | 64.92<br /> | 26/25, 27/26, 28/27<br /> |-<br /> | 9<br /> | 748.04<br /> | 54/35<br /> | 148.04<br /> | 12/11<br /> |-<br /> | 10<br /> | 831.16<br /> | 21/13<br /> | 231.16<br /> | '''8/7'''<br /> |-<br /> | 11<br /> | 914.28<br /> | 22/13<br /> | 314.28<br /> | 6/5<br /> |-<br /> | 12<br /> | 997.39<br /> | 16/9<br /> | 397.39<br /> | 44/35, 63/50<br /> |-<br /> | 13<br /> | 1080.51<br /> | 28/15<br /> | 480.51<br /> | 33/25<br /> |-<br /> | 14<br /> | 1163.62<br /> | 49/25, 88/45, 108/55<br /> | 563.62<br /> | 18/13<br /> |-<br /> | 15<br /> | 46.74<br /> | 36/35<br /> | 646.74<br /> | '''16/11'''<br /> |}<br /> <br /> == Chords ==<br /> {{main| Chords of harry }}<br /> <br /> == Scales ==<br /> * [[Harry58]]<br /> <br /> == Tuning spectrum ==<br /> <br /> {| class=&quot;wikitable center-all&quot;<br /> |-<br /> ! [[eigenmonzo|eigenmonzo&lt;br&gt;(unchanged interval]])<br /> ! generator&lt;br&gt;(¢)<br /> ! comments<br /> |-<br /> | 9/7<br /> | 82.458<br /> |<br /> |-<br /> | 11/10<br /> | 82.502<br /> |<br /> |-<br /> | 15/13<br /> | 82.580<br /> |<br /> |-<br /> | 13/11<br /> | 82.799<br /> |<br /> |-<br /> | 13/10<br /> | 82.865<br /> |<br /> |-<br /> | 15/11<br /> | 82.881<br /> |<br /> |-<br /> | 4/3<br /> | 83.007<br /> |<br /> |-<br /> | 14/13<br /> | 83.019<br /> |<br /> |-<br /> | 16/13<br /> | 83.057<br /> |<br /> |-<br /> | 13/12<br /> | 83.071<br /> |<br /> |-<br /> | 18/13<br /> | 83.099<br /> | 13- and 15-odd-limit minimax<br /> |-<br /> | 8/7<br /> | 83.117<br /> |<br /> |-<br /> | 16/15<br /> | 83.119<br /> |<br /> |-<br /> | 15/14<br /> | 83.120<br /> |<br /> |-<br /> | 5/4<br /> | 83.158<br /> | 5-, 7- and 9-odd-limit minimax<br /> |-<br /> | 7/5<br /> | 83.216<br /> |<br /> |-<br /> | 6/5<br /> | 83.240<br /> |<br /> |-<br /> | 11/8<br /> | 83.245<br /> | 11-odd-limit minimax<br /> |-<br /> | 7/6<br /> | 83.282<br /> |<br /> |-<br /> | 12/11<br /> | 83.404<br /> |<br /> |-<br /> | 14/11<br /> | 83.502<br /> |<br /> |-<br /> | 10/9<br /> | 83.519<br /> |<br /> |-<br /> | 11/9<br /> | 84.197<br /> |<br /> |}<br /> <br /> [[Category:Harry| ]] &lt;!-- main article --&gt;<br /> [[Category:Gravity family]]<br /> [[Category:Breedsmic temperaments]]<br /> [[Category:Cataharry temperaments]]<br /> {{IoT}}</div> Keenan Pepper https://en.xen.wiki/index.php?title=User:Keenan_Pepper&diff=83251 User:Keenan Pepper 2022-01-04T22:13:18Z <p>Keenan Pepper: </p> <hr /> <div>Keenan plays a lot of Balinese gamelan music but unfortunately not a lot of other xenharmonic music at this time. Keenan is a bit of an expert on mathematical theory and would love to chat with you about it.<br /> <br /> ==Project ideas==<br /> * &lt;s&gt;JS synth that can be played by computer keyboard and can take scale info passed in the URL (for linking from wiki).&lt;/s&gt; - [https://sevish.com/scaleworkshop/ Scale Workshop] pretty much provides this.<br /> * Hack up http://fritzo.org/keys to support regular temperament.<br /> * &lt;s&gt;Template thingy for Lumatone mappings.&lt;/s&gt; '''DONE'''<br /> * Write up no-limit TOP tuning definition and algorithm<br /> <br /> ==Temperaments that ought to have their own articles==<br /> * Chain of fourths ones:<br /> ** [[Archy]]<br /> ** [[Cassandra]]<br /> ** [[Dominant]]<br /> ** [[Father]]<br /> ** [[Garibaldi]]<br /> ** [[Helmholtz]]<br /> ** [[Meantone]]<br /> ** [[Superpyth]]<br /> ** [[Supra]]<br /> * Split fourth:<br /> ** [[Godzilla]]<br /> ** [[Semaphore]]<br /> * Split fifth:<br /> ** [[Mohaha]]<br /> ** [[Mohajira]]<br /> * Split octave:<br /> ** [[Pajara]]<br /> ** [[Srutal]]<br /> * [[Porcupine]]<br /> * [[Hanson]], [[Keemun]]<br /> * [[Magic]]<br /> * [[Tetracot]]<br /> * [[Slendric]]<br /> * [[Sensi]]<br /> * [[Negri]]<br /> * [[Orwell]]<br /> * [[Miracle]]<br /> * [[Valentine]]<br /> * [[Blackwood]], [[Blacksmith]]<br /> * [[Catler]]<br /> * [[Compton]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Talk:Trivial_temperament&diff=83250 Talk:Trivial temperament 2022-01-04T22:09:17Z <p>Keenan Pepper: </p> <hr /> <div>= OM =<br /> Is '''OM''' an acronym, and if so, what does it stand for? --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 18:07, 1 January 2022 (UTC)<br /> <br /> No, It's a reference to Hindu meditation practices, where said syllables are supposed to encompass the entire universe. https://en.wikipedia.org/wiki/Om --[[User:Yourmusic Productions|Yourmusic Productions]] ([[User talk:Yourmusic Productions|talk]]) 18:39, 1 January 2022 (UTC)<br /> <br /> : Ah, thanks for explaining, Yourmusic. Well, I was asking because I thought that whatever the answer was should be explained in the article itself. But if it's some Hindu meditation practice reference — not a simple acronym for a math or music term — then I don't understand enough to explain the connection and/or motivation myself, so I must ask someone else to take care of explaining it, then. Perhaps you're up to the task, Yourmusic?<br /> <br /> : What I can tell at a glance from this Wikipedia article is that this Hindu sense of &quot;Om&quot; is typically capitalized, but ''not'' in all caps. So if this xenharmonic object's name is meant as a reference to this Hindu sense of Om, then it should match its capitalization, unless there's some other consideration. If there is, then ''that'' consideration should also be surfaced, as well as explained in the article itself. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 19:14, 1 January 2022 (UTC)<br /> <br /> :: Yeah, a lot of temperament and comma names are in-jokes made by the original creator without explaining and it can be very hard to find out when and why they were called that, and if it has any deeper significance or a backronym attached. I've been irritated trying to track down info like that in the past as well. Looking at the revisions list, Keenan Pepper would be the person to ask in this case, as it's present right from the first version of the article and he created it. --[[User:Yourmusic Productions|Yourmusic Productions]] ([[User talk:Yourmusic Productions|talk]]) 21:38, 1 January 2022 (UTC)<br /> <br /> :::Exactly, the &quot;syllable encompassing the entire universe&quot; thing is spot on. I just called it Om temperament because there's only one temperament-distinct pitch in the whole system, kind of like &quot;Om&quot; is the only word you need to create the whole universe. —[[User:Keenan Pepper|Keenan Pepper]] ([[User talk:Keenan Pepper|talk]]) 22:09, 4 January 2022 (UTC)</div> Keenan Pepper https://en.xen.wiki/index.php?title=Lumatone_mapping_for_tetracot&diff=83013 Lumatone mapping for tetracot 2021-12-31T21:51:06Z <p>Keenan Pepper: monkey harmonics, youtube link</p> <hr /> <div>This [[Lumatone]] keyboard mapping is for temperaments shaped like [[tetracot family|tetracot]], which divides 3/2 into four equal parts resulting in a [[6L 1s]] scale. The notation used here is that A-G is Tetracot[7], where G-A is the unique small step. In other words, every pair of consecutive letters of the alphabet (so not G-A) is a tetracot generator.<br /> <br /> This mapping has the same overall shape as the [[Lumatone mapping for Porcupine#Compressed|&quot;compressed&quot; mapping for porcupine]], but because the chroma goes in the other direction, this is already optimal and there is no reason to go to a more &quot;expanded&quot; mapping.<br /> {{Lumatone mapping|<br /> <br /> {{Lumatone key|x=3|y=5|label=F^}}<br /> {{Lumatone key|x=4|y=5|label=G^}}<br /> <br /> {{Lumatone key|x=3|y=6|label=F}}<br /> {{Lumatone key|x=4|y=6|label=G}}<br /> {{Lumatone key|x=5|y=6|label=A^}}<br /> {{Lumatone key|x=6|y=6|label=B^}}<br /> {{Lumatone key|x=7|y=6|label=C^}}<br /> {{Lumatone key|x=8|y=6|label=D^}}<br /> {{Lumatone key|x=9|y=6|label=E^}}<br /> {{Lumatone key|x=10|y=6|label=F^}}<br /> {{Lumatone key|x=11|y=6|label=G^}}<br /> <br /> {{Lumatone key|x=4|y=7|label=Gv}}<br /> {{Lumatone key|x=5|y=7|label=A}}<br /> {{Lumatone key|x=6|y=7|label=B}}<br /> {{Lumatone key|x=7|y=7|label=C}}<br /> {{Lumatone key|x=8|y=7|label=D}}<br /> {{Lumatone key|x=9|y=7|label=E}}<br /> {{Lumatone key|x=10|y=7|label=F}}<br /> {{Lumatone key|x=11|y=7|label=G}}<br /> {{Lumatone key|x=12|y=7|label=A^}}<br /> {{Lumatone key|x=13|y=7|label=B^}}<br /> {{Lumatone key|x=14|y=7|label=C^}}<br /> {{Lumatone key|x=15|y=7|label=D^}}<br /> {{Lumatone key|x=16|y=7|label=E^}}<br /> {{Lumatone key|x=17|y=7|label=F^}}<br /> {{Lumatone key|x=18|y=7|label=G^}}<br /> <br /> {{Lumatone key|x=5|y=8|label=Av}}<br /> {{Lumatone key|x=6|y=8|label=Bv}}<br /> {{Lumatone key|x=7|y=8|label=Cv}}<br /> {{Lumatone key|x=8|y=8|label=Dv}}<br /> {{Lumatone key|x=9|y=8|label=Ev}}<br /> {{Lumatone key|x=10|y=8|label=Fv}}<br /> {{Lumatone key|x=11|y=8|label=Gv}}<br /> {{Lumatone key|x=12|y=8|label=A}}<br /> {{Lumatone key|x=13|y=8|label=B}}<br /> {{Lumatone key|x=14|y=8|label=C}}<br /> {{Lumatone key|x=15|y=8|label=D}}<br /> {{Lumatone key|x=16|y=8|label=E}}<br /> {{Lumatone key|x=17|y=8|label=F}}<br /> {{Lumatone key|x=18|y=8|label=G}}<br /> {{Lumatone key|x=19|y=8|label=A^}}<br /> {{Lumatone key|x=20|y=8|label=B^}}<br /> {{Lumatone key|x=21|y=8|label=C^}}<br /> {{Lumatone key|x=22|y=8|label=D^}}<br /> {{Lumatone key|x=23|y=8|label=E^}}<br /> {{Lumatone key|x=24|y=8|label=F^}}<br /> {{Lumatone key|x=25|y=8|label=G^}}<br /> <br /> {{Lumatone key|x=12|y=9|label=Av}}<br /> {{Lumatone key|x=13|y=9|label=Bv}}<br /> {{Lumatone key|x=14|y=9|label=Cv}}<br /> {{Lumatone key|x=15|y=9|label=Dv}}<br /> {{Lumatone key|x=16|y=9|label=Ev}}<br /> {{Lumatone key|x=17|y=9|label=Fv}}<br /> {{Lumatone key|x=18|y=9|label=Gv}}<br /> {{Lumatone key|x=19|y=9|label=A}}<br /> {{Lumatone key|x=20|y=9|label=B}}<br /> {{Lumatone key|x=21|y=9|label=C}}<br /> {{Lumatone key|x=22|y=9|label=D}}<br /> {{Lumatone key|x=23|y=9|label=E}}<br /> {{Lumatone key|x=24|y=9|label=F}}<br /> {{Lumatone key|x=25|y=9|label=G}}<br /> {{Lumatone key|x=26|y=9|label=A^}}<br /> {{Lumatone key|x=27|y=9|label=B^}}<br /> {{Lumatone key|x=28|y=9|label=C^}}<br /> {{Lumatone key|x=29|y=9|label=D^}}<br /> {{Lumatone key|x=30|y=9|label=E^}}<br /> {{Lumatone key|x=31|y=9|label=F^}}<br /> {{Lumatone key|x=32|y=9|label=G^}}<br /> <br /> {{Lumatone key|x=19|y=10|label=Av}}<br /> {{Lumatone key|x=20|y=10|label=Bv}}<br /> {{Lumatone key|x=21|y=10|label=Cv}}<br /> {{Lumatone key|x=22|y=10|label=Dv}}<br /> {{Lumatone key|x=23|y=10|label=Ev}}<br /> {{Lumatone key|x=24|y=10|label=Fv}}<br /> {{Lumatone key|x=25|y=10|label=Gv}}<br /> {{Lumatone key|x=26|y=10|label=A}}<br /> {{Lumatone key|x=27|y=10|label=B}}<br /> {{Lumatone key|x=28|y=10|label=C}}<br /> {{Lumatone key|x=29|y=10|label=D}}<br /> {{Lumatone key|x=30|y=10|label=E}}<br /> {{Lumatone key|x=31|y=10|label=F}}<br /> {{Lumatone key|x=32|y=10|label=G}}<br /> {{Lumatone key|x=33|y=10|label=A^}}<br /> {{Lumatone key|x=34|y=10|label=B^}}<br /> <br /> {{Lumatone key|x=26|y=11|label=Av}}<br /> {{Lumatone key|x=27|y=11|label=Bv}}<br /> {{Lumatone key|x=28|y=11|label=Cv}}<br /> {{Lumatone key|x=29|y=11|label=Dv}}<br /> {{Lumatone key|x=30|y=11|label=Ev}}<br /> {{Lumatone key|x=31|y=11|label=Fv}}<br /> {{Lumatone key|x=32|y=11|label=Gv}}<br /> {{Lumatone key|x=33|y=11|label=A}}<br /> {{Lumatone key|x=34|y=11|label=B}}<br /> {{Lumatone key|x=35|y=11|label=C}}<br /> <br /> {{Lumatone key|x=33|y=12|label=Av}}<br /> {{Lumatone key|x=34|y=12|label=Bv}}<br /> {{Lumatone key|x=35|y=12|label=Cv}}<br /> <br /> }}<br /> <br /> ==Locations of harmonics in Monkey mapping==<br /> <br /> The specific temperament mapping used here is 13-limit [[Tetracot family#Monkey|monkey]].<br /> {{Lumatone mapping|<br /> <br /> {{Lumatone key|x=6|y=6|label=9/8}}<br /> {{Lumatone key|x=7|y=6|label=5/4}}<br /> {{Lumatone key|x=8|y=6|label=11/8}}<br /> {{Lumatone key|x=11|y=6|label=15/8}}<br /> <br /> {{Lumatone key|x=5|y=7|label=1/1}}<br /> {{Lumatone key|x=9|y=7|label=3/2}}<br /> {{Lumatone key|x=13|y=7|label=9/8}}<br /> {{Lumatone key|x=14|y=7|label=5/4}}<br /> {{Lumatone key|x=15|y=7|label=11/8}}<br /> {{Lumatone key|x=18|y=7|label=15/8}}<br /> <br /> {{Lumatone key|x=10|y=8|label=13/8}}<br /> {{Lumatone key|x=12|y=8|label=1/1}}<br /> {{Lumatone key|x=16|y=8|label=3/2}}<br /> {{Lumatone key|x=20|y=8|label=9/8}}<br /> {{Lumatone key|x=21|y=8|label=5/4}}<br /> {{Lumatone key|x=22|y=8|label=11/8}}<br /> {{Lumatone key|x=25|y=8|label=15/8}}<br /> <br /> {{Lumatone key|x=17|y=9|label=13/8}}<br /> {{Lumatone key|x=19|y=9|label=1/1}}<br /> {{Lumatone key|x=23|y=9|label=3/2}}<br /> {{Lumatone key|x=27|y=9|label=9/8}}<br /> {{Lumatone key|x=28|y=9|label=5/4}}<br /> {{Lumatone key|x=29|y=9|label=11/8}}<br /> {{Lumatone key|x=32|y=9|label=15/8}}<br /> <br /> {{Lumatone key|x=11|y=10|label=7/4}}<br /> {{Lumatone key|x=24|y=10|label=13/8}}<br /> {{Lumatone key|x=26|y=10|label=1/1}}<br /> {{Lumatone key|x=30|y=10|label=3/2}}<br /> {{Lumatone key|x=34|y=10|label=9/8}}<br /> <br /> {{Lumatone key|x=18|y=11|label=7/4}}<br /> {{Lumatone key|x=31|y=11|label=13/8}}<br /> {{Lumatone key|x=33|y=11|label=1/1}}<br /> <br /> {{Lumatone key|x=25|y=12|label=7/4}}<br /> <br /> {{Lumatone key|x=32|y=13|label=7/4}}<br /> <br /> }}<br /> <br /> ==External links==<br /> * [https://www.youtube.com/watch?v=SueBUSvkTEg The monkey puzzle] by Herman Miller<br /> <br /> [[Category:Lumatone mappings]]<br /> [[Category:Tetracot family]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Lumatone_mapping_for_tetracot&diff=83012 Lumatone mapping for tetracot 2021-12-31T21:34:06Z <p>Keenan Pepper: Created page with &quot;This Lumatone keyboard mapping is for temperaments shaped like tetracot, which divides 3/2 into four equal parts resulting in a 6L 1s scale. The no...&quot;</p> <hr /> <div>This [[Lumatone]] keyboard mapping is for temperaments shaped like [[tetracot family|tetracot]], which divides 3/2 into four equal parts resulting in a [[6L 1s]] scale. The notation used here is that A-G is Tetracot[7], where G-A is the unique small step. In other words every pair of consecutive letters of the alphabet (so not G-A) is a tetracot generator.<br /> <br /> This mapping has the same overall shape as the [[Lumatone mapping for Porcupine#Compressed|&quot;compressed&quot; mapping for porcupine]], but because the chroma goes in the other direction, this is already optimal and there is no reason to go to a more &quot;expanded&quot; mapping.<br /> <br /> {{Lumatone mapping|<br /> <br /> {{Lumatone key|x=3|y=5|label=F^}}<br /> {{Lumatone key|x=4|y=5|label=G^}}<br /> <br /> {{Lumatone key|x=3|y=6|label=F}}<br /> {{Lumatone key|x=4|y=6|label=G}}<br /> {{Lumatone key|x=5|y=6|label=A^}}<br /> {{Lumatone key|x=6|y=6|label=B^}}<br /> {{Lumatone key|x=7|y=6|label=C^}}<br /> {{Lumatone key|x=8|y=6|label=D^}}<br /> {{Lumatone key|x=9|y=6|label=E^}}<br /> {{Lumatone key|x=10|y=6|label=F^}}<br /> {{Lumatone key|x=11|y=6|label=G^}}<br /> <br /> {{Lumatone key|x=4|y=7|label=Gv}}<br /> {{Lumatone key|x=5|y=7|label=A}}<br /> {{Lumatone key|x=6|y=7|label=B}}<br /> {{Lumatone key|x=7|y=7|label=C}}<br /> {{Lumatone key|x=8|y=7|label=D}}<br /> {{Lumatone key|x=9|y=7|label=E}}<br /> {{Lumatone key|x=10|y=7|label=F}}<br /> {{Lumatone key|x=11|y=7|label=G}}<br /> {{Lumatone key|x=12|y=7|label=A^}}<br /> {{Lumatone key|x=13|y=7|label=B^}}<br /> {{Lumatone key|x=14|y=7|label=C^}}<br /> {{Lumatone key|x=15|y=7|label=D^}}<br /> {{Lumatone key|x=16|y=7|label=E^}}<br /> {{Lumatone key|x=17|y=7|label=F^}}<br /> {{Lumatone key|x=18|y=7|label=G^}}<br /> <br /> {{Lumatone key|x=5|y=8|label=Av}}<br /> {{Lumatone key|x=6|y=8|label=Bv}}<br /> {{Lumatone key|x=7|y=8|label=Cv}}<br /> {{Lumatone key|x=8|y=8|label=Dv}}<br /> {{Lumatone key|x=9|y=8|label=Ev}}<br /> {{Lumatone key|x=10|y=8|label=Fv}}<br /> {{Lumatone key|x=11|y=8|label=Gv}}<br /> {{Lumatone key|x=12|y=8|label=A}}<br /> {{Lumatone key|x=13|y=8|label=B}}<br /> {{Lumatone key|x=14|y=8|label=C}}<br /> {{Lumatone key|x=15|y=8|label=D}}<br /> {{Lumatone key|x=16|y=8|label=E}}<br /> {{Lumatone key|x=17|y=8|label=F}}<br /> {{Lumatone key|x=18|y=8|label=G}}<br /> {{Lumatone key|x=19|y=8|label=A^}}<br /> {{Lumatone key|x=20|y=8|label=B^}}<br /> {{Lumatone key|x=21|y=8|label=C^}}<br /> {{Lumatone key|x=22|y=8|label=D^}}<br /> {{Lumatone key|x=23|y=8|label=E^}}<br /> {{Lumatone key|x=24|y=8|label=F^}}<br /> {{Lumatone key|x=25|y=8|label=G^}}<br /> <br /> {{Lumatone key|x=12|y=9|label=Av}}<br /> {{Lumatone key|x=13|y=9|label=Bv}}<br /> {{Lumatone key|x=14|y=9|label=Cv}}<br /> {{Lumatone key|x=15|y=9|label=Dv}}<br /> {{Lumatone key|x=16|y=9|label=Ev}}<br /> {{Lumatone key|x=17|y=9|label=Fv}}<br /> {{Lumatone key|x=18|y=9|label=Gv}}<br /> {{Lumatone key|x=19|y=9|label=A}}<br /> {{Lumatone key|x=20|y=9|label=B}}<br /> {{Lumatone key|x=21|y=9|label=C}}<br /> {{Lumatone key|x=22|y=9|label=D}}<br /> {{Lumatone key|x=23|y=9|label=E}}<br /> {{Lumatone key|x=24|y=9|label=F}}<br /> {{Lumatone key|x=25|y=9|label=G}}<br /> {{Lumatone key|x=26|y=9|label=A^}}<br /> {{Lumatone key|x=27|y=9|label=B^}}<br /> {{Lumatone key|x=28|y=9|label=C^}}<br /> {{Lumatone key|x=29|y=9|label=D^}}<br /> {{Lumatone key|x=30|y=9|label=E^}}<br /> {{Lumatone key|x=31|y=9|label=F^}}<br /> {{Lumatone key|x=32|y=9|label=G^}}<br /> <br /> {{Lumatone key|x=19|y=10|label=Av}}<br /> {{Lumatone key|x=20|y=10|label=Bv}}<br /> {{Lumatone key|x=21|y=10|label=Cv}}<br /> {{Lumatone key|x=22|y=10|label=Dv}}<br /> {{Lumatone key|x=23|y=10|label=Ev}}<br /> {{Lumatone key|x=24|y=10|label=Fv}}<br /> {{Lumatone key|x=25|y=10|label=Gv}}<br /> {{Lumatone key|x=26|y=10|label=A}}<br /> {{Lumatone key|x=27|y=10|label=B}}<br /> {{Lumatone key|x=28|y=10|label=C}}<br /> {{Lumatone key|x=29|y=10|label=D}}<br /> {{Lumatone key|x=30|y=10|label=E}}<br /> {{Lumatone key|x=31|y=10|label=F}}<br /> {{Lumatone key|x=32|y=10|label=G}}<br /> {{Lumatone key|x=33|y=10|label=A^}}<br /> {{Lumatone key|x=34|y=10|label=B^}}<br /> <br /> {{Lumatone key|x=26|y=11|label=Av}}<br /> {{Lumatone key|x=27|y=11|label=Bv}}<br /> {{Lumatone key|x=28|y=11|label=Cv}}<br /> {{Lumatone key|x=29|y=11|label=Dv}}<br /> {{Lumatone key|x=30|y=11|label=Ev}}<br /> {{Lumatone key|x=31|y=11|label=Fv}}<br /> {{Lumatone key|x=32|y=11|label=Gv}}<br /> {{Lumatone key|x=33|y=11|label=A}}<br /> {{Lumatone key|x=34|y=11|label=B}}<br /> {{Lumatone key|x=35|y=11|label=C}}<br /> <br /> {{Lumatone key|x=33|y=12|label=Av}}<br /> {{Lumatone key|x=34|y=12|label=Bv}}<br /> {{Lumatone key|x=35|y=12|label=Cv}}<br /> <br /> }}<br /> <br /> [[Category:Lumatone mappings]]<br /> [[Category:Tetracot family]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Lumatone_mapping_for_ennealimmal&diff=83009 Lumatone mapping for ennealimmal 2021-12-31T20:37:11Z <p>Keenan Pepper: explain JI labels for temperament</p> <hr /> <div>This mapping for [[ennealimmal]] temperament contains 1/1 in 4 different octaves, and contains the complete 9-limit tonality diamond in the middle octave.