Meantone family: Difference between revisions
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The [[5-limit]] parent [[comma]] of the '''meantone family''' is the Didymus or [[Wikipedia: syntonic comma|syntonic comma]], [[81/80]]. This is the one they all temper out. The period is an octave, the generator is a fifth, and four fifths go to make up a 5/1 interval. | The [[5-limit]] parent [[comma]] of the '''meantone family''' is the Didymus or [[Wikipedia: syntonic comma|syntonic comma]], [[81/80]]. This is the one they all temper out. The period is an octave, the generator is a fifth, and four fifths go to make up a 5/1 interval. | ||
= Meantone (12&19, 2.3.5) = | == Meantone (12&19, 2.3.5) == | ||
{{main| Meantone }} | {{main| Meantone }} | ||
| Line 33: | Line 33: | ||
Scales: [[meantone5]], [[meantone7]], [[meantone12]] | Scales: [[meantone5]], [[meantone7]], [[meantone12]] | ||
== Seven-limit extensions == | === Seven-limit extensions === | ||
The [[7-limit]] [[extension]]s of meantone are: | The [[7-limit]] [[extension]]s of meantone are: | ||
* Septimal meantone, with normal comma list [{{Monzo| -4 4 -1 }}, [[Harrison's comma|{{Monzo| -13 10 0 -1 }}]]], | * Septimal meantone, with normal comma list [{{Monzo| -4 4 -1 }}, [[Harrison's comma|{{Monzo| -13 10 0 -1 }}]]], | ||
| Line 46: | Line 46: | ||
* Liese, with normal list [{{Monzo| -4 4 -1 }}, {{Monzo| -9 11 0 -3 }}]. | * Liese, with normal list [{{Monzo| -4 4 -1 }}, {{Monzo| -9 11 0 -3 }}]. | ||
= Septimal meantone = | == Septimal meantone == | ||
<div style="float:right">[[:de:septimal-mitteltönig|Deutsch]]</div> | <div style="float:right">[[:de:septimal-mitteltönig|Deutsch]]</div> | ||
{{see also| Meantone }} | {{see also| Meantone }} | ||
| Line 81: | Line 81: | ||
Scales: [[meantone5]], [[meantone7]], [[meantone12]] | Scales: [[meantone5]], [[meantone7]], [[meantone12]] | ||
== Unidecimal meantone aka Huygens == | === Unidecimal meantone aka Huygens === | ||
{{see also| Meantone vs meanpop }} | {{see also| Meantone vs meanpop }} | ||
| Line 111: | Line 111: | ||
* [http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-74-edo.mp3 Twinkle canon – 74 edo] by [http://soonlabel.com/xenharmonic/archives/573 Claudi Meneghin] | * [http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-74-edo.mp3 Twinkle canon – 74 edo] by [http://soonlabel.com/xenharmonic/archives/573 Claudi Meneghin] | ||
=== Tridecimal meantone === | ==== Tridecimal meantone ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 124: | Line 124: | ||
Badness: 0.018048 | Badness: 0.018048 | ||
=== Grosstone === | ==== Grosstone ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 142: | Line 142: | ||
Badness: 0.025899 | Badness: 0.025899 | ||
=== Meridetone === | ==== Meridetone ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 155: | Line 155: | ||
Badness: 0.026421 | Badness: 0.026421 | ||
=== Hemimeantone === | ==== Hemimeantone ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 170: | Line 170: | ||
Badness: 0.031433 | Badness: 0.031433 | ||
== Meanpop == | === Meanpop === | ||
{{see also| Meantone vs meanpop }} | {{see also| Meantone vs meanpop }} | ||
| Line 203: | Line 203: | ||
* [http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-50-edo.mp3 Twinkle canon – 50 edo] by [http://soonlabel.com/xenharmonic/archives/573 Claudi Meneghin] | * [http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-50-edo.mp3 Twinkle canon – 50 edo] by [http://soonlabel.com/xenharmonic/archives/573 Claudi Meneghin] | ||
=== Tridecimal Meanpop === | ==== Tridecimal Meanpop ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 223: | Line 223: | ||
Badness: 0.020883 | Badness: 0.020883 | ||
=== Meanplop === | ==== Meanplop ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 236: | Line 236: | ||
Badness: 0.027666 | Badness: 0.027666 | ||
