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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | __FORCETOC__ |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | Below are some subgroups and temperaments for them. Obviously, no attempt has been made at completeness; attention is focused on subgroups containing interesting chords. The reader may also want to consult the page on [[Chromatic_pairs|Chromatic pairs]]. |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2016-09-23 16:44:41 UTC</tt>.<br>
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| : The original revision id was <tt>593183188</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| |
| <h4>Original Wikitext content:</h4>
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| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]]
| |
| Below are some subgroups and temperaments for them. Obviously, no attempt has been made at completeness; attention is focused on subgroups containing interesting chords. The reader may also want to consult the page on [[Chromatic pairs]]. | |
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| =2.3.7= | | =2.3.7= |
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| ==[[Semaphore and Godzilla|Semaphore]]== | | ==[[Semaphore_and_Godzilla|Semaphore]]== |
| Comma: 49/48 | | Comma: 49/48 |
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| [[Lp tuning|POL2 generator]]: ~8/7~7/6 = 250.385 | | [[Lp_tuning|POL2 generator]]: ~8/7~7/6 = 250.385 |
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| | [[Gencom|Gencom]]: [2 8/7; 49/48] |
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| [[Gencom]]: [2 8/7; 49/48]
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| Gencom mapping: [<1 2 0 3|, <0 -2 0 -1|] | | Gencom mapping: [<1 2 0 3|, <0 -2 0 -1|] |
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| Map: [<1 2 3|, <0 -2 -1|] | | Map: [<1 2 3|, <0 -2 -1|] |
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| EDOs: 5, 14, 19, 24, 67c, 91c | | EDOs: 5, 14, 19, 24, 67c, 91c |
| [[Tp tuning#T2%20tuning|RMS error]]: 2.523 cents
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| ==Archy== | | [[Tp_tuning#T2 tuning|RMS error]]: 2.523 cents |
| Archy can be thought of as "no-5's [[dominant]]" or "no-5's [[superpyth]]". The name comes from the fact that it tempers out 64/63, the Archytas comma. | | |
| | ==Archy== |
| | Archy can be thought of as "no-5's [[dominant|dominant]]" or "no-5's [[Superpyth|superpyth]]". The name comes from the fact that it tempers out 64/63, the Archytas comma. |
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| Comma: 64/63 | | Comma: 64/63 |
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| [[Lp tuning|POL2 generator]]: ~3/2 = 709.321 | | [[Lp_tuning|POL2 generator]]: ~3/2 = 709.321 |
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| Gencom: [2 3/2; 64/63] | | Gencom: [2 3/2; 64/63] |
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| Gencom mapping: [<1 1 0 4|, <0 1 0 -2|] | | Gencom mapping: [<1 1 0 4|, <0 1 0 -2|] |
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| Map: [<1 2 2|, <0 -1 2|] | | Map: [<1 2 2|, <0 -1 2|] |
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| EDOs: 5, 12, 17, 22, 27, 137bc | | EDOs: 5, 12, 17, 22, 27, 137bc |
| [[Tp tuning#T2%20tuning|RMS error]]: 1.856 cents
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| ==[[Slendric]]== | | [[Tp_tuning#T2 tuning|RMS error]]: 1.856 cents |
| | |
| | ==[[Slendric|Slendric]]== |
| Comma: 1029/1024 | | Comma: 1029/1024 |
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| [[Lp tuning|POL2 generator]]: ~8/7 = 233.688 | | [[Lp_tuning|POL2 generator]]: ~8/7 = 233.688 |
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| Gencom: [2 8/7; 1029/1024] | | Gencom: [2 8/7; 1029/1024] |
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| Gencom mapping: [<1 1 0 3|, <0 3 0 -1|] | | Gencom mapping: [<1 1 0 3|, <0 3 0 -1|] |
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| Map: [<1 1 3|, <0 3 -1|] | | Map: [<1 1 3|, <0 3 -1|] |
| | |
| EDOs: 5, 21, 26, 31, 36, 77, 113, 190 | | EDOs: 5, 21, 26, 31, 36, 77, 113, 190 |
| [[Tp tuning#T2%20tuning|RMS error]]: 0.3202 cents
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| ==Lee== | | [[Tp_tuning#T2 tuning|RMS error]]: 0.3202 cents |
| | |
| | ==Lee== |
| Comma: 177147/175616 | | Comma: 177147/175616 |
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| [[Lp tuning|POL2 generator]]: ~81/56 = 633.525 | | [[Lp_tuning|POL2 generator]]: ~81/56 = 633.525 |
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| Map: [<1 0 -3|, <0 3 11|] | | Map: [<1 0 -3|, <0 3 11|] |
| | |
| EDOs: 17, 36, 89, 125, 161, 358, 519b | | EDOs: 17, 36, 89, 125, 161, 358, 519b |
| [[Tp tuning#T2%20tuning|RMS error]]: 0.3519 cents
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| ==Skwares== | | [[Tp_tuning#T2 tuning|RMS error]]: 0.3519 cents |
| | |
| | ==Skwares== |
| Comma: 19683/19208 | | Comma: 19683/19208 |
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| [[Lp tuning|POL2 generator]]: ~9/7 = 425.365 cents | | [[Lp_tuning|POL2 generator]]: ~9/7 = 425.365 cents |
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| Map: [<1 3 6|, <0 -4 -9|] | | Map: [<1 3 6|, <0 -4 -9|] |
| | |
| EDOs: 14, 17, 31, 48, 79, 189b, 268bc, 347bc | | EDOs: 14, 17, 31, 48, 79, 189b, 268bc, 347bc |
| [[Tp tuning#T2%20tuning|RMS error]]: 1.149 cents
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| =2.3.11= | | [[Tp_tuning#T2 tuning|RMS error]]: 1.149 cents |
| | |
| | =2.3.11= |
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| ==Neuter== | | ==Neuter== |
| Neuter can be thought of as the 2.3.11 version of either [[mohajira]] or [[maqamic]], as well as suhajira (further down on this page) and ringo. Among other things, it is the temperament optimizing the [[neutral tetrad]]. | | Neuter can be thought of as the 2.3.11 version of either [[Mohajira|mohajira]] or [[maqamic|maqamic]], as well as suhajira (further down on this page) and ringo. Among other things, it is the temperament optimizing the [[neutral_tetrad|neutral tetrad]]. |
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| Comma: 243/242 | | Comma: 243/242 |
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| [[Lp tuning|POL2 generator]]: ~11/9 = 350.525 | | [[Lp_tuning|POL2 generator]]: ~11/9 = 350.525 |
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| Gencom: [2 11/9; 243/242] | | Gencom: [2 11/9; 243/242] |
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| Gencom mapping: [<1 1 0 0 2|, <0 2 0 0 5|] | | Gencom mapping: [<1 1 0 0 2|, <0 2 0 0 5|] |
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| Map: [<1 1 2|, <0 2 5|] | | Map: [<1 1 2|, <0 2 5|] |
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| EDOs: 7, 10, 17, 24, 41, 65, 89, 202, 291, 380 | | EDOs: 7, 10, 17, 24, 41, 65, 89, 202, 291, 380 |
| [[Tp tuning#T2%20tuning|RMS error]]: 0.3021 cents