<br /> <br /> (Note that JI ratios are used for labels, even tho ennealimmal is a temperament. Since ennealimmal is so remarkably accurate, this should not cause much confusion.)<br /> <br /> {{Lumatone mapping|<br /> {{Lumatone key|x=14|y=4|label=16/15|size=10px}}<br /> <br /> {{Lumatone key|x=12|y=5|label=16/9}}<br /> {{Lumatone key|x=13|y=5|label=48/25|size=10px}}<br /> {{Lumatone key|x=14|y=5|label=28/27|size=10px}}<br /> {{Lumatone key|x=15|y=5|label=28/25|size=10px}}<br /> {{Lumatone key|x=19|y=5|label=32/21|size=10px}}<br /> <br /> {{Lumatone key|x=19|y=6|label=40/27|size=10px}}<br /> {{Lumatone key|x=20|y=6|label=8/5}}<br /> {{Lumatone key|x=22|y=6|label=28/15|size=10px}}<br /> <br /> {{Lumatone key|x=16|y=7|label=8/7}}<br /> {{Lumatone key|x=18|y=7|label=4/3}}<br /> {{Lumatone key|x=19|y=7|label=36/25|size=10px}}<br /> {{Lumatone key|x=20|y=7|label=14/9}}<br /> {{Lumatone key|x=21|y=7|label=42/25|size=10px}}<br /> <br /> {{Lumatone key|x=14|y=8|label=40/21|size=10px}}<br /> {{Lumatone key|x=15|y=8|label=36/35|size=10px}}<br /> {{Lumatone key|x=16|y=8|label=10/9}}<br /> {{Lumatone key|x=17|y=8|label=6/5}}<br /> {{Lumatone key|x=19|y=8|label=7/5}}<br /> {{Lumatone key|x=23|y=8|label=40/21|size=10px}}<br /> {{Lumatone key|x=24|y=8|label=36/35|size=10px}}<br /> <br /> {{Lumatone key|x=6|y=9|label=1/1}}<br /> {{Lumatone key|x=14|y=9|label=50/27|size=10px}}<br /> {{Lumatone key|x=15|y=9|label=1/1}}<br /> {{Lumatone key|x=16|y=9|label=27/25|size=10px}}<br /> {{Lumatone key|x=17|y=9|label=7/6}}<br /> {{Lumatone key|x=18|y=9|label=(400)|size=10px}}<br /> {{Lumatone key|x=19|y=9|label=(533)|size=10px}}<br /> {{Lumatone key|x=20|y=9|label=(666)|size=10px}}<br /> {{Lumatone key|x=21|y=9|label=(800)|size=10px}}<br /> {{Lumatone key|x=22|y=9|label=12/7}}<br /> {{Lumatone key|x=23|y=9|label=50/27|size=10px}}<br /> {{Lumatone key|x=24|y=9|label=1/1}}<br /> {{Lumatone key|x=25|y=9|label=27/25|size=10px}}<br /> {{Lumatone key|x=33|y=9|label=1/1}}<br /> <br /> {{Lumatone key|x=15|y=10|label=35/18|size=10px}}<br /> {{Lumatone key|x=16|y=10|label=21/20|size=10px}}<br /> {{Lumatone key|x=20|y=10|label=10/7}}<br /> {{Lumatone key|x=22|y=10|label=5/3}}<br /> {{Lumatone key|x=23|y=10|label=9/5}}<br /> {{Lumatone key|x=24|y=10|label=35/18|size=10px}}<br /> {{Lumatone key|x=25|y=10|label=21/20|size=10px}}<br /> <br /> {{Lumatone key|x=16|y=11|label=49/48|size=10px}}<br /> {{Lumatone key|x=18|y=11|label=25/21|size=10px}}<br /> {{Lumatone key|x=19|y=11|label=9/7}}<br /> {{Lumatone key|x=20|y=11|label=25/18|size=10px}}<br /> {{Lumatone key|x=21|y=11|label=3/2}}<br /> {{Lumatone key|x=23|y=11|label=7/4}}<br /> {{Lumatone key|x=25|y=11|label=49/48|size=10px}}<br /> <br /> {{Lumatone key|x=17|y=12|label=15/14|size=10px}}<br /> {{Lumatone key|x=19|y=12|label=5/4}}<br /> {{Lumatone key|x=20|y=12|label=27/20|size=10px}}<br /> <br /> {{Lumatone key|x=20|y=13|label=21/16|size=10px}}<br /> {{Lumatone key|x=24|y=13|label=25/14|size=10px}}<br /> {{Lumatone key|x=25|y=13|label=27/14|size=10px}}<br /> {{Lumatone key|x=26|y=13|label=25/24|size=10px}}<br /> {{Lumatone key|x=27|y=13|label=9/8}}<br /> <br /> {{Lumatone key|x=25|y=14|label=15/8}}<br /> {{Lumatone key|x=26|y=14|label=81/80|size=10px}}<br /> }}<br /> <br /> [[Category:Lumatone mappings]]<br /> [[Category:Ennealimmal]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Lumatone_mapping_for_porcupine&diff=83008 Lumatone mapping for porcupine 2021-12-31T20:30:04Z <p>Keenan Pepper: overall approach</p> <hr /> <div>There are several ways to map [[porcupine]] temperament onto the [[Lumatone]] keyboard. This article uses the Porcupine[7] notation convention from [[Porcupine Notation]].<br /> <br /> The mappings pictured below are based on mapping consecutive porcupine generator steps (~160 cents) to adjacent keys going generally left-to-right across the keyboard.<br /> <br /> A completely different approach to playing porcupine music on the Lumatone would be to use a standard mapping for some porcupine EDO (e.g. the [[Lumatone mapping for 22edo]]) and learn the shapes of porcupine scales in that layout. For example in 22edo, porcupine steps go roughly vertically rather than roughly horizontally, thus requiring a lot of &quot;wrapping around&quot;. But if you just learn the shape of a &quot;porcupine tetrachord&quot; that could be a fruitful approach.<br /> <br /> ==Ultra-compressed==<br /> <br /> This has the largest range of any mapping shown here (5 complete octaves), but the sequence of nearby pitches can be confusing. In particular, notes separated by the Porcupine[7] chroma (denoted by ^/v here) are not mapped to adjacent keys.<br /> {{Lumatone mapping|<br /> <br /> {{Lumatone key|x=3|y=5|label=Ev}}<br /> {{Lumatone key|x=4|y=5|label=Fv}}<br /> {{Lumatone key|x=5|y=5|label=Gv}}<br /> <br /> {{Lumatone key|x=3|y=6|label=F}}<br /> {{Lumatone key|x=4|y=6|label=G}}<br /> {{Lumatone key|x=5|y=6|label=Av}}<br /> {{Lumatone key|x=6|y=6|label=Bv}}<br /> {{Lumatone key|x=7|y=6|label=Cv}}<br /> {{Lumatone key|x=8|y=6|label=Dv}}<br /> {{Lumatone key|x=9|y=6|label=Ev}}<br /> {{Lumatone key|x=10|y=6|label=Fv}}<br /> {{Lumatone key|x=11|y=6|label=Gv}}<br /> <br /> {{Lumatone key|x=4|y=7|label=A}}<br /> {{Lumatone key|x=5|y=7|label=B}}<br /> {{Lumatone key|x=6|y=7|label=C}}<br /> {{Lumatone key|x=7|y=7|label=D}}<br /> {{Lumatone key|x=8|y=7|label=E}}<br /> {{Lumatone key|x=9|y=7|label=F}}<br /> {{Lumatone key|x=10|y=7|label=G}}<br /> {{Lumatone key|x=11|y=7|label=Av}}<br /> {{Lumatone key|x=12|y=7|label=Bv}}<br /> {{Lumatone key|x=13|y=7|label=Cv}}<br /> {{Lumatone key|x=14|y=7|label=Dv}}<br /> {{Lumatone key|x=15|y=7|label=Ev}}<br /> {{Lumatone key|x=16|y=7|label=Fv}}<br /> {{Lumatone key|x=17|y=7|label=Gv}}<br /> <br /> {{Lumatone key|x=4|y=8|label=B^}}<br /> {{Lumatone key|x=5|y=8|label=C^}}<br /> {{Lumatone key|x=6|y=8|label=D^}}<br /> {{Lumatone key|x=7|y=8|label=E^}}<br /> {{Lumatone key|x=8|y=8|label=F^}}<br /> {{Lumatone key|x=9|y=8|label=G^}}<br /> {{Lumatone key|x=10|y=8|label=A}}<br /> {{Lumatone key|x=11|y=8|label=B}}<br /> {{Lumatone key|x=12|y=8|label=C}}<br /> {{Lumatone key|x=13|y=8|label=D}}<br /> {{Lumatone key|x=14|y=8|label=E}}<br /> {{Lumatone key|x=15|y=8|label=F}}<br /> {{Lumatone key|x=16|y=8|label=G}}<br /> {{Lumatone key|x=17|y=8|label=Av}}<br /> {{Lumatone key|x=18|y=8|label=Bv}}<br /> {{Lumatone key|x=19|y=8|label=Cv}}<br /> {{Lumatone key|x=20|y=8|label=Dv}}<br /> {{Lumatone key|x=21|y=8|label=Ev}}<br /> {{Lumatone key|x=22|y=8|label=Fv}}<br /> {{Lumatone key|x=23|y=8|label=Gv}}<br /> <br /> {{Lumatone key|x=9|y=9|label=A^}}<br /> {{Lumatone key|x=10|y=9|label=B^}}<br /> {{Lumatone key|x=11|y=9|label=C^}}<br /> {{Lumatone key|x=12|y=9|label=D^}}<br /> {{Lumatone key|x=13|y=9|label=E^}}<br /> {{Lumatone key|x=14|y=9|label=F^}}<br /> {{Lumatone key|x=15|y=9|label=G^}}<br /> {{Lumatone key|x=16|y=9|label=A}}<br /> {{Lumatone key|x=17|y=9|label=B}}<br /> {{Lumatone key|x=18|y=9|label=C}}<br /> {{Lumatone key|x=19|y=9|label=D}}<br /> {{Lumatone key|x=20|y=9|label=E}}<br /> {{Lumatone key|x=21|y=9|label=F}}<br /> {{Lumatone key|x=22|y=9|label=G}}<br /> {{Lumatone key|x=23|y=9|label=Av}}<br /> {{Lumatone key|x=24|y=9|label=Bv}}<br /> {{Lumatone key|x=25|y=9|label=Cv}}<br /> {{Lumatone key|x=26|y=9|label=Dv}}<br /> {{Lumatone key|x=27|y=9|label=Ev}}<br /> {{Lumatone key|x=28|y=9|label=Fv}}<br /> {{Lumatone key|x=29|y=9|label=Gv}}<br /> <br /> {{Lumatone key|x=15|y=10|label=A^}}<br /> {{Lumatone key|x=16|y=10|label=B^}}<br /> {{Lumatone key|x=17|y=10|label=C^}}<br /> {{Lumatone key|x=18|y=10|label=D^}}<br /> {{Lumatone key|x=19|y=10|label=E^}}<br /> {{Lumatone key|x=20|y=10|label=F^}}<br /> {{Lumatone key|x=21|y=10|label=G^}}<br /> {{Lumatone key|x=22|y=10|label=A}}<br /> {{Lumatone key|x=23|y=10|label=B}}<br /> {{Lumatone key|x=24|y=10|label=C}}<br /> {{Lumatone key|x=25|y=10|label=D}}<br /> {{Lumatone key|x=26|y=10|label=E}}<br /> {{Lumatone key|x=27|y=10|label=F}}<br /> {{Lumatone key|x=28|y=10|label=G}}<br /> {{Lumatone key|x=29|y=10|label=Av}}<br /> {{Lumatone key|x=30|y=10|label=Bv}}<br /> {{Lumatone key|x=31|y=10|label=Cv}}<br /> {{Lumatone key|x=32|y=10|label=Dv}}<br /> {{Lumatone key|x=33|y=10|label=Ev}}<br /> {{Lumatone key|x=34|y=10|label=Fv}}<br /> <br /> {{Lumatone key|x=21|y=11|label=A^}}<br /> {{Lumatone key|x=22|y=11|label=B^}}<br /> {{Lumatone key|x=23|y=11|label=C^}}<br /> {{Lumatone key|x=24|y=11|label=D^}}<br /> {{Lumatone key|x=25|y=11|label=E^}}<br /> {{Lumatone key|x=26|y=11|label=F^}}<br /> {{Lumatone key|x=27|y=11|label=G^}}<br /> {{Lumatone key|x=28|y=11|label=A}}<br /> {{Lumatone key|x=29|y=11|label=B}}<br /> {{Lumatone key|x=30|y=11|label=C}}<br /> {{Lumatone key|x=31|y=11|label=D}}<br /> {{Lumatone key|x=32|y=11|label=E}}<br /> {{Lumatone key|x=33|y=11|label=F}}<br /> {{Lumatone key|x=34|y=11|label=G}}<br /> {{Lumatone key|x=35|y=11|label=Av}}<br /> <br /> {{Lumatone key|x=27|y=12|label=A^}}<br /> {{Lumatone key|x=28|y=12|label=B^}}<br /> {{Lumatone key|x=29|y=12|label=C^}}<br /> {{Lumatone key|x=30|y=12|label=D^}}<br /> {{Lumatone key|x=31|y=12|label=E^}}<br /> {{Lumatone key|x=32|y=12|label=F^}}<br /> {{Lumatone key|x=33|y=12|label=G^}}<br /> {{Lumatone key|x=34|y=12|label=A}}<br /> {{Lumatone key|x=35|y=12|label=B}}<br /> <br /> {{Lumatone key|x=33|y=13|label=A^}}<br /> {{Lumatone key|x=34|y=13|label=B^}}<br /> {{Lumatone key|x=35|y=13|label=C^}}<br /> {{Lumatone key|x=36|y=13|label=D^}}<br /> <br /> }}<br /> <br /> ==Compressed==<br /> <br /> This is a compromise intermediate between the &quot;ultra-compressed&quot; and &quot;expanded&quot; mappings. It covers 4 complete octaves, and the Porcupine[7] chroma is now mapped to adjacent keys in the &quot;vertical&quot; direction. The sequence of pitches is still not completely intuitive, however: the Porcupine[15] chromatic scale still zigzags back and forth leaping over keys, rather than proceeding in mostly the same direction. This is because the Porcupine[8] chroma (denoted #/b on [[Porcupine Notation]] - for example the notes A and Bv are separated by this chroma) is still not mapped to adjacent keys.<br /> {{Lumatone mapping|<br /> <br /> {{Lumatone key|x=3|y=5|label=Fv}}<br /> {{Lumatone key|x=4|y=5|label=Gv}}<br /> <br /> {{Lumatone key|x=3|y=6|label=F}}<br /> {{Lumatone key|x=4|y=6|label=G}}<br /> {{Lumatone key|x=5|y=6|label=Av}}<br /> {{Lumatone key|x=6|y=6|label=Bv}}<br /> {{Lumatone key|x=7|y=6|label=Cv}}<br /> {{Lumatone key|x=8|y=6|label=Dv}}<br /> {{Lumatone key|x=9|y=6|label=Ev}}<br /> {{Lumatone key|x=10|y=6|label=Fv}}<br /> {{Lumatone key|x=11|y=6|label=Gv}}<br /> <br /> {{Lumatone key|x=4|y=7|label=G^}}<br /> {{Lumatone key|x=5|y=7|label=A}}<br /> {{Lumatone key|x=6|y=7|label=B}}<br /> {{Lumatone key|x=7|y=7|label=C}}<br /> {{Lumatone key|x=8|y=7|label=D}}<br /> {{Lumatone key|x=9|y=7|label=E}}<br /> {{Lumatone key|x=10|y=7|label=F}}<br /> {{Lumatone key|x=11|y=7|label=G}}<br /> {{Lumatone key|x=12|y=7|label=Av}}<br /> {{Lumatone key|x=13|y=7|label=Bv}}<br /> {{Lumatone key|x=14|y=7|label=Cv}}<br /> {{Lumatone key|x=15|y=7|label=Dv}}<br /> {{Lumatone key|x=16|y=7|label=Ev}}<br /> {{Lumatone key|x=17|y=7|label=Fv}}<br /> {{Lumatone key|x=18|y=7|label=Gv}}<br /> <br /> {{Lumatone key|x=5|y=8|label=A^}}<br /> {{Lumatone key|x=6|y=8|label=B^}}<br /> {{Lumatone key|x=7|y=8|label=C^}}<br /> {{Lumatone key|x=8|y=8|label=D^}}<br /> {{Lumatone key|x=9|y=8|label=E^}}<br /> {{Lumatone key|x=10|y=8|label=F^}}<br /> {{Lumatone key|x=11|y=8|label=G^}}<br /> {{Lumatone key|x=12|y=8|label=A}}<br /> {{Lumatone key|x=13|y=8|label=B}}<br /> {{Lumatone key|x=14|y=8|label=C}}<br /> {{Lumatone key|x=15|y=8|label=D}}<br /> {{Lumatone key|x=16|y=8|label=E}}<br /> {{Lumatone key|x=17|y=8|label=F}}<br /> {{Lumatone key|x=18|y=8|label=G}}<br /> {{Lumatone key|x=19|y=8|label=Av}}<br /> {{Lumatone key|x=20|y=8|label=Bv}}<br /> {{Lumatone key|x=21|y=8|label=Cv}}<br /> {{Lumatone key|x=22|y=8|label=Dv}}<br /> {{Lumatone key|x=23|y=8|label=Ev}}<br /> {{Lumatone key|x=24|y=8|label=Fv}}<br /> {{Lumatone key|x=25|y=8|label=Gv}}<br /> <br /> {{Lumatone key|x=12|y=9|label=A^}}<br /> {{Lumatone key|x=13|y=9|label=B^}}<br /> {{Lumatone key|x=14|y=9|label=C^}}<br /> {{Lumatone key|x=15|y=9|label=D^}}<br /> {{Lumatone key|x=16|y=9|label=E^}}<br /> {{Lumatone key|x=17|y=9|label=F^}}<br /> {{Lumatone key|x=18|y=9|label=G^}}<br /> {{Lumatone key|x=19|y=9|label=A}}<br /> {{Lumatone key|x=20|y=9|label=B}}<br /> {{Lumatone key|x=21|y=9|label=C}}<br /> {{Lumatone key|x=22|y=9|label=D}}<br /> {{Lumatone key|x=23|y=9|label=E}}<br /> {{Lumatone key|x=24|y=9|label=F}}<br /> {{Lumatone key|x=25|y=9|label=G}}<br /> {{Lumatone key|x=26|y=9|label=Av}}<br /> {{Lumatone key|x=27|y=9|label=Bv}}<br /> {{Lumatone key|x=28|y=9|label=Cv}}<br /> {{Lumatone key|x=29|y=9|label=Dv}}<br /> {{Lumatone key|x=30|y=9|label=Ev}}<br /> {{Lumatone key|x=31|y=9|label=Fv}}<br /> {{Lumatone key|x=32|y=9|label=Gv}}<br /> <br /> {{Lumatone key|x=19|y=10|label=A^}}<br /> {{Lumatone key|x=20|y=10|label=B^}}<br /> {{Lumatone key|x=21|y=10|label=C^}}<br /> {{Lumatone key|x=22|y=10|label=D^}}<br /> {{Lumatone key|x=23|y=10|label=E^}}<br /> {{Lumatone key|x=24|y=10|label=F^}}<br /> {{Lumatone key|x=25|y=10|label=G^}}<br /> {{Lumatone key|x=26|y=10|label=A}}<br /> {{Lumatone key|x=27|y=10|label=B}}<br /> {{Lumatone key|x=28|y=10|label=C}}<br /> {{Lumatone key|x=29|y=10|label=D}}<br /> {{Lumatone key|x=30|y=10|label=E}}<br /> {{Lumatone key|x=31|y=10|label=F}}<br /> {{Lumatone key|x=32|y=10|label=G}}<br /> {{Lumatone key|x=33|y=10|label=Av}}<br /> {{Lumatone key|x=34|y=10|label=Bv}}<br /> <br /> {{Lumatone key|x=26|y=11|label=A^}}<br /> {{Lumatone key|x=27|y=11|label=B^}}<br /> {{Lumatone key|x=28|y=11|label=C^}}<br /> {{Lumatone key|x=29|y=11|label=D^}}<br /> {{Lumatone key|x=30|y=11|label=E^}}<br /> {{Lumatone key|x=31|y=11|label=F^}}<br /> {{Lumatone key|x=32|y=11|label=G^}}<br /> {{Lumatone key|x=33|y=11|label=A}}<br /> {{Lumatone key|x=34|y=11|label=B}}<br /> {{Lumatone key|x=35|y=11|label=C}}<br /> <br /> {{Lumatone key|x=33|y=12|label=A^}}<br /> {{Lumatone key|x=34|y=12|label=B^}}<br /> {{Lumatone key|x=35|y=12|label=C^}}<br /> <br /> }}<br /> <br /> ==Expanded==<br /> <br /> This mapping has the smallest range of any presented here - less than 4 complete octaves - but its main advantage is mapping the Porcupine[15] scale to an intuitive zigzag pattern. In-between pitches always appear in-between on the keyboard, rather than off to the side.<br /> {{Lumatone mapping|<br /> <br /> {{Lumatone key|x=3|y=6|label=Gv}}<br /> <br /> {{Lumatone key|x=4|y=7|label=G}}<br /> {{Lumatone key|x=5|y=7|label=Av}}<br /> {{Lumatone key|x=6|y=7|label=Bv}}<br /> {{Lumatone key|x=7|y=7|label=Cv}}<br /> {{Lumatone key|x=8|y=7|label=Dv}}<br /> {{Lumatone key|x=9|y=7|label=Ev}}<br /> {{Lumatone key|x=10|y=7|label=Fv}}<br /> {{Lumatone key|x=11|y=7|label=Gv}}<br /> <br /> {{Lumatone key|x=4|y=8|label=F^}}<br /> {{Lumatone key|x=5|y=8|label=G^}}<br /> {{Lumatone key|x=6|y=8|label=A}}<br /> {{Lumatone key|x=7|y=8|label=B}}<br /> {{Lumatone key|x=8|y=8|label=C}}<br /> {{Lumatone key|x=9|y=8|label=D}}<br /> {{Lumatone key|x=10|y=8|label=E}}<br /> {{Lumatone key|x=11|y=8|label=F}}<br /> {{Lumatone key|x=12|y=8|label=G}}<br /> {{Lumatone key|x=13|y=8|label=Av}}<br /> {{Lumatone key|x=14|y=8|label=Bv}}<br /> {{Lumatone key|x=15|y=8|label=Cv}}<br /> {{Lumatone key|x=16|y=8|label=Dv}}<br /> {{Lumatone key|x=17|y=8|label=Ev}}<br /> {{Lumatone key|x=18|y=8|label=Fv}}<br /> {{Lumatone key|x=19|y=8|label=Gv}}<br /> <br /> {{Lumatone key|x=7|y=9|label=A^}}<br /> {{Lumatone key|x=8|y=9|label=B^}}<br /> {{Lumatone key|x=9|y=9|label=C^}}<br /> {{Lumatone key|x=10|y=9|label=D^}}<br /> {{Lumatone key|x=11|y=9|label=E^}}<br /> {{Lumatone key|x=12|y=9|label=F^}}<br /> {{Lumatone key|x=13|y=9|label=G^}}<br /> {{Lumatone key|x=14|y=9|label=A}}<br /> {{Lumatone key|x=15|y=9|label=B}}<br /> {{Lumatone key|x=16|y=9|label=C}}<br /> {{Lumatone key|x=17|y=9|label=D}}<br /> {{Lumatone key|x=18|y=9|label=E}}<br /> {{Lumatone key|x=19|y=9|label=F}}<br /> {{Lumatone key|x=20|y=9|label=G}}<br /> {{Lumatone key|x=21|y=9|label=Av}}<br /> {{Lumatone key|x=22|y=9|label=Bv}}<br /> {{Lumatone key|x=23|y=9|label=Cv}}<br /> {{Lumatone key|x=24|y=9|label=Dv}}<br /> {{Lumatone key|x=25|y=9|label=Ev}}<br /> {{Lumatone key|x=26|y=9|label=Fv}}<br /> {{Lumatone key|x=27|y=9|label=Gv}}<br /> <br /> {{Lumatone key|x=15|y=10|label=A^}}<br /> {{Lumatone key|x=16|y=10|label=B^}}<br /> {{Lumatone key|x=17|y=10|label=C^}}<br /> {{Lumatone key|x=18|y=10|label=D^}}<br /> {{Lumatone key|x=19|y=10|label=E^}}<br /> {{Lumatone key|x=20|y=10|label=F^}}<br /> {{Lumatone key|x=21|y=10|label=G^}}<br /> {{Lumatone key|x=22|y=10|label=A}}<br /> {{Lumatone key|x=23|y=10|label=B}}<br /> {{Lumatone key|x=24|y=10|label=C}}<br /> {{Lumatone key|x=25|y=10|label=D}}<br /> {{Lumatone key|x=26|y=10|label=E}}<br /> {{Lumatone key|x=27|y=10|label=F}}<br /> {{Lumatone key|x=28|y=10|label=G}}<br /> {{Lumatone key|x=29|y=10|label=Av}}<br /> {{Lumatone key|x=30|y=10|label=Bv}}<br /> {{Lumatone key|x=31|y=10|label=Cv}}<br /> {{Lumatone key|x=32|y=10|label=Dv}}<br /> {{Lumatone key|x=33|y=10|label=Ev}}<br /> {{Lumatone key|x=34|y=10|label=Fv}}<br /> <br /> {{Lumatone key|x=23|y=11|label=A^}}<br /> {{Lumatone key|x=24|y=11|label=B^}}<br /> {{Lumatone key|x=25|y=11|label=C^}}<br /> {{Lumatone key|x=26|y=11|label=D^}}<br /> {{Lumatone key|x=27|y=11|label=E^}}<br /> {{Lumatone key|x=28|y=11|label=F^}}<br /> {{Lumatone key|x=29|y=11|label=G^}}<br /> {{Lumatone key|x=30|y=11|label=A}}<br /> {{Lumatone key|x=31|y=11|label=B}}<br /> {{Lumatone key|x=32|y=11|label=C}}<br /> {{Lumatone key|x=33|y=11|label=D}}<br /> {{Lumatone key|x=34|y=11|label=E}}<br /> {{Lumatone key|x=35|y=11|label=F}}<br /> <br /> {{Lumatone key|x=31|y=12|label=A^}}<br /> {{Lumatone key|x=32|y=12|label=B^}}<br /> {{Lumatone key|x=33|y=12|label=C^}}<br /> {{Lumatone key|x=34|y=12|label=D^}}<br /> {{Lumatone key|x=35|y=12|label=E^}}<br /> <br /> }}<br /> <br /> [[Category:Lumatone mappings]]<br /> [[Category:Porcupine]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Lumatone&diff=83006 Lumatone 2021-12-31T20:23:12Z <p>Keenan Pepper: see also :Category:Lumatone mappings</p> <hr /> <div>The '''Lumatone''' is an [[isomorphic keyboard]] with 280 hexagonal keys arranged in a Bosanquet-Wilson pattern. Each key contains a light of a configurable color, and there are no other markings on the keys, so it is ideal for using with different xenharmonic key arrangements. Its direct predecessor was the Terpstra Keyboard.