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| <h2>IMPORTED REVISION FROM WIKISPACES</h2> | | <span style="display: block; text-align: right;"> |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | __FORCETOC__ |
| : This revision was by author [[User:Gedankenwelt|Gedankenwelt]] and made on <tt>2015-12-12 05:08:36 UTC</tt>.<br>
| | Other languages: [[:de:Hanson_Kleismisch Deutsch]]</span> |
| : The original revision id was <tt>569913707</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>
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| <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"><span style="display: block; text-align: right;">[[toc]]
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| | The [[5-limit|5-limit]] parent comma for the '''kleismic family''' is 15625/15552, the kleisma. Its monzo is |-6 -5 6>, and flipping that yields <<6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. This 5-limit temperament (virtually a microtemperament) is commonly called '''Hanson''', and 14\53 is about perfect as a hanson generator, though 9\34 also makes sense, and 5\19 and 4\15 are possible. Other tunings include [[72edo|72edo]], [[87edo|87edo]] and [[140edo|140edo]]. |
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| | [[Tuning_Ranges_of_Regular_Temperaments|valid range]]: [300.000, 327.273] (4 to 11b) |
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| Other languages: [[xenharmonie/Hanson Kleismisch|Deutsch]]
| | nice range: [315.641, 317.263] |
| </span>
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| The [[5-limit]] parent comma for the **kleismic family** is 15625/15552, the kleisma. Its monzo is |-6 -5 6>, and flipping that yields <<6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. This 5-limit temperament (virtually a microtemperament) is commonly called **Hanson**, and 14\53 is about perfect as a hanson generator, though 9\34 also makes sense, and 5\19 and 4\15 are possible. Other tunings include [[72edo]], [[87edo]] and [[140edo]].
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| [[Tuning Ranges of Regular Temperaments|valid range]]: [300.000, 327.273] (4 to 11b)
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| nice range: [315.641, 317.263]
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| strict range: [315.641, 317.263] | | strict range: [315.641, 317.263] |
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| [[POTE tuning|POTE generator]]: 317.007 | | [[POTE_tuning|POTE generator]]: 317.007 |
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| Map: [<1 0 1|, <0 6 5|] | | Map: [<1 0 1|, <0 6 5|] |
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| EDOs: [[15edo|15]], [[19edo|19]], [[34edo|34]], [[53edo|53]], [[458edo|458]], [[882edo|882c]] | | EDOs: [[15edo|15]], [[19edo|19]], [[34edo|34]], [[53edo|53]], [[458edo|458]], [[882edo|882c]] |
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| Music: | | Music: |
| [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Parizek/Hanson%20%20Improv.mp3|Hanson Improv]] by [[Petr Parizek]]
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| [[http://clones.soonlabel.com/public/micro/Hanson/daily20110127-in-hanson11.mp3|In Hanson11]] by [[Chris Vaisvil]]
| | [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Parizek/Hanson%20%20Improv.mp3 Hanson Improv] by [[Petr_Parizek|Petr Parizek]] |
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| | [http://clones.soonlabel.com/public/micro/Hanson/daily20110127-in-hanson11.mp3 In Hanson11] by [[Chris_Vaisvil|Chris Vaisvil]] |
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| Analysis and diagrams: | | Analysis and diagrams: |
| <span class="wiki_link_ext">[[@http://dkeenan.com/Music/ChainOfMinor3rds.htm|11 note chain-of-minor-thirds scale]], by David Keenan</span>
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| | <span style="">[http://dkeenan.com/Music/ChainOfMinor3rds.htm 11 note chain-of-minor-thirds scale], by David Keenan</span> |
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| =Seven limit children= | | =Seven limit children= |
| The second comma of the [[Normal lists|normal comma list]] defines which [[7-limit]] family member we are looking at. 875/864, the keemic comma, gives keemun, 4375/4374, the ragisma, gives catakleismic, 5120/5103, hemifamity, gives countercata, 6144/6125, the porwell comma, gives hemikleismic, 245/243, sensamagic, gives clyde, 1029/1024, the gamelisma, gives tritikleismic, and 2401/2400, the breedsma, gives quadritikleismic. Keemun, catakleismic and countercata all have octave period and use the minor third as a generator; catakleismic and countercata define the 7/4 more complexly but more accurately than keemun. Hemikleismic splits the 6/5 in half to get a neutral second generator of 35/32, and clyde similarly splits the 5/3 in half to get a 9/7 generator. Finally, tritikleismic has a 1/3 octave period with minor third generator, and quadritikleismic a 1/4 octave period with the minor third generator. | | The second comma of the [[Normal_lists|normal comma list]] defines which [[7-limit|7-limit]] family member we are looking at. 875/864, the keemic comma, gives keemun, 4375/4374, the ragisma, gives catakleismic, 5120/5103, hemifamity, gives countercata, 6144/6125, the porwell comma, gives hemikleismic, 245/243, sensamagic, gives clyde, 1029/1024, the gamelisma, gives tritikleismic, and 2401/2400, the breedsma, gives quadritikleismic. Keemun, catakleismic and countercata all have octave period and use the minor third as a generator; catakleismic and countercata define the 7/4 more complexly but more accurately than keemun. Hemikleismic splits the 6/5 in half to get a neutral second generator of 35/32, and clyde similarly splits the 5/3 in half to get a 9/7 generator. Finally, tritikleismic has a 1/3 octave period with minor third generator, and quadritikleismic a 1/4 octave period with the minor third generator. |
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| =Keemun= | | =Keemun= |
| [[Comma|Commas]]: 49/48, 126/125 | | [[Comma|Commas]]: 49/48, 126/125 |
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| valid range: [300.000, 327.273] (4 to 11b) | | valid range: [300.000, 327.273] (4 to 11b) |
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| nice range: [308.744, 322.942] | | nice range: [308.744, 322.942] |
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| strict range: [308.744, 322.942] | | strict range: [308.744, 322.942] |
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| [[POTE tuning|POTE generator]]: ~6/5 = 316.473 | | [[POTE_tuning|POTE generator]]: ~6/5 = 316.473 |
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| Map: [<1 0 1 2|, <0 6 5 3|] | | Map: [<1 0 1 2|, <0 6 5 3|] |
| [[Wedgie]]: <<6 5 3 -6 -12 -7|| | | |
| | [[wedgie|Wedgie]]: <<6 5 3 -6 -12 -7|| |
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| EDOs: [[15edo|15]], [[19edo|19]], [[53edo|53d]], [[72edo|72d]], [[91edo|91d]] | | EDOs: [[15edo|15]], [[19edo|19]], [[53edo|53d]], [[72edo|72d]], [[91edo|91d]] |
| [[Badness]]: 0.0274
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| ==11-limit== | | [[Badness|Badness]]: 0.0274 |
| [[Comma]]s: 49/48, 56/55, 100/99 | | |
| | ==11-limit== |
| | [[Comma|Comma]]s: 49/48, 56/55, 100/99 |
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| valid range: [315.789, 320.000] (19 to 15) | | valid range: [315.789, 320.000] (19 to 15) |
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| nice range: [308.744, 324.341] | | nice range: [308.744, 324.341] |
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| strict range: [315.789, 320.000] | | strict range: [315.789, 320.000] |
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| [[POTE tuning|POTE generator]]: ~6/5 = 317.576 | | [[POTE_tuning|POTE generator]]: ~6/5 = 317.576 |
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| Map: [<1 0 1 2 4|, <0 6 5 3 -2|] | | Map: [<1 0 1 2 4|, <0 6 5 3 -2|] |
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| EDOs: [[4edo|4]], [[15edo|15]], [[19edo|19]], [[34edo|34]], [[102edo|102de]] | | EDOs: [[4edo|4]], [[15edo|15]], [[19edo|19]], [[34edo|34]], [[102edo|102de]] |
| [[Badness]]: 0.0274
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| ==13-limit== | | [[Badness|Badness]]: 0.0274 |
| [[Comma]]s: 49/48, 56/55, 78/77, 100/99 | | |
| | ==13-limit== |
| | [[Comma|Comma]]s: 49/48, 56/55, 78/77, 100/99 |
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| valid range: 315.789 (19) | | valid range: 315.789 (19) |
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| nice range: [303.597, 324.341] | | nice range: [303.597, 324.341] |
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| strict range: 315.789 | | strict range: 315.789 |
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| [[POTE tuning|POTE generator]]: ~6/5 = 316.611 | | [[POTE_tuning|POTE generator]]: ~6/5 = 316.611 |
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| Map: [<1 0 1 2 4 5|, <0 6 5 3 -2 -5|] | | Map: [<1 0 1 2 4 5|, <0 6 5 3 -2 -5|] |
| EDOs: [[4edo|4]], [[15edo|15]], [[19edo|19]], [[53def]], [[72edo|72def]]
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| [[Badness]]: 0.0297
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| ===Kema=== | | EDOs: [[4edo|4]], [[15edo|15]], [[19edo|19]], [[53def|53def]], [[72edo|72def]] |
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| | [[Badness|Badness]]: 0.0297 |
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| | ===Kema=== |
| Commas: 49/48, 56/55, 91/90, 100/99 | | Commas: 49/48, 56/55, 91/90, 100/99 |
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| valid range: [315.789, 320.000] (19 to 15) | | valid range: [315.789, 320.000] (19 to 15) |
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| nice range: [308.744, 324.341] | | nice range: [308.744, 324.341] |
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| strict range: [315.789, 320.000] | | strict range: [315.789, 320.000] |
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| Line 84: |
Line 95: |
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| Map: [<1 0 1 2 4 0|, <0 6 5 3 -2 14|] | | Map: [<1 0 1 2 4 0|, <0 6 5 3 -2 14|] |
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| EDOs: 15, 19, 34, 87de | | EDOs: 15, 19, 34, 87de |
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| Badness: 0.0227 | | Badness: 0.0227 |
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| ===Kumbaya=== | | ===Kumbaya=== |
| Commas: 40/39, 49/48, 56/55, 66/65 | | Commas: 40/39, 49/48, 56/55, 66/65 |
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| Line 93: |
Line 106: |
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| Map: [<1 0 1 2 4 4|, <0 6 5 3 -2 -1|] | | Map: [<1 0 1 2 4 4|, <0 6 5 3 -2 -1|] |
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| EDOs: 15, 34f | | EDOs: 15, 34f |
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| Badness: 0.0316 | | Badness: 0.0316 |
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| ==Qeema== | | ==Qeema== |
| Commas: 45/44, 49/48, 126/125 | | Commas: 45/44, 49/48, 126/125 |
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| Line 102: |
Line 117: |
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| Map: [<1 0 1 2 -1|, <0 6 5 3 17|] | | Map: [<1 0 1 2 -1|, <0 6 5 3 17|] |
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| EDOs: 19, 42bcd, 61bcd | | EDOs: 19, 42bcd, 61bcd |