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| [[xenharmonic/neutraltet7|Seven note albitonic scale]] | | [[Tp_tuning#T2 tuning|RMS error]]: 0.3021 cents |
| [[xenharmonic/neutraltet10|Ten note chromatic scale]]
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| [[xenharmonic/neutraltet17|Seventeen note mega chromatic scale]] | | [[neutraltet7|Seven note albitonic scale]] |
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| =2.3.5.11=
| | [[neutraltet10|Ten note chromatic scale]] |
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| ==Porkypine== | | [[neutraltet17|Seventeen note mega chromatic scale]] |
| | |
| | =2.3.5.11= |
| | |
| | ==Porkypine== |
| Commas: 55/54, 100/99 | | Commas: 55/54, 100/99 |
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| [[Lp tuning|POL2 generator]]: ~10/9 = 164.078 | | [[Lp_tuning|POL2 generator]]: ~10/9 = 164.078 |
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| Gencom: [2 10/9; 55/54, 100/99] | | Gencom: [2 10/9; 55/54, 100/99] |
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| Gencom mapping: [<1 2 3 0 4|, <0 -3 -5 0 -4|] | | Gencom mapping: [<1 2 3 0 4|, <0 -3 -5 0 -4|] |
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| Map: [<1 2 3 4|, <0 -3 -5 -4|] | | Map: [<1 2 3 4|, <0 -3 -5 -4|] |
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| EDOs: 7, 15, 22, 37, 73cd, 95cd, 117bcd | | EDOs: 7, 15, 22, 37, 73cd, 95cd, 117bcd |
| [[Tp tuning#T2%20tuning|RMS error]]: 2.287 cents
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| ==Mohaha== | | [[Tp_tuning#T2 tuning|RMS error]]: 2.287 cents |
| | |
| | ==Mohaha== |
| Commas: 81/80, 121/120 | | Commas: 81/80, 121/120 |
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| [[Lp tuning|POL2 generator]]: ~11/9 = 348.094 | | [[Lp_tuning|POL2 generator]]: ~11/9 = 348.094 |
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| Gencom: [2 11/9; 81/80 121/120] | | Gencom: [2 11/9; 81/80 121/120] |
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| Gencom mapping: [<1 1 0 0 2|, <0 2 8 0 5|] | | Gencom mapping: [<1 1 0 0 2|, <0 2 8 0 5|] |
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| Map: [<1 1 0 2|, <0 2 8 5|] | | Map: [<1 1 0 2|, <0 2 8 5|] |
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| EDOs: 7, 10, 17, 24, 31, 55, 69d, 100d, 131bd | | EDOs: 7, 10, 17, 24, 31, 55, 69d, 100d, 131bd |
| [[Tp tuning#T2%20tuning|RMS error]]: 1.392 cents
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| ===Music=== | | [[Tp_tuning#T2 tuning|RMS error]]: 1.392 cents |
| [[http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/mohaha10ping2.mp3|Mohaha10ping2]] by [[Billy Stiltner]]
| | |
| | ===Music=== |
| | [http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/mohaha10ping2.mp3 Mohaha10ping2] by [[Billy_Stiltner|Billy Stiltner]] |
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| =2.3.7.11= | | =2.3.7.11= |
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| ==Ennea== | | ==Ennea== |
| Commas: 41503/41472, 43923/43904 | | Commas: 41503/41472, 43923/43904 |
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| [[Lp tuning|POL2 generator]]: ~99/98 = 17.6258 | | [[Lp_tuning|POL2 generator]]: ~99/98 = 17.6258 |
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| Gencom: [2 99/98; 41503/41472, 43923/43904] | | Gencom: [2 99/98; 41503/41472, 43923/43904] |
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| Gencom mapping: [<1 14/9 0 25/9 31/9|, <0 2 0 2 1|] | | Gencom mapping: [<1 14/9 0 25/9 31/9|, <0 2 0 2 1|] |
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| Sval map: [<9 0 11 24|, <0 2 2 1|] | | Sval map: [<9 0 11 24|, <0 2 2 1|] |
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| EDOs: 54, 63, 68, 72, 135, 342, 477, 525, 613, 681, 749, 817, 2159bcd, 3336bcd, 4153bcd | | EDOs: 54, 63, 68, 72, 135, 342, 477, 525, 613, 681, 749, 817, 2159bcd, 3336bcd, 4153bcd |
| [[Tp tuning#T2%20tuning|RMS error]]: 0.0383 cents
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| ==Supra== | | [[Tp_tuning#T2 tuning|RMS error]]: 0.0383 cents |
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| | ==Supra== |
| Commas: 64/63, 99/98 | | Commas: 64/63, 99/98 |
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| [[POTE tuning|POTE generator]]: ~3/2 = 707.192 | | [[POTE_tuning|POTE generator]]: ~3/2 = 707.192 |
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| Gencom: [2 3/2; 64/63 99/98] | | Gencom: [2 3/2; 64/63 99/98] |
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| Gencom mapping: [<1 1 0 4 7|, <0 1 0 -2 -6|] | | Gencom mapping: [<1 1 0 4 7|, <0 1 0 -2 -6|] |
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| Sval map: [<1 0 6 13|, <0 1 -2 -6|] | | Sval map: [<1 0 6 13|, <0 1 -2 -6|] |
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| EDOs: 5, 12, 17, 39c, 56c | | EDOs: 5, 12, 17, 39c, 56c |
| [[Tp tuning#T2%20tuning|RMS error]]: 1.977 cents
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| ==Skwares== | | [[Tp_tuning#T2 tuning|RMS error]]: 1.977 cents |
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| | ==Skwares== |
| Commas: 99/98, 243/242 | | Commas: 99/98, 243/242 |
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| [[POTE tuning|POTE generator]]: ~9/7 = 425.244 | | [[POTE_tuning|POTE generator]]: ~9/7 = 425.244 |
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| Gencom: [2 9/7; 99/98 243/242] | | Gencom: [2 9/7; 99/98 243/242] |
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| Gencom mapping: [<1 3 0 6 7|, <0 -4 0 -9 -10]] | | Gencom mapping: [<1 3 0 6 7|, <0 -4 0 -9 -10]] |
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| Sval map: [<1 3 6 7|, <0 -4 -9 -10|] | | Sval map: [<1 3 6 7|, <0 -4 -9 -10|] |
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| EDOs: 14, 17, 31, 48, 79, 127, 206bcd | | EDOs: 14, 17, 31, 48, 79, 127, 206bcd |
| [[Tp tuning#T2%20tuning|RMS error]]: 1.099 cents
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| ==Hemif== | | [[Tp_tuning#T2 tuning|RMS error]]: 1.099 cents |
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| | ==Hemif== |
| Commas: 243/242, 896/891 | | Commas: 243/242, 896/891 |
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| Line 160: |
Line 186: |
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| Gencom: [2 11/9; 243/242 896/891] | | Gencom: [2 11/9; 243/242 896/891] |
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| Gencom mapping: [<1 1 0 -1 2|, <0 2 0 13 5|] | | Gencom mapping: [<1 1 0 -1 2|, <0 2 0 13 5|] |
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| Sval map: [<1 1 -1 2|, <0 2 13 5|] | | Sval map: [<1 1 -1 2|, <0 2 13 5|] |
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| EDOs: 7, 17, 41, 58, 99d | | EDOs: 7, 17, 41, 58, 99d |
| [[Tp tuning#T2%20tuning|RMS error]]: 0.6108 cents
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| ==Bleu== | | [[Tp_tuning#T2 tuning|RMS error]]: 0.6108 cents |
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| | ==Bleu== |
| Commas: 99/98, 864/847 | | Commas: 99/98, 864/847 |