<br /> <br /> [[Image:Lumatone.svg|thumb|500px|280-key Lumatone layout]]<br /> <br /> ==See also==<br /> * [[:Category:Lumatone mappings]]<br /> <br /> ==External links==<br /> * [https://www.lumatone.io/ Official website]<br /> * [http://terpstrakeyboard.com/ Terpstra keyboard website]<br /> * [http://terpstrakeyboard.com/web-app/keys.htm Playable Terpstra simulator app]<br /> <br /> [[Category:Instruments]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Lumatone_mapping_for_porcupine&diff=83005 Lumatone mapping for porcupine 2021-12-31T20:22:10Z <p>Keenan Pepper: Created page with &quot;==Ultra-compressed== This has the largest range of any mapping shown here (5 complete octaves), but the sequence of nearby pitches can be confusing. In particular, notes sepa...&quot;</p> <hr /> <div>==Ultra-compressed==<br /> <br /> This has the largest range of any mapping shown here (5 complete octaves), but the sequence of nearby pitches can be confusing. In particular, notes separated by the Porcupine[7] chroma (denoted by ^/v here) are not mapped to adjacent keys.<br /> {{Lumatone mapping|<br /> <br /> {{Lumatone key|x=3|y=5|label=Ev}}<br /> {{Lumatone key|x=4|y=5|label=Fv}}<br /> {{Lumatone key|x=5|y=5|label=Gv}}<br /> <br /> {{Lumatone key|x=3|y=6|label=F}}<br /> {{Lumatone key|x=4|y=6|label=G}}<br /> {{Lumatone key|x=5|y=6|label=Av}}<br /> {{Lumatone key|x=6|y=6|label=Bv}}<br /> {{Lumatone key|x=7|y=6|label=Cv}}<br /> {{Lumatone key|x=8|y=6|label=Dv}}<br /> {{Lumatone key|x=9|y=6|label=Ev}}<br /> {{Lumatone key|x=10|y=6|label=Fv}}<br /> {{Lumatone key|x=11|y=6|label=Gv}}<br /> <br /> {{Lumatone key|x=4|y=7|label=A}}<br /> {{Lumatone key|x=5|y=7|label=B}}<br /> {{Lumatone key|x=6|y=7|label=C}}<br /> {{Lumatone key|x=7|y=7|label=D}}<br /> {{Lumatone key|x=8|y=7|label=E}}<br /> {{Lumatone key|x=9|y=7|label=F}}<br /> {{Lumatone key|x=10|y=7|label=G}}<br /> {{Lumatone key|x=11|y=7|label=Av}}<br /> {{Lumatone key|x=12|y=7|label=Bv}}<br /> {{Lumatone key|x=13|y=7|label=Cv}}<br /> {{Lumatone key|x=14|y=7|label=Dv}}<br /> {{Lumatone key|x=15|y=7|label=Ev}}<br /> {{Lumatone key|x=16|y=7|label=Fv}}<br /> {{Lumatone key|x=17|y=7|label=Gv}}<br /> <br /> {{Lumatone key|x=4|y=8|label=B^}}<br /> {{Lumatone key|x=5|y=8|label=C^}}<br /> {{Lumatone key|x=6|y=8|label=D^}}<br /> {{Lumatone key|x=7|y=8|label=E^}}<br /> {{Lumatone key|x=8|y=8|label=F^}}<br /> {{Lumatone key|x=9|y=8|label=G^}}<br /> {{Lumatone key|x=10|y=8|label=A}}<br /> {{Lumatone key|x=11|y=8|label=B}}<br /> {{Lumatone key|x=12|y=8|label=C}}<br /> {{Lumatone key|x=13|y=8|label=D}}<br /> {{Lumatone key|x=14|y=8|label=E}}<br /> {{Lumatone key|x=15|y=8|label=F}}<br /> {{Lumatone key|x=16|y=8|label=G}}<br /> {{Lumatone key|x=17|y=8|label=Av}}<br /> {{Lumatone key|x=18|y=8|label=Bv}}<br /> {{Lumatone key|x=19|y=8|label=Cv}}<br /> {{Lumatone key|x=20|y=8|label=Dv}}<br /> {{Lumatone key|x=21|y=8|label=Ev}}<br /> {{Lumatone key|x=22|y=8|label=Fv}}<br /> {{Lumatone key|x=23|y=8|label=Gv}}<br /> <br /> {{Lumatone key|x=9|y=9|label=A^}}<br /> {{Lumatone key|x=10|y=9|label=B^}}<br /> {{Lumatone key|x=11|y=9|label=C^}}<br /> {{Lumatone key|x=12|y=9|label=D^}}<br /> {{Lumatone key|x=13|y=9|label=E^}}<br /> {{Lumatone key|x=14|y=9|label=F^}}<br /> {{Lumatone key|x=15|y=9|label=G^}}<br /> {{Lumatone key|x=16|y=9|label=A}}<br /> {{Lumatone key|x=17|y=9|label=B}}<br /> {{Lumatone key|x=18|y=9|label=C}}<br /> {{Lumatone key|x=19|y=9|label=D}}<br /> {{Lumatone key|x=20|y=9|label=E}}<br /> {{Lumatone key|x=21|y=9|label=F}}<br /> {{Lumatone key|x=22|y=9|label=G}}<br /> {{Lumatone key|x=23|y=9|label=Av}}<br /> {{Lumatone key|x=24|y=9|label=Bv}}<br /> {{Lumatone key|x=25|y=9|label=Cv}}<br /> {{Lumatone key|x=26|y=9|label=Dv}}<br /> {{Lumatone key|x=27|y=9|label=Ev}}<br /> {{Lumatone key|x=28|y=9|label=Fv}}<br /> {{Lumatone key|x=29|y=9|label=Gv}}<br /> <br /> {{Lumatone key|x=15|y=10|label=A^}}<br /> {{Lumatone key|x=16|y=10|label=B^}}<br /> {{Lumatone key|x=17|y=10|label=C^}}<br /> {{Lumatone key|x=18|y=10|label=D^}}<br /> {{Lumatone key|x=19|y=10|label=E^}}<br /> {{Lumatone key|x=20|y=10|label=F^}}<br /> {{Lumatone key|x=21|y=10|label=G^}}<br /> {{Lumatone key|x=22|y=10|label=A}}<br /> {{Lumatone key|x=23|y=10|label=B}}<br /> {{Lumatone key|x=24|y=10|label=C}}<br /> {{Lumatone key|x=25|y=10|label=D}}<br /> {{Lumatone key|x=26|y=10|label=E}}<br /> {{Lumatone key|x=27|y=10|label=F}}<br /> {{Lumatone key|x=28|y=10|label=G}}<br /> {{Lumatone key|x=29|y=10|label=Av}}<br /> {{Lumatone key|x=30|y=10|label=Bv}}<br /> {{Lumatone key|x=31|y=10|label=Cv}}<br /> {{Lumatone key|x=32|y=10|label=Dv}}<br /> {{Lumatone key|x=33|y=10|label=Ev}}<br /> {{Lumatone key|x=34|y=10|label=Fv}}<br /> <br /> {{Lumatone key|x=21|y=11|label=A^}}<br /> {{Lumatone key|x=22|y=11|label=B^}}<br /> {{Lumatone key|x=23|y=11|label=C^}}<br /> {{Lumatone key|x=24|y=11|label=D^}}<br /> {{Lumatone key|x=25|y=11|label=E^}}<br /> {{Lumatone key|x=26|y=11|label=F^}}<br /> {{Lumatone key|x=27|y=11|label=G^}}<br /> {{Lumatone key|x=28|y=11|label=A}}<br /> {{Lumatone key|x=29|y=11|label=B}}<br /> {{Lumatone key|x=30|y=11|label=C}}<br /> {{Lumatone key|x=31|y=11|label=D}}<br /> {{Lumatone key|x=32|y=11|label=E}}<br /> {{Lumatone key|x=33|y=11|label=F}}<br /> {{Lumatone key|x=34|y=11|label=G}}<br /> {{Lumatone key|x=35|y=11|label=Av}}<br /> <br /> {{Lumatone key|x=27|y=12|label=A^}}<br /> {{Lumatone key|x=28|y=12|label=B^}}<br /> {{Lumatone key|x=29|y=12|label=C^}}<br /> {{Lumatone key|x=30|y=12|label=D^}}<br /> {{Lumatone key|x=31|y=12|label=E^}}<br /> {{Lumatone key|x=32|y=12|label=F^}}<br /> {{Lumatone key|x=33|y=12|label=G^}}<br /> {{Lumatone key|x=34|y=12|label=A}}<br /> {{Lumatone key|x=35|y=12|label=B}}<br /> <br /> {{Lumatone key|x=33|y=13|label=A^}}<br /> {{Lumatone key|x=34|y=13|label=B^}}<br /> {{Lumatone key|x=35|y=13|label=C^}}<br /> {{Lumatone key|x=36|y=13|label=D^}}<br /> <br /> }}<br /> <br /> ==Compressed==<br /> <br /> This is a compromise intermediate between the &quot;ultra-compressed&quot; and &quot;expanded&quot; mappings. It covers 4 complete octaves, and the Porcupine[7] chroma is now mapped to adjacent keys in the &quot;vertical&quot; direction. The sequence of pitches is still not completely intuitive, however: the Porcupine[15] chromatic scale still zigzags back and forth leaping over keys, rather than proceeding in mostly the same direction. This is because the Porcupine[8] chroma (denoted #/b on [[Porcupine Notation]] - for example the notes A and Bv are separated by this chroma) is still not mapped to adjacent keys.<br /> {{Lumatone mapping|<br /> <br /> {{Lumatone key|x=3|y=5|label=Fv}}<br /> {{Lumatone key|x=4|y=5|label=Gv}}<br /> <br /> {{Lumatone key|x=3|y=6|label=F}}<br /> {{Lumatone key|x=4|y=6|label=G}}<br /> {{Lumatone key|x=5|y=6|label=Av}}<br /> {{Lumatone key|x=6|y=6|label=Bv}}<br /> {{Lumatone key|x=7|y=6|label=Cv}}<br /> {{Lumatone key|x=8|y=6|label=Dv}}<br /> {{Lumatone key|x=9|y=6|label=Ev}}<br /> {{Lumatone key|x=10|y=6|label=Fv}}<br /> {{Lumatone key|x=11|y=6|label=Gv}}<br /> <br /> {{Lumatone key|x=4|y=7|label=G^}}<br /> {{Lumatone key|x=5|y=7|label=A}}<br /> {{Lumatone key|x=6|y=7|label=B}}<br /> {{Lumatone key|x=7|y=7|label=C}}<br /> {{Lumatone key|x=8|y=7|label=D}}<br /> {{Lumatone key|x=9|y=7|label=E}}<br /> {{Lumatone key|x=10|y=7|label=F}}<br /> {{Lumatone key|x=11|y=7|label=G}}<br /> {{Lumatone key|x=12|y=7|label=Av}}<br /> {{Lumatone key|x=13|y=7|label=Bv}}<br /> {{Lumatone key|x=14|y=7|label=Cv}}<br /> {{Lumatone key|x=15|y=7|label=Dv}}<br /> {{Lumatone key|x=16|y=7|label=Ev}}<br /> {{Lumatone key|x=17|y=7|label=Fv}}<br /> {{Lumatone key|x=18|y=7|label=Gv}}<br /> <br /> {{Lumatone key|x=5|y=8|label=A^}}<br /> {{Lumatone key|x=6|y=8|label=B^}}<br /> {{Lumatone key|x=7|y=8|label=C^}}<br /> {{Lumatone key|x=8|y=8|label=D^}}<br /> {{Lumatone key|x=9|y=8|label=E^}}<br /> {{Lumatone key|x=10|y=8|label=F^}}<br /> {{Lumatone key|x=11|y=8|label=G^}}<br /> {{Lumatone key|x=12|y=8|label=A}}<br /> {{Lumatone key|x=13|y=8|label=B}}<br /> {{Lumatone key|x=14|y=8|label=C}}<br /> {{Lumatone key|x=15|y=8|label=D}}<br /> {{Lumatone key|x=16|y=8|label=E}}<br /> {{Lumatone key|x=17|y=8|label=F}}<br /> {{Lumatone key|x=18|y=8|label=G}}<br /> {{Lumatone key|x=19|y=8|label=Av}}<br /> {{Lumatone key|x=20|y=8|label=Bv}}<br /> {{Lumatone key|x=21|y=8|label=Cv}}<br /> {{Lumatone key|x=22|y=8|label=Dv}}<br /> {{Lumatone key|x=23|y=8|label=Ev}}<br /> {{Lumatone key|x=24|y=8|label=Fv}}<br /> {{Lumatone key|x=25|y=8|label=Gv}}<br /> <br /> {{Lumatone key|x=12|y=9|label=A^}}<br /> {{Lumatone key|x=13|y=9|label=B^}}<br /> {{Lumatone key|x=14|y=9|label=C^}}<br /> {{Lumatone key|x=15|y=9|label=D^}}<br /> {{Lumatone key|x=16|y=9|label=E^}}<br /> {{Lumatone key|x=17|y=9|label=F^}}<br /> {{Lumatone key|x=18|y=9|label=G^}}<br /> {{Lumatone key|x=19|y=9|label=A}}<br /> {{Lumatone key|x=20|y=9|label=B}}<br /> {{Lumatone key|x=21|y=9|label=C}}<br /> {{Lumatone key|x=22|y=9|label=D}}<br /> {{Lumatone key|x=23|y=9|label=E}}<br /> {{Lumatone key|x=24|y=9|label=F}}<br /> {{Lumatone key|x=25|y=9|label=G}}<br /> {{Lumatone key|x=26|y=9|label=Av}}<br /> {{Lumatone key|x=27|y=9|label=Bv}}<br /> {{Lumatone key|x=28|y=9|label=Cv}}<br /> {{Lumatone key|x=29|y=9|label=Dv}}<br /> {{Lumatone key|x=30|y=9|label=Ev}}<br /> {{Lumatone key|x=31|y=9|label=Fv}}<br /> {{Lumatone key|x=32|y=9|label=Gv}}<br /> <br /> {{Lumatone key|x=19|y=10|label=A^}}<br /> {{Lumatone key|x=20|y=10|label=B^}}<br /> {{Lumatone key|x=21|y=10|label=C^}}<br /> {{Lumatone key|x=22|y=10|label=D^}}<br /> {{Lumatone key|x=23|y=10|label=E^}}<br /> {{Lumatone key|x=24|y=10|label=F^}}<br /> {{Lumatone key|x=25|y=10|label=G^}}<br /> {{Lumatone key|x=26|y=10|label=A}}<br /> {{Lumatone key|x=27|y=10|label=B}}<br /> {{Lumatone key|x=28|y=10|label=C}}<br /> {{Lumatone key|x=29|y=10|label=D}}<br /> {{Lumatone key|x=30|y=10|label=E}}<br /> {{Lumatone key|x=31|y=10|label=F}}<br /> {{Lumatone key|x=32|y=10|label=G}}<br /> {{Lumatone key|x=33|y=10|label=Av}}<br /> {{Lumatone key|x=34|y=10|label=Bv}}<br /> <br /> {{Lumatone key|x=26|y=11|label=A^}}<br /> {{Lumatone key|x=27|y=11|label=B^}}<br /> {{Lumatone key|x=28|y=11|label=C^}}<br /> {{Lumatone key|x=29|y=11|label=D^}}<br /> {{Lumatone key|x=30|y=11|label=E^}}<br /> {{Lumatone key|x=31|y=11|label=F^}}<br /> {{Lumatone key|x=32|y=11|label=G^}}<br /> {{Lumatone key|x=33|y=11|label=A}}<br /> {{Lumatone key|x=34|y=11|label=B}}<br /> {{Lumatone key|x=35|y=11|label=C}}<br /> <br /> {{Lumatone key|x=33|y=12|label=A^}}<br /> {{Lumatone key|x=34|y=12|label=B^}}<br /> {{Lumatone key|x=35|y=12|label=C^}}<br /> <br /> }}<br /> <br /> ==Expanded==<br /> <br /> This mapping has the smallest range of any presented here - less than 4 complete octaves - but its main advantage is mapping the Porcupine[15] scale to an intuitive zigzag pattern. In-between pitches always appear in-between on the keyboard, rather than off to the side.<br /> {{Lumatone mapping|<br /> <br /> {{Lumatone key|x=3|y=6|label=Gv}}<br /> <br /> {{Lumatone key|x=4|y=7|label=G}}<br /> {{Lumatone key|x=5|y=7|label=Av}}<br /> {{Lumatone key|x=6|y=7|label=Bv}}<br /> {{Lumatone key|x=7|y=7|label=Cv}}<br /> {{Lumatone key|x=8|y=7|label=Dv}}<br /> {{Lumatone key|x=9|y=7|label=Ev}}<br /> {{Lumatone key|x=10|y=7|label=Fv}}<br /> {{Lumatone key|x=11|y=7|label=Gv}}<br /> <br /> {{Lumatone key|x=4|y=8|label=F^}}<br /> {{Lumatone key|x=5|y=8|label=G^}}<br /> {{Lumatone key|x=6|y=8|label=A}}<br /> {{Lumatone key|x=7|y=8|label=B}}<br /> {{Lumatone key|x=8|y=8|label=C}}<br /> {{Lumatone key|x=9|y=8|label=D}}<br /> {{Lumatone key|x=10|y=8|label=E}}<br /> {{Lumatone key|x=11|y=8|label=F}}<br /> {{Lumatone key|x=12|y=8|label=G}}<br /> {{Lumatone key|x=13|y=8|label=Av}}<br /> {{Lumatone key|x=14|y=8|label=Bv}}<br /> {{Lumatone key|x=15|y=8|label=Cv}}<br /> {{Lumatone key|x=16|y=8|label=Dv}}<br /> {{Lumatone key|x=17|y=8|label=Ev}}<br /> {{Lumatone key|x=18|y=8|label=Fv}}<br /> {{Lumatone key|x=19|y=8|label=Gv}}<br /> <br /> {{Lumatone key|x=7|y=9|label=A^}}<br /> {{Lumatone key|x=8|y=9|label=B^}}<br /> {{Lumatone key|x=9|y=9|label=C^}}<br /> {{Lumatone key|x=10|y=9|label=D^}}<br /> {{Lumatone key|x=11|y=9|label=E^}}<br /> {{Lumatone key|x=12|y=9|label=F^}}<br /> {{Lumatone key|x=13|y=9|label=G^}}<br /> {{Lumatone key|x=14|y=9|label=A}}<br /> {{Lumatone key|x=15|y=9|label=B}}<br /> {{Lumatone key|x=16|y=9|label=C}}<br /> {{Lumatone key|x=17|y=9|label=D}}<br /> {{Lumatone key|x=18|y=9|label=E}}<br /> {{Lumatone key|x=19|y=9|label=F}}<br /> {{Lumatone key|x=20|y=9|label=G}}<br /> {{Lumatone key|x=21|y=9|label=Av}}<br /> {{Lumatone key|x=22|y=9|label=Bv}}<br /> {{Lumatone key|x=23|y=9|label=Cv}}<br /> {{Lumatone key|x=24|y=9|label=Dv}}<br /> {{Lumatone key|x=25|y=9|label=Ev}}<br /> {{Lumatone key|x=26|y=9|label=Fv}}<br /> {{Lumatone key|x=27|y=9|label=Gv}}<br /> <br /> {{Lumatone key|x=15|y=10|label=A^}}<br /> {{Lumatone key|x=16|y=10|label=B^}}<br /> {{Lumatone key|x=17|y=10|label=C^}}<br /> {{Lumatone key|x=18|y=10|label=D^}}<br /> {{Lumatone key|x=19|y=10|label=E^}}<br /> {{Lumatone key|x=20|y=10|label=F^}}<br /> {{Lumatone key|x=21|y=10|label=G^}}<br /> {{Lumatone key|x=22|y=10|label=A}}<br /> {{Lumatone key|x=23|y=10|label=B}}<br /> {{Lumatone key|x=24|y=10|label=C}}<br /> {{Lumatone key|x=25|y=10|label=D}}<br /> {{Lumatone key|x=26|y=10|label=E}}<br /> {{Lumatone key|x=27|y=10|label=F}}<br /> {{Lumatone key|x=28|y=10|label=G}}<br /> {{Lumatone key|x=29|y=10|label=Av}}<br /> {{Lumatone key|x=30|y=10|label=Bv}}<br /> {{Lumatone key|x=31|y=10|label=Cv}}<br /> {{Lumatone key|x=32|y=10|label=Dv}}<br /> {{Lumatone key|x=33|y=10|label=Ev}}<br /> {{Lumatone key|x=34|y=10|label=Fv}}<br /> <br /> {{Lumatone key|x=23|y=11|label=A^}}<br /> {{Lumatone key|x=24|y=11|label=B^}}<br /> {{Lumatone key|x=25|y=11|label=C^}}<br /> {{Lumatone key|x=26|y=11|label=D^}}<br /> {{Lumatone key|x=27|y=11|label=E^}}<br /> {{Lumatone key|x=28|y=11|label=F^}}<br /> {{Lumatone key|x=29|y=11|label=G^}}<br /> {{Lumatone key|x=30|y=11|label=A}}<br /> {{Lumatone key|x=31|y=11|label=B}}<br /> {{Lumatone key|x=32|y=11|label=C}}<br /> {{Lumatone key|x=33|y=11|label=D}}<br /> {{Lumatone key|x=34|y=11|label=E}}<br /> {{Lumatone key|x=35|y=11|label=F}}<br /> <br /> {{Lumatone key|x=31|y=12|label=A^}}<br /> {{Lumatone key|x=32|y=12|label=B^}}<br /> {{Lumatone key|x=33|y=12|label=C^}}<br /> {{Lumatone key|x=34|y=12|label=D^}}<br /> {{Lumatone key|x=35|y=12|label=E^}}<br /> <br /> }}<br /> <br /> [[Category:Lumatone mappings]]<br /> [[Category:Porcupine]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Lumatone_mapping_for_slendric&diff=82901 Lumatone mapping for slendric 2021-12-30T22:46:52Z <p>Keenan Pepper: add expanded layout</p> <hr /> <div>This is one proposed mapping of [[slendric]] temperament to the [[Lumatone]] keyboard. 6 complete octaves are available, and modulation to distant keys is possible.<br /> <br /> The keys marked &quot;c&quot; are one chroma up from 1/1, representing both 64/63 and 49/48. They keys marked &quot;-c&quot; are one chroma down from 1/1 (so 63/32 and 96/49).<br /> <br /> The same mapping could be used for any extension of slendric that has the same period and generator, including [[Cynder]], [[Rodan]], and [[Guiron]].