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| Badness: 0.0401 | | Badness: 0.0401 |
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| ===13-limit=== | | ===13-limit=== |
| Commas: 45/44, 49/48, 78/77, 126/125 | | Commas: 45/44, 49/48, 78/77, 126/125 |
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| Line 111: |
Line 128: |
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| Map: [<1 0 1 2 -1 0|, <0 6 5 3 17 14|] | | Map: [<1 0 1 2 -1 0|, <0 6 5 3 17 14|] |
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| EDOs: 19 | | EDOs: 19 |
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| Badness: 0.0294 | | Badness: 0.0294 |
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| ==Darjeeling== | | ==Darjeeling== |
| Commas: 49/48, 55/54, 77/75 | | Commas: 49/48, 55/54, 77/75 |
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| Line 120: |
Line 139: |
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| Map: [<1 0 1 2 0|, <0 6 5 3 13|] | | Map: [<1 0 1 2 0|, <0 6 5 3 13|] |
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| EDOs: 15, 19e, 34e | | EDOs: 15, 19e, 34e |
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| Badness: 0.0276 | | Badness: 0.0276 |
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| ===13-limit Darjeeling=== | | ===13-limit Darjeeling=== |
| Commas: 49/48, 55/54, 66/65, 77/75 | | Commas: 49/48, 55/54, 66/65, 77/75 |
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| Line 129: |
Line 150: |
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| Map: [<1 0 1 2 0 0|, <0 6 5 3 13 14|] | | Map: [<1 0 1 2 0 0|, <0 6 5 3 13 14|] |
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| EDOs: 15, 19e, 34e, 53de | | EDOs: 15, 19e, 34e, 53de |
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| Badness: 0.02144 | | Badness: 0.02144 |
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| =Catalan= | | =Catalan= |
| Commas: 64/63, 15625/15552 | | Commas: 64/63, 15625/15552 |
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| Line 138: |
Line 161: |
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| Map: [<1 0 1 6|, <0 6 5 -12|] | | Map: [<1 0 1 6|, <0 6 5 -12|] |
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| Wedgie: <<6 5 -12 -6 -36 -42|| | | Wedgie: <<6 5 -12 -6 -36 -42|| |
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| EDOs: 15, 34d, 49, 132bcd | | EDOs: 15, 34d, 49, 132bcd |
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| Badness: 0.0949 | | Badness: 0.0949 |
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| ==11-limit== | | ==11-limit== |
| Commas: 64/63, 100/99, 1331/1323 | | Commas: 64/63, 100/99, 1331/1323 |
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| Line 148: |
Line 174: |
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| Map: [<1 0 1 6 4|, <0 6 5 -12 -2|] | | Map: [<1 0 1 6 4|, <0 6 5 -12 -2|] |
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| EDOs: 15, 34d, 49 | | EDOs: 15, 34d, 49 |
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| Badness: 0.0369 | | Badness: 0.0369 |
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| =Catakleismic= | | =Catakleismic= |
| [[Comma|Commas]]: 225/224, 4375/4374 | | [[Comma|Commas]]: 225/224, 4375/4374 |
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| valid range: [315.789, 317.647] (19 to 34) | | valid range: [315.789, 317.647] (19 to 34) |
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| nice range: [315.641, 317.263] | | nice range: [315.641, 317.263] |
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| strict range: [315.789, 317.263] | | strict range: [315.789, 317.263] |
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| [[POTE tuning|POTE generator]]: 316.732 | | [[POTE_tuning|POTE generator]]: 316.732 |
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| Map: [<1 0 1 -3|, <0 6 5 22|] | | Map: [<1 0 1 -3|, <0 6 5 22|] |
| [[Wedgie]]: <<6 5 22 -6 18 37|| | | |
| | [[wedgie|Wedgie]]: <<6 5 22 -6 18 37|| |
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| EDOs: [[19edo|19]], [[53edo|53]], [[72edo|72]], [[197edo|197]], [[269edo|269c]] | | EDOs: [[19edo|19]], [[53edo|53]], [[72edo|72]], [[197edo|197]], [[269edo|269c]] |
| [[Badness]]: 0.0215
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| ==11-limit== | | [[Badness|Badness]]: 0.0215 |
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| | ==11-limit== |
| [[Comma|Commas]]: 225/224, 385/384, 4375/4374 | | [[Comma|Commas]]: 225/224, 385/384, 4375/4374 |
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| valid range: [315.789, 316.981] (19 to 53) | | valid range: [315.789, 316.981] (19 to 53) |
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| nice range: [315.641, 317.263] | | nice range: [315.641, 317.263] |
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| strict range: [315.789, 316.981] | | strict range: [315.789, 316.981] |
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| [[POTE tuning|POTE generator]]: 316.719 | | [[POTE_tuning|POTE generator]]: 316.719 |
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| Map: [<1 0 1 -3 9|, <0 6 5 22 -21|] | | Map: [<1 0 1 -3 9|, <0 6 5 22 -21|] |
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| EDOs: [[19edo|19]], [[53edo|53]], [[72edo|72]], [[197edo|197e]], [[269edo|269ce]], [[341edo|341ce]], [[610edo|610bce]] | | EDOs: [[19edo|19]], [[53edo|53]], [[72edo|72]], [[197edo|197e]], [[269edo|269ce]], [[341edo|341ce]], [[610edo|610bce]] |
| [[Badness]]: 0.0218
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| ==13-limit== | | [[Badness|Badness]]: 0.0218 |
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| | ==13-limit== |
| [[Comma|Commas]]: 169/168, 225/224, 325/324, 540/539 | | [[Comma|Commas]]: 169/168, 225/224, 325/324, 540/539 |
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| valid range: [315.789, 316.981] (19 to 53) | | valid range: [315.789, 316.981] (19 to 53) |
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| nice range: [315.641, 318.309] | | nice range: [315.641, 318.309] |
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| strict range: [315.789, 316.981] | | strict range: [315.789, 316.981] |
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| [[POTE tuning|POTE generator]]: 316.738 | | [[POTE_tuning|POTE generator]]: 316.738 |
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| Map: [<1 0 1 -3 9 0|, <0 6 5 22 -21 14|] | | Map: [<1 0 1 -3 9 0|, <0 6 5 22 -21 14|] |
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| EDOs: [[19edo|19]], [[53edo|53]], [[72edo|72]], [[125edo|125f]], [[197edo|197ef]], [[269edo|269cef]] | | EDOs: [[19edo|19]], [[53edo|53]], [[72edo|72]], [[125edo|125f]], [[197edo|197ef]], [[269edo|269cef]] |
| [[Badness]]: 0.0169
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| =Cataclysmic= | | [[Badness|Badness]]: 0.0169 |
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| | =Cataclysmic= |
| Commas: 99/98, 176/175, 2200/2187 | | Commas: 99/98, 176/175, 2200/2187 |
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| Line 197: |
Line 238: |
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| Map: [<1 0 1 -3 -5|, <0 6 5 22 32|] | | Map: [<1 0 1 -3 -5|, <0 6 5 22 32|] |
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| EDOs: 53, 87d, 140d, 171de, 181de, 193de, 224de, 246de, 277de | | EDOs: 53, 87d, 140d, 171de, 181de, 193de, 224de, 246de, 277de |
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| Badness: 0.0400 | | Badness: 0.0400 |
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| ==13-limit== | | ==13-limit== |
| Commas: 99/98, 169/168, 176/175, 275/273 | | Commas: 99/98, 169/168, 176/175, 275/273 |
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| Line 206: |
Line 249: |
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| Map: [<1 0 1 -3 -5 0|, <0 6 5 22 32 14|] | | Map: [<1 0 1 -3 -5 0|, <0 6 5 22 32 14|] |
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| EDOs: 53, 87d, 140d, 193de, 246de | | EDOs: 53, 87d, 140d, 193de, 246de |
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| Badness: 0.0226 | | Badness: 0.0226 |
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| =Catalytic= | | =Catalytic= |
| Commas: 225/224, 441/440, 4375/4374 | | Commas: 225/224, 441/440, 4375/4374 |
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| Line 215: |
Line 260: |
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| Map: [<1 0 1 -3 -10|, <0 6 5 22 51|] | | Map: [<1 0 1 -3 -10|, <0 6 5 22 51|] |
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| EDOs: 53e, 72 | | EDOs: 53e, 72 |
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| Badness: 0.0304 | | Badness: 0.0304 |
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| ==13-limit== | | ==13-limit== |
| Commas: 169/168 225/224 325/324 1716/1715 | | Commas: 169/168 225/224 325/324 1716/1715 |
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| Line 224: |
Line 271: |
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| Map: [<1 0 1 -3 -10 0|, <0 6 5 22 51 14|] | | Map: [<1 0 1 -3 -10 0|, <0 6 5 22 51 14|] |
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| EDOs: 19e, 53e, 72 | | EDOs: 19e, 53e, 72 |
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| Badness: 0.0223 | | Badness: 0.0223 |
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| =Cataleptic= | | =Cataleptic= |
| Commas: 100/99, 225/224, 864/847 | | Commas: 100/99, 225/224, 864/847 |
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| Line 233: |
Line 282: |
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| Map: [<1 0 1 -3 4|, <0 6 5 22 -2|] | | Map: [<1 0 1 -3 4|, <0 6 5 22 -2|] |
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| EDOs: 19, 34d, 53e | | EDOs: 19, 34d, 53e |
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| Badness: 0.0443 | | Badness: 0.0443 |
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| ==13-limit== | | ==13-limit== |
| Commas: 78/77, 100/99, 144/143, 676/675 | | Commas: 78/77, 100/99, 144/143, 676/675 |
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| Line 242: |
Line 293: |
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| Map: [<1 0 1 -3 4 0|, <0 6 5 22 -2 14|] | | Map: [<1 0 1 -3 4 0|, <0 6 5 22 -2 14|] |
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| EDOs: 19, 34d, 53e, 87de | | EDOs: 19, 34d, 53e, 87de |
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| Badness: 0.0273 | | Badness: 0.0273 |
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| =Countercata= | | =Countercata= |
| [[Comma|Commas]]: 15625/15552, 5120/5103 | | [[Comma|Commas]]: 15625/15552, 5120/5103 |
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| [[POTE tuning|POTE generator]]: 317.121 | | [[POTE_tuning|POTE generator]]: 317.121 |
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| Map: [<1 0 1 11|, <0 6 5 -31|] | | Map: [<1 0 1 11|, <0 6 5 -31|] |
| [[Wedgie]]: <<6 5 -31 -6 -66 -86|| | | |
| | [[wedgie|Wedgie]]: <<6 5 -31 -6 -66 -86|| |
| | |
| EDOs: [[15edo|15]], [[19edo|19]], [[34edo|34]], [[53edo|53]], [[87edo|87]], [[140edo|140]], [[333edo|333]], [[473edo|473]], [[806edo|806b]] | | EDOs: [[15edo|15]], [[19edo|19]], [[34edo|34]], [[53edo|53]], [[87edo|87]], [[140edo|140]], [[333edo|333]], [[473edo|473]], [[806edo|806b]] |
| [[Badness]]: 0.0521
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|
| ==11-limit== | | [[Badness|Badness]]: 0.0521 |