== Meanenneadecal == | === Meanenneadecal === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 249: | Line 249: | ||
Badness: 0.021423 | Badness: 0.021423 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 262: | Line 262: | ||
Badness: 0.021182 | Badness: 0.021182 | ||
=== Vincenzo === | ==== Vincenzo ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 275: | Line 275: | ||
Badness: 0.024763 | Badness: 0.024763 | ||
==== 17-limit ==== | ===== 17-limit ===== | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 288: | Line 288: | ||
Badness: 0.025535 | Badness: 0.025535 | ||
==== 19-limit ==== | ===== 19-limit ===== | ||
Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
| Line 301: | Line 301: | ||
Badness: 0.022302 | Badness: 0.022302 | ||
==== 23-limit ==== | ===== 23-limit ===== | ||
Subgroup: 2.3.5.7.11.13.17.19.23 | Subgroup: 2.3.5.7.11.13.17.19.23 | ||
| Line 314: | Line 314: | ||
Badness: 0.020139 | Badness: 0.020139 | ||
==== 29-limit ==== | ===== 29-limit ===== | ||
Subgroup: 2.3.5.7.11.13.17.19.23.29 | Subgroup: 2.3.5.7.11.13.17.19.23.29 | ||
| Line 327: | Line 327: | ||
Badness: 0.018168 | Badness: 0.018168 | ||
==== 31-limit ==== | ===== 31-limit ===== | ||
Subgroup: 2.3.5.7.11.13.17.19.23.29.31 | Subgroup: 2.3.5.7.11.13.17.19.23.29.31 | ||
| Line 340: | Line 340: | ||
Badness: 0.017069 | Badness: 0.017069 | ||
==== 37-limit ==== | ===== 37-limit ===== | ||
Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37 | Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37 | ||
| Line 353: | Line 353: | ||
Badness: 0.016129 | Badness: 0.016129 | ||
==== 41-limit ==== | ===== 41-limit ===== | ||
Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41 | Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41 | ||
| Line 366: | Line 366: | ||
Badness: 0.015356 | Badness: 0.015356 | ||
==== 43-limit ==== | ===== 43-limit ===== | ||
Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41.43 | Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41.43 | ||
| Line 379: | Line 379: | ||
Badness: 0.013906 | Badness: 0.013906 | ||
==== 47-limit ==== | ===== 47-limit ===== | ||
Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41.43.47 | Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41.43.47 | ||
| Line 392: | Line 392: | ||
Badness: 0.013818 | Badness: 0.013818 | ||
=== Meanundec === | ==== Meanundec ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 405: | Line 405: | ||
Badness: 0.024243 | Badness: 0.024243 | ||
== Meanundeci == | === Meanundeci === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 418: | Line 418: | ||
Badness: 0.031539 | Badness: 0.031539 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 431: | Line 431: | ||
Badness: 0.026288 | Badness: 0.026288 | ||
== Migration == | === Migration === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 446: | Line 446: | ||
Badness: 0.025516 | Badness: 0.025516 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 461: | Line 461: | ||
Badness: 0.028071 | Badness: 0.028071 | ||
== Bimeantone == | === Bimeantone === | ||
11/8 is mapped to half octave minus the [[meantone diesis]]. | 11/8 is mapped to half octave minus the [[meantone diesis]]. | ||
| Line 478: | Line 478: | ||
Badness: 0.038122 | Badness: 0.038122 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 493: | Line 493: | ||
Badness: 0.028817 | Badness: 0.028817 | ||
=== 17-limit === | ==== 17-limit ==== | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 508: | Line 508: | ||
Badness: 0.022666 | Badness: 0.022666 | ||
= Flattone = | == Flattone == | ||
In flattone, 9 generator steps of 4/3 get to the interval class for 7, meaning that [[7/4]] is a diminished seventh interval (C-Bbb). Other intervals are [[7/6]], a diminished third (C-Ebb), and [[7/5]], a doubly diminshed fifth (C-Gbb). Good tunings for flattone are [[26edo|26EDO]], [[45edo|45EDO]] and [[64edo|64EDO]]. | In flattone, 9 generator steps of 4/3 get to the interval class for 7, meaning that [[7/4]] is a diminished seventh interval (C-Bbb). Other intervals are [[7/6]], a diminished third (C-Ebb), and [[7/5]], a doubly diminshed fifth (C-Gbb). Good tunings for flattone are [[26edo|26EDO]], [[45edo|45EDO]] and [[64edo|64EDO]]. | ||