<br /> <br /> {{Lumatone mapping|<br /> <br /> {{Lumatone key|x=3|y=4|label=27/16|size=10px}}<br /> {{Lumatone key|x=4|y=4|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=3|y=5|label=12/7}}<br /> {{Lumatone key|x=4|y=5|label=-c}}<br /> {{Lumatone key|x=5|y=5|label=9/8}}<br /> {{Lumatone key|x=6|y=5|label=9/7}}<br /> {{Lumatone key|x=7|y=5|label=}}<br /> {{Lumatone key|x=8|y=5|label=27/16|size=10px}}<br /> {{Lumatone key|x=9|y=5|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=3|y=6|label=7/4}}<br /> {{Lumatone key|x=4|y=6|label=1/1}}<br /> {{Lumatone key|x=5|y=6|label=8/7}}<br /> {{Lumatone key|x=6|y=6|label=21/16|size=10px}}<br /> {{Lumatone key|x=7|y=6|label=3/2}}<br /> {{Lumatone key|x=8|y=6|label=12/7}}<br /> {{Lumatone key|x=9|y=6|label=-c}}<br /> {{Lumatone key|x=10|y=6|label=9/8}}<br /> {{Lumatone key|x=11|y=6|label=9/7}}<br /> {{Lumatone key|x=12|y=6|label=}}<br /> {{Lumatone key|x=13|y=6|label=27/16|size=10px}}<br /> {{Lumatone key|x=14|y=6|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=21|y=6|label=Y}}<br /> <br /> {{Lumatone key|x=4|y=7|label=c}}<br /> {{Lumatone key|x=5|y=7|label=7/6}}<br /> {{Lumatone key|x=6|y=7|label=4/3}}<br /> {{Lumatone key|x=7|y=7|label=32/21|size=10px}}<br /> {{Lumatone key|x=8|y=7|label=7/4}}<br /> {{Lumatone key|x=9|y=7|label=1/1}}<br /> {{Lumatone key|x=10|y=7|label=8/7}}<br /> {{Lumatone key|x=11|y=7|label=21/16|size=10px}}<br /> {{Lumatone key|x=12|y=7|label=3/2}}<br /> {{Lumatone key|x=13|y=7|label=12/7}}<br /> {{Lumatone key|x=14|y=7|label=-c}}<br /> {{Lumatone key|x=15|y=7|label=9/8}}<br /> {{Lumatone key|x=16|y=7|label=9/7}}<br /> {{Lumatone key|x=17|y=7|label=}}<br /> {{Lumatone key|x=18|y=7|label=27/16|size=10px}}<br /> {{Lumatone key|x=19|y=7|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=21|y=7|label=X}}<br /> <br /> {{Lumatone key|x=4|y=8|label=28/27|size=10px}}<br /> {{Lumatone key|x=5|y=8|label=32/27|size=10px}}<br /> {{Lumatone key|x=6|y=8|label=}}<br /> {{Lumatone key|x=7|y=8|label=14/9}}<br /> {{Lumatone key|x=8|y=8|label=16/9}}<br /> {{Lumatone key|x=9|y=8|label=c}}<br /> {{Lumatone key|x=10|y=8|label=7/6}}<br /> {{Lumatone key|x=11|y=8|label=4/3}}<br /> {{Lumatone key|x=12|y=8|label=32/21|size=10px}}<br /> {{Lumatone key|x=13|y=8|label=7/4}}<br /> {{Lumatone key|x=14|y=8|label=1/1}}<br /> {{Lumatone key|x=15|y=8|label=8/7}}<br /> {{Lumatone key|x=16|y=8|label=21/16|size=10px}}<br /> {{Lumatone key|x=17|y=8|label=3/2}}<br /> {{Lumatone key|x=18|y=8|label=12/7}}<br /> {{Lumatone key|x=19|y=8|label=-c}}<br /> {{Lumatone key|x=20|y=8|label=9/8}}<br /> {{Lumatone key|x=21|y=8|label=9/7}}<br /> {{Lumatone key|x=22|y=8|label=}}<br /> {{Lumatone key|x=23|y=8|label=27/16|size=10px}}<br /> {{Lumatone key|x=24|y=8|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=9|y=9|label=28/27|size=10px}}<br /> {{Lumatone key|x=10|y=9|label=32/27|size=10px}}<br /> {{Lumatone key|x=11|y=9|label=}}<br /> {{Lumatone key|x=12|y=9|label=14/9}}<br /> {{Lumatone key|x=13|y=9|label=16/9}}<br /> {{Lumatone key|x=14|y=9|label=c}}<br /> {{Lumatone key|x=15|y=9|label=7/6}}<br /> {{Lumatone key|x=16|y=9|label=4/3}}<br /> {{Lumatone key|x=17|y=9|label=32/21|size=10px}}<br /> {{Lumatone key|x=18|y=9|label=7/4}}<br /> {{Lumatone key|x=19|y=9|label=1/1}}<br /> {{Lumatone key|x=20|y=9|label=8/7}}<br /> {{Lumatone key|x=21|y=9|label=21/16|size=10px}}<br /> {{Lumatone key|x=22|y=9|label=3/2}}<br /> {{Lumatone key|x=23|y=9|label=12/7}}<br /> {{Lumatone key|x=24|y=9|label=-c}}<br /> {{Lumatone key|x=25|y=9|label=9/8}}<br /> {{Lumatone key|x=26|y=9|label=9/7}}<br /> {{Lumatone key|x=27|y=9|label=}}<br /> {{Lumatone key|x=28|y=9|label=27/16|size=10px}}<br /> {{Lumatone key|x=29|y=9|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=14|y=10|label=28/27|size=10px}}<br /> {{Lumatone key|x=15|y=10|label=32/27|size=10px}}<br /> {{Lumatone key|x=16|y=10|label=}}<br /> {{Lumatone key|x=17|y=10|label=14/9}}<br /> {{Lumatone key|x=18|y=10|label=16/9}}<br /> {{Lumatone key|x=19|y=10|label=c}}<br /> {{Lumatone key|x=20|y=10|label=7/6}}<br /> {{Lumatone key|x=21|y=10|label=4/3}}<br /> {{Lumatone key|x=22|y=10|label=32/21|size=10px}}<br /> {{Lumatone key|x=23|y=10|label=7/4}}<br /> {{Lumatone key|x=24|y=10|label=1/1}}<br /> {{Lumatone key|x=25|y=10|label=8/7}}<br /> {{Lumatone key|x=26|y=10|label=21/16|size=10px}}<br /> {{Lumatone key|x=27|y=10|label=3/2}}<br /> {{Lumatone key|x=28|y=10|label=12/7}}<br /> {{Lumatone key|x=29|y=10|label=-c}}<br /> {{Lumatone key|x=30|y=10|label=9/8}}<br /> {{Lumatone key|x=31|y=10|label=9/7}}<br /> {{Lumatone key|x=32|y=10|label=}}<br /> {{Lumatone key|x=33|y=10|label=27/16|size=10px}}<br /> {{Lumatone key|x=34|y=10|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=19|y=11|label=28/27|size=10px}}<br /> {{Lumatone key|x=20|y=11|label=32/27|size=10px}}<br /> {{Lumatone key|x=21|y=11|label=}}<br /> {{Lumatone key|x=22|y=11|label=14/9}}<br /> {{Lumatone key|x=23|y=11|label=16/9}}<br /> {{Lumatone key|x=24|y=11|label=c}}<br /> {{Lumatone key|x=25|y=11|label=7/6}}<br /> {{Lumatone key|x=26|y=11|label=4/3}}<br /> {{Lumatone key|x=27|y=11|label=32/21|size=10px}}<br /> {{Lumatone key|x=28|y=11|label=7/4}}<br /> {{Lumatone key|x=29|y=11|label=1/1}}<br /> {{Lumatone key|x=30|y=11|label=8/7}}<br /> {{Lumatone key|x=31|y=11|label=21/16|size=10px}}<br /> {{Lumatone key|x=32|y=11|label=3/2}}<br /> {{Lumatone key|x=33|y=11|label=12/7}}<br /> {{Lumatone key|x=34|y=11|label=-c}}<br /> {{Lumatone key|x=35|y=11|label=9/8}}<br /> <br /> {{Lumatone key|x=24|y=12|label=28/27|size=10px}}<br /> {{Lumatone key|x=25|y=12|label=32/27|size=10px}}<br /> {{Lumatone key|x=26|y=12|label=}}<br /> {{Lumatone key|x=27|y=12|label=14/9}}<br /> {{Lumatone key|x=28|y=12|label=16/9}}<br /> {{Lumatone key|x=29|y=12|label=c}}<br /> {{Lumatone key|x=30|y=12|label=7/6}}<br /> {{Lumatone key|x=31|y=12|label=4/3}}<br /> {{Lumatone key|x=32|y=12|label=32/21|size=10px}}<br /> {{Lumatone key|x=33|y=12|label=7/4}}<br /> {{Lumatone key|x=34|y=12|label=1/1}}<br /> {{Lumatone key|x=35|y=12|label=8/7}}<br /> <br /> {{Lumatone key|x=29|y=13|label=28/27|size=10px}}<br /> {{Lumatone key|x=30|y=13|label=32/27|size=10px}}<br /> {{Lumatone key|x=31|y=13|label=}}<br /> {{Lumatone key|x=32|y=13|label=14/9}}<br /> {{Lumatone key|x=33|y=13|label=16/9}}<br /> {{Lumatone key|x=34|y=13|label=c}}<br /> {{Lumatone key|x=35|y=13|label=7/6}}<br /> {{Lumatone key|x=36|y=13|label=4/3}}<br /> <br /> {{Lumatone key|x=34|y=14|label=28/27|size=10px}}<br /> {{Lumatone key|x=35|y=14|label=32/27|size=10px}}<br /> <br /> {{Lumatone key|x=30|y=16|label=Z}}<br /> <br /> }}<br /> <br /> The differences between the extensions of slendric to the prime 5 can be visualized on this keyboard.<br /> * Cynder tempers out 81/80, so 9/8 above 9/8 is equivalent to 5/4 so 5/4 is mapped to the key marked &quot;X&quot;.<br /> * Rodan, on the other hand, makes 81/80 the same as the chroma c, so 5/4 is instead mapped to the key mapped &quot;Y&quot;, one chroma lower than &quot;X&quot;.<br /> * Guiron maps 5/4 to the key marked &quot;Z&quot;.<br /> <br /> Cynder and guiron intersect in 36edo, so in 36edo both &quot;X&quot; and &quot;Z&quot; represent 5/4. Rodan and guiron intersect in 41edo, so in 41edo both &quot;Y&quot; and &quot;Z&quot; represent 5/4.<br /> <br /> If the above layout is the &quot;compressed&quot; one then the below is an &quot;expanded&quot; one which has a range of only 5 octaves, but whose layout may make more intuitive sense:<br /> <br /> {{Lumatone mapping|<br /> <br /> {{Lumatone key|x=2|y=4|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=3|y=5|label=-c}}<br /> {{Lumatone key|x=4|y=5|label=9/8}}<br /> {{Lumatone key|x=5|y=5|label=9/7}}<br /> {{Lumatone key|x=6|y=5|label=}}<br /> {{Lumatone key|x=7|y=5|label=27/16|size=10px}}<br /> {{Lumatone key|x=8|y=5|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=3|y=6|label=7/4}}<br /> {{Lumatone key|x=4|y=6|label=1/1}}<br /> {{Lumatone key|x=5|y=6|label=8/7}}<br /> {{Lumatone key|x=6|y=6|label=21/16|size=10px}}<br /> {{Lumatone key|x=7|y=6|label=3/2}}<br /> {{Lumatone key|x=8|y=6|label=12/7}}<br /> {{Lumatone key|x=9|y=6|label=-c}}<br /> {{Lumatone key|x=10|y=6|label=9/8}}<br /> {{Lumatone key|x=11|y=6|label=9/7}}<br /> {{Lumatone key|x=12|y=6|label=}}<br /> {{Lumatone key|x=13|y=6|label=27/16|size=10px}}<br /> {{Lumatone key|x=14|y=6|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=21|y=6|label=Y}}<br /> <br /> {{Lumatone key|x=4|y=7|label=16/9}}<br /> {{Lumatone key|x=5|y=7|label=c}}<br /> {{Lumatone key|x=6|y=7|label=7/6}}<br /> {{Lumatone key|x=7|y=7|label=4/3}}<br /> {{Lumatone key|x=8|y=7|label=32/21|size=10px}}<br /> {{Lumatone key|x=9|y=7|label=7/4}}<br /> {{Lumatone key|x=10|y=7|label=1/1}}<br /> {{Lumatone key|x=11|y=7|label=8/7}}<br /> {{Lumatone key|x=12|y=7|label=21/16|size=10px}}<br /> {{Lumatone key|x=13|y=7|label=3/2}}<br /> {{Lumatone key|x=14|y=7|label=12/7}}<br /> {{Lumatone key|x=15|y=7|label=-c}}<br /> {{Lumatone key|x=16|y=7|label=9/8}}<br /> {{Lumatone key|x=17|y=7|label=9/7}}<br /> {{Lumatone key|x=18|y=7|label=}}<br /> {{Lumatone key|x=19|y=7|label=27/16|size=10px}}<br /> {{Lumatone key|x=20|y=7|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=22|y=7|label=X}}<br /> <br /> {{Lumatone key|x=6|y=8|label=28/27|size=10px}}<br /> {{Lumatone key|x=7|y=8|label=32/27|size=10px}}<br /> {{Lumatone key|x=8|y=8|label=}}<br /> {{Lumatone key|x=9|y=8|label=14/9}}<br /> {{Lumatone key|x=10|y=8|label=16/9}}<br /> {{Lumatone key|x=11|y=8|label=c}}<br /> {{Lumatone key|x=12|y=8|label=7/6}}<br /> {{Lumatone key|x=13|y=8|label=4/3}}<br /> {{Lumatone key|x=14|y=8|label=32/21|size=10px}}<br /> {{Lumatone key|x=15|y=8|label=7/4}}<br /> {{Lumatone key|x=16|y=8|label=1/1}}<br /> {{Lumatone key|x=17|y=8|label=8/7}}<br /> {{Lumatone key|x=18|y=8|label=21/16|size=10px}}<br /> {{Lumatone key|x=19|y=8|label=3/2}}<br /> {{Lumatone key|x=20|y=8|label=12/7}}<br /> {{Lumatone key|x=21|y=8|label=-c}}<br /> {{Lumatone key|x=22|y=8|label=9/8}}<br /> {{Lumatone key|x=23|y=8|label=9/7}}<br /> {{Lumatone key|x=24|y=8|label=}}<br /> {{Lumatone key|x=25|y=8|label=27/16|size=10px}}<br /> {{Lumatone key|x=26|y=8|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=12|y=9|label=28/27|size=10px}}<br /> {{Lumatone key|x=13|y=9|label=32/27|size=10px}}<br /> {{Lumatone key|x=14|y=9|label=}}<br /> {{Lumatone key|x=15|y=9|label=14/9}}<br /> {{Lumatone key|x=16|y=9|label=16/9}}<br /> {{Lumatone key|x=17|y=9|label=c}}<br /> {{Lumatone key|x=18|y=9|label=7/6}}<br /> {{Lumatone key|x=19|y=9|label=4/3}}<br /> {{Lumatone key|x=20|y=9|label=32/21|size=10px}}<br /> {{Lumatone key|x=21|y=9|label=7/4}}<br /> {{Lumatone key|x=22|y=9|label=1/1}}<br /> {{Lumatone key|x=23|y=9|label=8/7}}<br /> {{Lumatone key|x=24|y=9|label=21/16|size=10px}}<br /> {{Lumatone key|x=25|y=9|label=3/2}}<br /> {{Lumatone key|x=26|y=9|label=12/7}}<br /> {{Lumatone key|x=27|y=9|label=-c}}<br /> {{Lumatone key|x=28|y=9|label=9/8}}<br /> {{Lumatone key|x=29|y=9|label=9/7}}<br /> {{Lumatone key|x=30|y=9|label=}}<br /> {{Lumatone key|x=31|y=9|label=27/16|size=10px}}<br /> {{Lumatone key|x=32|y=9|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=18|y=10|label=28/27|size=10px}}<br /> {{Lumatone key|x=19|y=10|label=32/27|size=10px}}<br /> {{Lumatone key|x=20|y=10|label=}}<br /> {{Lumatone key|x=21|y=10|label=14/9}}<br /> {{Lumatone key|x=22|y=10|label=16/9}}<br /> {{Lumatone key|x=23|y=10|label=c}}<br /> {{Lumatone key|x=24|y=10|label=7/6}}<br /> {{Lumatone key|x=25|y=10|label=4/3}}<br /> {{Lumatone key|x=26|y=10|label=32/21|size=10px}}<br /> {{Lumatone key|x=27|y=10|label=7/4}}<br /> {{Lumatone key|x=28|y=10|label=1/1}}<br /> {{Lumatone key|x=29|y=10|label=8/7}}<br /> {{Lumatone key|x=30|y=10|label=21/16|size=10px}}<br /> {{Lumatone key|x=31|y=10|label=3/2}}<br /> {{Lumatone key|x=32|y=10|label=12/7}}<br /> {{Lumatone key|x=33|y=10|label=-c}}<br /> {{Lumatone key|x=34|y=10|label=9/8}}<br /> <br /> {{Lumatone key|x=24|y=11|label=28/27|size=10px}}<br /> {{Lumatone key|x=25|y=11|label=32/27|size=10px}}<br /> {{Lumatone key|x=26|y=11|label=}}<br /> {{Lumatone key|x=27|y=11|label=14/9}}<br /> {{Lumatone key|x=28|y=11|label=16/9}}<br /> {{Lumatone key|x=29|y=11|label=c}}<br /> {{Lumatone key|x=30|y=11|label=7/6}}<br /> {{Lumatone key|x=31|y=11|label=4/3}}<br /> {{Lumatone key|x=32|y=11|label=32/21|size=10px}}<br /> {{Lumatone key|x=33|y=11|label=7/4}}<br /> {{Lumatone key|x=34|y=11|label=1/1}}<br /> {{Lumatone key|x=35|y=11|label=8/7}}<br /> <br /> {{Lumatone key|x=30|y=12|label=28/27|size=10px}}<br /> {{Lumatone key|x=31|y=12|label=32/27|size=10px}}<br /> {{Lumatone key|x=32|y=12|label=}}<br /> {{Lumatone key|x=33|y=12|label=14/9}}<br /> {{Lumatone key|x=34|y=12|label=16/9}}<br /> {{Lumatone key|x=35|y=12|label=c}}<br /> <br /> {{Lumatone key|x=36|y=13|label=28/27|size=10px}}<br /> <br /> {{Lumatone key|x=34|y=15|label=Z}}<br /> <br /> }}<br /> <br /> [[Category:Lumatone mappings]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Map&diff=82348 Map 2021-12-21T01:32:44Z <p>Keenan Pepper: make into more of a disambiguation page</p> <hr /> <div>The word '''map''' could refer to:<br /> <br /> * In [[regular temperament theory]], a single row of a [[mapping]], including a mapping with only one row (an [[ET]] map). &quot;Map&quot; is usually synonymous with &quot;[[val]]&quot;, except that [[tuning map]]s and keyboard maps are not vals because they may contain non-integer entries.<br /> <br /> * In mathematics generally, any function from one set to another. See [https://en.wikipedia.org/wiki/Map_(mathematics) Wikipedia]<br /> <br /> * In RTT, a [[Wikipedia:Linear_form|linear form]], which is a function that can be represented by a [[Wikipedia:Covector|covector]], and &quot;mapping&quot; has the more specific meaning given here: [[Mapping#math|mapping]]. The shorter word refers to the simpler object.<br /> <br /> [[Category:Temperament]]<br /> [[Category:Regular temperament theory]]<br /> [[Category:Theory]]<br /> [[Category:Terms]]<br /> [[Category:Math]]<br /> [[Category:Val]]<br /> [[Category:Mapping]]<br /> [[Category:Tuning]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Lumatone_mapping_for_slendric&diff=80051 Lumatone mapping for slendric 2021-10-28T22:35:03Z <p>Keenan Pepper: </p> <hr /> <div>This is one proposed mapping of [[slendric]] temperament to the [[Lumatone]] keyboard. 6 complete octaves are available, and modulation to distant keys is possible.<br /> <br /> The keys marked &quot;c&quot; are one chroma up from 1/1, representing both 64/63 and 49/48. They keys marked &quot;-c&quot; are one chroma down from 1/1 (so 63/32 and 96/49).<br /> <br /> The same mapping could be used for any extension of slendric that has the same period and generator, including [[Cynder]], [[Rodan]], and [[Guiron]].<br /> <br /> {{Lumatone mapping|<br /> <br /> {{Lumatone key|x=3|y=4|label=27/16|size=10px}}<br /> {{Lumatone key|x=4|y=4|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=3|y=5|label=12/7}}<br /> {{Lumatone key|x=4|y=5|label=-c}}<br /> {{Lumatone key|x=5|y=5|label=9/8}}<br /> {{Lumatone key|x=6|y=5|label=9/7}}<br /> {{Lumatone key|x=7|y=5|label=}}<br /> {{Lumatone key|x=8|y=5|label=27/16|size=10px}}<br /> {{Lumatone key|x=9|y=5|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=3|y=6|label=7/4}}<br /> {{Lumatone key|x=4|y=6|label=1/1}}<br /> {{Lumatone key|x=5|y=6|label=8/7}}<br /> {{Lumatone key|x=6|y=6|label=21/16|size=10px}}<br /> {{Lumatone key|x=7|y=6|label=3/2}}<br /> {{Lumatone key|x=8|y=6|label=12/7}}<br /> {{Lumatone key|x=9|y=6|label=-c}}<br /> {{Lumatone key|x=10|y=6|label=9/8}}<br /> {{Lumatone key|x=11|y=6|label=9/7}}<br /> {{Lumatone key|x=12|y=6|label=}}<br /> {{Lumatone key|x=13|y=6|label=27/16|size=10px}}<br /> {{Lumatone key|x=14|y=6|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=21|y=6|label=Y}}<br /> <br /> {{Lumatone key|x=4|y=7|label=c}}<br /> {{Lumatone key|x=5|y=7|label=7/6}}<br /> {{Lumatone key|x=6|y=7|label=4/3}}<br /> {{Lumatone key|x=7|y=7|label=32/21|size=10px}}<br /> {{Lumatone key|x=8|y=7|label=7/4}}<br /> {{Lumatone key|x=9|y=7|label=1/1}}<br /> {{Lumatone key|x=10|y=7|label=8/7}}<br /> {{Lumatone key|x=11|y=7|label=21/16|size=10px}}<br /> {{Lumatone key|x=12|y=7|label=3/2}}<br /> {{Lumatone key|x=13|y=7|label=12/7}}<br /> {{Lumatone key|x=14|y=7|label=-c}}<br /> {{Lumatone key|x=15|y=7|label=9/8}}<br /> {{Lumatone key|x=16|y=7|label=9/7}}<br /> {{Lumatone key|x=17|y=7|label=}}<br /> {{Lumatone key|x=18|y=7|label=27/16|size=10px}}<br /> {{Lumatone key|x=19|y=7|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=21|y=7|label=X}}<br /> <br /> {{Lumatone key|x=4|y=8|label=28/27|size=10px}}<br /> {{Lumatone key|x=5|y=8|label=32/27|size=10px}}<br /> {{Lumatone key|x=6|y=8|label=}}<br /> {{Lumatone key|x=7|y=8|label=14/9}}<br /> {{Lumatone key|x=8|y=8|label=16/9}}<br /> {{Lumatone key|x=9|y=8|label=c}}<br /> {{Lumatone key|x=10|y=8|label=7/6}}<br /> {{Lumatone key|x=11|y=8|label=4/3}}<br /> {{Lumatone key|x=12|y=8|label=32/21|size=10px}}<br /> {{Lumatone key|x=13|y=8|label=7/4}}<br /> {{Lumatone key|x=14|y=8|label=1/1}}<br /> {{Lumatone key|x=15|y=8|label=8/7}}<br /> {{Lumatone key|x=16|y=8|label=21/16|size=10px}}<br /> {{Lumatone key|x=17|y=8|label=3/2}}<br /> {{Lumatone key|x=18|y=8|label=12/7}}<br /> {{Lumatone key|x=19|y=8|label=-c}}<br /> {{Lumatone key|x=20|y=8|label=9/8}}<br /> {{Lumatone key|x=21|y=8|label=9/7}}<br /> {{Lumatone key|x=22|y=8|label=}}<br /> {{Lumatone key|x=23|y=8|label=27/16|size=10px}}<br /> {{Lumatone key|x=24|y=8|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=9|y=9|label=28/27|size=10px}}<br /> {{Lumatone key|x=10|y=9|label=32/27|size=10px}}<br /> {{Lumatone key|x=11|y=9|label=}}<br /> {{Lumatone key|x=12|y=9|label=14/9}}<br /> {{Lumatone key|x=13|y=9|label=16/9}}<br /> {{Lumatone key|x=14|y=9|label=c}}<br /> {{Lumatone key|x=15|y=9|label=7/6}}<br /> {{Lumatone key|x=16|y=9|label=4/3}}<br /> {{Lumatone key|x=17|y=9|label=32/21|size=10px}}<br /> {{Lumatone key|x=18|y=9|label=7/4}}<br /> {{Lumatone key|x=19|y=9|label=1/1}}<br /> {{Lumatone key|x=20|y=9|label=8/7}}<br /> {{Lumatone key|x=21|y=9|label=21/16|size=10px}}<br /> {{Lumatone key|x=22|y=9|label=3/2}}<br /> {{Lumatone key|x=23|y=9|label=12/7}}<br /> {{Lumatone key|x=24|y=9|label=-c}}<br /> {{Lumatone key|x=25|y=9|label=9/8}}<br /> {{Lumatone key|x=26|y=9|label=9/7}}<br /> {{Lumatone key|x=27|y=9|label=}}<br /> {{Lumatone key|x=28|y=9|label=27/16|size=10px}}<br /> {{Lumatone key|x=29|y=9|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=14|y=10|label=28/27|size=10px}}<br /> {{Lumatone key|x=15|y=10|label=32/27|size=10px}}<br /> {{Lumatone key|x=16|y=10|label=}}<br /> {{Lumatone key|x=17|y=10|label=14/9}}<br /> {{Lumatone key|x=18|y=10|label=16/9}}<br /> {{Lumatone key|x=19|y=10|label=c}}<br /> {{Lumatone key|x=20|y=10|label=7/6}}<br /> {{Lumatone key|x=21|y=10|label=4/3}}<br /> {{Lumatone key|x=22|y=10|label=32/21|size=10px}}<br /> {{Lumatone key|x=23|y=10|label=7/4}}<br /> {{Lumatone key|x=24|y=10|label=1/1}}<br /> {{Lumatone key|x=25|y=10|label=8/7}}<br /> {{Lumatone key|x=26|y=10|label=21/16|size=10px}}<br /> {{Lumatone key|x=27|y=10|label=3/2}}<br /> {{Lumatone key|x=28|y=10|label=12/7}}<br /> {{Lumatone key|x=29|y=10|label=-c}}<br /> {{Lumatone key|x=30|y=10|label=9/8}}<br /> {{Lumatone key|x=31|y=10|label=9/7}}<br /> {{Lumatone key|x=32|y=10|label=}}<br /> {{Lumatone key|x=33|y=10|label=27/16|size=10px}}<br /> {{Lumatone key|x=34|y=10|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=19|y=11|label=28/27|size=10px}}<br /> {{Lumatone key|x=20|y=11|label=32/27|size=10px}}<br /> {{Lumatone key|x=21|y=11|label=}}<br /> {{Lumatone key|x=22|y=11|label=14/9}}<br /> {{Lumatone key|x=23|y=11|label=16/9}}<br /> {{Lumatone key|x=24|y=11|label=c}}<br /> {{Lumatone key|x=25|y=11|label=7/6}}<br /> {{Lumatone key|x=26|y=11|label=4/3}}<br /> {{Lumatone key|x=27|y=11|label=32/21|size=10px}}<br /> {{Lumatone key|x=28|y=11|label=7/4}}<br /> {{Lumatone key|x=29|y=11|label=1/1}}<br /> {{Lumatone key|x=30|y=11|label=8/7}}<br /> {{Lumatone key|x=31|y=11|label=21/16|size=10px}}<br /> {{Lumatone key|x=32|y=11|label=3/2}}<br /> {{Lumatone key|x=33|y=11|label=12/7}}<br /> {{Lumatone key|x=34|y=11|label=-c}}<br /> {{Lumatone key|x=35|y=11|label=9/8}}<br /> <br /> {{Lumatone key|x=24|y=12|label=28/27|size=10px}}<br /> {{Lumatone key|x=25|y=12|label=32/27|size=10px}}<br /> {{Lumatone key|x=26|y=12|label=}}<br /> {{Lumatone key|x=27|y=12|label=14/9}}<br /> {{Lumatone key|x=28|y=12|label=16/9}}<br /> {{Lumatone key|x=29|y=12|label=c}}<br /> {{Lumatone key|x=30|y=12|label=7/6}}<br /> {{Lumatone key|x=31|y=12|label=4/3}}<br /> {{Lumatone key|x=32|y=12|label=32/21|size=10px}}<br /> {{Lumatone key|x=33|y=12|label=7/4}}<br /> {{Lumatone key|x=34|y=12|label=1/1}}<br /> {{Lumatone key|x=35|y=12|label=8/7}}<br /> <br /> {{Lumatone key|x=29|y=13|label=28/27|size=10px}}<br /> {{Lumatone key|x=30|y=13|label=32/27|size=10px}}<br /> {{Lumatone key|x=31|y=13|label=}}<br /> {{Lumatone key|x=32|y=13|label=14/9}}<br /> {{Lumatone key|x=33|y=13|label=16/9}}<br /> {{Lumatone key|x=34|y=13|label=c}}<br /> {{Lumatone key|x=35|y=13|label=7/6}}<br /> {{Lumatone key|x=36|y=13|label=4/3}}<br /> <br /> {{Lumatone key|x=34|y=14|label=28/27|size=10px}}<br /> {{Lumatone key|x=35|y=14|label=32/27|size=10px}}<br /> <br /> {{Lumatone key|x=30|y=16|label=Z}}<br /> <br /> }}<br /> <br /> The differences between the extensions of slendric to the prime 5 can be visualized on this keyboard.