| [[Comma]]s: 385/384, 2200/2187, 3388/3375 | | |
| | ==11-limit== |
| | [[Comma|Comma]]s: 385/384, 2200/2187, 3388/3375 |
|
| |
|
| POTE generator: ~6/5 = 317.162 | | POTE generator: ~6/5 = 317.162 |
|
| |
|
| Map: [<1 0 1 11 -5|, <0 6 5 -31 32|] | | Map: [<1 0 1 11 -5|, <0 6 5 -31 32|] |
| | |
| EDOs: [[34edo|34]], [[53edo|53]], [[87edo|87]], [[140edo|140]], [[227edo|227]] | | EDOs: [[34edo|34]], [[53edo|53]], [[87edo|87]], [[140edo|140]], [[227edo|227]] |
| [[Badness]]: 0.0398
| |
|
| |
|
| ==13-limit== | | [[Badness|Badness]]: 0.0398 |
| [[Comma]]s: 325/324, 352/351, 385/384, 625/624 | | |
| | ==13-limit== |
| | [[Comma|Comma]]s: 325/324, 352/351, 385/384, 625/624 |
|
| |
|
| POTE generator: ~6/5 = 317.162 | | POTE generator: ~6/5 = 317.162 |
|
| |
|
| Map: [<1 0 1 11 -5 0|, <0 6 5 -31 32 14|] | | Map: [<1 0 1 11 -5 0|, <0 6 5 -31 32 14|] |
| | |
| EDOs: [[34edo|34]], [[53edo|53]], [[87edo|87]], [[140edo|140]], [[227edo|227]], [[367edo|367e]], [[507edo|507e]] | | EDOs: [[34edo|34]], [[53edo|53]], [[87edo|87]], [[140edo|140]], [[227edo|227]], [[367edo|367e]], [[507edo|507e]] |
| [[Badness]]: 0.0202
| |
|
| |
|
| =Metakleismic= | | [[Badness|Badness]]: 0.0202 |
| [[Comma]]s: 15625/15552, 179200/177147 | | |
| | =Metakleismic= |
| | [[Comma|Comma]]s: 15625/15552, 179200/177147 |
|
| |
|
| POTE generator: ~6/5 = 317.314 | | POTE generator: ~6/5 = 317.314 |
|
| |
|
| Map: [<1 0 1 -12|, <0 6 5 56|] | | Map: [<1 0 1 -12|, <0 6 5 56|] |
| | |
| Wedgie: <<6 5 56 -6 72 116|| | | Wedgie: <<6 5 56 -6 72 116|| |
| | |
| EDOs: [[15edo|15]], [[19edo|19]], [[34edo|34]], [[87edo|87]], [[121edo|121]], [[208edo|208]] | | EDOs: [[15edo|15]], [[19edo|19]], [[34edo|34]], [[87edo|87]], [[121edo|121]], [[208edo|208]] |
| [[Badness]]: 0.1635
| |
|
| |
|
| ==11-limit== | | [[Badness|Badness]]: 0.1635 |
| [[Comma]]s: 896/891, 2200/2187, 14700/14641 | | |
| | ==11-limit== |
| | [[Comma|Comma]]s: 896/891, 2200/2187, 14700/14641 |
|
| |
|
| POTE generator: ~6/5 = 317.311 | | POTE generator: ~6/5 = 317.311 |
|
| |
|
| Map: [<1 0 1 -12 -5|, <0 6 5 56 32|] | | Map: [<1 0 1 -12 -5|, <0 6 5 56 32|] |
| | |
| EDOs: [[15edo|15]], [[19edo|19]], [[34edo|34]], [[87edo|87]], [[121edo|121]], [[208edo|208]] | | EDOs: [[15edo|15]], [[19edo|19]], [[34edo|34]], [[87edo|87]], [[121edo|121]], [[208edo|208]] |
| [[Badness]]: 0.0486
| |
|
| |
|
| ==13-limit== | | [[Badness|Badness]]: 0.0486 |
| [[Comma]]s: 325/324, 352/351, 364/363, 625/624 | | |
| | ==13-limit== |
| | [[Comma|Comma]]s: 325/324, 352/351, 364/363, 625/624 |
|
| |
|
| POTE generator: ~6/5 = 317.311 | | POTE generator: ~6/5 = 317.311 |
|
| |
|
| Map: [<1 0 1 -12 -5 0|, <0 6 5 56 32 14|] | | Map: [<1 0 1 -12 -5 0|, <0 6 5 56 32 14|] |
| | |
| EDOs: [[15edo|15]], [[19edo|19]], [[34edo|34]], [[87edo|87]], [[121edo|121]], [[208edo|208]] | | EDOs: [[15edo|15]], [[19edo|19]], [[34edo|34]], [[87edo|87]], [[121edo|121]], [[208edo|208]] |
| [[Badness]]: 0.0244
| |
|
| |
|
| =Hemikleismic= | | [[Badness|Badness]]: 0.0244 |
| | |
| | =Hemikleismic= |
| Commas: 4000/3969, 6144/6125 | | Commas: 4000/3969, 6144/6125 |
|
| |
|
| [[POTE tuning|POTE generator]]: 158.649 | | [[POTE_tuning|POTE generator]]: 158.649 |
|
| |
|
| Map: [<1 0 1 4|, <0 12 10 -9|] | | Map: [<1 0 1 4|, <0 12 10 -9|] |
| | |
| EDOs: [[53edo|53]], [[121edo|121]] | | EDOs: [[53edo|53]], [[121edo|121]] |
| | |
| Badness: 0.0521 | | Badness: 0.0521 |
|
| |
|
| ==11-limit== | | ==11-limit== |
| Commas: 121/120, 176/175, 4000/3969 | | Commas: 121/120, 176/175, 4000/3969 |
|
| |
|
| Line 316: |
Line 385: |
|
| |
|
| Map: [<1 0 1 4 2|, <0 12 10 -9 11|] | | Map: [<1 0 1 4 2|, <0 12 10 -9 11|] |
| | |
| EDOs: 15, 38, 53, 68, 121e | | EDOs: 15, 38, 53, 68, 121e |
| | |
| Badness: 0.0380 | | Badness: 0.0380 |
|
| |
|
| ==13-limit== | | ==13-limit== |
| Commas: 121/120, 176/175, 275/273, 325/324 | | Commas: 121/120, 176/175, 275/273, 325/324 |
|
| |
|
| Line 325: |
Line 396: |
|
| |
|
| Map: [<1 0 1 4 2 0|, <0 12 10 -9 11 28|] | | Map: [<1 0 1 4 2 0|, <0 12 10 -9 11 28|] |
| | |
| EDOs: 15, 53, 121e | | EDOs: 15, 53, 121e |
| | |
| Badness: 0.0260 | | Badness: 0.0260 |
|
| |
|
| =Clyde= | | =Clyde= |
| [[Comma|Commas]]: 245/243, 3136/3125 | | [[Comma|Commas]]: 245/243, 3136/3125 |
|
| |
|
| 7 and 9 limit minimax | | 7 and 9 limit minimax |
| | |
| [|1 0 0 0>, |6/25 0 0 12/25>, |6/5 0 0 2/5>, |0 0 0 1>] | | [|1 0 0 0>, |6/25 0 0 12/25>, |6/5 0 0 2/5>, |0 0 0 1>] |
| | |
| [[Eigenmonzo|Eigenmonzos]]: 2, 7 | | [[Eigenmonzo|Eigenmonzos]]: 2, 7 |
|
| |
|
| [[POTE tuning|POTE generator]]: ~9/7 = 441.335 | | [[POTE_tuning|POTE generator]]: ~9/7 = 441.335 |
|
| |
|
| Algebraic generator: real root of 5x^3-6x-3, the Poussami generator. Approximately 441.309 [[Cent|cents]]. Associated recurrence relationship quickly converges. | | Algebraic generator: real root of 5x^3-6x-3, the Poussami generator. Approximately 441.309 [[cent|cents]]. Associated recurrence relationship quickly converges. |
|
| |
|
| Map: [<1 6 6 12|, <0 -12 -10 -25|] | | Map: [<1 6 6 12|, <0 -12 -10 -25|] |
| [[Generator|Generators]]: 2, 9/7 | | |
| [[Edo|Edos]]: [[19edo|19]], [[49edo|49]], [[68edo|68]], [[87edo|87]], [[155edo|155]] | | [[generator|Generators]]: 2, 9/7 |
| | |
| | [[EDO|Edos]]: [[19edo|19]], [[49edo|49]], [[68edo|68]], [[87edo|87]], [[155edo|155]] |
| | |
| Badness: 0.0473 | | Badness: 0.0473 |
|
| |
|
| ==11-limit== | | ==11-limit== |
| Commas: 245/243, 3136/3125, 385/384 | | Commas: 245/243, 3136/3125, 385/384 |
|
| |
|
| Line 350: |
Line 428: |
|
| |
|
| Map: [<1 6 6 12 -5|, <0 -12 -10 -25 23|] | | Map: [<1 6 6 12 -5|, <0 -12 -10 -25 23|] |
| | |
| EDOs: 19, 68, 87, 329bd, 419bd, 503bd, 590bd | | EDOs: 19, 68, 87, 329bd, 419bd, 503bd, 590bd |
| | |
| Badness: 0.0474 | | Badness: 0.0474 |
|
| |
|
| ==13-limit== | | ==13-limit== |
| Commas: 196/195, 245/243, 385/384, 625/624 | | Commas: 196/195, 245/243, 385/384, 625/624 |
|
| |
|
| Line 359: |
Line 439: |
|
| |
|
| Map: [<1 6 6 12 -5 14|, <0 -12 -10 -25 23 -28|] | | Map: [<1 6 6 12 -5 14|, <0 -12 -10 -25 23 -28|] |
| | |
| EDOs: 19, 68, 87, 503bdf, 590bdf | | EDOs: 19, 68, 87, 503bdf, 590bdf |
| | |
| Badness: 0.0268 | | Badness: 0.0268 |
|
| |
|
| =Bikleismic= | | =Bikleismic= |
| Commas: 225/224, 243/242, 4375/4356 | | Commas: 225/224, 243/242, 4375/4356 |
|
| |
|
| Line 368: |
Line 450: |
|
| |
|
| Map: [<2 0 2 -6 -1|, <0 6 5 22 15|] | | Map: [<2 0 2 -6 -1|, <0 6 5 22 15|] |
| | |
| EDOs: 72, 106, 178, 250, 322c, 394c, 466bc, 538bc, 610bc | | EDOs: 72, 106, 178, 250, 322c, 394c, 466bc, 538bc, 610bc |
| | |
| Badness: 0.0293 | | Badness: 0.0293 |
|
| |
|
| ==13-limit== | | ==13-limit== |
| Commas: 169/168, 225/224, 243/242, 325/324 | | Commas: 169/168, 225/224, 243/242, 325/324 |
|
| |
|
| Line 377: |
Line 461: |
|
| |
|
| Map: [<2 0 2 -6 -1 0|, <0 6 5 22 15 14|] | | Map: [<2 0 2 -6 -1 0|, <0 6 5 22 15 14|] |
| | |
| EDOs: 72, 106, 322cff, 394cff, 466bcff, 538bcfff | | EDOs: 72, 106, 322cff, 394cff, 466bcff, 538bcfff |
| | |
| Badness: 0.0218 | | Badness: 0.0218 |
|
| |
|
| =Tritikleismic= | | =Tritikleismic= |
| [[Comma]]s: 15625/15552, 1029/1024 | | [[Comma|Comma]]s: 15625/15552, 1029/1024 |
|
| |
|
| [[POTE tuning|POTE generator]]: 316.872 | | [[POTE_tuning|POTE generator]]: 316.872 |
|
| |
|
| Map: [<3 0 3 10|, <0 6 5 -2|] | | Map: [<3 0 3 10|, <0 6 5 -2|] |
| [[Wedgie]]: <<18 15 -6 -18 -60 -56|| | | |
| | [[wedgie|Wedgie]]: <<18 15 -6 -18 -60 -56|| |
| | |
| EDOs: [[15edo|15]], [[57edo|57]], [[72edo|72]], [[159edo|159]], [[231edo|231]] | | EDOs: [[15edo|15]], [[57edo|57]], [[72edo|72]], [[159edo|159]], [[231edo|231]] |
| [[Badness]]: 0.0563
| |
|
| |
|
| ==11-limit== | | [[Badness|Badness]]: 0.0563 |
| [[Comma]]s: 385/384, 441/440, 4000/3993 | | |
| | ==11-limit== |
| | [[Comma|Comma]]s: 385/384, 441/440, 4000/3993 |
|
| |
|
| [[POTE tuning|POTE generator]]: 316.881 | | [[POTE_tuning|POTE generator]]: 316.881 |
|
| |
|
| Map: [<3 0 3 10 8|, <0 6 5 -2 3|] | | Map: [<3 0 3 10 8|, <0 6 5 -2 3|] |
| | |
| EDOs: [[15edo|15]], [[57edo|57]], [[72edo|72]], [[159edo|159]], [[231edo|231]] | | EDOs: [[15edo|15]], [[57edo|57]], [[72edo|72]], [[159edo|159]], [[231edo|231]] |
| [[Badness]]: 0.0193
| |
|
| |
|
| ==13-limit== | | [[Badness|Badness]]: 0.0193 |
| [[Comma]]s: 325/324, 364/363, 441/440, 625/624 | | |
| | ==13-limit== |
| | [[Comma|Comma]]s: 325/324, 364/363, 441/440, 625/624 |
|
| |
|
| [[POTE tuning|POTE generator]]: 316.959 | | [[POTE_tuning|POTE generator]]: 316.959 |
|
| |
|
| Map: [<3 0 3 10 8 0|, <0 6 5 -2 3 14|] | | Map: [<3 0 3 10 8 0|, <0 6 5 -2 3 14|] |
| | |
| EDOs: [[15edo|15]], [[72edo|72]], 87, 159, 867, 1026 | | EDOs: [[15edo|15]], [[72edo|72]], 87, 159, 867, 1026 |
| [[Badness]]: 0.0157
| |
|
| |
|
| =Quadritikleismic= | | [[Badness|Badness]]: 0.0157 |
| [[Comma]]s: 15625/15552, 2401/2400 | | |
| | =Quadritikleismic= |
| | [[Comma|Comma]]s: 15625/15552, 2401/2400 |
|
| |
|
| [[POTE tuning|POTE generator]]: 316.9999 | | [[POTE_tuning|POTE generator]]: 316.9999 |
|
| |
|
| Map: [<4 0 4 7|, <0 6 5 4|] | | Map: [<4 0 4 7|, <0 6 5 4|] |
| | |
| Wedgie: <<24 20 16 -24 -42 -19|| | | Wedgie: <<24 20 16 -24 -42 -19|| |
| | |
| EDOs: [[68edo|68]], [[72edo|72]], [[140edo|140]], [[212edo|212]], [[1200edo|1200]] | | EDOs: [[68edo|68]], [[72edo|72]], [[140edo|140]], [[212edo|212]], [[1200edo|1200]] |
| [[Badness]]: 0.0392
| |
|
| |
|
| ==11-limit== | | [[Badness|Badness]]: 0.0392 |
| | |
| | ==11-limit== |
| Commas: 385/384, 1375/1372, 6250/6237 | | Commas: 385/384, 1375/1372, 6250/6237 |
|
| |
|
| [[POTE tuning|POTE generator]]: 316.925 | | [[POTE_tuning|POTE generator]]: 316.925 |
|
| |
|
| Map: [<4 0 4 7 17|, <0 6 5 4 -3|] | | Map: [<4 0 4 7 17|, <0 6 5 4 -3|] |
| | |
| EDOs: [[68edo|68]], [[72edo|72]], [[140edo|140]], [[212edo|212]], [[284edo|284]], [[496edo|496]], [[780edo|780]] | | EDOs: [[68edo|68]], [[72edo|72]], [[140edo|140]], [[212edo|212]], [[284edo|284]], [[496edo|496]], [[780edo|780]] |
| [[Badness]]: 0.0234
| |
|
| |
|
| ==13-limit== | | [[Badness|Badness]]: 0.0234 |
| | |
| | ==13-limit== |
| Commas: 325/324, 385/384, 625/624, 1573/1568 | | Commas: 325/324, 385/384, 625/624, 1573/1568 |
|
| |
|
| [[POTE tuning|POTE generator]]: 316.989 | | [[POTE_tuning|POTE generator]]: 316.989 |
|
| |
|
| Map: [<4 0 4 7 17 0|, <0 6 5 4 -3 14|] | | Map: [<4 0 4 7 17 0|, <0 6 5 4 -3 14|] |
| | |
| EDOs: [[68edo|68]], [[72edo|72]], [[140edo|140]], [[212edo|212]] | | EDOs: [[68edo|68]], [[72edo|72]], [[140edo|140]], [[212edo|212]] |
| [[Badness]]: 0.0187
| |
|
| |
|
| =Kleiboh= | | [[Badness|Badness]]: 0.0187 |
| | |
| | =Kleiboh= |
| Commas: 1728/1715, 3125/3087 | | Commas: 1728/1715, 3125/3087 |
|
| |
|
| Line 442: |
Line 542: |
|
| |
|
| Map: [<1 6 6 6|, <0 -18 -15 -13|] | | Map: [<1 6 6 6|, <0 -18 -15 -13|] |
| | |
| Wedgie: <<18 15 13 -18 -30 -12|| | | Wedgie: <<18 15 13 -18 -30 -12|| |
| | |
| EDOs: 49, 53, 314d | | EDOs: 49, 53, 314d |
| | |
| Badness: 0.0765 | | Badness: 0.0765 |
|
| |
|
| ==11-limit== | | ==11-limit== |
| Commas: 176/175, 540/539, 3125/3087 | | Commas: 176/175, 540/539, 3125/3087 |
|
| |
|
| Line 452: |
Line 555: |
|
| |
|
| Map: [<1 6 6 6 14|, <0 -18 -15 -13 -43|] | | Map: [<1 6 6 6 14|, <0 -18 -15 -13 -43|] |
| | |
| EDOs: 49, 53, 102d, 155d | | EDOs: 49, 53, 102d, 155d |
| | |
| Badness: 0.0528 | | Badness: 0.0528 |
|
| |
|
| ==13-limit== | | ==13-limit== |
| Commas: 176/175, 275/273, 325/324, 540/539 | | Commas: 176/175, 275/273, 325/324, 540/539 |
|
| |
|
| Line 461: |