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| Line 172: |
Line 201: |
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| Map: [<1 1 2 3|, <0 5 7 4|] | | Map: [<1 1 2 3|, <0 5 7 4|] |
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| EDOs: 9, 17, 43, 60c | | EDOs: 9, 17, 43, 60c |
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| RMS error: 1.829 cents | | RMS error: 1.829 cents |
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| =2.3.7.11.13= | | =2.3.7.11.13= |
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| ==Suhajira== | | ==Suhajira== |
| Commas: 64/63, 78/77, 144/143 | | Commas: 64/63, 78/77, 144/143 |
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| Gencom: [2 11/9; 64/63 78/77 144/143] | | Gencom: [2 11/9; 64/63 78/77 144/143] |
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| Gencom map: [<1 1 0 4 2 4|, <0 2 0 -4 5 -1|] | | Gencom map: [<1 1 0 4 2 4|, <0 2 0 -4 5 -1|] |
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| [[Tp tuning|POT2 generator]]: ~11/9 = 353.775 | | [[Tp_tuning|POT2 generator]]: ~11/9 = 353.775 |
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| Map: [<1 1 4 2 4|, <0 2 -4 5 -1|] | | Map: [<1 1 4 2 4|, <0 2 -4 5 -1|] |
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| EDOs: 7, 10, 17, 44d, 61cd, 78cd | | EDOs: 7, 10, 17, 44d, 61cd, 78cd |
| [[Tp tuning#T2%20tuning|RMS error]]: 1.953 cents
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| ==Hemif== | | [[Tp_tuning#T2 tuning|RMS error]]: 1.953 cents |
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| | ==Hemif== |
| Commas: 144/143, 243/242, 364/363 | | Commas: 144/143, 243/242, 364/363 |
| Related temperament: [[xenharmonic/Breedsmic temperaments|Hemififths]], namo
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| [[Tp tuning|POT2 generator]]: ~11/9 = 351.691 | | Related temperament: [[Breedsmic_temperaments|Hemififths]], namo |
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| | [[Tp_tuning|POT2 generator]]: ~11/9 = 351.691 |
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| | [[Gencom|Gencom]]: [2 11/9; 144/143 243/242 364/363] |
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| [[Gencom]]: [2 11/9; 144/143 243/242 364/363]
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| Gencom map: [<1 1 0 -1 2 4|, <0 2 0 13 5 -1|] | | Gencom map: [<1 1 0 -1 2 4|, <0 2 0 13 5 -1|] |
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| Map: [<1 1 -1 2 4|, <0 2 13 5 -1|] | | Map: [<1 1 -1 2 4|, <0 2 13 5 -1|] |
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| EDOs: 7, 10, 17, 24, 41, 58 | | EDOs: 7, 10, 17, 24, 41, 58 |
| [[Tp tuning#T2%20tuning|RMS error]]: 0.7167 cents
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| ==Skwares== | | [[Tp_tuning#T2 tuning|RMS error]]: 0.7167 cents |
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| | ==Skwares== |
| Commas: 78/77, 99/98, 243/242 | | Commas: 78/77, 99/98, 243/242 |
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| [[Tp tuning|POT2 generator]]: ~9/7 = 424.457 | | [[Tp_tuning|POT2 generator]]: ~9/7 = 424.457 |
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| Map: [<1 3 6 7 9|, <0 -4 -9 -10 -15|] | | Map: [<1 3 6 7 9|, <0 -4 -9 -10 -15|] |
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| EDOs: 17, 48e, 65de, 82c, 147ce | | EDOs: 17, 48e, 65de, 82c, 147ce |
| [[Tp tuning#T2%20tuning|RMS error]]: 1.769 cents
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| ==Leapfrog== | | [[Tp_tuning#T2 tuning|RMS error]]: 1.769 cents |
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| | ==Leapfrog== |
| Commas: 169/168, 352/351, 364/363 | | Commas: 169/168, 352/351, 364/363 |
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| [[Lp tuning|POL2 generator]]: ~3/2 = 704.745 cents | | [[Lp_tuning|POL2 generator]]: ~3/2 = 704.745 cents |
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| Gencom: [2 3/2; 169/169 352/351 364/363] | | Gencom: [2 3/2; 169/169 352/351 364/363] |
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| Gencom mapping: [<1 1 0 -6 -3 -1|, <0 1 0 15 11 8|] | | Gencom mapping: [<1 1 0 -6 -3 -1|, <0 1 0 15 11 8|] |
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| Sval map: [<1 0 -21 -14 -9|, <0 1 15 11 8|] | | Sval map: [<1 0 -21 -14 -9|, <0 1 15 11 8|] |
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| EDOs: 17, 46, 63 | | EDOs: 17, 46, 63 |
| [[Tp tuning#T2%20tuning|RMS error]]: 0.7541 cents
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| ==Bleu== | | [[Tp_tuning#T2 tuning|RMS error]]: 0.7541 cents |
| | |
| | ==Bleu== |
| Group: 2.3.7.11.13 | | Group: 2.3.7.11.13 |
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| Commas: 78/77, 99/98, 144/143 | | Commas: 78/77, 99/98, 144/143 |
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| Sval name: 9&17 | | Sval name: 9&17 |
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| [[Tp tuning|POL2 generator]]: ~13/12 = 139.990 | | [[Tp_tuning|POL2 generator]]: ~13/12 = 139.990 |
| | |
| | [[Gencom|Gencom]]: [2 13/12; 78/77 99/98 144/143] |
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| [[Gencom]]: [2 13/12; 78/77 99/98 144/143]
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| Gencom map: [<1 1 0 2 3 3|, <0 5 0 7 4 6|] | | Gencom map: [<1 1 0 2 3 3|, <0 5 0 7 4 6|] |
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| Map: [<1 1 2 3 3|, <0 5 7 4 6|] | | Map: [<1 1 2 3 3|, <0 5 7 4 6|] |
| EDOs: [[xenharmonic/17edo|17]], [[xenharmonic/43edo|43]], [[xenharmonic/60edo|60c]]
| |
| [[Tp tuning#T2%20tuning|RMS error]]: 1.752 cents
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| ==Parapyth (Rank 3)== | | EDOs: [[17edo|17]], [[43edo|43]], [[60edo|60c]] |
| | |
| | [[Tp_tuning#T2 tuning|RMS error]]: 1.752 cents |
| | |
| | ==Parapyth (Rank 3)== |
| Commas: 352/351, 364/363 | | Commas: 352/351, 364/363 |
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| [[Lp tuning|POL2 tuning]]: <1200.000 1903.856 (2787.774) 3369.907 4154.482 4442.913| | | [[Lp_tuning|POL2 tuning]]: <1200.000 1903.856 (2787.774) 3369.907 4154.482 4442.913| |
| | |
| | The gencom below gives [[Margo_Schulter|Margo Schulter]]'s favored basis |
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| The gencom below gives [[Margo Schulter]]'s favored basis
| |
| Gencom: [2 3/2 28/27; 352/351 364/363] | | Gencom: [2 3/2 28/27; 352/351 364/363] |
| | |
| Gencom mapping: [<1 1 0 1 4 6|, <0 1 0 3 -1 -4|, <0 0 0 1 1 1|] | | Gencom mapping: [<1 1 0 1 4 6|, <0 1 0 3 -1 -4|, <0 0 0 1 1 1|] |
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| Sval map: [<1 0 0 7 12|, <0 1 0 -4 -7|, <0 0 1 1 1|] | | Sval map: [<1 0 0 7 12|, <0 1 0 -4 -7|, <0 0 1 1 1|] |
| | |
| EDOs: 17, 41, 46, 58, 87, 104 | | EDOs: 17, 41, 46, 58, 87, 104 |
| [[Tp tuning#T2%20tuning|RMS error]]: 0.3789 cents
| |
|
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| =2.3.5.11=
| | [[Tp_tuning#T2 tuning|RMS error]]: 0.3789 cents |
|
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| ==Larry== | | =2.3.5.11= |
| | |
| | ==Larry== |