| Line 542: | Line 542: | ||
Scales: [[flattone12]] | Scales: [[flattone12]] | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 562: | Line 562: | ||
Scales: [[flattone12]] | Scales: [[flattone12]] | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 582: | Line 582: | ||
Scales: [[flattone12]] | Scales: [[flattone12]] | ||
== Ptolemy == | === Ptolemy === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 595: | Line 595: | ||
Badness: 0.058785 | Badness: 0.058785 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 608: | Line 608: | ||
Badness: 0.034316 | Badness: 0.034316 | ||
= Dominant = | == Dominant == | ||
The interval class for 7 is obtained from two fourths in succession, so that 7/4 is a minor seventh. The 7/6 interval is, like 6/5, now a minor third, and 7/5 is a diminished fifth. An excellent tuning for dominant is [[12edo|12EDO]], but it also works well with the Pythagorean tuning of pure [[3/2]] fifths, and with [[29edo|29EDO]], [[41edo|41EDO]], or [[53edo|53EDO]]. | The interval class for 7 is obtained from two fourths in succession, so that 7/4 is a minor seventh. The 7/6 interval is, like 6/5, now a minor third, and 7/5 is a diminished fifth. An excellent tuning for dominant is [[12edo|12EDO]], but it also works well with the Pythagorean tuning of pure [[3/2]] fifths, and with [[29edo|29EDO]], [[41edo|41EDO]], or [[53edo|53EDO]]. | ||
| Line 630: | Line 630: | ||
[[Badness]]: 0.020690 | [[Badness]]: 0.020690 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 648: | Line 648: | ||
Badness: 0.024180 | Badness: 0.024180 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 666: | Line 666: | ||
Badness: 0.024108 | Badness: 0.024108 | ||
=== Dominion === | ==== Dominion ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 679: | Line 679: | ||
Badness: 0.027295 | Badness: 0.027295 | ||
== Domineering == | === Domineering === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 692: | Line 692: | ||
Badness: 0.021978 | Badness: 0.021978 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 705: | Line 705: | ||
Badness: 0.027039 | Badness: 0.027039 | ||
==== 17-limit ==== | ===== 17-limit ===== | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 718: | Line 718: | ||
Badness: 0.024539 | Badness: 0.024539 | ||
==== 19-limit ==== | ===== 19-limit ===== | ||
Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
| Line 731: | Line 731: | ||
Badness: 0.020398 | Badness: 0.020398 | ||
=== Dominatrix === | ==== Dominatrix ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 744: | Line 744: | ||
Badness: 0.018289 | Badness: 0.018289 | ||
== Domination == | === Domination === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 757: | Line 757: | ||
Badness: 0.036562 | Badness: 0.036562 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 770: | Line 770: | ||
Badness: 0.027435 | Badness: 0.027435 | ||
== Arnold == | === Arnold === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 783: | Line 783: | ||
Badness: 0.026141 | Badness: 0.026141 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 796: | Line 796: | ||
Badness: 0.023300 | Badness: 0.023300 | ||
=== 17-limit === | ==== 17-limit ==== | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 809: | Line 809: | ||
Badness: 0.024535 | Badness: 0.024535 | ||
=== 19-limit === | ==== 19-limit ==== | ||
Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
| Line 822: | Line 822: | ||
Badness: 0.021098 | Badness: 0.021098 | ||
== Maqamic == | === Maqamic === | ||