Line 566: |
|
| |
|
| Map: [<1 6 6 6 14 14|, <0 -18 -15 -13 -43 -42|] | | Map: [<1 6 6 6 14 14|, <0 -18 -15 -13 -43 -42|] |
| | |
| EDOs: 53, 102df, 155d | | EDOs: 53, 102df, 155d |
| | |
| Badness: 0.0311 | | Badness: 0.0311 |
|
| |
|
| =Novemkleismic= | | =Novemkleismic= |
| Commas: 15625/15552, 40353607/40310784 | | Commas: 15625/15552, 40353607/40310784 |
|
| |
|
| Line 470: |
Line 577: |
|
| |
|
| Map: [<9 0 9 11|, <0 6 5 6|] | | Map: [<9 0 9 11|, <0 6 5 6|] |
| | |
| Wedgie: <<54 45 54 -54 -66 -1|| | | Wedgie: <<54 45 54 -54 -66 -1|| |
| | |
| EDOs: 72, 261, 333, 405, 477c, 882c | | EDOs: 72, 261, 333, 405, 477c, 882c |
| | |
| Badness: 0.1934 | | Badness: 0.1934 |
|
| |
|
| ==11-limit== | | ==11-limit== |
| Commas: 1375/1372, 4000/3993, 15625/15552 | | Commas: 1375/1372, 4000/3993, 15625/15552 |
|
| |
|
| Line 480: |
Line 590: |
|
| |
|
| Map: [<9 0 9 11 24|, <0 6 5 6 3|] | | Map: [<9 0 9 11 24|, <0 6 5 6 3|] |
| | |
| EDOs: 72, 261, 333, 405, 882c | | EDOs: 72, 261, 333, 405, 882c |
| | |
| Badness: 0.05172 | | Badness: 0.05172 |
|
| |
|
| ==13-limit== | | ==13-limit== |
| Commas: 325/324, 625/624, 1375/1372, 4000/3993 | | Commas: 325/324, 625/624, 1375/1372, 4000/3993 |
|
| |
|
| Line 489: |
Line 601: |
|
| |
|
| Map: [<9 0 9 11 24 0|, <0 6 5 6 3 14|] | | Map: [<9 0 9 11 24 0|, <0 6 5 6 3 14|] |
| | |
| EDOs: 72, 261, 333, 738cf, 1071bcf | | EDOs: 72, 261, 333, 738cf, 1071bcf |
| | |
| Badness: 0.0391 | | Badness: 0.0391 |
|
| |
|
| =Sqrtphi= | | =Sqrtphi= |
| Commas: 15625/15552, 16875/16807 | | Commas: 15625/15552, 16875/16807 |
|
| |
|
| [[POTE tuning|POTE generator]]: ~125/98 = 416.603 cents | | [[POTE_tuning|POTE generator]]: ~125/98 = 416.603 cents |
|
| |
|
| Sqrt(phi) = 416.545 cents | | Sqrt(phi) = 416.545 cents |
|
| |
|
| Map: [<1 12 11 16|, <0 -30 -25 -38|] | | Map: [<1 12 11 16|, <0 -30 -25 -38|] |
| | |
| EDOs: [[49edo|49]], 72, [[193edo|193]], [[265edo|265]] | | EDOs: [[49edo|49]], 72, [[193edo|193]], [[265edo|265]] |
| | |
| Badness: 0.0704 | | Badness: 0.0704 |
|
| |
|
| ==11-limit== | | ==11-limit== |
| Commas: 540/539, 1375/1372, 4375/4356 | | Commas: 540/539, 1375/1372, 4375/4356 |
|
| |
|
| Line 509: |
Line 625: |
|
| |
|
| Map: [<1 12 11 16 17|, <0 -30 -25 -38 -39|] | | Map: [<1 12 11 16 17|, <0 -30 -25 -38 -39|] |
| | |
| EDOs: 49, 72, 193, 265 | | EDOs: 49, 72, 193, 265 |
| | |
| Badness: 0.0255 | | Badness: 0.0255 |
|
| |
|
| ==13-limit== | | ==13-limit== |
| Commas: 325/324, 364/363, 625/624, 1375/1372 | | Commas: 325/324, 364/363, 625/624, 1375/1372 |
|
| |
|
| Line 518: |
Line 636: |
|
| |
|
| Map: [<1 12 11 16 17 28|, <0 -30 -25 -38 -39 -70|] | | Map: [<1 12 11 16 17 28|, <0 -30 -25 -38 -39 -70|] |
| | |
| EDOs: 72, 121, 193 | | EDOs: 72, 121, 193 |
| | |
| Badness: 0.0200 | | Badness: 0.0200 |
|
| |
|
| ==17-limit== | | ==17-limit== |
| Commas: 325/324, 364/363, 375/374, 540/539, 595/594 | | Commas: 325/324, 364/363, 375/374, 540/539, 595/594 |
|
| |
|
| Line 527: |
Line 647: |
|
| |
|
| Map: [<1 12 11 16 17 28 27|, <0 -30 -25 -38 -39 -70 -66|] | | Map: [<1 12 11 16 17 28 27|, <0 -30 -25 -38 -39 -70 -66|] |
| | |
| EDOs: 72, 121, 193 | | EDOs: 72, 121, 193 |
| | |
| Badness: 0.0130 | | Badness: 0.0130 |
|
| |
|
| ==19-limit== | | ==19-limit== |
| Commas: 325/324, 364/363, 375/374, 400/399, 442/441, 595/594 | | Commas: 325/324, 364/363, 375/374, 400/399, 442/441, 595/594 |
|
| |
|
| Line 536: |
Line 658: |
|
| |
|
| Map: [<1 12 11 16 17 28 27 -2|, <0 -30 -25 -38 -39 -70 -66 18|] | | Map: [<1 12 11 16 17 28 27 -2|, <0 -30 -25 -38 -39 -70 -66 18|] |
| | |
| EDOs: 72, 121, 193 | | EDOs: 72, 121, 193 |
| | |
| Badness: 0.0147 | | Badness: 0.0147 |
|
| |
|
| ==Scales== | | ==Scales== |
| [[sqrtphi17]] | | [[sqrtphi17|sqrtphi17]] |
| [[sqrtphi23]] | | |
| [[sqrtphi49]] | | [[sqrtphi23|sqrtphi23]] |
| | |
| | [[sqrtphi49|sqrtphi49]] |
| | |
| | ==Music== |
| | [http://micro.soonlabel.com/sqrt_phi/daily20111123a-sqrt-phi-17.mp3 Prelude for Piano in Square root of Phi Tuning] by [[Chris_Vaisvil|Chris Vaisvil]] |
|
| |
|
| ==Music==
| | [http://micro.soonlabel.com/gene_ward_smith/Others/Sicurella/A%20Fight%20For%20Phi.mp3 A Fight for Phi] by Vito Sicurella |
| [[http://micro.soonlabel.com/sqrt_phi/daily20111123a-sqrt-phi-17.mp3|Prelude for Piano in Square root of Phi Tuning]] by [[Chris Vaisvil]]
| | [[Category:family]] |
| [[http://micro.soonlabel.com/gene_ward_smith/Others/Sicurella/A%20Fight%20For%20Phi.mp3|A Fight for Phi]] by Vito Sicurella</pre></div>
| | [[Category:kleismic]] |
| <h4>Original HTML content:</h4>
| | [[Category:list]] |
| <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>Kleismic family</title></head><body><span style="display: block; text-align: right;"><!-- ws:start:WikiTextTocRule:108:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:108 --><!-- ws:start:WikiTextTocRule:109: --><div style="margin-left: 1em;"><a href="#Seven limit children">Seven limit children</a></div>
| | [[Category:listen]] |
| <!-- ws:end:WikiTextTocRule:109 --><!-- ws:start:WikiTextTocRule:110: --><div style="margin-left: 1em;"><a href="#Keemun">Keemun</a></div>
| | [[Category:overview]] |
| <!-- ws:end:WikiTextTocRule:110 --><!-- ws:start:WikiTextTocRule:111: --><div style="margin-left: 2em;"><a href="#Keemun-11-limit">11-limit</a></div>
| | [[Category:theory]] |
| <!-- ws:end:WikiTextTocRule:111 --><!-- ws:start:WikiTextTocRule:112: --><div style="margin-left: 2em;"><a href="#Keemun-13-limit">13-limit</a></div>
| | [[Category:todo:add_definition]] |
| <!-- ws:end:WikiTextTocRule:112 --><!-- ws:start:WikiTextTocRule:113: --><div style="margin-left: 3em;"><a href="#Keemun-13-limit-Kema">Kema</a></div>
| |
| <!-- ws:end:WikiTextTocRule:113 --><!-- ws:start:WikiTextTocRule:114: --><div style="margin-left: 3em;"><a href="#Keemun-13-limit-Kumbaya">Kumbaya</a></div>
| |
| <!-- ws:end:WikiTextTocRule:114 --><!-- ws:start:WikiTextTocRule:115: --><div style="margin-left: 2em;"><a href="#Keemun-Qeema">Qeema</a></div>
| |
| <!-- ws:end:WikiTextTocRule:115 --><!-- ws:start:WikiTextTocRule:116: --><div style="margin-left: 3em;"><a href="#Keemun-Qeema-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:116 --><!-- ws:start:WikiTextTocRule:117: --><div style="margin-left: 2em;"><a href="#Keemun-Darjeeling">Darjeeling</a></div>
| |
| <!-- ws:end:WikiTextTocRule:117 --><!-- ws:start:WikiTextTocRule:118: --><div style="margin-left: 3em;"><a href="#Keemun-Darjeeling-13-limit Darjeeling">13-limit Darjeeling</a></div>
| |
| <!-- ws:end:WikiTextTocRule:118 --><!-- ws:start:WikiTextTocRule:119: --><div style="margin-left: 1em;"><a href="#Catalan">Catalan</a></div>
| |
| <!-- ws:end:WikiTextTocRule:119 --><!-- ws:start:WikiTextTocRule:120: --><div style="margin-left: 2em;"><a href="#Catalan-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:120 --><!-- ws:start:WikiTextTocRule:121: --><div style="margin-left: 1em;"><a href="#Catakleismic">Catakleismic</a></div>
| |
| <!-- ws:end:WikiTextTocRule:121 --><!-- ws:start:WikiTextTocRule:122: --><div style="margin-left: 2em;"><a href="#Catakleismic-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:122 --><!-- ws:start:WikiTextTocRule:123: --><div style="margin-left: 2em;"><a href="#Catakleismic-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:123 --><!-- ws:start:WikiTextTocRule:124: --><div style="margin-left: 1em;"><a href="#Cataclysmic">Cataclysmic</a></div>
| |
| <!-- ws:end:WikiTextTocRule:124 --><!-- ws:start:WikiTextTocRule:125: --><div style="margin-left: 2em;"><a href="#Cataclysmic-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:125 --><!-- ws:start:WikiTextTocRule:126: --><div style="margin-left: 1em;"><a href="#Catalytic">Catalytic</a></div>
| |
| <!-- ws:end:WikiTextTocRule:126 --><!-- ws:start:WikiTextTocRule:127: --><div style="margin-left: 2em;"><a href="#Catalytic-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:127 --><!-- ws:start:WikiTextTocRule:128: --><div style="margin-left: 1em;"><a href="#Cataleptic">Cataleptic</a></div>
| |
| <!-- ws:end:WikiTextTocRule:128 --><!-- ws:start:WikiTextTocRule:129: --><div style="margin-left: 2em;"><a href="#Cataleptic-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:129 --><!-- ws:start:WikiTextTocRule:130: --><div style="margin-left: 1em;"><a href="#Countercata">Countercata</a></div>
| |
| <!-- ws:end:WikiTextTocRule:130 --><!-- ws:start:WikiTextTocRule:131: --><div style="margin-left: 2em;"><a href="#Countercata-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:131 --><!-- ws:start:WikiTextTocRule:132: --><div style="margin-left: 2em;"><a href="#Countercata-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:132 --><!-- ws:start:WikiTextTocRule:133: --><div style="margin-left: 1em;"><a href="#Metakleismic">Metakleismic</a></div>
| |
| <!-- ws:end:WikiTextTocRule:133 --><!-- ws:start:WikiTextTocRule:134: --><div style="margin-left: 2em;"><a href="#Metakleismic-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:134 --><!-- ws:start:WikiTextTocRule:135: --><div style="margin-left: 2em;"><a href="#Metakleismic-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:135 --><!-- ws:start:WikiTextTocRule:136: --><div style="margin-left: 1em;"><a href="#Hemikleismic">Hemikleismic</a></div>
| |
| <!-- ws:end:WikiTextTocRule:136 --><!-- ws:start:WikiTextTocRule:137: --><div style="margin-left: 2em;"><a href="#Hemikleismic-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:137 --><!-- ws:start:WikiTextTocRule:138: --><div style="margin-left: 2em;"><a href="#Hemikleismic-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:138 --><!-- ws:start:WikiTextTocRule:139: --><div style="margin-left: 1em;"><a href="#Clyde">Clyde</a></div>
| |
| <!-- ws:end:WikiTextTocRule:139 --><!-- ws:start:WikiTextTocRule:140: --><div style="margin-left: 2em;"><a href="#Clyde-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:140 --><!-- ws:start:WikiTextTocRule:141: --><div style="margin-left: 2em;"><a href="#Clyde-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:141 --><!-- ws:start:WikiTextTocRule:142: --><div style="margin-left: 1em;"><a href="#Bikleismic">Bikleismic</a></div>
| |
| <!-- ws:end:WikiTextTocRule:142 --><!-- ws:start:WikiTextTocRule:143: --><div style="margin-left: 2em;"><a href="#Bikleismic-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:143 --><!-- ws:start:WikiTextTocRule:144: --><div style="margin-left: 1em;"><a href="#Tritikleismic">Tritikleismic</a></div>
| |
| <!-- ws:end:WikiTextTocRule:144 --><!-- ws:start:WikiTextTocRule:145: --><div style="margin-left: 2em;"><a href="#Tritikleismic-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:145 --><!-- ws:start:WikiTextTocRule:146: --><div style="margin-left: 2em;"><a href="#Tritikleismic-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:146 --><!-- ws:start:WikiTextTocRule:147: --><div style="margin-left: 1em;"><a href="#Quadritikleismic">Quadritikleismic</a></div>
| |
| <!-- ws:end:WikiTextTocRule:147 --><!-- ws:start:WikiTextTocRule:148: --><div style="margin-left: 2em;"><a href="#Quadritikleismic-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:148 --><!-- ws:start:WikiTextTocRule:149: --><div style="margin-left: 2em;"><a href="#Quadritikleismic-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:149 --><!-- ws:start:WikiTextTocRule:150: --><div style="margin-left: 1em;"><a href="#Kleiboh">Kleiboh</a></div>
| |