| Commas: 243/242, 4000/3993 | | Commas: 243/242, 4000/3993 |
| Related temperaments: [[Gravity family#Gravity|gravity]], [[Gravity family#Harry|harry]] | | |
| | Related temperaments: [[Gravity_family#Gravity|gravity]], [[Gravity_family#Harry|harry]] |
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| POTE generator: ~40/27 = 683.166 | | POTE generator: ~40/27 = 683.166 |
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| |
|
| Gencom: [2 40/27; 243/242 4000/3993] | | Gencom: [2 40/27; 243/242 4000/3993] |
| | |
| Gencom mapping: [<1 5 12 0 12|, <0 -6 -17 0 -15|] | | Gencom mapping: [<1 5 12 0 12|, <0 -6 -17 0 -15|] |
|
| |
|
| Map: [<1 5 12 12|, <0 -6 -17 -15|] | | Map: [<1 5 12 12|, <0 -6 -17 -15|] |
| | |
| EDOs: 7, 58, 65, 137, 202 | | EDOs: 7, 58, 65, 137, 202 |
| [[Tp tuning#T2%20tuning|RMS error]]: 0.3025 cents
| |
|
| |
|
| =2.9.7.11=
| | [[Tp_tuning#T2 tuning|RMS error]]: 0.3025 cents |
|
| |
|
| ==Machine== | | =2.9.7.11= |
| | |
| | ==Machine== |
| Commas: 64/63, 99/98 | | Commas: 64/63, 99/98 |
|
| |
|
| [[POTE tuning|POTE generator]]: ~8/7 = 214.384 | | [[POTE_tuning|POTE generator]]: ~8/7 = 214.384 |
|
| |
|
| Gencom: [2 8/7; 64/63 99/98] | | Gencom: [2 8/7; 64/63 99/98] |
| | |
| Gencom mapping: [<1 3/2 0 3 4|, <0 1/2 0 -1 -3|] | | Gencom mapping: [<1 3/2 0 3 4|, <0 1/2 0 -1 -3|] |
|
| |
|
| [[Smonzos and Svals|Sval map]]: [<1 0 6 13|, <0 1 -1 -3|] | | [[Smonzos_and_Svals|Sval map]]: [<1 0 6 13|, <0 1 -1 -3|] |
| | |
| EDOs: 5, 6, 11, 17, 28 | | EDOs: 5, 6, 11, 17, 28 |
| [[Tp tuning#T2%20tuning|RMS error]]: 1.977 cents
| |
|
| |
|
| ==Apparatus== | | [[Tp_tuning#T2 tuning|RMS error]]: 1.977 cents |
| | |
| | ==Apparatus== |
| Commas: 41503/41472, 322102/321489 | | Commas: 41503/41472, 322102/321489 |
|
| |
|
| [[POTE tuning|POTE generator]]: ~77/72 = 115.570 | | [[POTE_tuning|POTE generator]]: ~77/72 = 115.570 |
|
| |
|
| Gencom: [2 77/72; 41503/41472 322102/321489] | | Gencom: [2 77/72; 41503/41472 322102/321489] |
| | |
| Gencom mapping: [<1 5/2 0 3 5|, <0 -19/2 0 -2 -16|] | | Gencom mapping: [<1 5/2 0 3 5|, <0 -19/2 0 -2 -16|] |
|
| |
|
| [[Smonzos and Svals|Sval map]]: [<1 5 3 5|, <0 -19 -2 -16|] | | [[Smonzos_and_Svals|Sval map]]: [<1 5 3 5|, <0 -19 -2 -16|] |
| | |
| EDOs: 10, 21, 31, 52, 83, 135, 353, 488, 623 | | EDOs: 10, 21, 31, 52, 83, 135, 353, 488, 623 |
| [[Tp tuning#T2%20tuning|RMS error]]: 0.0673 cents
| |
|
| |
|
| ==Mechanism== | | [[Tp_tuning#T2 tuning|RMS error]]: 0.0673 cents |
| | |
| | ==Mechanism== |
| Commas: 896/891, 26411/26244 | | Commas: 896/891, 26411/26244 |
|
| |
|
| [[POTE tuning|POTE generator]]: ~9/7 = 438.465 | | [[POTE_tuning|POTE generator]]: ~9/7 = 438.465 |
|
| |
|
| Gencom: [2 9/7; 896/891 26411/26244] | | Gencom: [2 9/7; 896/891 26411/26244] |
| | |
| Gencom mapping: [<1 5/2 0 5 2|, <0 -5/2 0 -6 4|] | | Gencom mapping: [<1 5/2 0 5 2|, <0 -5/2 0 -6 4|] |
|
| |
|
| [[Smonzos and Svals|Sval map]]: [<1 5 5 2|, <0 -5 -6 4|] | | [[Smonzos_and_Svals|Sval map]]: [<1 5 5 2|, <0 -5 -6 4|] |
| | |
| EDOs: 8, 11, 30, 41, 52 | | EDOs: 8, 11, 30, 41, 52 |
| [[Tp tuning#T2%20tuning|RMS error]]: 0.4262 cents
| |
|
| |
|
| =2.9.15.7.11.13=
| | [[Tp_tuning#T2 tuning|RMS error]]: 0.4262 cents |
|
| |
|
| ==Stacks (aka 2magic)== | | =2.9.15.7.11.13= |
| | |
| | ==Stacks (aka 2magic)== |
| Commas: 100/99, 105/104, 144/143, 196/195 | | Commas: 100/99, 105/104, 144/143, 196/195 |
|
| |
|
| [[Lp tuning|POL2 generator]]: ~9/7 = 438.977 | | [[Lp_tuning|POL2 generator]]: ~9/7 = 438.977 |
|
| |
|
| Gencom: [2 9/7; 100/99 105/104 144/143 196/195] | | Gencom: [2 9/7; 100/99 105/104 144/143 196/195] |
| | |
| Gencom mapping: [<1 5/2 5/2 5 2 7|, <0 -5/2 -1/2 -6 4 -9|] | | Gencom mapping: [<1 5/2 5/2 5 2 7|, <0 -5/2 -1/2 -6 4 -9|] |
|
| |
|
| Sval map: [<1 0 2 -1 6 -2|, <0 5 3 6 -4 9|] | | Sval map: [<1 0 2 -1 6 -2|, <0 5 3 6 -4 9|] |
| | |
| EDOs: 11, 30, 41, 153cdef, 194cdef, 235cdef | | EDOs: 11, 30, 41, 153cdef, 194cdef, 235cdef |
| [[Tp tuning#T2%20tuning|RMS error]]: 1.540 cents
| |
|
| |
|
| ===2.9.15.7.11 stacks=== | | [[Tp_tuning#T2 tuning|RMS error]]: 1.540 cents |
| | |
| | ===2.9.15.7.11 stacks=== |
| Commas: 100/99, 225/224, 245/243 | | Commas: 100/99, 225/224, 245/243 |
|
| |
|
| [[Lp tuning|POL2 generator]]: ~9/7 = 438.607 | | [[Lp_tuning|POL2 generator]]: ~9/7 = 438.607 |
|
| |
|
| Gencom: [2 9/7; 100/99 225/224 245/243] | | Gencom: [2 9/7; 100/99 225/224 245/243] |
| | |
| Gencom mapping: [<1 5/2 5/2 5 2|, <0 -5/2 -1/2 -6 4|] | | Gencom mapping: [<1 5/2 5/2 5 2|, <0 -5/2 -1/2 -6 4|] |
|
| |
|
| Sval map: [<1 0 2 -1 6|, <0 5 3 6 -4|] | | Sval map: [<1 0 2 -1 6|, <0 5 3 6 -4|] |
| | |
| EDOs: 8, 11, 30, 41, 52, 93, 145, 342bce, | | EDOs: 8, 11, 30, 41, 52, 93, 145, 342bce, |
| [[Tp tuning#T2%20tuning|RMS error]]: 1.226 cents
| |
|
| |
|
| ===2.9.15.7 stacks=== | | [[Tp_tuning#T2 tuning|RMS error]]: 1.226 cents |
| | |
| | ===2.9.15.7 stacks=== |
| Commas: 225/224, 245/243 | | Commas: 225/224, 245/243 |
|
| |
|
| [[Lp tuning|POL2 generator]]: ~9/7 = 439.296 | | [[Lp_tuning|POL2 generator]]: ~9/7 = 439.296 |
|
| |
|
| Gencom: [2 9/7; 225/224 245/243] | | Gencom: [2 9/7; 225/224 245/243] |
| | |
| Gencom mapping: [<1 5/2 5/2 5|, <0 -5/2 -1/2 -6|] | | Gencom mapping: [<1 5/2 5/2 5|, <0 -5/2 -1/2 -6|] |
|
| |
|
| Sval map: [<1 0 2 -1|, <0 5 3 6|] | | Sval map: [<1 0 2 -1|, <0 5 3 6|] |
| | |
| EDOs: 8, 11, 30, 41, 71, 93, 112c, 134c, 175c | | EDOs: 8, 11, 30, 41, 71, 93, 112c, 134c, 175c |
| [[Tp tuning#T2%20tuning|RMS error]]: 1.074 cents
| |
|
| |
|
| =2.9.21= | | [[Tp_tuning#T2 tuning|RMS error]]: 1.074 cents |
| ==A-team== | | |
| | =2.9.21= |
| | |
| | ==A-team== |
| Commas: 1029/1024 | | Commas: 1029/1024 |
|
| |
|
| [[Lp tuning|POL2 generator]]: ~21/16 = 467.375 | | [[Lp_tuning|POL2 generator]]: ~21/16 = 467.375 |
|
| |
|
| Gencom: [2 21/16; 1029/1024] | | Gencom: [2 21/16; 1029/1024] |
| | |
| Gencom mapping: [<1 1 0 3|, <0 3/2 0 -1/2|] | | Gencom mapping: [<1 1 0 3|, <0 3/2 0 -1/2|] |
|
| |
|
| Sval map: [<1 2 4|, <0 3 1|] | | Sval map: [<1 2 4|, <0 3 1|] |
| | |
| EDOs: 5, 13, 18, 41, 59, 77, 95 | | EDOs: 5, 13, 18, 41, 59, 77, 95 |
| [[Tp tuning#T2%20tuning|RMS error]]: 0.3202 cents
| |
|
| |
|
| =2.3.7/5.11/5.13/5= | | [[Tp_tuning#T2 tuning|RMS error]]: 0.3202 cents |
| ==Historical== | | |
| | =2.3.7/5.11/5.13/5= |
| | |
| | ==Historical== |
| Subgroup: 2.3.7/5.11/5.13/5 | | Subgroup: 2.3.7/5.11/5.13/5 |
| | |
| Commas: 364/363, 441/440, 1001/1000 | | Commas: 364/363, 441/440, 1001/1000 |
|
| |
|
| [[Lp tuning|POL2 generator]]: ~21/20 = 83.016 | | [[Lp_tuning|POL2 generator]]: ~21/20 = 83.016 |
| | |
| | [[Gencom|Gencom]]: [2 21/20; 364/363 441/440 1001/1000] |
|
| |
|
| [[Gencom]]: [2 21/20; 364/363 441/440 1001/1000]
| |
| Gencom map: [<1 2 -3/4 -3/4 1/4 5/4|, <0 -6 0 7 2 -9|] | | Gencom map: [<1 2 -3/4 -3/4 1/4 5/4|, <0 -6 0 7 2 -9|] |
|
| |
|
| Sval map: [<1 2 0 1 2|, <0 -6 7 2 -9|] | | Sval map: [<1 2 0 1 2|, <0 -6 7 2 -9|] |
| | |
| EDOs: 14, 29, 72, 101, 130, 159 | | EDOs: 14, 29, 72, 101, 130, 159 |
