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Meantone family: Difference between revisions

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Line 1: Line 1:
<span style="display: block; text-align: right;">
<span style="display: block; text-align: right;">
__FORCETOC__
[[de:mitteltönig]]</span>
[[de:mitteltönig]]</span>


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 [[monzo]] for 81/80 goes {{monzo| -4 4 -1 }}, and that can be flipped around to the corresponding [[Wedgies and Multivals|wedgie]], &lt;&lt;1 4 4||, which tells us that 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 [[monzo]] for 81/80 goes {{monzo| -4 4 -1 }}, and that can be flipped around to the corresponding [[Wedgies and Multivals|wedgie]], &lt;&lt;1 4 4||, which tells us that the period is an octave, the generator is a fifth, and four fifths go to make up a 5/1 interval.


=5-limit meantone=
= 5-limit meantone =
Comma: 81/80
Comma: 81/80


Line 24: Line 23:
[[Badness]]: 0.00736
[[Badness]]: 0.00736


==Seven limit children==
== Seven limit children ==
The [[7-limit]] children of 81/80 are septimal meantone, with normal comma list [|-4 4 -1&gt;, |-13 10 0 -1&gt;], flattone, with normal list [|-4 4 -1&gt;, |-17 9 0 1&gt;], dominant, with normal list [|-4 4 -1&gt;, |6 -2 0 -1&gt;], sharptone, with normal list [|-4 4 -1&gt;, |2 -3 0 1&gt;], injera, with normal list [|-4 4 -1&gt;, |-7 8 0 -2&gt;], mohajira, with normal list [|-4 4 -1&gt;, |-23 11 0 2&gt;], godzilla, with normal list [|-4 4 -1&gt;, |-4 -1 0 2&gt;], mothra, with normal list [|-4 4 -1&gt;, |-10 1 0 3&gt;], squares, with normal list [|-4 4 -1&gt;, |-3 9 0 -4&gt;], and liese, with normal list [|-4 4 -1&gt;, |-9 11 0 -3&gt;].
The [[7-limit]] children of 81/80 are septimal meantone, with normal comma list [{{Monzo| -4 4 -1 }}, {{Monzo| -13 10 0 -1 }}], flattone, with normal list [{{Monzo| -4 4 -1 }}, {{Monzo| -17 9 0 1 }}], dominant, with normal list [{{Monzo| -4 4 -1 }}, {{Monzo| 6 -2 0 -1 }}], sharptone, with normal list [{{Monzo| -4 4 -1 }}, {{Monzo| 2 -3 0 1 }}], injera, with normal list [{{Monzo| -4 4 -1 }}, {{Monzo| -7 8 0 -2 }}], mohajira, with normal list [{{Monzo| -4 4 -1 }}, {{Monzo| -23 11 0 2 }}], godzilla, with normal list [{{Monzo| -4 4 -1 }}, {{Monzo| -4 -1 0 2 }}], mothra, with normal list [{{Monzo| -4 4 -1 }}, {{Monzo| -10 1 0 3 }}], squares, with normal list [{{Monzo| -4 4 -1 }}, {{Monzo| -3 9 0 -4 }}], and liese, with normal list [{{Monzo| -4 4 -1 }}, {{Monzo| -9 11 0 -3 }}].


=Septimal meantone=
= Septimal meantone =
<span style="display: block; text-align: right;">[[:de:septimal-mitteltönig|Deutsch]]</span>
<span style="display: block; text-align: right;">[[:de:septimal-mitteltönig|Deutsch]]</span>


[https://en.wikipedia.org/wiki/Septimal_meantone_temperament Wikipedia article]
[https://en.wikipedia.org/wiki/Septimal_meantone_temperament Wikipedia article]


The comma |-13 10 0 -1&gt; for septimal meantone tells us that the interval class for 7 is 10 generator steps up. Hence, the [[7/4]] of septimal meantone is the augmented sixth, C-A#, and other septimal intervals are 7/6, C-D#, the augmented second, and [[7/5]], C-F#, the tritone. The [[Wedgies_and_Multivals|wedgie]] for septimal meantone is &lt;&lt;1 4 10 4 13 12||, again telling us how to get to 5 and 7 in terms of generator steps. The temperament, aside from what is on the normal list, tempers out 126/125 and 225/224, and [[31edo]] is a good tuning for it.
The comma {{Monzo| -13 10 0 -1 }} for septimal meantone tells us that the interval class for 7 is 10 generator steps up. Hence, the [[7/4]] of septimal meantone is the augmented sixth, C-A#, and other septimal intervals are 7/6, C-D#, the augmented second, and [[7/5]], C-F#, the tritone. The [[Wedgies_and_Multivals|wedgie]] for septimal meantone is &lt;&lt;1 4 10 4 13 12||, again telling us how to get to 5 and 7 in terms of generator steps. The temperament, aside from what is on the normal list, tempers out 126/125 and 225/224, and [[31edo]] is a good tuning for it.