<br /> * Cynder tempers out 81/80, so 9/8 above 9/8 is equivalent to 5/4 so 5/4 is mapped to the key marked &quot;X&quot;.<br /> * Rodan, on the other hand, makes 81/80 the same as the chroma c, so 5/4 is instead mapped to the key mapped &quot;Y&quot;, one chroma lower than &quot;X&quot;.<br /> * Guiron maps 5/4 to the key marked &quot;Z&quot;.<br /> <br /> Cynder and guiron intersect in 36edo, so in 36edo both &quot;X&quot; and &quot;Z&quot; represent 5/4. Rodan and guiron intersect in 41edo, so in 41edo both &quot;Y&quot; and &quot;Z&quot; represent 5/4.<br /> <br /> [[Category:Lumatone mappings]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Lumatone_mapping_for_slendric&diff=80050 Lumatone mapping for slendric 2021-10-28T22:20:59Z <p>Keenan Pepper: create</p> <hr /> <div>This is one proposed mapping of [[slendric]] temperament to the [[Lumatone]] keyboard. 6 complete octaves are available, and modulation to distant keys is possible.<br /> <br /> The keys marked &quot;c&quot; are one chroma up from 1/1, representing both 64/63 and 49/48. They keys marked &quot;-c&quot; are one chroma down from 1/1 (so 63/32 and 96/49).<br /> <br /> The same mapping could be used for any extension of slendric that has the same period and generator, including [[Cynder]], [[Rodan]], and [[Guiron]].<br /> <br /> {{Lumatone mapping|<br /> <br /> {{Lumatone key|x=2|y=4|label=}}<br /> {{Lumatone key|x=3|y=4|label=27/16|size=10px}}<br /> {{Lumatone key|x=4|y=4|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=3|y=5|label=12/7}}<br /> {{Lumatone key|x=4|y=5|label=-c}}<br /> {{Lumatone key|x=5|y=5|label=9/8}}<br /> {{Lumatone key|x=6|y=5|label=9/7}}<br /> {{Lumatone key|x=7|y=5|label=}}<br /> {{Lumatone key|x=8|y=5|label=27/16|size=10px}}<br /> {{Lumatone key|x=9|y=5|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=3|y=6|label=7/4}}<br /> {{Lumatone key|x=4|y=6|label=1/1}}<br /> {{Lumatone key|x=5|y=6|label=8/7}}<br /> {{Lumatone key|x=6|y=6|label=21/16|size=10px}}<br /> {{Lumatone key|x=7|y=6|label=3/2}}<br /> {{Lumatone key|x=8|y=6|label=12/7}}<br /> {{Lumatone key|x=9|y=6|label=-c}}<br /> {{Lumatone key|x=10|y=6|label=9/8}}<br /> {{Lumatone key|x=11|y=6|label=9/7}}<br /> {{Lumatone key|x=12|y=6|label=}}<br /> {{Lumatone key|x=13|y=6|label=27/16|size=10px}}<br /> {{Lumatone key|x=14|y=6|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=4|y=7|label=c}}<br /> {{Lumatone key|x=5|y=7|label=7/6}}<br /> {{Lumatone key|x=6|y=7|label=4/3}}<br /> {{Lumatone key|x=7|y=7|label=32/21|size=10px}}<br /> {{Lumatone key|x=8|y=7|label=7/4}}<br /> {{Lumatone key|x=9|y=7|label=1/1}}<br /> {{Lumatone key|x=10|y=7|label=8/7}}<br /> {{Lumatone key|x=11|y=7|label=21/16|size=10px}}<br /> {{Lumatone key|x=12|y=7|label=3/2}}<br /> {{Lumatone key|x=13|y=7|label=12/7}}<br /> {{Lumatone key|x=14|y=7|label=-c}}<br /> {{Lumatone key|x=15|y=7|label=9/8}}<br /> {{Lumatone key|x=16|y=7|label=9/7}}<br /> {{Lumatone key|x=17|y=7|label=}}<br /> {{Lumatone key|x=18|y=7|label=27/16|size=10px}}<br /> {{Lumatone key|x=19|y=7|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=4|y=8|label=28/27|size=10px}}<br /> {{Lumatone key|x=5|y=8|label=32/27|size=10px}}<br /> {{Lumatone key|x=6|y=8|label=}}<br /> {{Lumatone key|x=7|y=8|label=14/9}}<br /> {{Lumatone key|x=8|y=8|label=16/9}}<br /> {{Lumatone key|x=9|y=8|label=c}}<br /> {{Lumatone key|x=10|y=8|label=7/6}}<br /> {{Lumatone key|x=11|y=8|label=4/3}}<br /> {{Lumatone key|x=12|y=8|label=32/21|size=10px}}<br /> {{Lumatone key|x=13|y=8|label=7/4}}<br /> {{Lumatone key|x=14|y=8|label=1/1}}<br /> {{Lumatone key|x=15|y=8|label=8/7}}<br /> {{Lumatone key|x=16|y=8|label=21/16|size=10px}}<br /> {{Lumatone key|x=17|y=8|label=3/2}}<br /> {{Lumatone key|x=18|y=8|label=12/7}}<br /> {{Lumatone key|x=19|y=8|label=-c}}<br /> {{Lumatone key|x=20|y=8|label=9/8}}<br /> {{Lumatone key|x=21|y=8|label=9/7}}<br /> {{Lumatone key|x=22|y=8|label=}}<br /> {{Lumatone key|x=23|y=8|label=27/16|size=10px}}<br /> {{Lumatone key|x=24|y=8|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=9|y=9|label=28/27|size=10px}}<br /> {{Lumatone key|x=10|y=9|label=32/27|size=10px}}<br /> {{Lumatone key|x=11|y=9|label=}}<br /> {{Lumatone key|x=12|y=9|label=14/9}}<br /> {{Lumatone key|x=13|y=9|label=16/9}}<br /> {{Lumatone key|x=14|y=9|label=c}}<br /> {{Lumatone key|x=15|y=9|label=7/6}}<br /> {{Lumatone key|x=16|y=9|label=4/3}}<br /> {{Lumatone key|x=17|y=9|label=32/21|size=10px}}<br /> {{Lumatone key|x=18|y=9|label=7/4}}<br /> {{Lumatone key|x=19|y=9|label=1/1}}<br /> {{Lumatone key|x=20|y=9|label=8/7}}<br /> {{Lumatone key|x=21|y=9|label=21/16|size=10px}}<br /> {{Lumatone key|x=22|y=9|label=3/2}}<br /> {{Lumatone key|x=23|y=9|label=12/7}}<br /> {{Lumatone key|x=24|y=9|label=-c}}<br /> {{Lumatone key|x=25|y=9|label=9/8}}<br /> {{Lumatone key|x=26|y=9|label=9/7}}<br /> {{Lumatone key|x=27|y=9|label=}}<br /> {{Lumatone key|x=28|y=9|label=27/16|size=10px}}<br /> {{Lumatone key|x=29|y=9|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=14|y=10|label=28/27|size=10px}}<br /> {{Lumatone key|x=15|y=10|label=32/27|size=10px}}<br /> {{Lumatone key|x=16|y=10|label=}}<br /> {{Lumatone key|x=17|y=10|label=14/9}}<br /> {{Lumatone key|x=18|y=10|label=16/9}}<br /> {{Lumatone key|x=19|y=10|label=c}}<br /> {{Lumatone key|x=20|y=10|label=7/6}}<br /> {{Lumatone key|x=21|y=10|label=4/3}}<br /> {{Lumatone key|x=22|y=10|label=32/21|size=10px}}<br /> {{Lumatone key|x=23|y=10|label=7/4}}<br /> {{Lumatone key|x=24|y=10|label=1/1}}<br /> {{Lumatone key|x=25|y=10|label=8/7}}<br /> {{Lumatone key|x=26|y=10|label=21/16|size=10px}}<br /> {{Lumatone key|x=27|y=10|label=3/2}}<br /> {{Lumatone key|x=28|y=10|label=12/7}}<br /> {{Lumatone key|x=29|y=10|label=-c}}<br /> {{Lumatone key|x=30|y=10|label=9/8}}<br /> {{Lumatone key|x=31|y=10|label=9/7}}<br /> {{Lumatone key|x=32|y=10|label=}}<br /> {{Lumatone key|x=33|y=10|label=27/16|size=10px}}<br /> {{Lumatone key|x=34|y=10|label=27/14|size=10px}}<br /> <br /> {{Lumatone key|x=19|y=11|label=28/27|size=10px}}<br /> {{Lumatone key|x=20|y=11|label=32/27|size=10px}}<br /> {{Lumatone key|x=21|y=11|label=}}<br /> {{Lumatone key|x=22|y=11|label=14/9}}<br /> {{Lumatone key|x=23|y=11|label=16/9}}<br /> {{Lumatone key|x=24|y=11|label=c}}<br /> {{Lumatone key|x=25|y=11|label=7/6}}<br /> {{Lumatone key|x=26|y=11|label=4/3}}<br /> {{Lumatone key|x=27|y=11|label=32/21|size=10px}}<br /> {{Lumatone key|x=28|y=11|label=7/4}}<br /> {{Lumatone key|x=29|y=11|label=1/1}}<br /> {{Lumatone key|x=30|y=11|label=8/7}}<br /> {{Lumatone key|x=31|y=11|label=21/16|size=10px}}<br /> {{Lumatone key|x=32|y=11|label=3/2}}<br /> {{Lumatone key|x=33|y=11|label=12/7}}<br /> {{Lumatone key|x=34|y=11|label=-c}}<br /> {{Lumatone key|x=35|y=11|label=9/8}}<br /> <br /> {{Lumatone key|x=24|y=12|label=28/27|size=10px}}<br /> {{Lumatone key|x=25|y=12|label=32/27|size=10px}}<br /> {{Lumatone key|x=26|y=12|label=}}<br /> {{Lumatone key|x=27|y=12|label=14/9}}<br /> {{Lumatone key|x=28|y=12|label=16/9}}<br /> {{Lumatone key|x=29|y=12|label=c}}<br /> {{Lumatone key|x=30|y=12|label=7/6}}<br /> {{Lumatone key|x=31|y=12|label=4/3}}<br /> {{Lumatone key|x=32|y=12|label=32/21|size=10px}}<br /> {{Lumatone key|x=33|y=12|label=7/4}}<br /> {{Lumatone key|x=34|y=12|label=1/1}}<br /> {{Lumatone key|x=35|y=12|label=8/7}}<br /> <br /> {{Lumatone key|x=29|y=13|label=28/27|size=10px}}<br /> {{Lumatone key|x=30|y=13|label=32/27|size=10px}}<br /> {{Lumatone key|x=31|y=13|label=}}<br /> {{Lumatone key|x=32|y=13|label=14/9}}<br /> {{Lumatone key|x=33|y=13|label=16/9}}<br /> {{Lumatone key|x=34|y=13|label=c}}<br /> {{Lumatone key|x=35|y=13|label=7/6}}<br /> {{Lumatone key|x=36|y=13|label=4/3}}<br /> <br /> {{Lumatone key|x=34|y=14|label=28/27|size=10px}}<br /> {{Lumatone key|x=35|y=14|label=32/27|size=10px}}<br /> {{Lumatone key|x=36|y=14|label=}}<br /> <br /> }}<br /> <br /> [[Category:Lumatone mappings]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Lumatone_mapping_for_miracle&diff=79102 Lumatone mapping for miracle 2021-10-06T16:58:39Z <p>Keenan Pepper: fix some instances of -c that should be c</p> <hr /> <div>This Lumatone mapping for [[miracle]] temperament spans 3 full octaves. The letter s refers to the secor (representing both 16/15 and 15/14). The letter c refers to the chroma (representing 45/44~49/48~50/49~55/54~56/55~64/63). The note labeled &quot;21/20&quot; also represents 22/21, and the note labeled &quot;21/11&quot; also represents 40/21.<br /> <br /> {{Lumatone mapping|<br /> <br /> {{Lumatone key|x=3|y=5|label=9/5}}<br /> {{Lumatone key|x=6|y=5|label=11/10|size=11px}}<br /> <br /> {{Lumatone key|x=3|y=6|label=11/6}}<br /> {{Lumatone key|x=4|y=6|label=-c}}<br /> {{Lumatone key|x=5|y=6|label=21/20|size=10px}}<br /> {{Lumatone key|x=6|y=6|label=9/8}}<br /> {{Lumatone key|x=7|y=6|label=6/5}}<br /> {{Lumatone key|x=8|y=6|label=9/7}}<br /> {{Lumatone key|x=9|y=6|label=11/8}}<br /> {{Lumatone key|x=10|y=6|label=22/15|size=11px}}<br /> {{Lumatone key|x=11|y=6|label=11/7}}<br /> {{Lumatone key|x=13|y=6|label=9/5}}<br /> {{Lumatone key|x=16|y=6|label=11/10|size=11px}}<br /> <br /> {{Lumatone key|x=4|y=7|label=1/1}}<br /> {{Lumatone key|x=5|y=7|label=s}}<br /> {{Lumatone key|x=6|y=7|label=8/7}}<br /> {{Lumatone key|x=7|y=7|label=11/9}}<br /> {{Lumatone key|x=8|y=7|label=21/16|size=10px}}<br /> {{Lumatone key|x=9|y=7|label=7/5}}<br /> {{Lumatone key|x=10|y=7|label=3/2}}<br /> {{Lumatone key|x=11|y=7|label=8/5}}<br /> {{Lumatone key|x=12|y=7|label=12/7}}<br /> {{Lumatone key|x=13|y=7|label=11/6}}<br /> {{Lumatone key|x=14|y=7|label=-c}}<br /> {{Lumatone key|x=15|y=7|label=21/20|size=10px}}<br /> {{Lumatone key|x=16|y=7|label=9/8}}<br /> {{Lumatone key|x=17|y=7|label=6/5}}<br /> {{Lumatone key|x=18|y=7|label=9/7}}<br /> {{Lumatone key|x=19|y=7|label=11/8}}<br /> {{Lumatone key|x=20|y=7|label=22/15|size=11px}}<br /> {{Lumatone key|x=21|y=7|label=11/7}}<br /> {{Lumatone key|x=23|y=7|label=9/5}}<br /> {{Lumatone key|x=26|y=7|label=11/10|size=11px}}<br /> <br /> {{Lumatone key|x=4|y=8|label=c}}<br /> {{Lumatone key|x=5|y=8|label=12/11|size=11px}}<br /> {{Lumatone key|x=6|y=8|label=7/6}}<br /> {{Lumatone key|x=7|y=8|label=5/4}}<br /> {{Lumatone key|x=8|y=8|label=4/3}}<br /> {{Lumatone key|x=9|y=8|label=10/7}}<br /> {{Lumatone key|x=10|y=8|label=32/21|size=10px}}<br /> {{Lumatone key|x=11|y=8|label=18/11|size=11px}}<br /> {{Lumatone key|x=12|y=8|label=7/4}}<br /> {{Lumatone key|x=13|y=8|label=-s}}<br /> {{Lumatone key|x=14|y=8|label=1/1}}<br /> {{Lumatone key|x=15|y=8|label=s}}<br /> {{Lumatone key|x=16|y=8|label=8/7}}<br /> {{Lumatone key|x=17|y=8|label=11/9}}<br /> {{Lumatone key|x=18|y=8|label=21/16|size=10px}}<br /> {{Lumatone key|x=19|y=8|label=7/5}}<br /> {{Lumatone key|x=20|y=8|label=3/2}}<br /> {{Lumatone key|x=21|y=8|label=8/5}}<br /> {{Lumatone key|x=22|y=8|label=12/7}}<br /> {{Lumatone key|x=23|y=8|label=11/6}}<br /> {{Lumatone key|x=24|y=8|label=-c}}<br /> {{Lumatone key|x=25|y=8|label=21/20|size=10px}}<br /> {{Lumatone key|x=26|y=8|label=9/8}}<br /> {{Lumatone key|x=27|y=8|label=6/5}}<br /> {{Lumatone key|x=28|y=8|label=9/7}}<br /> {{Lumatone key|x=29|y=8|label=11/8}}<br /> <br /> {{Lumatone key|x=7|y=9|label=14/11|size=11px}}<br /> {{Lumatone key|x=8|y=9|label=15/11|size=11px}}<br /> {{Lumatone key|x=9|y=9|label=16/11|size=11px}}<br /> {{Lumatone key|x=10|y=9|label=14/9}}<br /> {{Lumatone key|x=11|y=9|label=5/3}}<br /> {{Lumatone key|x=12|y=9|label=16/9}}<br /> {{Lumatone key|x=13|y=9|label=21/11|size=10px}}<br /> {{Lumatone key|x=14|y=9|label=c}}<br /> {{Lumatone key|x=15|y=9|label=12/11|size=11px}}<br /> {{Lumatone key|x=16|y=9|label=7/6}}<br /> {{Lumatone key|x=17|y=9|label=5/4}}<br /> {{Lumatone key|x=18|y=9|label=4/3}}<br /> {{Lumatone key|x=19|y=9|label=10/7}}<br /> {{Lumatone key|x=20|y=9|label=32/21|size=10px}}<br /> {{Lumatone key|x=21|y=9|label=18/11|size=11px}}<br /> {{Lumatone key|x=22|y=9|label=7/4}}<br /> {{Lumatone key|x=23|y=9|label=-s}}<br /> {{Lumatone key|x=24|y=9|label=1/1}}<br /> {{Lumatone key|x=25|y=9|label=s}}<br /> {{Lumatone key|x=26|y=9|label=8/7}}<br /> {{Lumatone key|x=27|y=9|label=11/9}}<br /> {{Lumatone key|x=28|y=9|label=21/16|size=10px}}<br /> {{Lumatone key|x=29|y=9|label=7/5}}<br /> {{Lumatone key|x=30|y=9|label=3/2}}<br /> {{Lumatone key|x=31|y=9|label=8/5}}<br /> {{Lumatone key|x=32|y=9|label=12/7}}<br /> {{Lumatone key|x=33|y=9|label=11/6}}<br /> <br /> {{Lumatone key|x=12|y=10|label=20/11|size=11px}}<br /> {{Lumatone key|x=15|y=10|label=10/9}}<br /> {{Lumatone key|x=17|y=10|label=14/11|size=11px}}<br /> {{Lumatone key|x=18|y=10|label=15/11|size=11px}}<br /> {{Lumatone key|x=19|y=10|label=16/11|size=11px}}<br /> {{Lumatone key|x=20|y=10|label=14/9}}<br /> {{Lumatone key|x=21|y=10|label=5/3}}<br /> {{Lumatone key|x=22|y=10|label=16/9}}<br /> {{Lumatone key|x=23|y=10|label=21/11|size=10px}}<br /> {{Lumatone key|x=24|y=10|label=c}}<br /> {{Lumatone key|x=25|y=10|label=12/11|size=11px}}<br /> {{Lumatone key|x=26|y=10|label=7/6}}<br /> {{Lumatone key|x=27|y=10|label=5/4}}<br /> {{Lumatone key|x=28|y=10|label=4/3}}<br /> {{Lumatone key|x=29|y=10|label=10/7}}<br /> {{Lumatone key|x=30|y=10|label=32/21|size=10px}}<br /> {{Lumatone key|x=31|y=10|label=18/11|size=11px}}<br /> {{Lumatone key|x=32|y=10|label=7/4}}<br /> {{Lumatone key|x=33|y=10|label=-s}}<br /> {{Lumatone key|x=34|y=10|label=1/1}}<br /> <br /> {{Lumatone key|x=22|y=11|label=20/11|size=11px}}<br /> {{Lumatone key|x=25|y=11|label=10/9}}<br /> {{Lumatone key|x=27|y=11|label=14/11|size=11px}}<br /> {{Lumatone key|x=28|y=11|label=15/11|size=11px}}<br /> {{Lumatone key|x=29|y=11|label=16/11|size=11px}}<br /> {{Lumatone key|x=30|y=11|label=14/9}}<br /> {{Lumatone key|x=31|y=11|label=5/3}}<br /> {{Lumatone key|x=32|y=11|label=16/9}}<br /> {{Lumatone key|x=33|y=11|label=21/11|size=10px}}<br /> {{Lumatone key|x=34|y=11|label=c}}<br /> {{Lumatone key|x=35|y=11|label=12/11|size=11px}}<br /> <br /> {{Lumatone key|x=32|y=12|label=20/11|size=11px}}<br /> {{Lumatone key|x=35|y=12|label=10/9}}<br /> <br /> }}<br /> <br /> [[Category:Lumatone mappings]]<br /> [[Category:Miracle]]</div> Keenan Pepper https://en.xen.wiki/index.php?title=Talk:Skip_fretting&diff=73420 Talk:Skip fretting 2021-06-29T20:36:16Z <p>Keenan Pepper: /* remove &quot;Thanos tuning&quot;? */</p> <hr /> <div>Nice work Jeff! BTW I like the terms skip-1 fretting for omitting 1/2 of the frets, skip-2 fretting for omitting 2/3, etc. Matthew Autry has built guitars with skip-2, skip-3, etc. See http://tallkite.com/misc_files/The%20Kite%20Tuning.pdf --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 02:52, 3 May 2021 (UTC)<br /> <br /> == remove &quot;Thanos tuning&quot;? ==<br /> <br /> Not only is it obscure, it's also wrong. &quot;Thanos tuning&quot; would literally be where a tuning has only half of the pitches at all (even if all pitch classes are available, only half of them in any given octave). &quot;Thanos fretting&quot; would be more appropriate, but it would only apply to every-other-fret and not other types of skip-frettings. I would urge that it be thrown away as just a funny joke that doesn't actually make sense and nobody should be using as an actual name for this. --[[User:Wolftune|Wolftune]] ([[User talk:Wolftune|talk]]) 22:42, 27 June 2021 (UTC)<br /> :Agreed and removed. —[[User:Keenan Pepper|Keenan Pepper]] ([[User talk:Keenan Pepper|talk]]) 20:36, 29 June 2021 (UTC)</div> Keenan Pepper https://en.xen.wiki/index.php?title=Skip_fretting&diff=73419 Skip fretting 2021-06-29T20:36:06Z <p>Keenan Pepper: rm &quot;Thanos tuning&quot;</p> <hr /> <div>(Note: Despite it's name, skip-fretting is relevant not only to fretted stringed instruments, but to the layout of other two-dimensional grid instruments like the Lumatone and the monome.)<br /> <br /> == Introduction ==<br /> <br /> Skip fretting allows a player of a fretted stringed instrument to play in a higher EDO than would otherwise be possible or convenient. In most skip-fretting systems, the guitar skips every other fret, so each string has only half of the notes.<br /> <br /> The most familiar skip-fretting systems allow someone with an ordinary 12-edo guitar to tune to 24-edo by retuning their guitar, for instance by tuning 450 cents between every pair of adjacent strings. 350 cents, 550 cents etc. would all work too. The even strings have half the notes, and the odd strings have the other half.