| [[Tp tuning#T2%20tuning|RMS error]]: 0.2562 cents
| |
|
| |
|
| =2.3.7.11/5.13= | | [[Tp_tuning#T2 tuning|RMS error]]: 0.2562 cents |
| ==Hypnosis== | | |
| | =2.3.7.11/5.13= |
| | |
| | ==Hypnosis== |
| Subgroup: 2.3.7.11/5.13 | | Subgroup: 2.3.7.11/5.13 |
| | |
| Commas: 169/168, 540/539, 729/728 | | Commas: 169/168, 540/539, 729/728 |
| Related temperament: [[Swetismic temperaments#Hypnos-13-limit|hypnos]], [[Hemifamity temperaments#Tricot-13-limit|tricot]]
| |
|
| |
|
| [[Gencom]]: [2 13/9; 169/168, 540/539, 729/728] | | Related temperament: [[Swetismic_temperaments#Hypnos-13-limit|hypnos]], [[Hemifamity_temperaments#Tricot-13-limit|tricot]] |
| | |
| | [[Gencom|Gencom]]: [2 13/9; 169/168, 540/539, 729/728] |
| | |
| Gencom map: [<1 0 -4 -3 4 0|, <0 3 13/2 11 -13/2 7|] | | Gencom map: [<1 0 -4 -3 4 0|, <0 3 13/2 11 -13/2 7|] |
|
| |
|
| Sval map: [<1 0 -3 8 0|, <0 3 11 -13 7|] | | Sval map: [<1 0 -3 8 0|, <0 3 11 -13 7|] |
| | |
| EDOs: 17, 36, 118e, 125e, 161e, 197e | | EDOs: 17, 36, 118e, 125e, 161e, 197e |
| [[Tp tuning#T2%20tuning|RMS error]]: 0.5379 cents | | |
| | [[Tp_tuning#T2 tuning|RMS error]]: 0.5379 cents |
|
| |
|
| =2.5.7= | | =2.5.7= |
| Line 385: |
Line 474: |
| ==Didacus== | | ==Didacus== |
| Subgroup: 2.5.7 | | Subgroup: 2.5.7 |
| | |
| Commas: 3136/3125 | | Commas: 3136/3125 |
| | |
| Related temperaments: [[Chromatic+pairs#Roulette]] | | Related temperaments: [[Chromatic+pairs#Roulette]] |
|
| |
|
| [[Gencom]]: [2 28/25 3136/3125] | | [[Gencom|Gencom]]: [2 28/25 3136/3125] |
| | |
| Gencom map: [<1 0 2 2|, <0 0 2 5|] | | Gencom map: [<1 0 2 2|, <0 0 2 5|] |
|
| |
|
| Sval map: [<1 2 2|, <0 2 5|] | | Sval map: [<1 2 2|, <0 2 5|] |
| | |
| EDOs: 6, 19, 25, 31, 37, 99, 130, 161, 353 | | EDOs: 6, 19, 25, 31, 37, 99, 130, 161, 353 |
| [[Tp tuning#T2%20tuning|RMS error]]: 0.2138 cents</pre></div>
| | |
| <h4>Original HTML content:</h4>
| | [[Tp_tuning#T2 tuning|RMS error]]: 0.2138 cents |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Subgroup temperaments</title></head><body><!-- ws:start:WikiTextTocRule:86:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:86 --><!-- ws:start:WikiTextTocRule:87: --><a href="#x2.3.7">2.3.7</a><!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --><!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --><!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --><!-- ws:end:WikiTextTocRule:90 --><!-- ws:start:WikiTextTocRule:91: --><!-- ws:end:WikiTextTocRule:91 --><!-- ws:start:WikiTextTocRule:92: --><!-- ws:end:WikiTextTocRule:92 --><!-- ws:start:WikiTextTocRule:93: --> | <a href="#x2.3.11">2.3.11</a><!-- ws:end:WikiTextTocRule:93 --><!-- ws:start:WikiTextTocRule:94: --><!-- ws:end:WikiTextTocRule:94 --><!-- ws:start:WikiTextTocRule:95: --> | <a href="#x2.3.5.11">2.3.5.11</a><!-- ws:end:WikiTextTocRule:95 --><!-- ws:start:WikiTextTocRule:96: --><!-- ws:end:WikiTextTocRule:96 --><!-- ws:start:WikiTextTocRule:97: --><!-- ws:end:WikiTextTocRule:97 --><!-- ws:start:WikiTextTocRule:98: --><!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --> | <a href="#x2.3.7.11">2.3.7.11</a><!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --><!-- ws:end:WikiTextTocRule:100 --><!-- ws:start:WikiTextTocRule:101: --><!-- ws:end:WikiTextTocRule:101 --><!-- ws:start:WikiTextTocRule:102: --><!-- ws:end:WikiTextTocRule:102 --><!-- ws:start:WikiTextTocRule:103: --><!-- ws:end:WikiTextTocRule:103 --><!-- ws:start:WikiTextTocRule:104: --><!-- ws:end:WikiTextTocRule:104 --><!-- ws:start:WikiTextTocRule:105: --> | <a href="#x2.3.7.11.13">2.3.7.11.13</a><!-- ws:end:WikiTextTocRule:105 --><!-- ws:start:WikiTextTocRule:106: --><!-- ws:end:WikiTextTocRule:106 --><!-- ws:start:WikiTextTocRule:107: --><!-- ws:end:WikiTextTocRule:107 --><!-- ws:start:WikiTextTocRule:108: --><!-- ws:end:WikiTextTocRule:108 --><!-- ws:start:WikiTextTocRule:109: --><!-- ws:end:WikiTextTocRule:109 --><!-- ws:start:WikiTextTocRule:110: --><!-- ws:end:WikiTextTocRule:110 --><!-- ws:start:WikiTextTocRule:111: --><!-- ws:end:WikiTextTocRule:111 --><!-- ws:start:WikiTextTocRule:112: --> | <a href="#x2.3.5.11">2.3.5.11</a><!-- ws:end:WikiTextTocRule:112 --><!-- ws:start:WikiTextTocRule:113: --><!-- ws:end:WikiTextTocRule:113 --><!-- ws:start:WikiTextTocRule:114: --> | <a href="#x2.9.7.11">2.9.7.11</a><!-- ws:end:WikiTextTocRule:114 --><!-- ws:start:WikiTextTocRule:115: --><!-- ws:end:WikiTextTocRule:115 --><!-- ws:start:WikiTextTocRule:116: --><!-- ws:end:WikiTextTocRule:116 --><!-- ws:start:WikiTextTocRule:117: --><!-- ws:end:WikiTextTocRule:117 --><!-- ws:start:WikiTextTocRule:118: --> | <a href="#x2.9.15.7.11.13">2.9.15.7.11.13</a><!-- ws:end:WikiTextTocRule:118 --><!-- ws:start:WikiTextTocRule:119: --><!-- ws:end:WikiTextTocRule:119 --><!-- ws:start:WikiTextTocRule:120: --><!-- ws:end:WikiTextTocRule:120 --><!-- ws:start:WikiTextTocRule:121: --><!-- ws:end:WikiTextTocRule:121 --><!-- ws:start:WikiTextTocRule:122: --> | <a href="#x2.9.21">2.9.21</a><!-- ws:end:WikiTextTocRule:122 --><!-- ws:start:WikiTextTocRule:123: --><!-- ws:end:WikiTextTocRule:123 --><!-- ws:start:WikiTextTocRule:124: --> | <a href="#x2.3.7/5.11/5.13/5">2.3.7/5.11/5.13/5</a><!-- ws:end:WikiTextTocRule:124 --><!-- ws:start:WikiTextTocRule:125: --><!-- ws:end:WikiTextTocRule:125 --><!-- ws:start:WikiTextTocRule:126: --> | <a href="#x2.3.7.11/5.13">2.3.7.11/5.13</a><!-- ws:end:WikiTextTocRule:126 --><!-- ws:start:WikiTextTocRule:127: --><!-- ws:end:WikiTextTocRule:127 --><!-- ws:start:WikiTextTocRule:128: --> | <a href="#x2.5.7">2.5.7</a><!-- ws:end:WikiTextTocRule:128 --><!-- ws:start:WikiTextTocRule:129: --><!-- ws:end:WikiTextTocRule:129 --><!-- ws:start:WikiTextTocRule:130: -->
| | [[Category:subgroup]] |
| <!-- ws:end:WikiTextTocRule:130 -->Below are some subgroups and temperaments for them. Obviously, no attempt has been made at completeness; attention is focused on subgroups containing interesting chords. The reader may also want to consult the page on <a class="wiki_link" href="/Chromatic%20pairs">Chromatic pairs</a>.<br />
| | [[Category:temperament]] |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x2.3.7"></a><!-- ws:end:WikiTextHeadingRule:0 -->2.3.7</h1>
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x2.3.7-Semaphore"></a><!-- ws:end:WikiTextHeadingRule:2 --><a class="wiki_link" href="/Semaphore%20and%20Godzilla">Semaphore</a></h2>
| |
| Comma: 49/48<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~8/7~7/6 = 250.385<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Gencom">Gencom</a>: [2 8/7; 49/48]<br />
| |
| Gencom mapping: [&lt;1 2 0 3|, &lt;0 -2 0 -1|]<br />
| |
| <br />
| |
| Map: [&lt;1 2 3|, &lt;0 -2 -1|]<br />
| |
| EDOs: 5, 14, 19, 24, 67c, 91c<br />
| |
| <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 2.523 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x2.3.7-Archy"></a><!-- ws:end:WikiTextHeadingRule:4 -->Archy</h2>
| |
| Archy can be thought of as &quot;no-5's <a class="wiki_link" href="/dominant">dominant</a>&quot; or &quot;no-5's <a class="wiki_link" href="/superpyth">superpyth</a>&quot;. The name comes from the fact that it tempers out 64/63, the Archytas comma.<br />