<span style="display: block; text-align: right;">[[:de:maqamisch|Deutsch]]</span> | <span style="display: block; text-align: right;">[[:de:maqamisch|Deutsch]]</span> | ||
{{main| Maqamic }} | {{main| Maqamic }} | ||
| Line 842: | Line 842: | ||
Badness: 0.040240 | Badness: 0.040240 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 857: | Line 857: | ||
Badness: 0.027214 | Badness: 0.027214 | ||
= Sharptone = | == Sharptone == | ||
Sharptone is a low-accuracy temperament tempering out 21/20 and 28/27. In sharptone, a 7/4 is a major sixth, a 7/6 a whole tone, and a 7/5 a fourth. Genuinely septimal sounding harmony therefore cannot be expected, but it can be used to translate, more or less, 7-limit JI into 5-limit meantone. [[12edo|12EDO]] tuning does sharptone about as well as such a thing can be done, of course not in its patent val. | Sharptone is a low-accuracy temperament tempering out 21/20 and 28/27. In sharptone, a 7/4 is a major sixth, a 7/6 a whole tone, and a 7/5 a fourth. Genuinely septimal sounding harmony therefore cannot be expected, but it can be used to translate, more or less, 7-limit JI into 5-limit meantone. [[12edo|12EDO]] tuning does sharptone about as well as such a thing can be done, of course not in its patent val. | ||
| Line 874: | Line 874: | ||
[[Badness]]: 0.024848 | [[Badness]]: 0.024848 | ||
== Meanertone == | === Meanertone === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 887: | Line 887: | ||
Badness: 0.025167 | Badness: 0.025167 | ||
= Plutus = | == Plutus == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 902: | Line 902: | ||
[[Badness]]: 0.045275 | [[Badness]]: 0.045275 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 915: | Line 915: | ||
Badness: 0.032521 | Badness: 0.032521 | ||
= Supermean = | == Supermean == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 928: | Line 928: | ||
[[Badness]]: 0.134204 | [[Badness]]: 0.134204 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 941: | Line 941: | ||
Badness: 0.063262 | Badness: 0.063262 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 954: | Line 954: | ||
Badness: 0.040324 | Badness: 0.040324 | ||
= Godzilla = | == Godzilla == | ||
<span style="display: block; text-align: right;">[[:de:Semiphor,_Semaphor,_Godzilla|Deutsch]]</span> | <span style="display: block; text-align: right;">[[:de:Semiphor,_Semaphor,_Godzilla|Deutsch]]</span> | ||
{{main| Semaphore and Godzilla }} | {{main| Semaphore and Godzilla }} | ||
| Line 981: | Line 981: | ||
[[Badness]]: 0.026747 | [[Badness]]: 0.026747 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,001: | Line 1,001: | ||
Badness: 0.028947 | Badness: 0.028947 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 1,021: | Line 1,021: | ||
Badness: 0.022503 | Badness: 0.022503 | ||
== Semafour == | === Semafour === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,036: | Line 1,036: | ||
Badness: 0.028510 | Badness: 0.028510 | ||
== Varan == | === Varan === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,051: | Line 1,051: | ||
Badness: 0.039647 | Badness: 0.039647 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 1,066: | Line 1,066: | ||
Badness: 0.025676 | Badness: 0.025676 | ||
== Baragon == | === Baragon === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,081: | Line 1,081: | ||
Badness: 0.035673 | Badness: 0.035673 | ||
= Injera = | == Injera == | ||
Injera has a half-octave period and a generator which can be taken as a fifth or fourth, but also as a 15/14 semitone difference between a half-octave and a perfect fifth. Injera tempers out 50/49, equating 7/5 with 10/7 and giving a tritone of half an octave. A major third up from this tritone is the 7/4. [[38edo|38EDO]], which is two parallel [[19edo|19EDOs]], is an excellent tuning for injera. | Injera has a half-octave period and a generator which can be taken as a fifth or fourth, but also as a 15/14 semitone difference between a half-octave and a perfect fifth. Injera tempers out 50/49, equating 7/5 with 10/7 and giving a tritone of half an octave. A major third up from this tritone is the 7/4. [[38edo|38EDO]], which is two parallel [[19edo|19EDOs]], is an excellent tuning for injera. | ||