<br /> <br /> === Partial skip-fretting ===<br /> <br /> Because the frets on a fretted instrument get closer together toward the bridge - at the first octave they are twice as dense, and at the second octave, four times -- it could be reasonable to include all the frets near the nut, and then switch to a skip-fretting system somewhere for the high notes. To this author's knowledge a partially skip-fretted instrument has not yet been made.<br /> <br /> == (edo, divisor, gap) notation ==<br /> <br /> Skip-fretting systems can be &quot;isomorphic&quot;, with the same distance between every pair of adjacent strings, but they don't have to be. An isomorphic skip-fretting system can be described with three numbers: The EDO it allows one to play, the fraction of that EDO's notes on any particular string, and the number of steps in the EDO between adjacent strings. So, for instance, the system described above for playing 24-edo on a 12-edo guitar could be called a &quot;24 2 9&quot; system (9\24 being equal to 450 cents).<br /> <br /> [In retrospect, I wish I had used notation like &quot;2,13\41&quot; instead of &quot;(41,2,13)&quot;. Both of those represent the [[Kite guitar]] tuning equally unambiguously, but I think the first is clearer.]<br /> <br /> == The relevance to keyboard players of skip-fretting ==<br /> <br /> Any skip-fretting system can be used on any two-dimensional grid instrument, such as the Lumatone or the monome. Whereas for a string player the numbers `div` and `gap` in an `(edo, div, gap)` system have different meanings, for a keyboardist they don't: Both `div` and `gap` describe the amount by which the pitch changes between two keys adjacent on a particular axis.<br /> <br /> For example, the Kite skip-fretting system (41,2,13) involves keeping only every 2nd fret from 41-edo and putting 13\41 between the strings. The reverse, keeping every 13th fret and putting 2\41 between every pair of strings, would be ridiculous on a guitar, but makes just as much sense on a keyboard, and in fact results in the same system, just swapping the two axes.<br /> <br /> == Tradeoffs inherent in skip-fretting systems ==<br /> <br /> The ideal skip-fretting system would be one that offers the player a big range without requiring too much movement or stretching, good approximations to the just intervals they want, and convenient unison or octave equivalents to any given note. These qualities are in tension.<br /> <br /> === Ease of reach vs. frequency range ===<br /> <br /> The smaller the interval between adjacent strings, the easier it becomes to reach all the notes of interest in a given octave, but this reduces the total range of the instrument.<br /> <br /> The narrow 11\41 and (standard) wide 13\41 Kite guitar tunings illustrate this tradeoff. In the narrow tuning, intervals based on the 7th and 13th harmonic are much easier to play, but the interval from the first string to the sixth is 1609 cents. In the wider tuning, by contrast, it is 1902 cents.<br /> <br /> === Ease of reach vs. harmonic accuracy ===<br /> <br /> The relationship is not linear, but as a loose rule, higher EDOs provide closer approxiamtions to the harmonic series. However, skip-frettings for higher EDOs provide fewer unisons and octaves. For instance, [[Skip fretting system 63 3 17]] is in general more faithful than 41-edo is to the harmonic series, but unisons lie 17 frets apart on a guitar with 21 frets per octave. That's equivalent to a stretch of 9.7 frets on a standard 12-edo guitar. By contrast, on the Kite guitar, which uses 41-edo, the distance between unisons is only 13 frets on a 20.5-fret guitar, equivalent to about 7.6 frets on a 12-edo guitar.<br /> <br /> == Finding unisons and octaves in a skip-fretting system ==<br /> In skip-fretting system `(edo, div, gap)`, the unison to any note lies `div` strings and `gap` frets away.<br /> <br /> This author has yet to find or see a formula for determining the octaves. However, the following procedure does the job: Let `n` be a number of strings. If `f = (edo - n*gap) / div` is a whole number, then an octave can be found `n` strings and `f` frets away.<br /> <br /> For instance, for the standard Kite tuning, `(edo, div, gap)` = `(41,2,13)`. Since `14 = (41 - 1*13)/2` is a whole number, there is an octave 1 string and 14 frets away. And since `1 = (41 - 3*13)/2` is another whole number, there is another octave 3 strings and 1 fret away.<br /> <br /> == Some skip-fretting systems ==<br /> <br /> * [[Skip fretting system 31 2 9]]: Make the higher register of a 31-edo guitar easier to play by omitting every other fret, while keeping all the frets in the lower register.<br /> * [[Skip fretting system 34 2 9]]: 34-edo on a 17-edo guitar.<br /> * [[Skip fretting system 41 2 11]]: Same fret layout as the Kite guitar, with narrower string gaps and easier-to-reach higher-limit intervals.<br /> * [[The Kite Guitar|The Kite Guitar, system 41 2 13]]: 41-edo on a 20.5-edo guitar.<br /> * [[Skip fretting system 44 2 11]]: 44-edo on a 22-edo guitar.<br /> * [[Skip fretting system 48 2 13]]: 48-edo on a 24-edo guitar.<br /> * [[Skip fretting system 58 2 15]]: 58-edo on a 29-edo guitar.<br /> * [[Skip fretting system 63 3 17]]: 63-edo on a 21-edo guitar.<br /> * [[Skip fretting system 90 5 17]]: 90-edo on an 18-edo guitar.<br /> * [[Isomorphic grid layout 7\94 x 16\94]]: 94-edo on a 13.429-edo guitar.<br /> <br /> [[Category:Guitar]]<br /> [[Category:Skip fretting| ]] &lt;!-- main category --&gt;</div> Keenan Pepper https://en.xen.wiki/index.php?title=Talk:Exotemperament&diff=73418 Talk:Exotemperament 2021-06-29T20:23:44Z <p>Keenan Pepper: </p> <hr /> <div>== Low complexity criterion ==<br /> <br /> When exactly do we speak of a low-complexity comma? Answering that question could open up options for '''new''' [[:category:comma|categories for commas]] (we currently sub-categorize them by size). --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 22:05, 27 June 2021 (UTC)<br /> :It's the [[complexity]] of the comma as an interval. So there are multiple ways to define it precisely, but they're all highly correlated. Examples: [[Benedetti height]]/[[Tenney height]], [[Tenney-Euclidean metrics#TE norm|TE norm]], [[Generalized Tenney Norms and Tp Interval Space]], [[Kees height]]... —[[User:Keenan Pepper|Keenan Pepper]] ([[User talk:Keenan Pepper|talk]]) 20:23, 29 June 2021 (UTC)</div> Keenan Pepper https://en.xen.wiki/index.php?title=22edo&diff=72970 22edo 2021-06-23T06:35:12Z <p>Keenan Pepper: /* Music */ use archive.org link for glassic</p> <hr /> <div>{{interwiki<br /> | de = 22edo<br /> | en = 22edo<br /> | es = <br /> | ja = 22平均律<br /> }}<br /> {{Infobox ET<br /> | Prime factorization = 2 × 11<br /> | Step size = 54.545¢<br /> | Fifth = 13\22 = 709.091¢<br /> | Major 2nd = 4\22 = 218¢<br /> | Minor 2nd = 1\22 = 55¢<br /> | Augmented 1sn = 3\22 = 164¢<br /> }}<br /> <br /> In music, '''22 equal temperament''', called '''22-tet''', '''22-edo''', or '''22-et''', is the scale derived by dividing the [[octave]] into 22 equally large steps. Each step represents a frequency ratio of the twenty-second root of 2, or 54.55 [[cent]]s. Because it distinguishes 10/9 and 9/8, it's not meantone.<br /> <br /> == Theory ==<br /> <br /> {| class=&quot;wikitable center-all&quot;<br /> ! colspan=&quot;2&quot; | &lt;!-- empty cell --&gt;<br /> ! prime 2<br /> ! prime 3<br /> ! prime 5<br /> ! prime 7<br /> ! prime 11<br /> ! prime 13<br /> ! prime 17<br /> |-<br /> ! rowspan=&quot;2&quot; | error<br /> ! absolute (¢)<br /> | 0<br /> | +7.2<br /> | -4.5<br /> | +13.0<br /> | -5.9<br /> | -22.3<br /> | +4.1<br /> |-<br /> ! [[Relative error|relative]] (%)<br /> | 0<br /> | +13<br /> | -8<br /> | +24<br /> | -11<br /> | -40<br /> | +7<br /> |-<br /> ! colspan=&quot;2&quot; | [[nearest edomapping]]<br /> | 22<br /> | 13<br /> | 7<br /> | 18<br /> | 10<br /> | 15<br /> | 2<br /> |-<br /> ! colspan=&quot;2&quot; | [[fifthspan]]<br /> | 0<br /> | +1<br /> | +9<br /> | -2<br /> | -6<br /> | -9<br /> | -10<br /> |}<br /> <br /> The idea of dividing the octave into 22 steps of equal size seems to have originated with nineteenth century music theorist RHM Bosanquet. Inspired by the division of the octave into 22 unequal parts in the [[Indian|music theory of India]], Bosenquet noted that such an equal division was capable of representing 5-limit music with tolerable accuracy. In this he was followed in the twentieth century by theorist José Würschmidt, who noted it as a possible next step after [[19edo|19 equal temperament]], and J. Murray Barbour in his classic survey of tuning history, ''Tuning and Temperament''.<br /> <br /> The 22-et system is in fact the third equal division, after 12 and 19, which is capable of approximating the [[5-limit]] to within a TE error of 4 cents/oct. While not an integral or gap edo it at least qualifies as a [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta peak]]. Moreover, there is more to it than just the 5-limit; unlike 12 or 19 it is able to approximate the [[7-limit|7-]] and [[11-limit]]s to within 3 cents/oct of error. While [[31edo|31 equal temperament]] does much better, 22-et still allows the use of these higher-limit harmonies, and in fact 22 is the smallest equal division to represent the 11-limit [[consistent|consistently]]. Furthermore, 22-et, unlike 12 and [[19edo|19]], is not a [[meantone]] system. The net effect is that 22 allows, and to some extent even forces, the exploration of less familiar musical territory, yet is small enough that it can be used in live performances with suitably designed instruments, such as 22-tone guitars and the like.<br /> <br /> 22-et can also be treated as adding harmonics 3 and 5 to 11-EDO's 2.7.9.11.15.17 subgroup, making it a (rather accurate) 2.3.5.7.11.17 subgroup temperament. Let us also mind it's approximation of the 31st harmonic is within half a cent, which is fairly accurate. It also approximates some intervals involving the 29th harmonic well, especially 29/24, which is also matched within half a cent. This leaves us with 2.3.5.7.11.17.29.31.<br /> <br /> 22-et is very close to an extended &quot;quarter-comma superpyth&quot;, a tuning analogous to quarter-comma meantone except that it tempers out the septimal comma 64:63 instead of the syntonic comma 81:80. Because of this it has nearly pure septimal major thirds (9:7).<br /> <br /> == Properties of 22 equal temperament ==<br /> <br /> Possibly the most striking characteristic of 22edo to those not used to it is that it does '''not''' &quot;temper out&quot; the syntonic comma of 81/80, and therefore is not a system of [[Regular Temperaments#meantone|meantone]] temperament. This means that 22 distinguishes a number of Pythagorean and 5-limit intervals that 12-EDO, 19-EDO, 31-EDO, ... do not distinguish, such as the two whole tones 9/8 and 10/9. Indeed, these distinctions are exaggerated in comparison to 5-limit JI and many more accurate temperaments such as [[34edo]], [[41edo]] and [[53edo]].<br /> <br /> The diatonic scale it produces is instead derived from [[superpyth]] temperament, which despite having the same melodic structure as meantone's diatonic scale (LLsLLLs or, [[5L 2s]]), has thirds approximating 9/7 and 7/6, rather than 5/4 and 6/5. This means that the septimal comma of 64/63 vanishes, rather than the syntonic comma of 81/80, which is one of the core features of 22-EDO. Superpyth is melodically interesting for having a quasi-equal pentatonic scale (as the large whole tone and subminor third are rather close in size) and a more uneven heptatonic scale, as compared with 12-equal and meantone systems: step patterns 4 4 5 4 5 and 4 4 1 4 4 4 1, respectively.<br /> <br /> It additionally tempers out the porcupine comma or maximal diesis of 250/243, which means that 22edo supports [[porcupine]] temperament. The generator for porcupine is a flat minor whole tone of [[10/9]], two of which is a slightly sharp [[6/5]], and three of which is a slightly flat [[4/3]], implying the existence of an equal-step tetrachord, which is characteristic of Porcupine. Porcupine is notable for being the 5-limit temperament lowest in [[badness]] which is ''not'' approximated by the familiar 12-tone equal temperament, and as such represents one excellent point of departure for examining the harmonic properties of 22-EDO. It forms [[MOSScales|MOS]]'s of 7 and 8, which in 22-EDO are tuned respectively as 4 3 3 3 3 3 3 and 3 1 3 3 3 3 3 3 (and their respective modes).<br /> <br /> The 164¢ &quot;flat minor whole tone&quot; is a key interval in 22edo, in part because it functions as no less than three different consonant ratios in the [[11-limit]]: 10/9, 11/10, and 12/11. It is thus extremely ambiguous and flexible. The trade-off is that it is very much in the cracks of the 12-equal piano, and so for most 12-equal listeners, it takes some getting used to. Simple translations of 5-limit music into 22-EDO can sound very different, with a more complex harmonic quality inevitably arising. 22edo does not contain a neutral third but both the 5-limit thirds have a &quot;neutral-like&quot; quality since they are tempered closer together rather than farther apart as in 12edo.<br /> <br /> 22-EDO also supports Orwell temperament, which uses the septimal subminor third as a generator (5 degrees) and forms MOS scales with step patterns 3 2 3 2 3 2 3 2 2 and 1 2 2 1 2 2 1 2 2 1 2 2 2. Harmonically, Orwell can be tuned more accurately in other temperaments, such as [[31edo]], [[53edo]] and [[84edo]]. But 22-equal Orwell has a leg-up on the others melodically, as the large and small steps of Orwell[9] are easier to distinguish in 22.<br /> <br /> Other 5-limit commas 22edo tempers out include the diaschisma, 2048/2025 and the magic comma or small diesis, 3125/3072. In a diaschismic system, such as 12-et or 22-et, the [[diatonic tritone]] [[45/32]], which is a major third above a [[major_whole_tone|major whole tone]] representing [[9/8]], is equated to its inverted form, [[64/45]]. That the magic comma is tempered out means that 22-et is a [[Regular_Temperaments#magic|magic]] system, where five major thirds make up a perfect fifth.<br /> <br /> In the 7-limit 22edo tempers out certain commas also tempered out by 12-et; this relates 12 equal to 22 in a way different from the way in which meantone systems are akin to it. Both [[50/49]], (the [[jubilee comma]]), and [[64/63]], (the [[septimal comma]]), are tempered out in both systems. Hence because of 50/49 they both equate the two septimal tritones of 7/5 and 10/7, and because of 64/63 they both do not distinguish between a dominant seventh chord and an otonal tetrad. Hence both also temper out (50/49)/(64/63) = 225/224, the [[septimal kleisma]], so that the septimal kleisma augmented triad is a chord of 22-et, as it also is of any meantone tuning. A septimal comma not tempered out by 12-et which 22-et does temper out is 1728/1715, the [[orwell comma]]; and the [[orwell tetrad]] is also a chord of 22-et.<br /> <br /> In the 11-limit, 22edo tempers out [[Quartisma|117440512/117406179]], leading to a stack of five 33/32 quartertones being equated with one 7/6 subminor third. This is a trait which, while shared with [[24edo]], is surprisingly ''not'' shared with a number of other relatively small EDOs such as [[17edo]], [[26edo]] and [[34edo]]. In fact, not even the famous [[53edo]] has this property- although it should be noted that the related [[159edo]] ''does''.<br /> <br /> As 22 is divisible by 11, a 22edo instrument can play any music in [[11edo|11edo]], in the same way that 12edo can play 6edo (the whole tone scale). 11-equal is interesting for sounding melodically very similar to 12-equal (whole steps, half steps and minor thirds in the familiar 1:2:3 ratio), but harmonically very different, in particular because it lacks perfect fifths/fourths and 5-limit major thirds/minor sixths. Similarly, 22edo is melodically similar to 24edo as both contain quarter-tones and minor, neutral, and major seconds; but 22edo offers much better all-around harmonies than 24. In [[Sagittal notation|Sagittal]], 11 can be notated as every other note of 22.<br /> <br /> == Notation ==<br /> <br /> {| class=&quot;wikitable center-all right-2&quot;<br /> |-<br /> ! Degree<br /> ! Cents<br /> ! Approximate Ratios*<br /> ! colspan=&quot;3&quot; |[[Ups and Downs Notation]]<br /> |-<br /> | 0<br /> | 0.000<br /> | [[1/1]]<br /> |perfect unison<br /> |P1<br /> |D<br /> |-<br /> | 1<br /> | 54.545<br /> | [[36/35]], [[34/33]], [[33/32]], [[32/31]]<br /> |minor 2nd<br /> |m2<br /> |Eb<br /> |-<br /> | 2<br /> | 109.091<br /> | [[18/17]], [[17/16]], [[16/15]], [[15/14]]<br /> |upminor 2nd<br /> |^m2<br /> |^Eb<br /> |-<br /> | 3<br /> | 163.636<br /> | [[12/11]], [[11/10]], [[10/9]]<br /> |downmajor 2nd<br /> |vM2<br /> |vE<br /> |-<br /> | 4<br /> | 218.182<br /> | [[9/8]], [[17/15]], [[8/7]]<br /> |major 2nd<br /> |M2<br /> |E<br /> |-<br /> | 5<br /> | 272.737<br /> | [[20/17]], [[7/6]]<br /> |minor 3rd<br /> |m3<br /> |F<br /> |-<br /> | 6<br /> | 327.273<br /> | [[6/5]], [[17/14]], [[11/9]]<br /> |upminor 3rd<br /> |^m3<br /> |^F<br /> |-<br /> | 7<br /> | 381.818<br /> | [[5/4]], [[96/77]]<br /> |downmajor 3rd<br /> |vM3<br /> |vF#<br /> |-<br /> | 8<br /> | 436.364<br /> | [[14/11]], [[9/7]], [[22/17]]<br /> |major 3rd<br /> |M3<br /> |F#<br /> |-<br /> | 9<br /> | 490.909<br /> | [[4/3]]<br /> |perfect fourth<br /> |P4<br /> |G<br /> |-<br /> | 10<br /> | 545.455<br /> | [[15/11]], [[11/8]]<br /> |up-4th, dim 5th<br /> |^4, d5<br /> |^G, Ab<br /> |-<br /> | 11<br /> | 600.000<br /> | [[7/5]], [[24/17]], [[17/12]], [[10/7]]<br /> |downaug 4th, updim 5th<br /> |vA4, ^d5<br /> |vG#, ^Ab<br /> |-<br /> | 12<br /> | 654.545<br /> | [[16/11]], [[22/15]]<br /> |aug 4th, down-5th<br /> |A4, v5<br /> |G#, vA<br /> |-<br /> | 13<br /> | 709.091<br /> | [[3/2]]<br /> |perfect 5th<br /> |P5<br /> |A<br /> |-<br /> | 14<br /> | 763.636<br /> | [[17/11]], [[14/9]], [[11/7]]<br /> |minor 6th<br /> |m6<br /> |Bb<br /> |-<br /> | 15<br /> | 818.182<br /> | [[8/5]], [[77/48]]<br /> |upminor 6th<br /> |^m6<br /> |^Bb<br /> |-<br /> | 16<br /> | 872.727<br /> | [[18/11]], [[28/17]], [[5/3]]<br /> |downmajor 6th<br /> |vM6<br /> |vB<br /> |-<br /> | 17<br /> | 927.273<br /> | [[17/10]], [[12/7]]<br /> |major 6th<br /> |M6<br /> |B<br /> |-<br /> | 18<br /> | 981.818<br /> | [[7/4]], [[30/17]], [[16/9]]<br /> |minor 7th<br /> |m7<br /> |C<br /> |-<br /> | 19<br /> | 1036.364<br /> | [[9/5]], [[11/6]], [[20/11]]<br /> |upminor 7th<br /> |^m7<br /> |^C<br /> |-<br /> | 20<br /> | 1090.909<br /> | [[28/15]], [[15/8]], [[32/17]], [[17/9]]<br /> |downmajor 7th<br /> |vM7<br /> |vC#<br /> |-<br /> | 21<br /> | 1145.455<br /> | [[31/16]], [[64/33]], [[33/17]], [[35/18]]<br /> |major 7th<br /> |M7<br /> |C#<br /> |-<br /> | 22<br /> | 1200.000<br /> | [[2/1]]<br /> |perfect octave<br /> |P8<br /> |D<br /> |}<br /> <br /> &lt;nowiki&gt;*&lt;/nowiki&gt; some simpler ratios, ordered by increasing size, based on treating 22-edo as a 2.3.5.7.11.17 subgroup temperament; other approaches are possible.