| |
| <br />
| |
| Comma: 64/63<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~3/2 = 709.321<br />
| |
| <br />
| |
| Gencom: [2 3/2; 64/63]<br />
| |
| Gencom mapping: [&lt;1 1 0 4|, &lt;0 1 0 -2|]<br />
| |
| <br />
| |
| Map: [&lt;1 2 2|, &lt;0 -1 2|]<br />
| |
| EDOs: 5, 12, 17, 22, 27, 137bc<br />
| |
| <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.856 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x2.3.7-Slendric"></a><!-- ws:end:WikiTextHeadingRule:6 --><a class="wiki_link" href="/Slendric">Slendric</a></h2>
| |
| Comma: 1029/1024<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~8/7 = 233.688<br />
| |
| <br />
| |
| Gencom: [2 8/7; 1029/1024]<br />
| |
| Gencom mapping: [&lt;1 1 0 3|, &lt;0 3 0 -1|]<br />
| |
| <br />
| |
| Map: [&lt;1 1 3|, &lt;0 3 -1|]<br />
| |
| EDOs: 5, 21, 26, 31, 36, 77, 113, 190<br />
| |
| <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.3202 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x2.3.7-Lee"></a><!-- ws:end:WikiTextHeadingRule:8 -->Lee</h2>
| |
| Comma: 177147/175616<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~81/56 = 633.525<br />
| |
| <br />
| |
| Map: [&lt;1 0 -3|, &lt;0 3 11|]<br />
| |
| EDOs: 17, 36, 89, 125, 161, 358, 519b<br />
| |
| <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.3519 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x2.3.7-Skwares"></a><!-- ws:end:WikiTextHeadingRule:10 -->Skwares</h2>
| |
| Comma: 19683/19208<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~9/7 = 425.365 cents<br />
| |
| <br />
| |
| Map: [&lt;1 3 6|, &lt;0 -4 -9|]<br />
| |
| EDOs: 14, 17, 31, 48, 79, 189b, 268bc, 347bc<br />
| |
| <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.149 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="x2.3.11"></a><!-- ws:end:WikiTextHeadingRule:12 -->2.3.11</h1>
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x2.3.11-Neuter"></a><!-- ws:end:WikiTextHeadingRule:14 -->Neuter</h2>
| |
| Neuter can be thought of as the 2.3.11 version of either <a class="wiki_link" href="/mohajira">mohajira</a> or <a class="wiki_link" href="/maqamic">maqamic</a>, as well as suhajira (further down on this page) and ringo. Among other things, it is the temperament optimizing the <a class="wiki_link" href="/neutral%20tetrad">neutral tetrad</a>.<br />
| |
| <br />
| |
| Comma: 243/242<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~11/9 = 350.525<br />
| |
| <br />
| |
| Gencom: [2 11/9; 243/242]<br />
| |
| Gencom mapping: [&lt;1 1 0 0 2|, &lt;0 2 0 0 5|]<br />
| |
| <br />
| |
| Map: [&lt;1 1 2|, &lt;0 2 5|]<br />
| |
| EDOs: 7, 10, 17, 24, 41, 65, 89, 202, 291, 380<br />
| |
| <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.3021 cents<br />
| |
| <br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/neutraltet7">Seven note albitonic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/neutraltet10">Ten note chromatic scale</a><br />
| |
| <a class="wiki_link" href="http://xenharmonic.wikispaces.com/neutraltet17">Seventeen note mega chromatic scale</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="x2.3.5.11"></a><!-- ws:end:WikiTextHeadingRule:16 -->2.3.5.11</h1>
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="x2.3.5.11-Porkypine"></a><!-- ws:end:WikiTextHeadingRule:18 -->Porkypine</h2>
| |
| Commas: 55/54, 100/99<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~10/9 = 164.078<br />
| |
| <br />
| |
| Gencom: [2 10/9; 55/54, 100/99]<br />
| |
| Gencom mapping: [&lt;1 2 3 0 4|, &lt;0 -3 -5 0 -4|]<br />
| |
| <br />
| |
| Map: [&lt;1 2 3 4|, &lt;0 -3 -5 -4|]<br />
| |
| EDOs: 7, 15, 22, 37, 73cd, 95cd, 117bcd<br />
| |
| <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 2.287 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="x2.3.5.11-Mohaha"></a><!-- ws:end:WikiTextHeadingRule:20 -->Mohaha</h2>
| |
| Commas: 81/80, 121/120<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~11/9 = 348.094<br />
| |
| <br />
| |
| Gencom: [2 11/9; 81/80 121/120]<br />
| |
| Gencom mapping: [&lt;1 1 0 0 2|, &lt;0 2 8 0 5|]<br />
| |
| <br />
| |
| Map: [&lt;1 1 0 2|, &lt;0 2 8 5|]<br />
| |
| EDOs: 7, 10, 17, 24, 31, 55, 69d, 100d, 131bd<br />
| |
| <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.392 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:22:&lt;h3&gt; --><h3 id="toc11"><a name="x2.3.5.11-Mohaha-Music"></a><!-- ws:end:WikiTextHeadingRule:22 -->Music</h3>
| |
| <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/mohaha10ping2.mp3" rel="nofollow">Mohaha10ping2</a> by <a class="wiki_link" href="/Billy%20Stiltner">Billy Stiltner</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc12"><a name="x2.3.7.11"></a><!-- ws:end:WikiTextHeadingRule:24 -->2.3.7.11</h1>
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc13"><a name="x2.3.7.11-Ennea"></a><!-- ws:end:WikiTextHeadingRule:26 -->Ennea</h2>
| |
| Commas: 41503/41472, 43923/43904<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~99/98 = 17.6258<br />
| |
| <br />
| |
| Gencom: [2 99/98; 41503/41472, 43923/43904]<br />
| |
| Gencom mapping: [&lt;1 14/9 0 25/9 31/9|, &lt;0 2 0 2 1|]<br />
| |
| <br />
| |
| Sval map: [&lt;9 0 11 24|, &lt;0 2 2 1|]<br />
| |
| EDOs: 54, 63, 68, 72, 135, 342, 477, 525, 613, 681, 749, 817, 2159bcd, 3336bcd, 4153bcd<br />
| |
| <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.0383 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="x2.3.7.11-Supra"></a><!-- ws:end:WikiTextHeadingRule:28 -->Supra</h2>
| |
| Commas: 64/63, 99/98<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~3/2 = 707.192<br />
| |
| <br />
| |
| Gencom: [2 3/2; 64/63 99/98]<br />
| |
| Gencom mapping: [&lt;1 1 0 4 7|, &lt;0 1 0 -2 -6|]<br />
| |
| <br />
| |
| Sval map: [&lt;1 0 6 13|, &lt;0 1 -2 -6|]<br />
| |
| EDOs: 5, 12, 17, 39c, 56c<br />
| |
| <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.977 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:30:&lt;h2&gt; --><h2 id="toc15"><a name="x2.3.7.11-Skwares"></a><!-- ws:end:WikiTextHeadingRule:30 -->Skwares</h2>
| |
| Commas: 99/98, 243/242<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~9/7 = 425.244<br />
| |
| <br />
| |
| Gencom: [2 9/7; 99/98 243/242]<br />
| |
| Gencom mapping: [&lt;1 3 0 6 7|, &lt;0 -4 0 -9 -10]]<br />
| |
| <br />
| |
| Sval map: [&lt;1 3 6 7|, &lt;0 -4 -9 -10|]<br />
| |
| EDOs: 14, 17, 31, 48, 79, 127, 206bcd<br />
| |
| <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.099 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="x2.3.7.11-Hemif"></a><!-- ws:end:WikiTextHeadingRule:32 -->Hemif</h2>
| |
| Commas: 243/242, 896/891<br />
| |
| <br />
| |
| POTE generator: ~11/9 = 351.535<br />
| |
| <br />
| |
| Gencom: [2 11/9; 243/242 896/891]<br />
| |
| Gencom mapping: [&lt;1 1 0 -1 2|, &lt;0 2 0 13 5|]<br />
| |
| <br />
| |
| Sval map: [&lt;1 1 -1 2|, &lt;0 2 13 5|]<br />
| |
| EDOs: 7, 17, 41, 58, 99d<br />
| |