| Line 1,110: | Line 1,110: | ||
* [http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Two%20Pairs%20of%20Socks.mp3 Two Pairs of Socks] (in [[26edo|26EDO]]) by [[Igliashon Jones]] | * [http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Two%20Pairs%20of%20Socks.mp3 Two Pairs of Socks] (in [[26edo|26EDO]]) by [[Igliashon Jones]] | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,130: | Line 1,130: | ||
Badness: 0.023124 | Badness: 0.023124 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 1,150: | Line 1,150: | ||
Badness: 0.021565 | Badness: 0.021565 | ||
=== Enjera === | ==== Enjera ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 1,165: | Line 1,165: | ||
Badness: 0.026542 | Badness: 0.026542 | ||
== Injerous == | === Injerous === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,180: | Line 1,180: | ||
Badness: 0.038577 | Badness: 0.038577 | ||
== Lahoh == | === Lahoh === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,195: | Line 1,195: | ||
Badness: 0.043062 | Badness: 0.043062 | ||
= Mohaha = | == Mohaha == | ||
{{see also| Subgroup temperaments #Mohaha }} | {{see also| Subgroup temperaments #Mohaha }} | ||
| Line 1,218: | Line 1,218: | ||
Scales: [[mohaha7]], [[mohaha10]] | Scales: [[mohaha7]], [[mohaha10]] | ||
== Mohoho == | === Mohoho === | ||
Subgroup: 2.3.5.11.13 | Subgroup: 2.3.5.11.13 | ||
| Line 1,237: | Line 1,237: | ||
Scales: [[mohaha7]], [[mohaha10]] | Scales: [[mohaha7]], [[mohaha10]] | ||
= Mohajira = | == Mohajira == | ||
{{main|Mohajira}} | {{main|Mohajira}} | ||
| Line 1,267: | Line 1,267: | ||
Scales: [[mohaha7]], [[mohaha10]] | Scales: [[mohaha7]], [[mohaha10]] | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Scales: [[mohaha7]], [[mohaha10]] | Scales: [[mohaha7]], [[mohaha10]] | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Scales: [[mohaha7]], [[mohaha10]] | Scales: [[mohaha7]], [[mohaha10]] | ||
== 17-limit == | === 17-limit === | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
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Scales: [[mohaha7]], [[mohaha10]] | Scales: [[mohaha7]], [[mohaha10]] | ||
== 19-limit == | === 19-limit === | ||
Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
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Scales: [[mohaha7]], [[mohaha10]] | Scales: [[mohaha7]], [[mohaha10]] | ||
= Mohamaq = | == Mohamaq == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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Scales: [[mohaha7]], [[mohaha10]] | Scales: [[mohaha7]], [[mohaha10]] | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,374: | Line 1,374: | ||
Scales: [[mohaha7]], [[mohaha10]] | Scales: [[mohaha7]], [[mohaha10]] | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Scales: [[mohaha7]], [[mohaha10]] | Scales: [[mohaha7]], [[mohaha10]] | ||
= Orphic = | == Orphic == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 1,408: | Line 1,408: | ||
[[Badness]]: 0.258825 | [[Badness]]: 0.258825 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,423: | Line 1,423: | ||
Badness: 0.101499 | Badness: 0.101499 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness: 0.053482 | Badness: 0.053482 | ||
= Mothra = | == Mothra == | ||
Mothra splits the fifth into three 8/7 generators. It uses [[1029/1024]], the gamelisma, to accomplish this deed and also tempers out [[1728/1715]], the orwell comma. Using [[31edo|31EDO]] with a generator of 6/31 is an excellent tuning choice. Once again something other than a MOS should be used as a scale to get the most out of mothra. In the 2.3.7 subgroup, mothra is identical to [[slendric]]. | Mothra splits the fifth into three 8/7 generators. It uses [[1029/1024]], the gamelisma, to accomplish this deed and also tempers out [[1728/1715]], the orwell comma. Using [[31edo|31EDO]] with a generator of 6/31 is an excellent tuning choice. Once again something other than a MOS should be used as a scale to get the most out of mothra. In the 2.3.7 subgroup, mothra is identical to [[slendric]]. | ||