<br /> <br /> === Superpyth/Porcupine Notation, Porcupine Notation and Pentatonic Notation ===<br /> Superpyth/Porcupine Notation is a system arising from both Superpyth and Porcupine temperament. It categorizes each 22edo interval as major and minor of one or both of those temperaments. s indicates superpyth and p indicates Porcupine. Because p now represents porcupine and not perfect, P in perfect intervals is no longer used in this system. Instead the number is used without P and is read as either just the number or &quot;Natural&quot;. Example: P5 becomes 5 or N5 = Perfect fifth becomes Natural fifth.<br /> <br /> Another possible notation uses the porcupine generator to generate the notation as well. The 2nd and 7th are perfect, and the 4th and 5th are imperfect like the 3rd and 6th. This is the only way to use a heptatonic notation without additional accidentals. The keyboard runs D * * E * * F * * G * * * A * * B * * C * * D. The natural notes represent a chain of 2nds ABCDEFG.<br /> <br /> Yet another notation is pentatonic. The degrees are unison, subthird, fourthoid, fifthoid, subseventh and octoid. This is the only way to use a chain-of-fifths notation without additional accidentals. The keyboard runs D * * * * F * * * G * * * A * * * * C * * * D. The natural notes represent a chain of 5ths FCGDA.<br /> <br /> {| class=&quot;wikitable center-all right-2&quot;<br /> |-<br /> ! [[Degree]]<br /> ! [[cent|Cents]]<br /> ! colspan=&quot;2&quot; | Superpyth/Porcupine Notation<br /> ! colspan=&quot;3&quot; | Porcupine<br /> ! colspan=&quot;3&quot; | Pentatonic<br /> |-<br /> | 0<br /> | 0<br /> | Natural Unison<br /> | 1<br /> | perfect unison<br /> | P1<br /> | D<br /> | perfect unison<br /> | P1<br /> | D<br /> |-<br /> | 1<br /> | 55<br /> | s-minor second<br /> | sm2<br /> | aug unison<br /> | A1<br /> | D#<br /> | aug unison<br /> | A1<br /> | D#<br /> |-<br /> | 2<br /> | 109<br /> | p-diminished second<br /> | pd2<br /> | dim 2nd<br /> | d2<br /> | Eb<br /> | double-aug unison, &lt;br&gt;double-dim sub3rd<br /> | AA1, &lt;br&gt;dds3<br /> | Dx, &lt;br&gt;Fb&lt;span style=&quot;vertical-align: super;&quot;&gt;3 &lt;/span&gt;<br /> |-<br /> | 3<br /> | 164<br /> | p-minor second<br /> | pm2<br /> | perfect 2nd<br /> | P2<br /> | E<br /> | dim sub3rd<br /> | ds3<br /> | Fbb<br /> |-<br /> | 4<br /> | 218<br /> | (s/p) Major second<br /> | M2<br /> | aug 2nd<br /> | A2<br /> | E#<br /> | minor sub3rd<br /> | ms3<br /> | Fb<br /> |-<br /> | 5<br /> | 273<br /> | s-minor third<br /> | sm3<br /> | dim 3rd<br /> | d3<br /> | Fb<br /> | major sub3rd<br /> | Ms3<br /> | F<br /> |-<br /> | 6<br /> | 327<br /> | p-minor third<br /> | pm3<br /> | minor 3rd<br /> | m3<br /> | F<br /> | aug sub3rd<br /> | As3<br /> | F#<br /> |-<br /> | 7<br /> | 382<br /> | p-Major third<br /> | pM3<br /> | major 3rd<br /> | M3<br /> | F#<br /> | double-aug sub3rd, &lt;br&gt;double-dim 4thoid<br /> | AAs3, &lt;br&gt;dd4d<br /> | Fx, &lt;br&gt;Gbb<br /> |-<br /> | 8<br /> | 436<br /> | s-Major third<br /> | sM3<br /> | aug 3rd, dim 4th<br /> | A3, d4<br /> | Fx, Gb<br /> | dim 4thoid<br /> | d4d<br /> | Gb<br /> |-<br /> | 9<br /> | 491<br /> | Natural Fourth<br /> | 4, N4<br /> | minor 4th<br /> | m4<br /> | G<br /> | perfect 4thoid<br /> | P4d<br /> | G<br /> |-<br /> | 10<br /> | 545<br /> | p-Major Fourth, s-dim fifth<br /> | pM4, sd5<br /> | major 4th<br /> | M4<br /> | G#<br /> | aug 4thoid<br /> | A4d<br /> | G#<br /> |-<br /> | 11<br /> | 600<br /> | Augmented Fourth, <br /> Half-Octave<br /> | A4, HO<br /> | aug 4th, &lt;br&gt;dim 5th<br /> | A4, d5<br /> | Gx, &lt;br&gt;Abb<br /> | double-aug 4thoid, &lt;br&gt;double-dim 5thoid<br /> | AA4d, &lt;br&gt;dd5d<br /> | Gx, &lt;br&gt;Abb<br /> |-<br /> | 12<br /> | 655<br /> | p-minor Fifth, s-aug Fourth<br /> | pm5, sA4<br /> | minor 5th<br /> | m5<br /> | Ab<br /> | dim 5thoid<br /> | d5d<br /> | Ab<br /> |-<br /> | 13<br /> | 709<br /> | Natural Fifth<br /> | 5, N5<br /> | major 5th<br /> | M5<br /> | A<br /> | perfect 5thoid<br /> | P5d<br /> | A<br /> |-<br /> | 14<br /> | 764<br /> | s-minor sixth<br /> | sm6<br /> | aug 5th, dim 6th<br /> | A5, d6<br /> | A#, Bbb<br /> | aug 5thoid<br /> | A5d<br /> | A#<br /> |-<br /> | 15<br /> | 818<br /> | p-minor sixth<br /> | pm6<br /> | minor 6th<br /> | m6<br /> | Bb<br /> | double-aug 5thoid, &lt;br&gt;double-dim sub7th<br /> | AA5d, &lt;br&gt;dds7<br /> | Ax, &lt;br&gt;Cb&lt;span style=&quot;vertical-align: super;&quot;&gt;3&lt;/span&gt;<br /> |-<br /> | 16<br /> | 873<br /> | p-Major sixth<br /> | pM6<br /> | major 6th<br /> | M6<br /> | B<br /> | dim sub7th<br /> | ds7<br /> | Cbb<br /> |-<br /> | 17<br /> | 927<br /> | s-Major sixth<br /> | sM6<br /> | aug 6th<br /> | A6<br /> | B#<br /> | minor sub7th<br /> | ms7<br /> | Cb<br /> |-<br /> | 18<br /> | 982<br /> | (s/p) minor seventh<br /> | m7<br /> | dim 7th<br /> | d7<br /> | Cb<br /> | major sub7th<br /> | Ms7<br /> | C<br /> |-<br /> | 19<br /> | 1036<br /> | p-Major seventh<br /> | pM7<br /> | perfect 7th<br /> | P7<br /> | C<br /> | aug sub7th<br /> | As7<br /> | C#<br /> |-<br /> | 20<br /> | 1091<br /> | p-Augmented Seventh<br /> | pA7<br /> | aug 7th<br /> | A7<br /> | C#<br /> | double-aug sub7th, &lt;br&gt;double-dim octave<br /> | AAs7, &lt;br&gt;dd8<br /> | Cx, &lt;br&gt;Dbb<br /> |-<br /> | 21<br /> | 1145<br /> | s-Major Seventh<br /> | sM7<br /> | dim 8ve<br /> | d8<br /> | Db<br /> | dim octave<br /> | d8<br /> | Db<br /> |-<br /> | 22<br /> | 1200<br /> | Octave<br /> | 8<br /> | perfect octave<br /> | P8<br /> | D<br /> | perfect octave<br /> | P8<br /> | D<br /> |}<br /> <br /> === Decatonic Notation ===<br /> The decatonic notation is based on Paul Erlich's decatonic scales. Unlike typical notation, the decatonic system is based on a scale of 10 tones rather than 7. This approach requires an entire re-learning of chords, intervals, and notation, but it allows 22EDO to be notated using only one pair of accidentals, and gives the opportunity to escape a heptatonic thinking pattern. The system is based on two chains of fifths: one represented by Latin letters, the other by Greek. The two chains can be looked at as two juxtaposed pentatonic scales.<br /> <br /> Chain 1: C G D A E<br /> <br /> Chain 2: γ δ α ε β<br /> <br /> The alphabet is, in ascending order: C δ D ε E γ G α A β C<br /> <br /> In this alphabet, a chain of fifths is preserved because equivalent Greek letters also represent fifths if they are the same as their Latin counterparts. For example G-D is a fifth, and so is γ-δ.<br /> <br /> ==Chord Names==<br /> <br /> See also [[22 EDO Chords]], [[Chords of orwell]].<br /> <br /> Combining ups and downs notation with [[color notation]], qualities can be loosely associated with colors:<br /> <br /> {| class=&quot;wikitable center-all&quot;<br /> |-<br /> ! quality<br /> ![[color name]]<br /> ! [[monzo]] format<br /> ! examples<br /> |-<br /> | rowspan=&quot;2&quot; | minor<br /> | zo<br /> | [a b 0 1&gt;<br /> | 7/6, 7/4<br /> |-<br /> | fourthward wa<br /> | [a b&gt; where b &amp;lt; -1<br /> | 32/27, 16/9<br /> |-<br /> | upminor<br /> | gu<br /> | [a b -1&gt;<br /> | 6/5, 9/5<br /> |-<br /> | downmajor<br /> | yo<br /> | [a b 1&gt;<br /> | 5/4, 5/3<br /> |-<br /> | rowspan=&quot;2&quot; | major<br /> | fifthward wa<br /> | [a b&gt; where b &amp;gt; 1<br /> | 9/8, 27/16<br /> |-<br /> | ru<br /> | [a b 0 -1&gt;<br /> | 9/7, 12/7<br /> |}<br /> <br /> All 31edo chords can be named using ups and downs. Alterations are always enclosed in parentheses, additions never are. An up or down immediately after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13).Here are the zo, gu, yo and ru triads:<br /> <br /> {| class=&quot;wikitable center-all&quot;<br /> |-<br /> ! [[Kite's color notation|color of the 3rd]]<br /> ! JI chord<br /> ! notes as edosteps<br /> ! notes of C chord<br /> ! written name<br /> ! spoken name<br /> |-<br /> | zo<br /> | 6:7:9<br /> | 0-5-13<br /> | C Eb G<br /> | Cm<br /> | C minor<br /> |-<br /> | gu<br /> | 10:12:15<br /> | 0-6-13<br /> | C ^Eb G<br /> | C^m<br /> | C upminor<br /> |-<br /> | yo<br /> | 4:5:6<br /> | 0-7-13<br /> | C vE G<br /> | Cv<br /> | C downmajor or C down<br /> |-<br /> | ru<br /> | 14:18:21<br /> | 0-8-13<br /> | C E G<br /> | C<br /> | C major or C<br /> |}<br /> <br /> 0-4-13 = C D G = C2<br /> <br /> 0-9-13 = C F G = C4<br /> <br /> 0-10-13 = C ^F G = C^4 or C(^4)<br /> <br /> 0-5-10 = C Eb Gb = Cd = Cdim<br /> <br /> 0-5-11 = C Eb ^Gb = Cd(^5)<br /> <br /> 0-5-12 = C Eb vG = Cm(v5)<br /> <br /> For a more complete list, see [[22edo Chord Names]] and [[Ups and Downs Notation #Chords and Chord Progressions]].<br /> <br /> == Just approximation ==<br /> <br /> === Selected just intervals by error ===<br /> <br /> ==== 15-odd-limit interval mappings ====<br /> <br /> The following tables show how [[15-odd-limit intervals]] are represented in 22edo. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italic''. <br /> <br /> {| class=&quot;wikitable center-1 right-2&quot;<br /> |+ Direct mapping (even if inconsistent)<br /> ! Interval, complement<br /> ! Error (abs, [[cent|¢]])<br /> |-<br /> | [[9/7]], [[14/9]]<br /> | 1.280<br /> |-<br /> | [[11/10]], [[20/11]]<br /> | 1.368<br /> |-<br /> | [[16/15]], [[15/8]]<br /> | 2.640<br /> |-<br /> | '''[[5/4]], [[8/5]]'''<br /> | '''4.496'''<br /> |-<br /> | [[7/6]], [[12/7]]<br /> | 5.856<br /> |-<br /> | '''[[11/8]], [[16/11]]'''<br /> | '''5.863'''<br /> |-<br /> | '''[[4/3]], [[3/2]]'''<br /> | '''7.136'''<br /> |-<br /> | [[15/11]], [[22/15]]<br /> | 8.504<br /> |-<br /> | [[15/14]], [[28/15]]<br /> | 10.352<br /> |-<br /> | [[6/5]], [[5/3]]<br /> | 11.631<br /> |-<br /> | '''[[8/7]], [[7/4]]'''<br /> | '''12.992'''<br /> |-<br /> | [[12/11]], [[11/6]]<br /> | 12.999<br /> |-<br /> | [[9/8]], [[16/9]]<br /> | 14.272<br /> |-<br /> | [[13/11]], [[22/13]]<br /> | 16.482<br /> |-<br /> | [[7/5]], [[10/7]]<br /> | 17.488<br /> |-<br /> | [[13/10]], [[20/13]]<br /> | 17.850<br /> |-<br /> | ''[[18/13]], [[13/9]]''<br /> | ''17.928''<br /> |-<br /> | [[10/9]], [[9/5]]<br /> | 18.767<br /> |-<br /> | [[14/11]], [[11/7]]<br /> | 18.856<br /> |-<br /> | ''[[14/13]], [[13/7]]''<br /> | ''19.207''<br /> |-<br /> | [[11/9]], [[18/11]]<br /> | 20.135<br /> |-<br /> | '''[[16/13]], [[13/8]]'''<br /> | '''22.346'''<br /> |-<br /> | [[15/13]], [[26/15]]<br /> | 24.986<br /> |-<br /> | ''[[13/12]], [[24/13]]''<br /> | ''25.064''<br /> |}<br /> <br /> {| class=&quot;wikitable center-1 right-2&quot;<br /> |+ Patent val mapping<br /> ! Interval, complement<br /> ! Error (abs, [[cent|¢]])<br /> |-<br /> | [[9/7]], [[14/9]]<br /> | 1.280<br /> |-<br /> | [[11/10]], [[20/11]]<br /> | 1.368<br /> |-<br /> | [[16/15]], [[15/8]]<br /> | 2.640<br /> |-<br /> | '''[[5/4]], [[8/5]]'''<br /> | '''4.496'''<br /> |-<br /> | [[7/6]], [[12/7]]<br /> | 5.856<br /> |-<br /> | '''[[11/8]], [[16/11]]'''<br /> | '''5.863'''<br /> |-<br /> | '''[[4/3]], [[3/2]]'''<br /> | '''7.136'''<br /> |-<br /> | [[15/11]], [[22/15]]<br /> | 8.504<br /> |-<br /> | [[15/14]], [[28/15]]<br /> | 10.352<br /> |-<br /> | [[6/5]], [[5/3]]<br /> | 11.631<br /> |-<br /> | '''[[8/7]], [[7/4]]'''<br /> | '''12.992'''<br /> |-<br /> | [[12/11]], [[11/6]]<br /> | 12.999<br /> |-<br /> | [[9/8]], [[16/9]]<br /> | 14.272<br /> |-<br /> | [[13/11]], [[22/13]]<br /> | 16.482<br /> |-<br /> | [[7/5]], [[10/7]]<br /> | 17.488<br /> |-<br /> | [[13/10]], [[20/13]]<br /> | 17.850<br /> |-<br /> | [[10/9]], [[9/5]]<br /> | 18.767<br /> |-<br /> | [[14/11]], [[11/7]]<br /> | 18.856<br /> |-<br /> | [[11/9]], [[18/11]]<br /> | 20.135<br /> |-<br /> | '''[[16/13]], [[13/8]]'''<br /> | '''22.346'''<br /> |-<br /> | [[15/13]], [[26/15]]<br /> | 24.986<br /> |-<br /> | ''[[13/12]], [[24/13]]''<br /> | ''29.482''<br /> |-<br /> | ''[[14/13]], [[13/7]]''<br /> | ''35.338''<br /> |-<br /> | ''[[18/13]], [[13/9]]''<br /> | ''36.618''<br /> |}<br /> <br /> ==== Selected 17-limit intervals ====<br /> <br /> [[File:22ed2-001e.svg|alt=alt : Your browser has no SVG support.]]<br /> <br /> ''See also: [[22edo Solfege]], [[22edo tetrachords]], [[22 EDO Chords]], [[22edo Modes]]''<br /> <br /> === Temperament measures ===<br /> The following table shows [[TE temperament measures]] (RMS normalized by the rank) of 22et. <br /> {| class=&quot;wikitable center-all&quot;<br /> ! colspan=&quot;2&quot; |<br /> ! 3-limit<br /> ! 5-limit<br /> ! 7-limit<br /> ! 11-limit<br /> ! 2.3.5.7.11.17<br /> |-<br /> ! colspan=&quot;2&quot; |Octave stretch (¢)<br /> | -2.25<br /> | -0.86<br /> | -1.80<br /> | -1.11<br /> | -1.09<br /> |-<br /> ! rowspan=&quot;2&quot; |Error<br /> ! [[TE error|absolute]] (¢)<br /> | 2.25<br /> | 2.70<br /> | 2.85<br /> | 2.90<br /> | 2.65<br /> |-<br /> ! [[TE simple badness|relative]] (%)<br /> | 4.12<br /> | 4.94<br /> | 5.23<br /> | 5.33<br /> | 4.87<br /> |}<br /> <br /> * 22et has a lower relative error than any previous ET in the 11-limit. The next ET that does better in this subgroup is 31. <br /> * 22et is most prominent in the 2.3.5.7.11.17 subgroup, and the next ET that does better in this is 46. <br /> <br /> == Rank Two Temperaments ==<br /> [[List of 22et rank two temperaments by badness]]<br /> <br /> [[List of 22et rank two temperaments by complexity]]<br /> <br /> [[List of edo-distinct 22et rank two temperaments]]<br /> <br /> Important MOSes include: <br /> <br /> * [[superpyth]] pentatonic 2L3s 44545 (13\22, 1\1)<br /> * [[superpyth]] diatonic 5L2s 1441444 (13\22, 1\1)<br /> * [[superpyth]] chromatic 5L7s 113131131313 (13\22, 1\1)<br /> * [[superpyth]] hyperchromatic 5L12s 11121121112112112 (13\22, 1\1)<br /> * [[porcupine]] 7L1s 13333333 (3\22, 1\1)<br /> * [[porcupine]] 7L8s 112121212121212 (3\22, 1\1)<br /> * [[pajara]] 2L8s 2232222322 (2\22, 1\2)<br /> * [[pajara]] 10L2s 221222221222 (2\22, 1\2)<br /> * [[orwell]] pentatonic 4L1s 55552 (5\22, 1\1)<br /> * [[orwell]] diatonic 4L5s 323232322 (5\22, 1\1)<br /> * [[orwell]] chromatic 9L4s 2122122122122 (5\22, 1\1)<br /> * [[magic]] diatonic 3L4s 1616161 (7\22, 1\1)<br /> * [[magic]] superdiatonic 3L7s 1511511511 (7\22, 1\1)<br /> * [[magic]] chromatic 3L10s 1411141114111 (7\22, 1\1)<br /> * [[magic]] mega chromatic 3L13s 1131111311113111 (7\22, 1\1)<br /> * Pathological [[magic]] enharmonic 3L16s 1112111112111112111 (7\22, 1\1)<br /> * [[hedgehog]] hexatonic 2L4s 353353 (3\22, 1\2)<br /> * [[hedgehog]] symmetric octatonic 6L2s 33233323 (3\22, 1\2)<br /> * [[hedgehog]] symmetric chromatic 8L6s 21212212121221 (3\22, 1\2)<br /> * [[astrology]] hexatonic 4L2s 434434 (4\22, 1\2)<br /> * [[astrology]] symmetric decatonic 6L4s 3133131331 (4\22, 1\2)<br /> * [[astrology]] symmetric hexadecatonic 6L10s 2112121121121211 (4\22, 1\2)<br /> * [[doublewide]] tetrad 2L2s 6565 (5\22, 1\2)<br /> * [[doublewide]] hexatonic 4L2s 515515 (5\22, 1\2)<br /> * [[doublewide]] symmetric decatonic 4L6s 4114141141 (5\22, 1\2)<br /> * [[Astrology|doublewide]] symmetric tetradecatonic 4L10s 31113113111311 (5\22, 1\2)<br /> * Pathological [[doublewide]] symmetric octokaidecatonic 4L14s 211112111211112111 (5\22, 1\2)<br /> <br /> {| class=&quot;wikitable&quot;<br /> |-<br /> ! Periods &lt;br&gt; per octave<br /> ! Period<br /> ! Generator<br /> ! Temperaments<br /> |-<br /> | 1<br /> | 22\22<br /> | 1\22<br /> | [[Sensamagic clan#Sensa|Sensa]]/chromo/ceratitid<br /> |-<br /> | 1<br /> | 22\22<br /> | 3\22<br /> | [[Porcupine]]<br /> |-<br /> | 1<br /> | 22\22<br /> | 5\22<br /> | [[Orwell]]/blair/orson<br /> |-<br /> | 1<br /> | 22\22<br /> | 7\22<br /> | [[Magic]]/telepathy<br /> |-<br /> | 1<br /> | 22\22<br /> | 9\22<br /> | [[Superpyth]]/[[Suprapyth]]<br /> |-<br /> | 2<br /> | 11\22<br /> | 1\22<br /> | [[Shrutar]]/hemipaj/comic<br /> |-<br /> | 2<br /> | 11\22<br /> | 2\22<br /> | [[Srutal]]/[[pajara]]/pajarous<br /> |-<br /> | 2<br /> | 11\22<br /> | 3\22<br /> | [[Porcupine family#Hedgehog|Hedgehog]]/[[echidna]]<br /> |-<br /> | 2<br /> | 11\22<br /> | 4\22<br /> | [[Astrology]]/[[wizard]]/[[antikythera]]<br /> |-<br /> | 2<br /> | 11\22<br /> | 5\22<br /> | [[Doublewide]]/fleetwood<br /> |-<br /> | 11<br /> | 2\22<br /> | 1\22<br /> | [[Hendecatonic]]/undeka<br /> |}<br /> <br /> == Scales ==<br /> Scales are written be steps in degrees of 22edo. [[MOS scale]]s are listed in their symmetric mode if one exists, and otherwise in the &quot;brightest&quot; mode - the mode with the highest average pitch height / the lexicographically highest mode<br /> <br /> === MOS scales ===<br /> <br /> :''See also [[22edo Modes]], [[22edo tetrachords]]<br /> <br /> * Porcupine[7] - 3334333<br /> * Porcupine[8] - 33333331<br /> * Porcupine[15] - 121212121212121<br /> * Orwell[5] - 55255<br /> * Orwell[9] - 232323232<br /> * Orwell[13] - 2122122212212<br /> * Magic[7] - 1616161<br /> * Magic[10] - 5115115111<br /> * Magic[13] - 1141114111411<br /> * Magic[16] - 3111131111311111<br /> * Magic[19] - 1112111112111112111<br /> * Superpyth[5] - pentatonic - 45454<br /> * Superpyth[7] - diatonic - 4144414<br /> * Superpyth[12] - chromatic - 313131131311<br /> * Superpyth[17] - hyperchromatic - 12111211211211121<br /> * Pajara[10] - symmetric decatonic - 2232222322<br /> * Pajara[12] - 222221222221<br /> * Hedgehog[6] - 353353<br /> * Hedgehog[8] - 33323332<br /> * Hedgehog[14] - 21212122121212<br /> * Astrology[6] - 434434<br /> * Astrology[10] - 3131331313<br /> * Astrology[16] - 2121121121211211<br /> * Doublewide[4] - 5656<br /> * Doublewide[6] - 551551<br /> * Doublewide[10] - 4141141411<br /> * Doublewide[14] - 31131113113111<br /> * Doublewide[18] - 211121111211121111<br /> <br /> === Other Scales ===<br /> <br /> * Pentachordal decatonic - Pajara[10] 4|4(2) #8 - 2232223222<br /> * Zarlino/Ptolemy diatonic, &quot;just&quot; major, Ma grama - 4324342<br /> * inverse of Zarlino/Ptolemy diatonic, natural minor - 4234243<br /> * tetrachordal major, Sa grama - 4324432<br /> * inverse of tetrachordal major, &quot;just&quot;/tetrachordal minor - 4234234<br /> * Porcupine bright major #7 - Porcupine[7] 6|0 #7 - 4333342<br /> * Porcupine bright major #6 #7 - Porcupine[7] 6|0 #6 #7 - 4333432<br /> * Porcupine bright minor #2 - Porcupine[7] 4|2 #2 4243333 (mode of bright major #7)<br /> * Porcupine dark minor #2 - Porcupine[7] 3|3 #2 4234333 (inverse of bright major #6 #7)<br /> * Porcupine bright harmonic 11th mode - Porcupine[7] 6|0 b7 4333324<br /> * Superpyth harmonic minor - Superpyth[7] 2|4 #7 - 4144171<br /> * Superpyth harmonic major - Superpyth[7] 5|1 b6 - 4414171 (inverse of harmonic minor)<br /> * Superpyth melodic minor - Superpyth[7] 5|1 b3 - 4144441<br /> * Superpyth double harmonic - Superpyth[7] 5|1 b2 b6 - 1714171<br /> * &quot;just&quot; harmonic minor - 4234252<br /> * &quot;just&quot; harmonic major - 4324252<br /> * &quot;just&quot; melodic minor - 4234342<br /> * &quot;just&quot; double harmonic - 2524252<br /> <br /> == Commas ==<br /> 22 EDO [[tempers out]] the following [[commas]]. (Note: This assumes the [[val]] {{val| 22 35 51 62 76 81 }}.)