| <!-- ws:end:WikiTextTocRule:150 --><!-- ws:start:WikiTextTocRule:151: --><div style="margin-left: 2em;"><a href="#Kleiboh-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:151 --><!-- ws:start:WikiTextTocRule:152: --><div style="margin-left: 2em;"><a href="#Kleiboh-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:152 --><!-- ws:start:WikiTextTocRule:153: --><div style="margin-left: 1em;"><a href="#Novemkleismic">Novemkleismic</a></div>
| |
| <!-- ws:end:WikiTextTocRule:153 --><!-- ws:start:WikiTextTocRule:154: --><div style="margin-left: 2em;"><a href="#Novemkleismic-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:154 --><!-- ws:start:WikiTextTocRule:155: --><div style="margin-left: 2em;"><a href="#Novemkleismic-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:155 --><!-- ws:start:WikiTextTocRule:156: --><div style="margin-left: 1em;"><a href="#Sqrtphi">Sqrtphi</a></div>
| |
| <!-- ws:end:WikiTextTocRule:156 --><!-- ws:start:WikiTextTocRule:157: --><div style="margin-left: 2em;"><a href="#Sqrtphi-11-limit">11-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:157 --><!-- ws:start:WikiTextTocRule:158: --><div style="margin-left: 2em;"><a href="#Sqrtphi-13-limit">13-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:158 --><!-- ws:start:WikiTextTocRule:159: --><div style="margin-left: 2em;"><a href="#Sqrtphi-17-limit">17-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:159 --><!-- ws:start:WikiTextTocRule:160: --><div style="margin-left: 2em;"><a href="#Sqrtphi-19-limit">19-limit</a></div>
| |
| <!-- ws:end:WikiTextTocRule:160 --><!-- ws:start:WikiTextTocRule:161: --><div style="margin-left: 2em;"><a href="#Sqrtphi-Scales">Scales</a></div>
| |
| <!-- ws:end:WikiTextTocRule:161 --><!-- ws:start:WikiTextTocRule:162: --><div style="margin-left: 2em;"><a href="#Sqrtphi-Music">Music</a></div>
| |
| <!-- ws:end:WikiTextTocRule:162 --><!-- ws:start:WikiTextTocRule:163: --></div>
| |
| <!-- ws:end:WikiTextTocRule:163 --><br />
| |
| <br />
| |
| <br />
| |
| <br />
| |
| Other languages: <a class="wiki_link" href="http://xenharmonie.wikispaces.com/Hanson%20Kleismisch">Deutsch</a><br />
| |
| </span><br />
| |
| The <a class="wiki_link" href="/5-limit">5-limit</a> parent comma for the <strong>kleismic family</strong> is 15625/15552, the kleisma. Its monzo is |-6 -5 6&gt;, and flipping that yields &lt;&lt;6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. This 5-limit temperament (virtually a microtemperament) is commonly called <strong>Hanson</strong>, and 14\53 is about perfect as a hanson generator, though 9\34 also makes sense, and 5\19 and 4\15 are possible. Other tunings include <a class="wiki_link" href="/72edo">72edo</a>, <a class="wiki_link" href="/87edo">87edo</a> and <a class="wiki_link" href="/140edo">140edo</a>.<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Tuning%20Ranges%20of%20Regular%20Temperaments">valid range</a>: [300.000, 327.273] (4 to 11b)<br />
| |
| nice range: [315.641, 317.263]<br />
| |
| strict range: [315.641, 317.263]<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 317.007<br />
| |
| <br />
| |
| Map: [&lt;1 0 1|, &lt;0 6 5|]<br />
| |
| EDOs: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/458edo">458</a>, <a class="wiki_link" href="/882edo">882c</a><br />
| |
| <br />
| |
| Music:<br />
| |
| <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Parizek/Hanson%20%20Improv.mp3" rel="nofollow">Hanson Improv</a> by <a class="wiki_link" href="/Petr%20Parizek">Petr Parizek</a><br />
| |
| <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/Hanson/daily20110127-in-hanson11.mp3" rel="nofollow">In Hanson11</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br />
| |
| <br />
| |
| Analysis and diagrams:<br />
| |
| <span class="wiki_link_ext"><a class="wiki_link_ext" href="http://dkeenan.com/Music/ChainOfMinor3rds.htm" rel="nofollow" target="_blank">11 note chain-of-minor-thirds scale</a>, by David Keenan</span><br />
| |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Seven limit children</h1>
| |
| The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which <a class="wiki_link" href="/7-limit">7-limit</a> family member we are looking at. 875/864, the keemic comma, gives keemun, 4375/4374, the ragisma, gives catakleismic, 5120/5103, hemifamity, gives countercata, 6144/6125, the porwell comma, gives hemikleismic, 245/243, sensamagic, gives clyde, 1029/1024, the gamelisma, gives tritikleismic, and 2401/2400, the breedsma, gives quadritikleismic. Keemun, catakleismic and countercata all have octave period and use the minor third as a generator; catakleismic and countercata define the 7/4 more complexly but more accurately than keemun. Hemikleismic splits the 6/5 in half to get a neutral second generator of 35/32, and clyde similarly splits the 5/3 in half to get a 9/7 generator. Finally, tritikleismic has a 1/3 octave period with minor third generator, and quadritikleismic a 1/4 octave period with the minor third generator.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Keemun"></a><!-- ws:end:WikiTextHeadingRule:2 -->Keemun</h1>
| |
| <a class="wiki_link" href="/Comma">Commas</a>: 49/48, 126/125<br />
| |
| <br />
| |
| valid range: [300.000, 327.273] (4 to 11b)<br />
| |
| nice range: [308.744, 322.942]<br />
| |
| strict range: [308.744, 322.942]<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~6/5 = 316.473<br />
| |
| <br />
| |
| Map: [&lt;1 0 1 2|, &lt;0 6 5 3|]<br />
| |
| <a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;6 5 3 -6 -12 -7||<br />
| |
| EDOs: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/53edo">53d</a>, <a class="wiki_link" href="/72edo">72d</a>, <a class="wiki_link" href="/91edo">91d</a><br />
| |
| <a class="wiki_link" href="/Badness">Badness</a>: 0.0274<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Keemun-11-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit</h2>
| |
| <a class="wiki_link" href="/Comma">Comma</a>s: 49/48, 56/55, 100/99<br />
| |
| <br />
| |
| valid range: [315.789, 320.000] (19 to 15)<br />
| |
| nice range: [308.744, 324.341]<br />
| |
| strict range: [315.789, 320.000]<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~6/5 = 317.576<br />
| |
| <br />
| |
| Map: [&lt;1 0 1 2 4|, &lt;0 6 5 3 -2|]<br />
| |
| EDOs: <a class="wiki_link" href="/4edo">4</a>, <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/102edo">102de</a><br />
| |
| <a class="wiki_link" href="/Badness">Badness</a>: 0.0274<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Keemun-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h2>
| |
| <a class="wiki_link" href="/Comma">Comma</a>s: 49/48, 56/55, 78/77, 100/99<br />
| |
| <br />
| |
| valid range: 315.789 (19)<br />
| |
| nice range: [303.597, 324.341]<br />
| |
| strict range: 315.789<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~6/5 = 316.611<br />
| |
| <br />
| |
| Map: [&lt;1 0 1 2 4 5|, &lt;0 6 5 3 -2 -5|]<br />
| |
| EDOs: <a class="wiki_link" href="/4edo">4</a>, <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/53def">53def</a>, <a class="wiki_link" href="/72edo">72def</a><br />
| |
| <a class="wiki_link" href="/Badness">Badness</a>: 0.0297<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="Keemun-13-limit-Kema"></a><!-- ws:end:WikiTextHeadingRule:8 -->Kema</h3>
| |
| Commas: 49/48, 56/55, 91/90, 100/99<br />
| |
| <br />
| |
| valid range: [315.789, 320.000] (19 to 15)<br />
| |
| nice range: [308.744, 324.341]<br />
| |
| strict range: [315.789, 320.000]<br />
| |
| <br />
| |
| POTE generator: ~6/5 = 317.423<br />
| |
| <br />
| |
| Map: [&lt;1 0 1 2 4 0|, &lt;0 6 5 3 -2 14|]<br />
| |
| EDOs: 15, 19, 34, 87de<br />
| |
| Badness: 0.0227<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="Keemun-13-limit-Kumbaya"></a><!-- ws:end:WikiTextHeadingRule:10 -->Kumbaya</h3>
| |
| Commas: 40/39, 49/48, 56/55, 66/65<br />
| |
| <br />
| |
| POTE generator: ~6/5 = 318.595<br />
| |
| <br />
| |
| Map: [&lt;1 0 1 2 4 4|, &lt;0 6 5 3 -2 -1|]<br />
| |
| EDOs: 15, 34f<br />
| |
| Badness: 0.0316<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Keemun-Qeema"></a><!-- ws:end:WikiTextHeadingRule:12 -->Qeema</h2>
| |
| Commas: 45/44, 49/48, 126/125<br />
| |
| <br />
| |
| POTE generator: ~6/5 = 314.730<br />
| |
| <br />
| |
| Map: [&lt;1 0 1 2 -1|, &lt;0 6 5 3 17|]<br />
| |
| EDOs: 19, 42bcd, 61bcd<br />
| |
| Badness: 0.0401<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="Keemun-Qeema-13-limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->13-limit</h3>
| |
| Commas: 45/44, 49/48, 78/77, 126/125<br />
| |
| <br />
| |
| POTE generator: ~6/5 = 315.044<br />
| |
| <br />
| |
| Map: [&lt;1 0 1 2 -1 0|, &lt;0 6 5 3 17 14|]<br />
| |
| EDOs: 19<br />
| |
| Badness: 0.0294<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Keemun-Darjeeling"></a><!-- ws:end:WikiTextHeadingRule:16 -->Darjeeling</h2>
| |
| Commas: 49/48, 55/54, 77/75<br />
| |
| <br />
| |
| POTE generator: ~6/5 = 317.656<br />
| |
| <br />
| |
| Map: [&lt;1 0 1 2 0|, &lt;0 6 5 3 13|]<br />
| |
| EDOs: 15, 19e, 34e<br />
| |
| Badness: 0.0276<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:18:&lt;h3&gt; --><h3 id="toc9"><a name="Keemun-Darjeeling-13-limit Darjeeling"></a><!-- ws:end:WikiTextHeadingRule:18 -->13-limit Darjeeling</h3>
| |
| Commas: 49/48, 55/54, 66/65, 77/75<br />
| |
| <br />
| |
| POTE generator: ~6/5 = 317.298<br />
| |
| <br />
| |
| Map: [&lt;1 0 1 2 0 0|, &lt;0 6 5 3 13 14|]<br />
| |
| EDOs: 15, 19e, 34e, 53de<br />
| |
| Badness: 0.02144<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Catalan"></a><!-- ws:end:WikiTextHeadingRule:20 -->Catalan</h1>
| |
| Commas: 64/63, 15625/15552<br />
| |
| <br />
| |
| POTE generator: ~6/5 = 318.267<br />
| |
| <br />
| |
| Map: [&lt;1 0 1 6|, &lt;0 6 5 -12|]<br />
| |
| Wedgie: &lt;&lt;6 5 -12 -6 -36 -42||<br />
| |
| EDOs: 15, 34d, 49, 132bcd<br />
| |
| Badness: 0.0949<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Catalan-11-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->11-limit</h2>
| |
| Commas: 64/63, 100/99, 1331/1323<br />
| |
| <br />
| |
| POTE generator: ~6/5 = 318.282<br />
| |
| <br />
| |
| Map: [&lt;1 0 1 6 4|, &lt;0 6 5 -12 -2|]<br />
| |
| EDOs: 15, 34d, 49<br />
| |
| Badness: 0.0369<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc12"><a name="Catakleismic"></a><!-- ws:end:WikiTextHeadingRule:24 -->Catakleismic</h1>
| |
| <a class="wiki_link" href="/Comma">Commas</a>: 225/224, 4375/4374<br />
| |
| <br />
| |
| valid range: [315.789, 317.647] (19 to 34)<br />
| |
| nice range: [315.641, 317.263]<br />
| |
| strict range: [315.789, 317.263]<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.732<br />
| |
| <br />
| |
| Map: [&lt;1 0 1 -3|, &lt;0 6 5 22|]<br />
| |
| <a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;6 5 22 -6 18 37||<br />
| |
| EDOs: <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/197edo">197</a>, <a class="wiki_link" href="/269edo">269c</a><br />
| |
| <a class="wiki_link" href="/Badness">Badness</a>: 0.0215<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc13"><a name="Catakleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->11-limit</h2>
| |
| <a class="wiki_link" href="/Comma">Commas</a>: 225/224, 385/384, 4375/4374<br />
| |
| <br />
| |
| valid range: [315.789, 316.981] (19 to 53)<br />
| |
| nice range: [315.641, 317.263]<br />
| |
| strict range: [315.789, 316.981]<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.719<br />