[[Comma]]s: 81/80, 126/125
[[Comma]]s: 81/80, 126/125
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7 and [[9-odd-limit|9-limit]] minimax
7 and [[9-odd-limit|9-limit]] minimax


[|1 0 0 0&gt;, |1 0 1/4 0&gt;, |0 0 1 0&gt;, |-3 0 5/2 0&gt;]
[{{Monzo| 1 0 0 0 }}, {{Monzo| 1 0 1/4 0 }}, {{Monzo| 0 0 1 0 }}, {{Monzo| -3 0 5/2 0 }}]


[[Eigenmonzo]]s: 2, 5
[[Eigenmonzo]]s: 2, 5
Line 64: Line 63:
[[Badness]]: 0.0137
[[Badness]]: 0.0137


==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 77: Line 76:
Badness: 0.0381
Badness: 0.0381


===13-limit===
=== 13-limit ===
Commas: 81/80, 105/104, 126/125, 245/242
Commas: 81/80, 105/104, 126/125, 245/242


Line 88: Line 87:
Badness: 0.0288
Badness: 0.0288


==Unidecimal meantone aka Huygens==
== Unidecimal meantone aka Huygens ==
See also [[Meantone_vs_meanpop|Meantone vs meanpop]]
See also [[Meantone_vs_meanpop|Meantone vs meanpop]]


Line 95: Line 94:
[[11-odd-limit|11-limit]] minimax
[[11-odd-limit|11-limit]] minimax


[|1 0 0 0 0&gt;, |25/16 -1/8 0 0 1/16&gt;, |9/4 -1/2 0 0 1/4&gt;,
[{{Monzo| 1 0 0 0 0 }}, {{Monzo| 25/16 -1/8 0 0 1/16 }}, {{Monzo| 9/4 -1/2 0 0 1/4 }},
|21/8 -5/4 0 0 5/8&gt;, |25/8 -9/4 0 0 9/8&gt;<nowiki>]</nowiki>
{{Monzo| 21/8 -5/4 0 0 5/8 }}, {{Monzo| 25/8 -9/4 0 0 9/8 }}<nowiki>]</nowiki>


[[Eigenmonzo]]s: 2, 11/9
[[Eigenmonzo]]s: 2, 11/9
Line 122: Line 121:
[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 ===
Commas: 66/65, 81/80, 99/98, 105/104
Commas: 66/65, 81/80, 99/98, 105/104


Line 135: Line 134:
Badness: 0.0180
Badness: 0.0180


===Grosstone===
=== Grosstone ===
Commas: 81/80, 99/98, 126/125, 144/143
Commas: 81/80, 99/98, 126/125, 144/143


Line 154: Line 153:
Badness: 0.0259
Badness: 0.0259


===Meridetone===
=== Meridetone ===
Commas: 78/77, 81/80, 99/98, 126/125
Commas: 78/77, 81/80, 99/98, 126/125


Line 167: Line 166:
Badness: 0.0264
Badness: 0.0264


===Hemimeantone===
=== Hemimeantone ===
Commas: 81/80, 99/98, 126/125, 169/168
Commas: 81/80, 99/98, 126/125, 169/168


Line 180: Line 179:
Badness: 0.0314
Badness: 0.0314


==Meanpop==
== Meanpop ==
See also [[Meantone_vs_meanpop|Meantone vs meanpop]]
See also [[Meantone_vs_meanpop|Meantone vs meanpop]]


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[[11-odd-limit|11-limit]] minimax 1/4 comma
[[11-odd-limit|11-limit]] minimax 1/4 comma