| <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.6108 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="x2.3.7.11-Bleu"></a><!-- ws:end:WikiTextHeadingRule:34 -->Bleu</h2>
| |
| Commas: 99/98, 864/847<br />
| |
| <br />
| |
| POTE generator: ~12/11 = 140.005<br />
| |
| <br />
| |
| Map: [&lt;1 1 2 3|, &lt;0 5 7 4|]<br />
| |
| EDOs: 9, 17, 43, 60c<br />
| |
| RMS error: 1.829 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:36:&lt;h1&gt; --><h1 id="toc18"><a name="x2.3.7.11.13"></a><!-- ws:end:WikiTextHeadingRule:36 -->2.3.7.11.13</h1>
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="x2.3.7.11.13-Suhajira"></a><!-- ws:end:WikiTextHeadingRule:38 -->Suhajira</h2>
| |
| Commas: 64/63, 78/77, 144/143<br />
| |
| <br />
| |
| Gencom: [2 11/9; 64/63 78/77 144/143]<br />
| |
| Gencom map: [&lt;1 1 0 4 2 4|, &lt;0 2 0 -4 5 -1|]<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~11/9 = 353.775<br />
| |
| <br />
| |
| Map: [&lt;1 1 4 2 4|, &lt;0 2 -4 5 -1|]<br />
| |
| EDOs: 7, 10, 17, 44d, 61cd, 78cd<br />
| |
| <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.953 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="x2.3.7.11.13-Hemif"></a><!-- ws:end:WikiTextHeadingRule:40 -->Hemif</h2>
| |
| Commas: 144/143, 243/242, 364/363<br />
| |
| Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Breedsmic%20temperaments">Hemififths</a>, namo<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~11/9 = 351.691<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Gencom">Gencom</a>: [2 11/9; 144/143 243/242 364/363]<br />
| |
| Gencom map: [&lt;1 1 0 -1 2 4|, &lt;0 2 0 13 5 -1|]<br />
| |
| <br />
| |
| Map: [&lt;1 1 -1 2 4|, &lt;0 2 13 5 -1|]<br />
| |
| EDOs: 7, 10, 17, 24, 41, 58<br />
| |
| <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.7167 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:42:&lt;h2&gt; --><h2 id="toc21"><a name="x2.3.7.11.13-Skwares"></a><!-- ws:end:WikiTextHeadingRule:42 -->Skwares</h2>
| |
| Commas: 78/77, 99/98, 243/242<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~9/7 = 424.457<br />
| |
| <br />
| |
| Map: [&lt;1 3 6 7 9|, &lt;0 -4 -9 -10 -15|]<br />
| |
| EDOs: 17, 48e, 65de, 82c, 147ce<br />
| |
| <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.769 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc22"><a name="x2.3.7.11.13-Leapfrog"></a><!-- ws:end:WikiTextHeadingRule:44 -->Leapfrog</h2>
| |
| Commas: 169/168, 352/351, 364/363<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~3/2 = 704.745 cents<br />
| |
| <br />
| |
| Gencom: [2 3/2; 169/169 352/351 364/363]<br />
| |
| Gencom mapping: [&lt;1 1 0 -6 -3 -1|, &lt;0 1 0 15 11 8|]<br />
| |
| <br />
| |
| Sval map: [&lt;1 0 -21 -14 -9|, &lt;0 1 15 11 8|]<br />
| |
| EDOs: 17, 46, 63<br />
| |
| <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.7541 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:46:&lt;h2&gt; --><h2 id="toc23"><a name="x2.3.7.11.13-Bleu"></a><!-- ws:end:WikiTextHeadingRule:46 -->Bleu</h2>
| |
| Group: 2.3.7.11.13<br />
| |
| Commas: 78/77, 99/98, 144/143<br />
| |
| Sval name: 9&amp;17<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Tp%20tuning">POL2 generator</a>: ~13/12 = 139.990<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Gencom">Gencom</a>: [2 13/12; 78/77 99/98 144/143]<br />
| |
| Gencom map: [&lt;1 1 0 2 3 3|, &lt;0 5 0 7 4 6|]<br />
| |
| <br />
| |
| Map: [&lt;1 1 2 3 3|, &lt;0 5 7 4 6|]<br />
| |
| EDOs: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/17edo">17</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/43edo">43</a>, <a class="wiki_link" href="http://xenharmonic.wikispaces.com/60edo">60c</a><br />
| |
| <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.752 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:48:&lt;h2&gt; --><h2 id="toc24"><a name="x2.3.7.11.13-Parapyth (Rank 3)"></a><!-- ws:end:WikiTextHeadingRule:48 -->Parapyth (Rank 3)</h2>
| |
| Commas: 352/351, 364/363<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Lp%20tuning">POL2 tuning</a>: &lt;1200.000 1903.856 (2787.774) 3369.907 4154.482 4442.913|<br />
| |
| <br />
| |
| The gencom below gives <a class="wiki_link" href="/Margo%20Schulter">Margo Schulter</a>'s favored basis<br />
| |
| Gencom: [2 3/2 28/27; 352/351 364/363]<br />
| |
| Gencom mapping: [&lt;1 1 0 1 4 6|, &lt;0 1 0 3 -1 -4|, &lt;0 0 0 1 1 1|]<br />
| |
| <br />
| |
| Sval map: [&lt;1 0 0 7 12|, &lt;0 1 0 -4 -7|, &lt;0 0 1 1 1|]<br />
| |
| EDOs: 17, 41, 46, 58, 87, 104<br />
| |
| <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.3789 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:50:&lt;h1&gt; --><h1 id="toc25"><a name="x2.3.5.11"></a><!-- ws:end:WikiTextHeadingRule:50 -->2.3.5.11</h1>
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:52:&lt;h2&gt; --><h2 id="toc26"><a name="x2.3.5.11-Larry"></a><!-- ws:end:WikiTextHeadingRule:52 -->Larry</h2>
| |
| Commas: 243/242, 4000/3993<br />
| |
| Related temperaments: <a class="wiki_link" href="/Gravity%20family#Gravity">gravity</a>, <a class="wiki_link" href="/Gravity%20family#Harry">harry</a><br />
| |
| <br />
| |
| POTE generator: ~40/27 = 683.166<br />
| |
| <br />
| |
| Gencom: [2 40/27; 243/242 4000/3993]<br />
| |
| Gencom mapping: [&lt;1 5 12 0 12|, &lt;0 -6 -17 0 -15|]<br />
| |
| <br />
| |
| Map: [&lt;1 5 12 12|, &lt;0 -6 -17 -15|]<br />
| |
| EDOs: 7, 58, 65, 137, 202<br />
| |
| <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.3025 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:54:&lt;h1&gt; --><h1 id="toc27"><a name="x2.9.7.11"></a><!-- ws:end:WikiTextHeadingRule:54 -->2.9.7.11</h1>
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:56:&lt;h2&gt; --><h2 id="toc28"><a name="x2.9.7.11-Machine"></a><!-- ws:end:WikiTextHeadingRule:56 -->Machine</h2>
| |
| Commas: 64/63, 99/98<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~8/7 = 214.384<br />
| |
| <br />
| |
| Gencom: [2 8/7; 64/63 99/98]<br />
| |
| Gencom mapping: [&lt;1 3/2 0 3 4|, &lt;0 1/2 0 -1 -3|]<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Smonzos%20and%20Svals">Sval map</a>: [&lt;1 0 6 13|, &lt;0 1 -1 -3|]<br />
| |
| EDOs: 5, 6, 11, 17, 28<br />
| |
| <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.977 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:58:&lt;h2&gt; --><h2 id="toc29"><a name="x2.9.7.11-Apparatus"></a><!-- ws:end:WikiTextHeadingRule:58 -->Apparatus</h2>
| |
| Commas: 41503/41472, 322102/321489<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~77/72 = 115.570<br />
| |
| <br />
| |
| Gencom: [2 77/72; 41503/41472 322102/321489]<br />
| |
| Gencom mapping: [&lt;1 5/2 0 3 5|, &lt;0 -19/2 0 -2 -16|]<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Smonzos%20and%20Svals">Sval map</a>: [&lt;1 5 3 5|, &lt;0 -19 -2 -16|]<br />
| |
| EDOs: 10, 21, 31, 52, 83, 135, 353, 488, 623<br />
| |
| <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.0673 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:60:&lt;h2&gt; --><h2 id="toc30"><a name="x2.9.7.11-Mechanism"></a><!-- ws:end:WikiTextHeadingRule:60 -->Mechanism</h2>