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[[Badness]]: 0.037146 | [[Badness]]: 0.037146 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Badness: 0.025642 | Badness: 0.025642 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness: 0.023954 | Badness: 0.023954 | ||
== Cynder == | === Cynder === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,511: | Line 1,511: | ||
Badness: 0.055706 | Badness: 0.055706 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 1,526: | Line 1,526: | ||
Badness: 0.034124 | Badness: 0.034124 | ||
== Mosura == | === Mosura === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Badness: 0.0313 | Badness: 0.0313 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness: 0.036857 | Badness: 0.036857 | ||
=== Music === | ==== Music ==== | ||
* [http://micro.soonlabel.com/16-ET/mothra/20141028_mothra16br4.mp3 Prelude for solo piano in mothra16, brat 4 tuning] by [http://chrisvaisvil.com/prelude-for-solo-piano-in-mothra16-brat-4-tuning/ Chris Vaisvil] | * [http://micro.soonlabel.com/16-ET/mothra/20141028_mothra16br4.mp3 Prelude for solo piano in mothra16, brat 4 tuning] by [http://chrisvaisvil.com/prelude-for-solo-piano-in-mothra16-brat-4-tuning/ Chris Vaisvil] | ||
= Squares = | == Squares == | ||
Squares splits the interval of an eleventh, or 8/3, into four supermajor third ([[9/7]]) intervals, and uses it for a generator. [[31edo|31EDO]], with a generator of 11/31, makes for a good squares tuning, with 8, 11, and 14 note MOS available. Squares tempers out [[2401/2400]], the breedsma, as well as [[2430/2401]]. | Squares splits the interval of an eleventh, or 8/3, into four supermajor third ([[9/7]]) intervals, and uses it for a generator. [[31edo|31EDO]], with a generator of 11/31, makes for a good squares tuning, with 8, 11, and 14 note MOS available. Squares tempers out [[2401/2400]], the breedsma, as well as [[2430/2401]]. | ||
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* [http://clones.soonlabel.com/public/micro/tuning-survey/daily20100603-squares8piano.mp3 Square 8] by [[Chris Vaisvil]] | * [http://clones.soonlabel.com/public/micro/tuning-survey/daily20100603-squares8piano.mp3 Square 8] by [[Chris Vaisvil]] | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Scales: [[skwares8]], [[skwares11]], [[skwares14]] | Scales: [[skwares8]], [[skwares11]], [[skwares14]] | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Scales: [[skwares8]], [[skwares11]], [[skwares14]] | Scales: [[skwares8]], [[skwares11]], [[skwares14]] | ||
=== Agora === | ==== Agora ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Scales: [[skwares8]], [[skwares11]], [[skwares14]] | Scales: [[skwares8]], [[skwares11]], [[skwares14]] | ||
==== 17-limit ==== | ===== 17-limit ===== | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
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Scales: [[skwares8]], [[skwares11]], [[skwares14]] | Scales: [[skwares8]], [[skwares11]], [[skwares14]] | ||
==== 19-limit ==== | ===== 19-limit ===== | ||
Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
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Scales: [[skwares8]], [[skwares11]], [[skwares14]] | Scales: [[skwares8]], [[skwares11]], [[skwares14]] | ||
== Cuboctahedra == | === Cuboctahedra === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Scales: [[skwares8]], [[skwares11]], [[skwares14]] | Scales: [[skwares8]], [[skwares11]], [[skwares14]] | ||
= Liese = | == Liese == | ||