[|1 0 0 0 0&gt;, |1 0 1/4 0 0&gt;, |0 0 1 0 0&gt;,
[{{Monzo| 1 0 0 0 0 }}, {{Monzo| 1 0 1/4 0 0 }}, {{Monzo| 0 0 1 0 0 }},
|-3 0 5/2 0 0&gt;, |11 0 -13/4 0 0&gt;<nowiki>&lt;nowiki&gt;&amp;lt;nowiki&amp;gt;&amp;amp;lt;nowiki&amp;amp;gt;]&amp;amp;lt;/nowiki&amp;amp;gt;&amp;lt;/nowiki&amp;gt;&lt;/nowiki&gt;</nowiki>
{{Monzo| -3 0 5/2 0 0 }}, {{Monzo| 11 0 -13/4 0 0 }}]


[[Eigenmonzo]]s: 2, 5
[[Eigenmonzo]]s: 2, 5
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[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]


===13-limit Meanpop===
=== 13-limit Meanpop ===
Commas: 81/80, 105/104, 126/125, 144/143
Commas: 81/80, 105/104, 126/125, 144/143


Line 235: Line 234:
Badness: 0.0209
Badness: 0.0209


===Meanplop===
=== Meanplop ===
Commas: 65/64, 78/77, 81/80, 91/90
Commas: 65/64, 78/77, 81/80, 91/90


Line 248: Line 247:
Badness: 0.0277
Badness: 0.0277


==Meanenneadecal==
== Meanenneadecal ==
Commas: 45/44, 56/55, 81/80
Commas: 45/44, 56/55, 81/80


Line 261: Line 260:
Badness: 0.0214
Badness: 0.0214


===13-limit===
=== 13-limit ===
Commas: 45/44, 56/55, 78/77, 81/80
Commas: 45/44, 56/55, 78/77, 81/80


Line 386: Line 385:
Badness: 0.0138
Badness: 0.0138


==Meanundeci==
== Meanundeci ==
Commas: 33/32, 55/54, 77/75
Commas: 33/32, 55/54, 77/75


Line 399: Line 398:
Badness: 0.0315
Badness: 0.0315


===13-limit===
=== 13-limit ===
Commas: 33/32, 55/54, 65/64, 77/75
Commas: 33/32, 55/54, 65/64, 77/75


Line 425: Line 424:
Badness: 0.0242
Badness: 0.0242


=Flattone=
= Flattone =
[[Comma]]s: 81/80, 525/512
[[Comma]]s: 81/80, 525/512


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[[7-odd-limit|7-limit]] minimax
[[7-odd-limit|7-limit]] minimax


[|1 0 0 0&gt;, |21/13 0 1/13 -1/13&gt;,
[{{Monzo| 1 0 0 0 }}, {{Monzo| 21/13 0 1/13 -1/13 }},
|32/13 0 4/13 -4/13&gt;, |32/13 0 -9/13 9/13&gt;<nowiki>]</nowiki>
{{Monzo| 32/13 0 4/13 -4/13 }}, {{Monzo| 32/13 0 -9/13 9/13 }}<nowiki>]</nowiki>


[[Eigenmonzo]]s: 2, 7/5
[[Eigenmonzo]]s: 2, 7/5
Line 439: Line 438:
[[9-odd-limit|9-limit]] minimax
[[9-odd-limit|9-limit]] minimax


[|1 0 0 0&gt;, |17/11 2/11 0 -1/11&gt;,
[{{Monzo| 1 0 0 0 }}, {{Monzo| 17/11 2/11 0 -1/11 }},
|24/11 8/11 0 -4/11&gt;, |34/11 -18/11 0 9/11&gt;<nowiki>]</nowiki>
{{Monzo| 24/11 8/11 0 -4/11 }}, {{Monzo| 34/11 -18/11 0 9/11 }}<nowiki>]</nowiki>


Eigenmonzos: 2, 9/7
Eigenmonzos: 2, 9/7
Line 466: Line 465:
[[Badness]]: 0.0386
[[Badness]]: 0.0386


==11-limit==
== 11-limit ==
Commas: 45/44, 81/80, 385/384
Commas: 45/44, 81/80, 385/384


Line 485: Line 484:
Badness: 0.0338
Badness: 0.0338


==13-limit==
== 13-limit ==
45/44, 65/64, 78/77, 81/80
45/44, 65/64, 78/77, 81/80