| |
| <br />
| |
| Map: [&lt;1 0 1 -3 9|, &lt;0 6 5 22 -21|]<br />
| |
| EDOs: <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/197edo">197e</a>, <a class="wiki_link" href="/269edo">269ce</a>, <a class="wiki_link" href="/341edo">341ce</a>, <a class="wiki_link" href="/610edo">610bce</a><br />
| |
| <a class="wiki_link" href="/Badness">Badness</a>: 0.0218<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="Catakleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:28 -->13-limit</h2>
| |
| <a class="wiki_link" href="/Comma">Commas</a>: 169/168, 225/224, 325/324, 540/539<br />
| |
| <br />
| |
| valid range: [315.789, 316.981] (19 to 53)<br />
| |
| nice range: [315.641, 318.309]<br />
| |
| strict range: [315.789, 316.981]<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.738<br />
| |
| <br />
| |
| Map: [&lt;1 0 1 -3 9 0|, &lt;0 6 5 22 -21 14|]<br />
| |
| EDOs: <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/125edo">125f</a>, <a class="wiki_link" href="/197edo">197ef</a>, <a class="wiki_link" href="/269edo">269cef</a><br />
| |
| <a class="wiki_link" href="/Badness">Badness</a>: 0.0169<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="Cataclysmic"></a><!-- ws:end:WikiTextHeadingRule:30 -->Cataclysmic</h1>
| |
| Commas: 99/98, 176/175, 2200/2187<br />
| |
| <br />
| |
| POTE generator: ~6/5 = 317.042<br />
| |
| <br />
| |
| Map: [&lt;1 0 1 -3 -5|, &lt;0 6 5 22 32|]<br />
| |
| EDOs: 53, 87d, 140d, 171de, 181de, 193de, 224de, 246de, 277de<br />
| |
| Badness: 0.0400<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Cataclysmic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->13-limit</h2>
| |
| Commas: 99/98, 169/168, 176/175, 275/273<br />
| |
| <br />
| |
| POTE generator: ~6/5 = 317.036<br />
| |
| <br />
| |
| Map: [&lt;1 0 1 -3 -5 0|, &lt;0 6 5 22 32 14|]<br />
| |
| EDOs: 53, 87d, 140d, 193de, 246de<br />
| |
| Badness: 0.0226<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:34:&lt;h1&gt; --><h1 id="toc17"><a name="Catalytic"></a><!-- ws:end:WikiTextHeadingRule:34 -->Catalytic</h1>
| |
| Commas: 225/224, 441/440, 4375/4374<br />
| |
| <br />
| |
| POTE generator: ~6/5 = 316.653<br />
| |
| <br />
| |
| Map: [&lt;1 0 1 -3 -10|, &lt;0 6 5 22 51|]<br />
| |
| EDOs: 53e, 72<br />
| |
| Badness: 0.0304<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Catalytic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:36 -->13-limit</h2>
| |
| Commas: 169/168 225/224 325/324 1716/1715<br />
| |
| <br />
| |
| POTE generator: ~6/5 = 316.639<br />
| |
| <br />
| |
| Map: [&lt;1 0 1 -3 -10 0|, &lt;0 6 5 22 51 14|]<br />
| |
| EDOs: 19e, 53e, 72<br />
| |
| Badness: 0.0223<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:38:&lt;h1&gt; --><h1 id="toc19"><a name="Cataleptic"></a><!-- ws:end:WikiTextHeadingRule:38 -->Cataleptic</h1>
| |
| Commas: 100/99, 225/224, 864/847<br />
| |
| <br />
| |
| POTE generator: ~6/5 = 317.083<br />
| |
| <br />
| |
| Map: [&lt;1 0 1 -3 4|, &lt;0 6 5 22 -2|]<br />
| |
| EDOs: 19, 34d, 53e<br />
| |
| Badness: 0.0443<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="Cataleptic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:40 -->13-limit</h2>
| |
| Commas: 78/77, 100/99, 144/143, 676/675<br />
| |
| <br />
| |
| POTE generator: ~6/5 = 317.118<br />
| |
| <br />
| |
| Map: [&lt;1 0 1 -3 4 0|, &lt;0 6 5 22 -2 14|]<br />
| |
| EDOs: 19, 34d, 53e, 87de<br />
| |
| Badness: 0.0273<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:42:&lt;h1&gt; --><h1 id="toc21"><a name="Countercata"></a><!-- ws:end:WikiTextHeadingRule:42 -->Countercata</h1>
| |
| <a class="wiki_link" href="/Comma">Commas</a>: 15625/15552, 5120/5103<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 317.121<br />
| |
| <br />
| |
| Map: [&lt;1 0 1 11|, &lt;0 6 5 -31|]<br />
| |
| <a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;6 5 -31 -6 -66 -86||<br />
| |
| EDOs: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/333edo">333</a>, <a class="wiki_link" href="/473edo">473</a>, <a class="wiki_link" href="/806edo">806b</a><br />
| |
| <a class="wiki_link" href="/Badness">Badness</a>: 0.0521<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc22"><a name="Countercata-11-limit"></a><!-- ws:end:WikiTextHeadingRule:44 -->11-limit</h2>
| |
| <a class="wiki_link" href="/Comma">Comma</a>s: 385/384, 2200/2187, 3388/3375<br />
| |
| <br />
| |
| POTE generator: ~6/5 = 317.162<br />
| |
| <br />
| |
| Map: [&lt;1 0 1 11 -5|, &lt;0 6 5 -31 32|]<br />
| |
| EDOs: <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/227edo">227</a><br />
| |
| <a class="wiki_link" href="/Badness">Badness</a>: 0.0398<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:46:&lt;h2&gt; --><h2 id="toc23"><a name="Countercata-13-limit"></a><!-- ws:end:WikiTextHeadingRule:46 -->13-limit</h2>
| |
| <a class="wiki_link" href="/Comma">Comma</a>s: 325/324, 352/351, 385/384, 625/624<br />
| |
| <br />
| |
| POTE generator: ~6/5 = 317.162<br />
| |
| <br />
| |
| Map: [&lt;1 0 1 11 -5 0|, &lt;0 6 5 -31 32 14|]<br />
| |
| EDOs: <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/227edo">227</a>, <a class="wiki_link" href="/367edo">367e</a>, <a class="wiki_link" href="/507edo">507e</a><br />
| |
| <a class="wiki_link" href="/Badness">Badness</a>: 0.0202<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:48:&lt;h1&gt; --><h1 id="toc24"><a name="Metakleismic"></a><!-- ws:end:WikiTextHeadingRule:48 -->Metakleismic</h1>
| |
| <a class="wiki_link" href="/Comma">Comma</a>s: 15625/15552, 179200/177147<br />
| |
| <br />
| |
| POTE generator: ~6/5 = 317.314<br />
| |
| <br />
| |
| Map: [&lt;1 0 1 -12|, &lt;0 6 5 56|]<br />
| |
| Wedgie: &lt;&lt;6 5 56 -6 72 116||<br />
| |
| EDOs: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/121edo">121</a>, <a class="wiki_link" href="/208edo">208</a><br />
| |
| <a class="wiki_link" href="/Badness">Badness</a>: 0.1635<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:50:&lt;h2&gt; --><h2 id="toc25"><a name="Metakleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:50 -->11-limit</h2>
| |
| <a class="wiki_link" href="/Comma">Comma</a>s: 896/891, 2200/2187, 14700/14641<br />
| |
| <br />
| |
| POTE generator: ~6/5 = 317.311<br />
| |
| <br />
| |
| Map: [&lt;1 0 1 -12 -5|, &lt;0 6 5 56 32|]<br />
| |
| EDOs: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/121edo">121</a>, <a class="wiki_link" href="/208edo">208</a><br />
| |
| <a class="wiki_link" href="/Badness">Badness</a>: 0.0486<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:52:&lt;h2&gt; --><h2 id="toc26"><a name="Metakleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:52 -->13-limit</h2>
| |
| <a class="wiki_link" href="/Comma">Comma</a>s: 325/324, 352/351, 364/363, 625/624<br />
| |
| <br />
| |
| POTE generator: ~6/5 = 317.311<br />
| |
| <br />
| |
| Map: [&lt;1 0 1 -12 -5 0|, &lt;0 6 5 56 32 14|]<br />
| |
| EDOs: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/34edo">34</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/121edo">121</a>, <a class="wiki_link" href="/208edo">208</a><br />
| |
| <a class="wiki_link" href="/Badness">Badness</a>: 0.0244<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:54:&lt;h1&gt; --><h1 id="toc27"><a name="Hemikleismic"></a><!-- ws:end:WikiTextHeadingRule:54 -->Hemikleismic</h1>
| |
| Commas: 4000/3969, 6144/6125<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 158.649<br />
| |
| <br />
| |
| Map: [&lt;1 0 1 4|, &lt;0 12 10 -9|]<br />
| |
| EDOs: <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/121edo">121</a><br />
| |
| Badness: 0.0521<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:56:&lt;h2&gt; --><h2 id="toc28"><a name="Hemikleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:56 -->11-limit</h2>
| |
| Commas: 121/120, 176/175, 4000/3969<br />
| |
| <br />
| |
| POTE generator: ~11/10 = 158.677<br />
| |
| <br />
| |
| Map: [&lt;1 0 1 4 2|, &lt;0 12 10 -9 11|]<br />
| |
| EDOs: 15, 38, 53, 68, 121e<br />
| |
| Badness: 0.0380<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:58:&lt;h2&gt; --><h2 id="toc29"><a name="Hemikleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:58 -->13-limit</h2>
| |
| Commas: 121/120, 176/175, 275/273, 325/324<br />
| |
| <br />
| |
| POTE generator: ~11/10 = 158.655<br />
| |
| <br />
| |
| Map: [&lt;1 0 1 4 2 0|, &lt;0 12 10 -9 11 28|]<br />
| |
| EDOs: 15, 53, 121e<br />
| |
| Badness: 0.0260<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:60:&lt;h1&gt; --><h1 id="toc30"><a name="Clyde"></a><!-- ws:end:WikiTextHeadingRule:60 -->Clyde</h1>
| |
| <a class="wiki_link" href="/Comma">Commas</a>: 245/243, 3136/3125<br />
| |
| <br />
| |
| 7 and 9 limit minimax<br />
| |
| [|1 0 0 0&gt;, |6/25 0 0 12/25&gt;, |6/5 0 0 2/5&gt;, |0 0 0 1&gt;]<br />
| |
| <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 7<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~9/7 = 441.335<br />
| |
| <br />
| |
| Algebraic generator: real root of 5x^3-6x-3, the Poussami generator. Approximately 441.309 <a class="wiki_link" href="/Cent">cents</a>. Associated recurrence relationship quickly converges.<br />
| |
| <br />
| |
| Map: [&lt;1 6 6 12|, &lt;0 -12 -10 -25|]<br />
| |
| <a class="wiki_link" href="/Generator">Generators</a>: 2, 9/7<br />
| |
| <a class="wiki_link" href="/Edo">Edos</a>: <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/49edo">49</a>, <a class="wiki_link" href="/68edo">68</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/155edo">155</a><br />
| |
| Badness: 0.0473<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:62:&lt;h2&gt; --><h2 id="toc31"><a name="Clyde-11-limit"></a><!-- ws:end:WikiTextHeadingRule:62 -->11-limit</h2>
| |
| Commas: 245/243, 3136/3125, 385/384<br />
| |
| <br />
| |
| POTE generator: ~9/7 = 441.355<br />
| |
| <br />
| |
| Map: [&lt;1 6 6 12 -5|, &lt;0 -12 -10 -25 23|]<br />
| |
| EDOs: 19, 68, 87, 329bd, 419bd, 503bd, 590bd<br />
| |
| Badness: 0.0474<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:64:&lt;h2&gt; --><h2 id="toc32"><a name="Clyde-13-limit"></a><!-- ws:end:WikiTextHeadingRule:64 -->13-limit</h2>
| |
| Commas: 196/195, 245/243, 385/384, 625/624<br />
| |
| <br />
| |
| POTE generator: ~9/7 = 441.363<br />
| |
| <br />
| |
| Map: [&lt;1 6 6 12 -5 14|, &lt;0 -12 -10 -25 23 -28|]<br />
| |
| EDOs: 19, 68, 87, 503bdf, 590bdf<br />
| |
| Badness: 0.0268<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:66:&lt;h1&gt; --><h1 id="toc33"><a name="Bikleismic"></a><!-- ws:end:WikiTextHeadingRule:66 -->Bikleismic</h1>
| |
| Commas: 225/224, 243/242, 4375/4356<br />
| |
| <br />
| |
| POTE generator: ~6/5 = 316.721<br />
| |
| <br />
| |
| Map: [&lt;2 0 2 -6 -1|, &lt;0 6 5 22 15|]<br />
| |
| EDOs: 72, 106, 178, 250, 322c, 394c, 466bc, 538bc, 610bc<br />
| |
| Badness: 0.0293<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:68:&lt;h2&gt; --><h2 id="toc34"><a name="Bikleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:68 -->13-limit</h2>
| |
| Commas: 169/168, 225/224, 243/242, 325/324<br />
| |
| <br />
| |
| POTE generator: ~6/5 = 316.726<br />
| |
| <br />
| |
| Map: [&lt;2 0 2 -6 -1 0|, &lt;0 6 5 22 15 14|]<br />
| |
| EDOs: 72, 106, 322cff, 394cff, 466bcff, 538bcfff<br />
| |
| Badness: 0.0218<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:70:&lt;h1&gt; --><h1 id="toc35"><a name="Tritikleismic"></a><!-- ws:end:WikiTextHeadingRule:70 -->Tritikleismic</h1>
| |