<span style="display: block; text-align: right;">[[:de:Liese|Deutsch]]</span> | <span style="display: block; text-align: right;">[[:de:Liese|Deutsch]]</span> | ||
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[[Badness]]: 0.046706 | [[Badness]]: 0.046706 | ||
== Liesel == | === Liesel === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Badness: 0.040721 | Badness: 0.040721 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Liesel is a very natural 13-limit tuning, given the generator is so near 13/9. | Liesel is a very natural 13-limit tuning, given the generator is so near 13/9. | ||
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Badness: 0.027304 | Badness: 0.027304 | ||
== Elisa == | === Elisa === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Badness: 0.041592 | Badness: 0.041592 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,782: | Line 1,782: | ||
Badness: 0.026922 | Badness: 0.026922 | ||
== Lisa == | === Lisa === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Badness: 0.054829 | Badness: 0.054829 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness: 0.036144 | Badness: 0.036144 | ||
= Jerome = | == Jerome == | ||
Jerome is related to [[20ed5|Hieronymus' tuning]]; the Hieronymus generator is 5<sup>1/20</sup>, or 139.316 cents. While the generator represents both 13/12 and 12/11, the POTE and Hieronymus generators are close to 13/12 in size. | Jerome is related to [[20ed5|Hieronymus' tuning]]; the Hieronymus generator is 5<sup>1/20</sup>, or 139.316 cents. While the generator represents both 13/12 and 12/11, the POTE and Hieronymus generators are close to 13/12 in size. | ||
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[[Badness]]: 0.108656 | [[Badness]]: 0.108656 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,846: | Line 1,846: | ||
Badness: 0.047914 | Badness: 0.047914 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness: 0.029285 | Badness: 0.029285 | ||
== 17-limit == | === 17-limit === | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
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Badness: 0.020878 | Badness: 0.020878 | ||
== 19-limit == | === 19-limit === | ||
Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
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Badness: 0.018229 | Badness: 0.018229 | ||
= Cloudtone = | == Cloudtone == | ||
The ''cloudtone'' temperament (5&50, named by [[User:Xenllium|Xenllium]]) tempers out the [[cloudy comma]], 16807/16384 and the [[81/80|syntonic comma]], 81/80 in the 7-limit. It can be extended to the 11- and 13-limit by adding 385/384 and 105/104 to the comma list in this order. | The ''cloudtone'' temperament (5&50, named by [[User:Xenllium|Xenllium]]) tempers out the [[cloudy comma]], 16807/16384 and the [[81/80|syntonic comma]], 81/80 in the 7-limit. It can be extended to the 11- and 13-limit by adding 385/384 and 105/104 to the comma list in this order. | ||
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[[Badness]]: 0.102256 | [[Badness]]: 0.102256 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,925: | Line 1,925: | ||
Badness: 0.070378 | Badness: 0.070378 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 1,940: | Line 1,940: | ||
Badness: 0.048829 | Badness: 0.048829 | ||
= Meanmag = | == Meanmag == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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[[Badness]]: 0.077023 | [[Badness]]: 0.077023 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 1,972: | Line 1,972: | ||
Badness: 0.066829 | Badness: 0.066829 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 1,987: | Line 1,987: | ||
Badness: 0.045844 | Badness: 0.045844 | ||
= Undevigintone = | == Undevigintone == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 2,002: | Line 2,002: | ||
Badness: 0.036387 | Badness: 0.036387 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||