Line 504: Line 503:
Badness: 0.0223
Badness: 0.0223


=Dominant=
= Dominant =
[[Comma|Comma]]s: 36/35, 64/63
[[Comma]]s: 36/35, 64/63


The wedgie for dominant is &lt;&lt;1 4 -2 4 -6 -16||. Now 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]], but it also works well with the Pythagorean tuning of pure [[3/2]] fifths, and with [[29edo]], [[41edo]], or [[53edo]].
The wedgie for dominant is &lt;&lt;1 4 -2 4 -6 -16||. Now 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]], but it also works well with the Pythagorean tuning of pure [[3/2]] fifths, and with [[29edo]], [[41edo]], or [[53edo]].
Line 527: Line 526:
[[Badness]]: 0.0207
[[Badness]]: 0.0207


==11-limit==
== 11-limit ==
Commas: 36/35, 64/63, 56/55
Commas: 36/35, 64/63, 56/55


Line 574: Line 573:
Badness: 0.0273
Badness: 0.0273


==Domineering==
== Domineering ==
Commas: 36/35, 45/44, 64/63
Commas: 36/35, 45/44, 64/63


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Badness: 0.0220
Badness: 0.0220


===13-limit===
=== 13-limit ===
Commas: 36/35, 45/44, 52/49, 64/63
Commas: 36/35, 45/44, 52/49, 64/63


Line 626: Line 625:
Badness: 0.0204
Badness: 0.0204


===Dominatrix===
=== Dominatrix ===
Commas: 27/26, 36/35, 45/44, 64/63
Commas: 27/26, 36/35, 45/44, 64/63


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EDOs: 5e, 7, 12f, 19df
EDOs: 5e, 7, 12f, 19df


==Domination==
== Domination ==
Commas: 36/35, 64/63, 77/75
Commas: 36/35, 64/63, 77/75


Line 650: Line 649:
Badness: 0.0366
Badness: 0.0366


===13-limit===
=== 13-limit ===
Commas: 26/25, 36/35, 64/63, 66/65
Commas: 26/25, 36/35, 64/63, 66/65


Line 663: Line 662:
Badness: 0.0274
Badness: 0.0274


==Arnold==
== Arnold ==
Commas: 22/21, 33/32, 36/35
Commas: 22/21, 33/32, 36/35


Line 676: Line 675:
Badness: 0.0261
Badness: 0.0261


===13-limit===
=== 13-limit ===
Commas: 22/21, 27/26, 33/32, 36/35
Commas: 22/21, 27/26, 33/32, 36/35


Line 687: Line 686:
Badness: 0.0233
Badness: 0.0233


===17-limit===
=== 17-limit ===
Commas: 22/21, 27/26, 33/32, 36/35, 51/49
Commas: 22/21, 27/26, 33/32, 36/35, 51/49


Line 698: Line 697:
Badness: 0.0245
Badness: 0.0245


===19-limit===
=== 19-limit ===
Commas: 22/21, 27/26, 33/32, 36/35, 51/49, 57/56
Commas: 22/21, 27/26, 33/32, 36/35, 51/49, 57/56


Line 709: Line 708:
Badness: 0.0211
Badness: 0.0211


=Sharptone=
= Sharptone =
[[Comma]]s: 21/20, 28/27
[[Comma]]s: 21/20, 28/27


Line 726: Line 725:
[[Badness]]: 0.0248
[[Badness]]: 0.0248


==Meanertone==
== Meanertone ==
Commas: 21/20, 28/27, 33/32
Commas: 21/20, 28/27, 33/32


Line 737: Line 736:
Badness: 0.0252
Badness: 0.0252


=Meansept=
= Meansept =
Commas: 15/14, 81/80
Commas: 15/14, 81/80


Line 752: Line 751:
Badness: 0.0453
Badness: 0.0453


==11-limit==
== 11-limit ==
Commas: 15/14, 22/21, 81/80
Commas: 15/14, 22/21, 81/80


Line 765: Line 764:
Badness: 0.0325
Badness: 0.0325


=Supermean=
= Supermean =
Commas: 81/80, 672/625
Commas: 81/80, 672/625


Line 776: Line 775:
Badness: 0.1342
Badness: 0.1342


==11-limit==
== 11-limit ==
Commas: 56/55, 81/80, 132/125
Commas: 56/55, 81/80, 132/125


Line 787: Line 786:
Badness: 0.0633
Badness: 0.0633


==13-limit==
== 13-limit ==
Commas: 26/25, 56/55, 66/65, 81/80
Commas: 26/25, 56/55, 66/65, 81/80