| <a class="wiki_link" href="/Comma">Comma</a>s: 15625/15552, 1029/1024<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.872<br />
| |
| <br />
| |
| Map: [&lt;3 0 3 10|, &lt;0 6 5 -2|]<br />
| |
| <a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;18 15 -6 -18 -60 -56||<br />
| |
| EDOs: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/57edo">57</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/159edo">159</a>, <a class="wiki_link" href="/231edo">231</a><br />
| |
| <a class="wiki_link" href="/Badness">Badness</a>: 0.0563<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:72:&lt;h2&gt; --><h2 id="toc36"><a name="Tritikleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:72 -->11-limit</h2>
| |
| <a class="wiki_link" href="/Comma">Comma</a>s: 385/384, 441/440, 4000/3993<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.881<br />
| |
| <br />
| |
| Map: [&lt;3 0 3 10 8|, &lt;0 6 5 -2 3|]<br />
| |
| EDOs: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/57edo">57</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/159edo">159</a>, <a class="wiki_link" href="/231edo">231</a><br />
| |
| <a class="wiki_link" href="/Badness">Badness</a>: 0.0193<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:74:&lt;h2&gt; --><h2 id="toc37"><a name="Tritikleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:74 -->13-limit</h2>
| |
| <a class="wiki_link" href="/Comma">Comma</a>s: 325/324, 364/363, 441/440, 625/624<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.959<br />
| |
| <br />
| |
| Map: [&lt;3 0 3 10 8 0|, &lt;0 6 5 -2 3 14|]<br />
| |
| EDOs: <a class="wiki_link" href="/15edo">15</a>, <a class="wiki_link" href="/72edo">72</a>, 87, 159, 867, 1026<br />
| |
| <a class="wiki_link" href="/Badness">Badness</a>: 0.0157<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:76:&lt;h1&gt; --><h1 id="toc38"><a name="Quadritikleismic"></a><!-- ws:end:WikiTextHeadingRule:76 -->Quadritikleismic</h1>
| |
| <a class="wiki_link" href="/Comma">Comma</a>s: 15625/15552, 2401/2400<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.9999<br />
| |
| <br />
| |
| Map: [&lt;4 0 4 7|, &lt;0 6 5 4|]<br />
| |
| Wedgie: &lt;&lt;24 20 16 -24 -42 -19||<br />
| |
| EDOs: <a class="wiki_link" href="/68edo">68</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/212edo">212</a>, <a class="wiki_link" href="/1200edo">1200</a><br />
| |
| <a class="wiki_link" href="/Badness">Badness</a>: 0.0392<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:78:&lt;h2&gt; --><h2 id="toc39"><a name="Quadritikleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:78 -->11-limit</h2>
| |
| Commas: 385/384, 1375/1372, 6250/6237<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.925<br />
| |
| <br />
| |
| Map: [&lt;4 0 4 7 17|, &lt;0 6 5 4 -3|]<br />
| |
| EDOs: <a class="wiki_link" href="/68edo">68</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/212edo">212</a>, <a class="wiki_link" href="/284edo">284</a>, <a class="wiki_link" href="/496edo">496</a>, <a class="wiki_link" href="/780edo">780</a><br />
| |
| <a class="wiki_link" href="/Badness">Badness</a>: 0.0234<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:80:&lt;h2&gt; --><h2 id="toc40"><a name="Quadritikleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:80 -->13-limit</h2>
| |
| Commas: 325/324, 385/384, 625/624, 1573/1568<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 316.989<br />
| |
| <br />
| |
| Map: [&lt;4 0 4 7 17 0|, &lt;0 6 5 4 -3 14|]<br />
| |
| EDOs: <a class="wiki_link" href="/68edo">68</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/140edo">140</a>, <a class="wiki_link" href="/212edo">212</a><br />
| |
| <a class="wiki_link" href="/Badness">Badness</a>: 0.0187<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:82:&lt;h1&gt; --><h1 id="toc41"><a name="Kleiboh"></a><!-- ws:end:WikiTextHeadingRule:82 -->Kleiboh</h1>
| |
| Commas: 1728/1715, 3125/3087<br />
| |
| <br />
| |
| POTE generator: ~25/21 = 294.303<br />
| |
| <br />
| |
| Map: [&lt;1 6 6 6|, &lt;0 -18 -15 -13|]<br />
| |
| Wedgie: &lt;&lt;18 15 13 -18 -30 -12||<br />
| |
| EDOs: 49, 53, 314d<br />
| |
| Badness: 0.0765<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:84:&lt;h2&gt; --><h2 id="toc42"><a name="Kleiboh-11-limit"></a><!-- ws:end:WikiTextHeadingRule:84 -->11-limit</h2>
| |
| Commas: 176/175, 540/539, 3125/3087<br />
| |
| <br />
| |
| POTE generator: ~25/21 = 294.181<br />
| |
| <br />
| |
| Map: [&lt;1 6 6 6 14|, &lt;0 -18 -15 -13 -43|]<br />
| |
| EDOs: 49, 53, 102d, 155d<br />
| |
| Badness: 0.0528<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:86:&lt;h2&gt; --><h2 id="toc43"><a name="Kleiboh-13-limit"></a><!-- ws:end:WikiTextHeadingRule:86 -->13-limit</h2>
| |
| Commas: 176/175, 275/273, 325/324, 540/539<br />
| |
| <br />
| |
| POTE generator: ~13/11 = 294.187<br />
| |
| <br />
| |
| Map: [&lt;1 6 6 6 14 14|, &lt;0 -18 -15 -13 -43 -42|]<br />
| |
| EDOs: 53, 102df, 155d<br />
| |
| Badness: 0.0311<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:88:&lt;h1&gt; --><h1 id="toc44"><a name="Novemkleismic"></a><!-- ws:end:WikiTextHeadingRule:88 -->Novemkleismic</h1>
| |
| Commas: 15625/15552, 40353607/40310784<br />
| |
| <br />
| |
| POTE generator: ~6/5 = 317.005<br />
| |
| <br />
| |
| Map: [&lt;9 0 9 11|, &lt;0 6 5 6|]<br />
| |
| Wedgie: &lt;&lt;54 45 54 -54 -66 -1||<br />
| |
| EDOs: 72, 261, 333, 405, 477c, 882c<br />
| |
| Badness: 0.1934<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:90:&lt;h2&gt; --><h2 id="toc45"><a name="Novemkleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:90 -->11-limit</h2>
| |
| Commas: 1375/1372, 4000/3993, 15625/15552<br />
| |
| <br />
| |
| POTE generator: ~6/5 = 317.010<br />
| |
| <br />
| |
| Map: [&lt;9 0 9 11 24|, &lt;0 6 5 6 3|]<br />
| |
| EDOs: 72, 261, 333, 405, 882c<br />
| |
| Badness: 0.05172<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:92:&lt;h2&gt; --><h2 id="toc46"><a name="Novemkleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:92 -->13-limit</h2>
| |
| Commas: 325/324, 625/624, 1375/1372, 4000/3993<br />
| |
| <br />
| |
| POTE generator: ~6/5 = 317.086<br />
| |
| <br />
| |
| Map: [&lt;9 0 9 11 24 0|, &lt;0 6 5 6 3 14|]<br />
| |
| EDOs: 72, 261, 333, 738cf, 1071bcf<br />
| |
| Badness: 0.0391<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:94:&lt;h1&gt; --><h1 id="toc47"><a name="Sqrtphi"></a><!-- ws:end:WikiTextHeadingRule:94 -->Sqrtphi</h1>
| |
| Commas: 15625/15552, 16875/16807<br />
| |
| <br />
| |
| <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~125/98 = 416.603 cents<br />
| |
| <br />
| |
| Sqrt(phi) = 416.545 cents<br />
| |
| <br />
| |
| Map: [&lt;1 12 11 16|, &lt;0 -30 -25 -38|]<br />
| |
| EDOs: <a class="wiki_link" href="/49edo">49</a>, 72, <a class="wiki_link" href="/193edo">193</a>, <a class="wiki_link" href="/265edo">265</a><br />
| |
| Badness: 0.0704<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:96:&lt;h2&gt; --><h2 id="toc48"><a name="Sqrtphi-11-limit"></a><!-- ws:end:WikiTextHeadingRule:96 -->11-limit</h2>
| |
| Commas: 540/539, 1375/1372, 4375/4356<br />
| |
| <br />
| |
| POTE generator: ~14/11 = 416.604<br />
| |
| <br />
| |
| Map: [&lt;1 12 11 16 17|, &lt;0 -30 -25 -38 -39|]<br />
| |
| EDOs: 49, 72, 193, 265<br />
| |
| Badness: 0.0255<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:98:&lt;h2&gt; --><h2 id="toc49"><a name="Sqrtphi-13-limit"></a><!-- ws:end:WikiTextHeadingRule:98 -->13-limit</h2>
| |
| Commas: 325/324, 364/363, 625/624, 1375/1372<br />
| |
| <br />
| |
| POTE generator: ~14/11 = 416.585<br />
| |
| <br />
| |
| Map: [&lt;1 12 11 16 17 28|, &lt;0 -30 -25 -38 -39 -70|]<br />
| |
| EDOs: 72, 121, 193<br />
| |
| Badness: 0.0200<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:100:&lt;h2&gt; --><h2 id="toc50"><a name="Sqrtphi-17-limit"></a><!-- ws:end:WikiTextHeadingRule:100 -->17-limit</h2>
| |
| Commas: 325/324, 364/363, 375/374, 540/539, 595/594<br />
| |
| <br />
| |
| POTE generator: ~14/11 = 416.585<br />
| |
| <br />
| |
| Map: [&lt;1 12 11 16 17 28 27|, &lt;0 -30 -25 -38 -39 -70 -66|]<br />
| |
| EDOs: 72, 121, 193<br />
| |
| Badness: 0.0130<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:102:&lt;h2&gt; --><h2 id="toc51"><a name="Sqrtphi-19-limit"></a><!-- ws:end:WikiTextHeadingRule:102 -->19-limit</h2>
| |
| Commas: 325/324, 364/363, 375/374, 400/399, 442/441, 595/594<br />
| |
| <br />
| |
| POTE generator: ~14/11 = 416.580<br />
| |
| <br />
| |
| Map: [&lt;1 12 11 16 17 28 27 -2|, &lt;0 -30 -25 -38 -39 -70 -66 18|]<br />
| |
| EDOs: 72, 121, 193<br />
| |
| Badness: 0.0147<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:104:&lt;h2&gt; --><h2 id="toc52"><a name="Sqrtphi-Scales"></a><!-- ws:end:WikiTextHeadingRule:104 -->Scales</h2>
| |
| <a class="wiki_link" href="/sqrtphi17">sqrtphi17</a><br />
| |
| <a class="wiki_link" href="/sqrtphi23">sqrtphi23</a><br />
| |
| <a class="wiki_link" href="/sqrtphi49">sqrtphi49</a><br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:106:&lt;h2&gt; --><h2 id="toc53"><a name="Sqrtphi-Music"></a><!-- ws:end:WikiTextHeadingRule:106 -->Music</h2>
| |
| <a class="wiki_link_ext" href="http://micro.soonlabel.com/sqrt_phi/daily20111123a-sqrt-phi-17.mp3" rel="nofollow">Prelude for Piano in Square root of Phi Tuning</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br />
| |
| <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Sicurella/A%20Fight%20For%20Phi.mp3" rel="nofollow">A Fight for Phi</a> by Vito Sicurella</body></html></pre></div>
| |
Other languages: de:Hanson_Kleismisch Deutsch
The 5-limit parent comma for the kleismic family is 15625/15552, the kleisma. Its monzo is |-6 -5 6>, and flipping that yields <<6 5 -6|| for the wedgie. This tells us the generator is a minor third, and that to get to the interval class of major thirds will require five of these, and so to get to fifths will require six. In fact, (6/5)^5 = 5/2 * 15625/15552. This 5-limit temperament (virtually a microtemperament) is commonly called Hanson, and 14\53 is about perfect as a hanson generator, though 9\34 also makes sense, and 5\19 and 4\15 are possible. Other tunings include 72edo, 87edo and 140edo.
valid range: [300.000, 327.273] (4 to 11b)
nice range: [315.641, 317.263]
strict range: [315.641, 317.263]
POTE generator: 317.007
Map: [<1 0 1|, <0 6 5|]
EDOs: 15, 19, 34, 53, 458, 882c
Music:
Hanson Improv by Petr Parizek
In Hanson11 by Chris Vaisvil
Analysis and diagrams:
11 note chain-of-minor-thirds scale, by David Keenan
Seven limit children
The second comma of the normal comma list defines which 7-limit family member we are looking at. 875/864, the keemic comma, gives keemun, 4375/4374, the ragisma, gives catakleismic, 5120/5103, hemifamity, gives countercata, 6144/6125, the porwell comma, gives hemikleismic, 245/243, sensamagic, gives clyde, 1029/1024, the gamelisma, gives tritikleismic, and 2401/2400, the breedsma, gives quadritikleismic. Keemun, catakleismic and countercata all have octave period and use the minor third as a generator; catakleismic and countercata define the 7/4 more complexly but more accurately than keemun. Hemikleismic splits the 6/5 in half to get a neutral second generator of 35/32, and clyde similarly splits the 5/3 in half to get a 9/7 generator. Finally, tritikleismic has a 1/3 octave period with minor third generator, and quadritikleismic a 1/4 octave period with the minor third generator.