| |
| Commas: 896/891, 26411/26244<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~9/7 = 438.465<br />
| |
| <br />
| |
| Gencom: [2 9/7; 896/891 26411/26244]<br />
| |
| Gencom mapping: [&lt;1 5/2 0 5 2|, &lt;0 -5/2 0 -6 4|]<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Smonzos%20and%20Svals">Sval map</a>: [&lt;1 5 5 2|, &lt;0 -5 -6 4|]<br />
| |
| EDOs: 8, 11, 30, 41, 52<br />
| |
| <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.4262 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:62:&lt;h1&gt; --><h1 id="toc31"><a name="x2.9.15.7.11.13"></a><!-- ws:end:WikiTextHeadingRule:62 -->2.9.15.7.11.13</h1>
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:64:&lt;h2&gt; --><h2 id="toc32"><a name="x2.9.15.7.11.13-Stacks (aka 2magic)"></a><!-- ws:end:WikiTextHeadingRule:64 -->Stacks (aka 2magic)</h2>
| |
| Commas: 100/99, 105/104, 144/143, 196/195<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~9/7 = 438.977<br />
| |
| <br />
| |
| Gencom: [2 9/7; 100/99 105/104 144/143 196/195]<br />
| |
| Gencom mapping: [&lt;1 5/2 5/2 5 2 7|, &lt;0 -5/2 -1/2 -6 4 -9|]<br />
| |
| <br />
| |
| Sval map: [&lt;1 0 2 -1 6 -2|, &lt;0 5 3 6 -4 9|]<br />
| |
| EDOs: 11, 30, 41, 153cdef, 194cdef, 235cdef<br />
| |
| <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.540 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:66:&lt;h3&gt; --><h3 id="toc33"><a name="x2.9.15.7.11.13-Stacks (aka 2magic)-2.9.15.7.11 stacks"></a><!-- ws:end:WikiTextHeadingRule:66 -->2.9.15.7.11 stacks</h3>
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| Commas: 100/99, 225/224, 245/243<br />
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| <br />
| |
| <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~9/7 = 438.607<br />
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| <br />
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| Gencom: [2 9/7; 100/99 225/224 245/243]<br />
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| Gencom mapping: [&lt;1 5/2 5/2 5 2|, &lt;0 -5/2 -1/2 -6 4|]<br />
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| <br />
| |
| Sval map: [&lt;1 0 2 -1 6|, &lt;0 5 3 6 -4|]<br />
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| EDOs: 8, 11, 30, 41, 52, 93, 145, 342bce,<br />
| |
| <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.226 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:68:&lt;h3&gt; --><h3 id="toc34"><a name="x2.9.15.7.11.13-Stacks (aka 2magic)-2.9.15.7 stacks"></a><!-- ws:end:WikiTextHeadingRule:68 -->2.9.15.7 stacks</h3>
| |
| Commas: 225/224, 245/243<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~9/7 = 439.296<br />
| |
| <br />
| |
| Gencom: [2 9/7; 225/224 245/243]<br />
| |
| Gencom mapping: [&lt;1 5/2 5/2 5|, &lt;0 -5/2 -1/2 -6|]<br />
| |
| <br />
| |
| Sval map: [&lt;1 0 2 -1|, &lt;0 5 3 6|]<br />
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| EDOs: 8, 11, 30, 41, 71, 93, 112c, 134c, 175c<br />
| |
| <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 1.074 cents<br />
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| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:70:&lt;h1&gt; --><h1 id="toc35"><a name="x2.9.21"></a><!-- ws:end:WikiTextHeadingRule:70 -->2.9.21</h1>
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| <!-- ws:start:WikiTextHeadingRule:72:&lt;h2&gt; --><h2 id="toc36"><a name="x2.9.21-A-team"></a><!-- ws:end:WikiTextHeadingRule:72 -->A-team</h2>
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| Commas: 1029/1024<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~21/16 = 467.375<br />
| |
| <br />
| |
| Gencom: [2 21/16; 1029/1024]<br />
| |
| Gencom mapping: [&lt;1 1 0 3|, &lt;0 3/2 0 -1/2|]<br />
| |
| <br />
| |
| Sval map: [&lt;1 2 4|, &lt;0 3 1|]<br />
| |
| EDOs: 5, 13, 18, 41, 59, 77, 95<br />
| |
| <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.3202 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:74:&lt;h1&gt; --><h1 id="toc37"><a name="x2.3.7/5.11/5.13/5"></a><!-- ws:end:WikiTextHeadingRule:74 -->2.3.7/5.11/5.13/5</h1>
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| <!-- ws:start:WikiTextHeadingRule:76:&lt;h2&gt; --><h2 id="toc38"><a name="x2.3.7/5.11/5.13/5-Historical"></a><!-- ws:end:WikiTextHeadingRule:76 -->Historical</h2>
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| Subgroup: 2.3.7/5.11/5.13/5<br />
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| Commas: 364/363, 441/440, 1001/1000<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~21/20 = 83.016<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Gencom">Gencom</a>: [2 21/20; 364/363 441/440 1001/1000]<br />
| |
| Gencom map: [&lt;1 2 -3/4 -3/4 1/4 5/4|, &lt;0 -6 0 7 2 -9|]<br />
| |
| <br />
| |
| Sval map: [&lt;1 2 0 1 2|, &lt;0 -6 7 2 -9|]<br />
| |
| EDOs: 14, 29, 72, 101, 130, 159<br />
| |
| <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.2562 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:78:&lt;h1&gt; --><h1 id="toc39"><a name="x2.3.7.11/5.13"></a><!-- ws:end:WikiTextHeadingRule:78 -->2.3.7.11/5.13</h1>
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| <!-- ws:start:WikiTextHeadingRule:80:&lt;h2&gt; --><h2 id="toc40"><a name="x2.3.7.11/5.13-Hypnosis"></a><!-- ws:end:WikiTextHeadingRule:80 -->Hypnosis</h2>
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| Subgroup: 2.3.7.11/5.13<br />
| |
| Commas: 169/168, 540/539, 729/728<br />
| |
| Related temperament: <a class="wiki_link" href="/Swetismic%20temperaments#Hypnos-13-limit">hypnos</a>, <a class="wiki_link" href="/Hemifamity%20temperaments#Tricot-13-limit">tricot</a><br />
| |
| <br />
| |
| <a class="wiki_link" href="/Gencom">Gencom</a>: [2 13/9; 169/168, 540/539, 729/728]<br />
| |
| Gencom map: [&lt;1 0 -4 -3 4 0|, &lt;0 3 13/2 11 -13/2 7|]<br />
| |
| <br />
| |
| Sval map: [&lt;1 0 -3 8 0|, &lt;0 3 11 -13 7|]<br />
| |
| EDOs: 17, 36, 118e, 125e, 161e, 197e<br />
| |
| <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.5379 cents<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:82:&lt;h1&gt; --><h1 id="toc41"><a name="x2.5.7"></a><!-- ws:end:WikiTextHeadingRule:82 -->2.5.7</h1>
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| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:84:&lt;h2&gt; --><h2 id="toc42"><a name="x2.5.7-Didacus"></a><!-- ws:end:WikiTextHeadingRule:84 -->Didacus</h2>
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| Subgroup: 2.5.7<br />
| |
| Commas: 3136/3125<br />
| |
| Related temperaments: [[Chromatic+pairs#Roulette]]<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Gencom">Gencom</a>: [2 28/25 3136/3125]<br />
| |
| Gencom map: [&lt;1 0 2 2|, &lt;0 0 2 5|]<br />
| |
| <br />
| |
| Sval map: [&lt;1 2 2|, &lt;0 2 5|]<br />
| |
| EDOs: 6, 19, 25, 31, 37, 99, 130, 161, 353<br />
| |
| <a class="wiki_link" href="/Tp%20tuning#T2%20tuning">RMS error</a>: 0.2138 cents</body></html></pre></div>
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