<br /> <br /> {{todo| cleanup }} &lt;!-- switch monzos to template in the following table --&gt;<br /> <br /> {| class=&quot;commatable wikitable center-all left-3 right-4 left-6&quot;<br /> |-<br /> ! [[Harmonic limit|Prime &lt;br&gt;limit]]<br /> ! [[Ratio]]&lt;ref&gt;Ratios longer than 10 digits are presented by placeholders with informative hints&lt;/ref&gt;<br /> ! [[Monzo]]<br /> ! [[Cents]]<br /> ! [[Color name]]<br /> ! Name(s)<br /> |-<br /> | 5<br /> | [[250/243]]<br /> | {{monzo| 1 -5 3 }}<br /> | 49.17<br /> | Triyo<br /> | Maximal diesis, Porcupine comma<br /> |-<br /> | 5<br /> | [[3125/3072]]<br /> | {{monzo| -10 -1 5 }}<br /> | 29.61<br /> | Laquinyo<br /> | Small diesis, Magic comma<br /> |-<br /> | 5<br /> | [[2048/2025]]<br /> | {{monzo| 11 -4 -2 }}<br /> | 19.55<br /> | Sagugu<br /> | Diaschisma<br /> |-<br /> | 5<br /> | [[2109375/2097152|(14 digits)]]<br /> | {{monzo| -21 3 7 }}<br /> | 10.06<br /> | Lasepyo<br /> | [[Semicomma]], Fokker comma<br /> |-<br /> | 5<br /> | &lt;abbr title=&quot;4294967296/4271484375&quot;&gt;(20 digits)&lt;/abbr&gt;<br /> | {{monzo| 32 -7 -9 }}<br /> | 9.49<br /> | Sasa-tritrigu<br /> | [[Escapade comma]]<br /> |-<br /> | 5<br /> | &lt;abbr title=&quot;9010162353515625/9007199254740992&quot;&gt;(32 digits)&lt;/abbr&gt;<br /> | {{monzo| -53 10 16 }}<br /> | 0.57<br /> | Quadla-quadquadyo<br /> | [[Kwazy]]<br /> |-<br /> | 7<br /> | [[50/49]]<br /> | {{monzo| 1 0 2 -2 }}<br /> | 34.98<br /> | Biruyo<br /> | Tritonic diesis, Jubilisma<br /> |-<br /> | 7<br /> | [[64/63]]<br /> | {{monzo| 6 -2 0 -1 }}<br /> | 27.26<br /> | Ru<br /> | Septimal comma, Archytas' comma, Leipziger Komma<br /> |-<br /> | 7<br /> | [[875/864]]<br /> | {{monzo| -5 -3 3 1 }}<br /> | 21.90<br /> | Zotriyo<br /> | Keema<br /> |-<br /> | 7<br /> | [[2430/2401]]<br /> | {{monzo| 1 5 1 -4 }}<br /> | 20.79<br /> | Quadru-ayo<br /> | Nuwell<br /> |-<br /> | 7<br /> | [[245/243]]<br /> | {{monzo| 0 -5 1 2 }}<br /> | 14.19<br /> | Zozoyo<br /> | Sensamagic<br /> |-<br /> | 7<br /> | [[1728/1715]]<br /> | {{monzo| 6 3 -1 -3 }}<br /> | 13.07<br /> | Triru-agu<br /> | Orwellisma, Orwell comma<br /> |-<br /> | 7<br /> | [[225/224]]<br /> | {{monzo| -5 2 2 -1 }}<br /> | 7.71<br /> | Ruyoyo<br /> | Septimal kleisma, Marvel comma<br /> |-<br /> | 7<br /> | [[10976/10935]]<br /> | {{monzo| 5 -7 -1 3 }}<br /> | 6.48<br /> | Trizo-agu<br /> | Hemimage<br /> |-<br /> | 7<br /> | [[6144/6125]]<br /> | {{monzo| 11 1 -3 -2 }}<br /> | 5.36<br /> | Saruru-atrigu<br /> | Porwell<br /> |-<br /> | 7<br /> | [[65625/65536]]<br /> | {{monzo| -16 1 5 1 }}<br /> | 2.35<br /> | Lazoquinyo<br /> | Horwell<br /> |-<br /> | 7<br /> | &lt;abbr title=&quot;420175/419904&quot;&gt;(12 digits)&lt;/abbr&gt;<br /> | {{monzo| -6 -8 2 5 }}<br /> | 1.12<br /> | Quinzo-ayoyo<br /> | [[Wizma]]<br /> |-<br /> | 11<br /> | [[99/98]]<br /> | {{monzo| -1 2 0 -2 1 }}<br /> | 17.58<br /> | Loruru<br /> | Mothwellsma<br /> |-<br /> | 11<br /> | [[100/99]]<br /> | {{monzo| 2 -2 2 0 -1 }}<br /> | 17.40<br /> | Luyoyo<br /> | Ptolemisma<br /> |-<br /> | 11<br /> | [[121/120]]<br /> | {{monzo| -3 -1 -1 0 2 }}<br /> | 14.37<br /> | Lologu<br /> | Biyatisma<br /> |-<br /> | 11<br /> | [[176/175]]<br /> | {{monzo| 4 0 -2 -1 1 }}<br /> | 9.86<br /> | Lorugugu<br /> | Valinorsma<br /> |-<br /> | 11<br /> | [[896/891]]<br /> | {{monzo| 7 -4 0 1 -1 }}<br /> | 9.69<br /> | Saluzo<br /> | Pentacircle<br /> |-<br /> | 11<br /> | [[65536/65219]]<br /> | {{monzo| 16 0 0 -2 -3 }}<br /> | 8.39<br /> | Satrilu-aruru<br /> | Orgonisma<br /> |-<br /> | 11<br /> | [[385/384]]<br /> | {{monzo| -7 -1 1 1 1 }}<br /> | 4.50<br /> | |Lozoyo<br /> | Keenanisma<br /> |-<br /> | 11<br /> | [[540/539]]<br /> | {{monzo| 2 3 1 -2 -1 }}<br /> | 3.21<br /> | Lururuyo<br /> | Swetisma<br /> |-<br /> | 11<br /> | [[4000/3993]]<br /> | {{monzo| 5 -1 3 0 -3 }}<br /> | 3.03<br /> | Triluyo<br /> | Wizardharry<br /> |-<br /> | 11<br /> | [[9801/9800]]<br /> | {{monzo| -3 4 -2 -2 2 }}<br /> | 0.18<br /> | Bilorugu<br /> | Kalisma, Gauss' comma<br /> |-<br /> | 13<br /> | [[91/90]]<br /> | {{monzo| -1 -2 -1 1 0 1 }}<br /> | 19.13<br /> | Thozogu<br /> | Superleap<br /> |-<br /> | 31<br /> | [[125/124]]<br /> | {{monzo| -2 0 3 0 0 0 0 0 0 0 -1 }}<br /> | 13.91<br /> | Thiwutriyo<br /> | Twizzler<br /> |}<br /> &lt;references/&gt;<br /> <br /> == Staff Notation ==<br /> <br /> ===How to Notate 22edo in Sagittal===<br /> <br /> When 22edo is treated as generated by a cycle of its fifths, the naturals F C G D A E B represent a chain of those 13\22 fifths; consequently, the whole tone comes out to four degrees and the apotome (pythagorean sharp/flat) comes out to three degrees. Three pairs of sagittal symbols, dividing that apotome into three parts, are all that is necessary, and offer plenty of enharmonic equivalents:<br /> <br /> [[File:22edo.png|alt=22edo.png|22edo.png]]<br /> <br /> This notation is consistent with Sagittal's notation of 5-limit JI harmony: &quot;major&quot; 3rds and 6ths appear as (super)pythagorean intervals flattened by a syntonic comma.<br /> <br /> The division of the apotome into three syntonic commas also indicates 22's tempering out of the [[250/243|porcupine comma]] (which is equivalent to three syntonic commas minus a Pythagorean apotome).<br /> <br /> We also have, from the appendix to [[The Sagittal Songbook]] by [[JacobBarton|Jacob A. Barton]], this diagram of how to notate 22-EDO in the Revo flavor of Sagittal:<br /> <br /> [[File:22edo Sagittal.png|800px]]<br /> <br /> ===How to Notate 22edo with Ups and Downs===<br /> <br /> Treating [[Ups_and_Downs_Notation|ups and downs]] as &quot;fused&quot; with sharps and flats, and never appearing separately:<br /> <br /> [[File:Tibia_22edo_ups_and_downs_guide_1.png|alt=Tibia 22edo ups and downs guide 1.png|800x147px|Tibia 22edo ups and downs guide 1.png]]<br /> <br /> Treating ups and downs as independent of sharps and flats, and sometimes appearing separately:<br /> <br /> [[File:Tibia_22edo_ups_and_downs_guide_2.png|alt=Tibia 22edo ups and downs guide 2.png|800x150px|Tibia 22edo ups and downs guide 2.png]]<br /> <br /> A D downmajor scale with mandatory accidentals (no key signature), with minimal accidentals (only when needed to override the key signature), and with independent ups and downs.<br /> <br /> [[File:Tibia_22edo_guide_D_major.png|alt=Tibia 22edo guide D major.png|800x68px|Tibia 22edo guide D major.png]]<br /> <br /> Paul Erlich's &quot;Tibia&quot; in G, with independent ups and downs:<br /> <br /> [[File:Tibia_in_G_for_the_book-1.png|alt=Tibia in G for the book-1.png|800x956px|Tibia in G for the book-1.png]]<br /> <br /> [[File:Tibia_in_G_for_the_book-2.png|alt=Tibia in G for the book-2.png|800x889px|Tibia in G for the book-2.png]]<br /> <br /> ==Internal links==<br /> &lt;ul&gt;&lt;li&gt;[[William_Lynch's_Thoughts_on_Septimal_Harmony_and_22_EDO|William Lynch's Thoughts on Septimal Harmony and 22 EDO]]&lt;/li&gt;&lt;/ul&gt;<br /> <br /> ==External links==<br /> &lt;ul&gt;&lt;li&gt;[http://lumma.org/tuning/erlich/erlich-decatonic.pdf Erlich, Paul, ''Tuning, Tonality, and Twenty-Two Tone Temperament'']&lt;/li&gt;&lt;li&gt;[http://porcupinemusic.weebly.com/ &quot;Porcupine Music&quot; - Website Focused on the Development of 22 EDO music]&lt;/li&gt;&lt;/ul&gt;<br /> <br /> ==References==<br /> *Barbour, James Murray, ''Tuning and temperament, a historical survey'', East Lansing, Michigan State College Press, 1953 [c1951]<br /> <br /> *Bosanquet, R.H.M. [http://www.webcitation.org/5kjJcrhEx ''On the Hindoo division of the octave, with additions to the theory of higher orders''], Proceedings of the Royal Society of London vol. 26, 1879, pp. 272-284. Reproduced in Tagore, Sourindro Mohun, ''Hindu Music from Various Authors'', Chowkhamba Sanskrit Series, Varanasi, India, 1965<br /> <br /> ==Music==<br /> <br /> * [https://soundcloud.com/overtoneshock/dose-of-familiarityode-to-microtonality-22-edo-studio-version Stephen Weigel · Dose Of Familiarity/Ode to Microtonality]<br /> * [https://soundcloud.com/metaclown/couples-therapy Couples' Therapy] by metaclown<br /> * [http://soonlabel.com/xenharmonic/archives/1145 Canon 2 in 1 upon a ground (22edo)] by [[Claudi Meneghin]]<br /> * [http://www.tallkite.com/words/Tibia.mp3 TIBIA] by [[Paul Erlich]]<br /> ** Sagittal score of Tibia, [[:File:TIBIA.pdf|in F||\]] or [[:File:tibia_in_g.pdf|in G]] (contains errors in measures 9, 19 and 20)<br /> ** Ups and Downs score of Tibia in G [[:File:Tibia_in_G_CORRECTED-1.png|page 1]] [[:File:Tibia_in_G_CORRECTED-2.png|page 2]] (no errors)<br /> * [https://web.archive.org/web/20070928093239/http://66.98.148.43/~xenharmo/mp3/erlich/glassic.mp3 Glassic] by Paul Erlich and [[Ara Sarkissian]]<br /> * [http://lumma.org/tuning/erlich/decatonic-swing.mp3 Decatonic Swing] by Paul Erlich and Ara Sarkissian (jazz)<br /> * [http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12-22hexachordal%20Dirge.mp3 12-22hexachordal Dirge] by [[Joel Grant Taylor]]<br /> * [https://soundcloud.com/jdfreivald/chord-sequence-in-paul-erlichs Chord sequence in Paul Erlich's 22 EDO decatonic major] by [[Jake Freivald]]<br /> * [https://soundcloud.com/jdfreivald/porcupine-comma-pump Porcupine Comma Pump] by [[Jake_Freivald|Jake Freivald]]<br /> * [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%20Dragged%20By%20a%20Storm%20Across%20the%20Desert%20Years.mp3 Dragged by a Storm Across the Desert Years] by * [[Igliashon Jones]] (synth with electric guitar)<br /> * [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2022-Numerology.mp3 Numerology] by Iglashion Jones (progressive metal)<br /> * [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2022-Revenge%20of%20the%20Inorganic%20Compounds.mp3 Revenge of the inorganic compounds] by Iglashion Jones (progressive metal)<br /> * [http://chrisvaisvil.com/?p=267 My Crazy Aunt Sophie] [http://micro.soonlabel.com/22-ET/22edo-piano-my-crazy-aunt-sophie.mp3 play] by [[Chris Vaisvil]]. Blatantly xenharmonic piano.<br /> * [http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/17%20-%2017.%2022%20octave.mp3 Comets Over Flatland 17] by [[Randy Winchester]]<br /> * [http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3 Night on Porcupine Mountain] Mussorgsky-Smith<br /> * [http://www.youtube.com/watch?v=lO5xSjIHyMg Paul Erlich 22-Equal Guitar Improvisation Shredfest Insanity] - youtube<br /> * [http://www.youtube.com/watch?v=WMtp9Wk0tO0 Improvisation in 22-equal temperament], Mike Battaglia - youtube<br /> * Boxwood Forest, Dream Tone, The Eternal Sleep, Sunday Pipes, Twisted Clowns - [http://www.angelfire.com/mo/oljare/midicomp.html MIDI files] by Mats Öljare<br /> ** [[:File:sunday3.pdf|Sagittal score of Sunday Pipes]]<br /> * [http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3 Phobos Light] by Chris Vaisvil in Hedgehog[14] [[hedgehog14|tuned]] to 22edo.<br /> * ''[http://micro.soonlabel.com/22-ET/20120716_theorbo_22edo.mp3 The Capture and Release of the Fairy]'' by [[Chris Vaisvil]] =&amp;gt; [http://chrisvaisvil.com/?p=2494 blog post presentation]<br /> * ''[http://www.youtube.com/watch?v=oNJr1YOOqF8 Yak Butter]'' by The Stern Brocot Band, 1L6s MOS, compressed period/generator<br /> * ''[http://micro.soonlabel.com/22-ET/20120726-from-the-sky-islands-they-came.mp3 From the Sky Islands They Came]'' by [[Chris Vaisvil]] =&amp;gt; [http://chrisvaisvil.com/?p=2523 blog post presentation]<br /> * [http://micro.soonlabel.com/22-ET/20120616-12-22h.scl-smoke-filled-bar.mp3 Smoke Filled Bar] by [[Chris Vaisvil]] =&amp;gt; [http://chrisvaisvil.com/smoke-filled-bar/ blog presentation]<br /> * [http://micro.soonlabel.com/gene_ward_smith/Others/Sultan/__Recurring_Mimosa_by_Redrick_Sultan.mp3 Recurring Mimosa] by [https://soundcloud.com/redrick-sultan/recurring-mimosa Redrick Sultan]<br /> * The Saharan Pump by Chris Vaisvil [http://chrisvaisvil.com/the-saharan-pump-22-edo-rock/ blog post]<br /> * [http://micro.soonlabel.com/22-ET/20150910_22edo.mp3 22 edo electric guitar duet] by [[Chris_Vaisvil|Chris Vaisvil]]<br /> * [https://soundcloud.com/gareth-hearne/mass-in-22edo-sanctus Mass in 22edo - Sanctus] by [[Gareth_Hearne|Gareth Hearne]]<br /> * [https://soundcloud.com/gareth-hearne/mass-in-22edo-agnus-dei Mass in 22edo - Agnus Dei] by Gareth Hearne<br /> * [http://chrisvaisvil.com/for-the-sunset/ For the Sunset] - 22 edo rock ensemble by [[Chris_Vaisvil|Chris Vaisvil]]<br /> * [https://drive.google.com/drive/folders/0BwsXD8q2VCYUNGZJOGRzSVdhRjg Rose, liz, printemps, verdure] by Alex Ness (in 22edo with stretched octaves)<br /> * [https://www.youtube.com/watch?v=jagxI__W-Mg Palinkalin Viharo (Flowers in the Mist)] by Jake Huryn ([https://drive.google.com/file/d/0BwJHTddN0-rdUFdwMEtfYnFJZ0E/view Score]); uses 11edo machine[6], 22edo orwell[9]<br /> * [https://youtu.be/0NtKxk8Aaz0 Little Brother by Diamond Doll (xen-pop)]<br /> * [https://www.youtube.com/watch?v=wYgGP50D4bA Octatonic Groove (22 EDO version) by Ray Perlner]<br /> <br /> === By Andrew Heathwaite ===<br /> * [http://soundclick.com/share?songid=8839058 where words are said to mean] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+wherewordsaresaidtomean.mp3 play] by [[Andrew Heathwaite]], a setting of a text by Herbert Brün to a 22-tone row, thrice repeated. This &amp;amp; the following pieces by Andrew are for 22-tone guitar &amp;amp; voice.<br /> * [http://soundclick.com/share?songid=9101704 I've come with a bucket of roses] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+ivecomewithabucketofroses.mp3 play] (orwell-9: 3 2 3 2 3 2 3 2 2).<br /> * [http://soundclick.com/share?songid=9101705 one drop of rain] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+onedropofrain.mp3 play] (orwell-9).<br /> * [http://soundclick.com/share?songid=8839060 being a] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+beinga.mp3 play] (porcupine-8: 3 1 3 3 3 3 3).<br /> * [http://soundclick.com/share?songid=8839071 my own house] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+myownhouse.mp3 play] (a pelog-flavored subset of orwell-9: 3 2 7 3 7).<br /> <br /> === By Brendan Byrnes ===<br /> * [https://soundcloud.com/ilevens/tracks tracks of ILEVENS] - all their tracks on SoundCloud are tagged with 22edo<br /> * [http://www.youtube.com/watch?v=qHHv3mwJTlg Short piece and demonstration] (video) by [http://brendanbyrnes.com/ Brendan Byrnes] (electric guitar)<br /> * [http://micro.soonlabel.com/gene_ward_smith/Others/Byrnes/Brendan%20Byrnes%20-%2022%20EDO%20Guitar%20Etude.mp3 22 EDO Guitar Etude] by [http://brendanbyrnes.bandcamp.com/ Brendan Byrnes]<br /> * [http://micro.soonlabel.com/gene_ward_smith/Others/Byrnes/Brendan%20Byrnes%20-%20Llurion.mp3 Llurion] by [http://brendanbyrnes.bandcamp.com/track/llurion Brendan Byrnes]<br /> * [https://youtu.be/XS6wxEtttU8 &quot;Unreachable Island&quot;] (from his 2020 album &quot;Realism&quot;)<br /> * [https://youtu.be/U5BZ2KncKs8 &quot;Hysteria&quot;] (from his 2017 album &quot;Neutral Paradise&quot;)<br /> === By Johann alias Circular17 ===<br /> * [https://d.tube/v/circular17/QmWDXi7hgSwZF9kRUUXUkCjEz8BMepoxehM9mRhUecTubQ Good devil]<br /> * [https://d.tube/v/circular17/QmazZ9NBed2LoJb1bauNuEsAztah6Jir2VVrX2wiG6rwVm Wave from the past]<br /> <br /> === By MÜÜR ===<br /> * [https://www.youtube.com/watch?v=Qgb59snzMII Nenio reala] by [https://muur-proj.web.app/ MÜÜR]<br /> * [https://www.youtube.com/watch?v=MuoZQqvR-gc Imzadi]<br /> * [https://www.youtube.com/watch?v=sK8lVDyvakE Imzadi (alie)]<br /> <br /> === By Sevish ===<br /> * [http://www.archive.org/download/Sevish_-_Golden_Hour/Sevish_-_03_-_Dirty_Drummer_vbr.mp3 Dirty Drummer]<br /> * [http://www.archive.org/download/Sevish_-_Golden_Hour/Sevish_-_12_-_Ganymede_vbr.mp3 Ganymede] (doesn't sound [[The Xen|that xen]], but it's in 22-edo)<br /> * [http://www.archive.org/download/HumanAstronomy/03Sevish-Ambrosia.mp3 Ambrosia]<br /> * [https://youtu.be/l9wINwlgxRU &quot;Gleam&quot;] (from his 2017 album &quot;Harmony Hacker&quot;)<br /> [[Category:22edo| ]] <br /> [[Category:Equal divisions of the octave]]<br /> [[Category:Listen]]<br /> [[Category:Theory]]<br /> [[Category:Twentuning]]<br /> [[Category:Alpharabian]]<br /> [[Category:Quartismic]]<br /> [[Category:Zeta]]</div> Keenan Pepper