Keemun
Commas: 49/48, 126/125
valid range: [300.000, 327.273] (4 to 11b)
nice range: [308.744, 322.942]
strict range: [308.744, 322.942]
POTE generator: ~6/5 = 316.473
Map: [<1 0 1 2|, <0 6 5 3|]
Wedgie: <<6 5 3 -6 -12 -7||
EDOs: 15, 19, 53d, 72d, 91d
Badness: 0.0274
11-limit
Commas: 49/48, 56/55, 100/99
valid range: [315.789, 320.000] (19 to 15)
nice range: [308.744, 324.341]
strict range: [315.789, 320.000]
POTE generator: ~6/5 = 317.576
Map: [<1 0 1 2 4|, <0 6 5 3 -2|]
EDOs: 4, 15, 19, 34, 102de
Badness: 0.0274
13-limit
Commas: 49/48, 56/55, 78/77, 100/99
valid range: 315.789 (19)
nice range: [303.597, 324.341]
strict range: 315.789
POTE generator: ~6/5 = 316.611
Map: [<1 0 1 2 4 5|, <0 6 5 3 -2 -5|]
EDOs: 4, 15, 19, 53def, 72def
Badness: 0.0297
Kema
Commas: 49/48, 56/55, 91/90, 100/99
valid range: [315.789, 320.000] (19 to 15)
nice range: [308.744, 324.341]
strict range: [315.789, 320.000]
POTE generator: ~6/5 = 317.423
Map: [<1 0 1 2 4 0|, <0 6 5 3 -2 14|]
EDOs: 15, 19, 34, 87de
Badness: 0.0227
Kumbaya
Commas: 40/39, 49/48, 56/55, 66/65
POTE generator: ~6/5 = 318.595
Map: [<1 0 1 2 4 4|, <0 6 5 3 -2 -1|]
EDOs: 15, 34f
Badness: 0.0316
Qeema
Commas: 45/44, 49/48, 126/125
POTE generator: ~6/5 = 314.730
Map: [<1 0 1 2 -1|, <0 6 5 3 17|]
EDOs: 19, 42bcd, 61bcd
Badness: 0.0401
13-limit
Commas: 45/44, 49/48, 78/77, 126/125
POTE generator: ~6/5 = 315.044
Map: [<1 0 1 2 -1 0|, <0 6 5 3 17 14|]
EDOs: 19
Badness: 0.0294
Darjeeling
Commas: 49/48, 55/54, 77/75
POTE generator: ~6/5 = 317.656
Map: [<1 0 1 2 0|, <0 6 5 3 13|]
EDOs: 15, 19e, 34e
Badness: 0.0276
13-limit Darjeeling
Commas: 49/48, 55/54, 66/65, 77/75
POTE generator: ~6/5 = 317.298
Map: [<1 0 1 2 0 0|, <0 6 5 3 13 14|]
EDOs: 15, 19e, 34e, 53de
Badness: 0.02144
Catalan
Commas: 64/63, 15625/15552
POTE generator: ~6/5 = 318.267
Map: [<1 0 1 6|, <0 6 5 -12|]
Wedgie: <<6 5 -12 -6 -36 -42||
EDOs: 15, 34d, 49, 132bcd
Badness: 0.0949
11-limit
Commas: 64/63, 100/99, 1331/1323
POTE generator: ~6/5 = 318.282
Map: [<1 0 1 6 4|, <0 6 5 -12 -2|]
EDOs: 15, 34d, 49
Badness: 0.0369
Catakleismic
Commas: 225/224, 4375/4374
valid range: [315.789, 317.647] (19 to 34)
nice range: [315.641, 317.263]
strict range: [315.789, 317.263]
POTE generator: 316.732
Map: [<1 0 1 -3|, <0 6 5 22|]
Wedgie: <<6 5 22 -6 18 37||
EDOs: 19, 53, 72, 197, 269c
Badness: 0.0215
11-limit
Commas: 225/224, 385/384, 4375/4374
valid range: [315.789, 316.981] (19 to 53)
nice range: [315.641, 317.263]
strict range: [315.789, 316.981]
POTE generator: 316.719
Map: [<1 0 1 -3 9|, <0 6 5 22 -21|]
EDOs: 19, 53, 72, 197e, 269ce, 341ce, 610bce
Badness: 0.0218
13-limit
Commas: 169/168, 225/224, 325/324, 540/539
valid range: [315.789, 316.981] (19 to 53)
nice range: [315.641, 318.309]
strict range: [315.789, 316.981]
POTE generator: 316.738
Map: [<1 0 1 -3 9 0|, <0 6 5 22 -21 14|]
EDOs: 19, 53, 72, 125f, 197ef, 269cef
Badness: 0.0169
Cataclysmic
Commas: 99/98, 176/175, 2200/2187
POTE generator: ~6/5 = 317.042
Map: [<1 0 1 -3 -5|, <0 6 5 22 32|]
EDOs: 53, 87d, 140d, 171de, 181de, 193de, 224de, 246de, 277de
Badness: 0.0400
13-limit
Commas: 99/98, 169/168, 176/175, 275/273
POTE generator: ~6/5 = 317.036
Map: [<1 0 1 -3 -5 0|, <0 6 5 22 32 14|]
EDOs: 53, 87d, 140d, 193de, 246de
Badness: 0.0226
Catalytic
Commas: 225/224, 441/440, 4375/4374
POTE generator: ~6/5 = 316.653
Map: [<1 0 1 -3 -10|, <0 6 5 22 51|]
EDOs: 53e, 72
Badness: 0.0304
13-limit
Commas: 169/168 225/224 325/324 1716/1715
POTE generator: ~6/5 = 316.639
Map: [<1 0 1 -3 -10 0|, <0 6 5 22 51 14|]
EDOs: 19e, 53e, 72
Badness: 0.0223
Cataleptic
Commas: 100/99, 225/224, 864/847
POTE generator: ~6/5 = 317.083
Map: [<1 0 1 -3 4|, <0 6 5 22 -2|]
EDOs: 19, 34d, 53e
Badness: 0.0443
13-limit
Commas: 78/77, 100/99, 144/143, 676/675
POTE generator: ~6/5 = 317.118
Map: [<1 0 1 -3 4 0|, <0 6 5 22 -2 14|]
EDOs: 19, 34d, 53e, 87de
Badness: 0.0273
Countercata
Commas: 15625/15552, 5120/5103
POTE generator: 317.121
Map: [<1 0 1 11|, <0 6 5 -31|]
Wedgie: <<6 5 -31 -6 -66 -86||
EDOs: 15, 19, 34, 53, 87, 140, 333, 473, 806b
Badness: 0.0521
11-limit
Commas: 385/384, 2200/2187, 3388/3375
POTE generator: ~6/5 = 317.162
Map: [<1 0 1 11 -5|, <0 6 5 -31 32|]
EDOs: 34, 53, 87, 140, 227
Badness: 0.0398
13-limit
Commas: 325/324, 352/351, 385/384, 625/624
POTE generator: ~6/5 = 317.162
Map: [<1 0 1 11 -5 0|, <0 6 5 -31 32 14|]
EDOs: 34, 53, 87, 140, 227, 367e, 507e
Badness: 0.0202
Metakleismic
Commas: 15625/15552, 179200/177147
POTE generator: ~6/5 = 317.314
Map: [<1 0 1 -12|, <0 6 5 56|]
Wedgie: <<6 5 56 -6 72 116||
EDOs: 15, 19, 34, 87, 121, 208
Badness: 0.1635
11-limit
Commas: 896/891, 2200/2187, 14700/14641
POTE generator: ~6/5 = 317.311
Map: [<1 0 1 -12 -5|, <0 6 5 56 32|]
EDOs: 15, 19, 34, 87, 121, 208
Badness: 0.0486
13-limit
Commas: 325/324, 352/351, 364/363, 625/624
POTE generator: ~6/5 = 317.311
Map: [<1 0 1 -12 -5 0|, <0 6 5 56 32 14|]
EDOs: 15, 19, 34, 87, 121, 208
Badness: 0.0244
Hemikleismic
Commas: 4000/3969, 6144/6125
POTE generator: 158.649
Map: [<1 0 1 4|, <0 12 10 -9|]
EDOs: 53, 121
Badness: 0.0521
11-limit
Commas: 121/120, 176/175, 4000/3969
POTE generator: ~11/10 = 158.677
Map: [<1 0 1 4 2|, <0 12 10 -9 11|]
EDOs: 15, 38, 53, 68, 121e
Badness: 0.0380
13-limit
Commas: 121/120, 176/175, 275/273, 325/324
POTE generator: ~11/10 = 158.655
Map: [<1 0 1 4 2 0|, <0 12 10 -9 11 28|]
EDOs: 15, 53, 121e
Badness: 0.0260
Clyde
Commas: 245/243, 3136/3125
7 and 9 limit minimax
[|1 0 0 0>, |6/25 0 0 12/25>, |6/5 0 0 2/5>, |0 0 0 1>]
Eigenmonzos: 2, 7
POTE generator: ~9/7 = 441.335
Algebraic generator: real root of 5x^3-6x-3, the Poussami generator. Approximately 441.309 cents. Associated recurrence relationship quickly converges.
Map: [<1 6 6 12|, <0 -12 -10 -25|]
Generators: 2, 9/7
Edos: 19, 49, 68, 87, 155
Badness: 0.0473
11-limit
Commas: 245/243, 3136/3125, 385/384
POTE generator: ~9/7 = 441.355
Map: [<1 6 6 12 -5|, <0 -12 -10 -25 23|]
EDOs: 19, 68, 87, 329bd, 419bd, 503bd, 590bd
Badness: 0.0474
13-limit
Commas: 196/195, 245/243, 385/384, 625/624
POTE generator: ~9/7 = 441.363
Map: [<1 6 6 12 -5 14|, <0 -12 -10 -25 23 -28|]
EDOs: 19, 68, 87, 503bdf, 590bdf
Badness: 0.0268
Bikleismic
Commas: 225/224, 243/242, 4375/4356
POTE generator: ~6/5 = 316.721
Map: [<2 0 2 -6 -1|, <0 6 5 22 15|]
EDOs: 72, 106, 178, 250, 322c, 394c, 466bc, 538bc, 610bc
Badness: 0.0293
13-limit
Commas: 169/168, 225/224, 243/242, 325/324
POTE generator: ~6/5 = 316.726
Map: [<2 0 2 -6 -1 0|, <0 6 5 22 15 14|]
EDOs: 72, 106, 322cff, 394cff, 466bcff, 538bcfff
Badness: 0.0218
Tritikleismic
Commas: 15625/15552, 1029/1024
POTE generator: 316.872
Map: [<3 0 3 10|, <0 6 5 -2|]
Wedgie: <<18 15 -6 -18 -60 -56||
EDOs: 15, 57, 72, 159, 231
Badness: 0.0563
11-limit
Commas: 385/384, 441/440, 4000/3993
POTE generator: 316.881
Map: [<3 0 3 10 8|, <0 6 5 -2 3|]
EDOs: 15, 57, 72, 159, 231
Badness: 0.0193
13-limit
Commas: 325/324, 364/363, 441/440, 625/624
POTE generator: 316.959
Map: [<3 0 3 10 8 0|, <0 6 5 -2 3 14|]
EDOs: 15, 72, 87, 159, 867, 1026
Badness: 0.0157
Quadritikleismic
Commas: 15625/15552, 2401/2400
POTE generator: 316.9999
Map: [<4 0 4 7|, <0 6 5 4|]
Wedgie: <<24 20 16 -24 -42 -19||
EDOs: 68, 72, 140, 212, 1200
Badness: 0.0392
11-limit
Commas: 385/384, 1375/1372, 6250/6237
POTE generator: 316.925
Map: [<4 0 4 7 17|, <0 6 5 4 -3|]
EDOs: 68, 72, 140, 212, 284, 496, 780
Badness: 0.0234
13-limit
Commas: 325/324, 385/384, 625/624, 1573/1568
POTE generator: 316.989
Map: [<4 0 4 7 17 0|, <0 6 5 4 -3 14|]
EDOs: 68, 72, 140, 212
Badness: 0.0187
Kleiboh
Commas: 1728/1715, 3125/3087
POTE generator: ~25/21 = 294.303
Map: [<1 6 6 6|, <0 -18 -15 -13|]
Wedgie: <<18 15 13 -18 -30 -12||
EDOs: 49, 53, 314d
Badness: 0.0765
11-limit
Commas: 176/175, 540/539, 3125/3087
POTE generator: ~25/21 = 294.181
Map: [<1 6 6 6 14|, <0 -18 -15 -13 -43|]
EDOs: 49, 53, 102d, 155d
Badness: 0.0528
13-limit
Commas: 176/175, 275/273, 325/324, 540/539
POTE generator: ~13/11 = 294.187
Map: [<1 6 6 6 14 14|, <0 -18 -15 -13 -43 -42|]
EDOs: 53, 102df, 155d
Badness: 0.0311
Novemkleismic
Commas: 15625/15552, 40353607/40310784
POTE generator: ~6/5 = 317.005
Map: [<9 0 9 11|, <0 6 5 6|]
Wedgie: <<54 45 54 -54 -66 -1||
EDOs: 72, 261, 333, 405, 477c, 882c
Badness: 0.1934
11-limit
Commas: 1375/1372, 4000/3993, 15625/15552
POTE generator: ~6/5 = 317.010
Map: [<9 0 9 11 24|, <0 6 5 6 3|]
EDOs: 72, 261, 333, 405, 882c
Badness: 0.05172
13-limit
Commas: 325/324, 625/624, 1375/1372, 4000/3993
POTE generator: ~6/5 = 317.086
Map: [<9 0 9 11 24 0|, <0 6 5 6 3 14|]
EDOs: 72, 261, 333, 738cf, 1071bcf
Badness: 0.0391
Sqrtphi
Commas: 15625/15552, 16875/16807
POTE generator: ~125/98 = 416.603 cents
Sqrt(phi) = 416.545 cents
Map: [<1 12 11 16|, <0 -30 -25 -38|]
EDOs: 49, 72, 193, 265
Badness: 0.0704
11-limit
Commas: 540/539, 1375/1372, 4375/4356
POTE generator: ~14/11 = 416.604
Map: [<1 12 11 16 17|, <0 -30 -25 -38 -39|]
EDOs: 49, 72, 193, 265
Badness: 0.0255
13-limit
Commas: 325/324, 364/363, 625/624, 1375/1372
POTE generator: ~14/11 = 416.585
Map: [<1 12 11 16 17 28|, <0 -30 -25 -38 -39 -70|]
EDOs: 72, 121, 193
Badness: 0.0200
17-limit
Commas: 325/324, 364/363, 375/374, 540/539, 595/594
POTE generator: ~14/11 = 416.585
Map: [<1 12 11 16 17 28 27|, <0 -30 -25 -38 -39 -70 -66|]
EDOs: 72, 121, 193
Badness: 0.0130
19-limit
Commas: 325/324, 364/363, 375/374, 400/399, 442/441, 595/594
POTE generator: ~14/11 = 416.580
Map: [<1 12 11 16 17 28 27 -2|, <0 -30 -25 -38 -39 -70 -66 18|]
EDOs: 72, 121, 193
Badness: 0.0147
Scales
sqrtphi17
sqrtphi23
sqrtphi49
Music
Prelude for Piano in Square root of Phi Tuning by Chris Vaisvil
A Fight for Phi by Vito Sicurella