Line 796: Line 795:
EDOs: 5de, 12de, 17c, 29c
EDOs: 5de, 12de, 17c, 29c


=Injera=
= Injera =
[[Comma]]s: 50/49, 81/80
[[Comma]]s: 50/49, 81/80


Line 821: Line 820:
[[Badness]]: 0.0311
[[Badness]]: 0.0311


==Music==
== Music ==
* [http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Two%20Pairs%20of%20Socks.mp3 Two Pairs of Socks] (in [[26edo]]) by [[Igliashon Jones]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Two%20Pairs%20of%20Socks.mp3 Two Pairs of Socks] (in [[26edo]]) by [[Igliashon Jones]]


==11-limit==
== 11-limit ==
Commas: 45/44, 50/49, 81/80
Commas: 45/44, 50/49, 81/80


Line 875: Line 874:
Badness: 0.0265
Badness: 0.0265


==Injerous==
== Injerous ==
Commas: 33/32, 50/49, 55/54
Commas: 33/32, 50/49, 55/54


Line 888: Line 887:
Badness: 0.0386
Badness: 0.0386


==Lahoh==
== Lahoh ==
Commas: 50/49, 56/55, 81/77
Commas: 50/49, 56/55, 81/77


Line 901: Line 900:
Badness: 0.0431
Badness: 0.0431


=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}}


[[Comma|Comma]]s: 49/48, 81/80
[[Comma]]s: 49/48, 81/80


Godzilla has wedgie &lt;&lt;2 8 1 8 -4 -20||, and tempers out 49/48, equating 8/7 with 7/6. Two of the step-and-a-quarter intervals these represent give a fourth, and so step-and-a-quarter generators generate godzilla. [[19edo]] is the perfect godzilla tuning, so much so that's there's not much point in looking elsewhere. Hence it can be more or less equated with taking 4\19 as a generator. MOS are of 5, 9, or 14 notes.
Godzilla has wedgie &lt;&lt;2 8 1 8 -4 -20||, and tempers out 49/48, equating 8/7 with 7/6. Two of the step-and-a-quarter intervals these represent give a fourth, and so step-and-a-quarter generators generate godzilla. [[19edo]] is the perfect godzilla tuning, so much so that's there's not much point in looking elsewhere. Hence it can be more or less equated with taking 4\19 as a generator. MOS are of 5, 9, or 14 notes.
Line 928: Line 927:
[[Badness]]: 0.0267
[[Badness]]: 0.0267


==11-limit==
== 11-limit ==
Commas: 45/44, 49/48, 81/80
Commas: 45/44, 49/48, 81/80


Line 966: Line 965:
Badness: 0.0225
Badness: 0.0225


==Semafour==
== Semafour ==
Commas: 33/32, 49/48, 55/54
Commas: 33/32, 49/48, 55/54


Line 979: Line 978:
Badness: 0.0285
Badness: 0.0285


==Varan==
== Varan ==
Commas: 49/48, 77/75, 81/80
Commas: 49/48, 77/75, 81/80


Line 992: Line 991:
Badness: 0.0396
Badness: 0.0396


===13-limit===
=== 13-limit ===
Commas: 49/48, 66/65, 77/75, 81/80
Commas: 49/48, 66/65, 77/75, 81/80


Line 1,005: Line 1,004:
Badness: 0.0257
Badness: 0.0257


==Baragon==
== Baragon ==
Commas: 49/48, 56/55, 81/80
Commas: 49/48, 56/55, 81/80


Line 1,018: Line 1,017:
Badness: 0.0357
Badness: 0.0357


==Music==
== Music ==
[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Bobro/GodzillaExample.mp3 Godzilla Example] by [[Cameron_Bobro|Cameron Bobro]]
[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Bobro/GodzillaExample.mp3 Godzilla Example] by [[Cameron_Bobro|Cameron Bobro]]


[http://tinyurl.com/4uyumk9 "Change is on the Wind"] in Godzilla[9] by [[Igliashon_Jones|Igliashon Jones]]
[http://tinyurl.com/4uyumk9 "Change is on the Wind"] in Godzilla[9] by [[Igliashon_Jones|Igliashon Jones]]


=Mohajira=
= Mohajira =


{{main|Mohajira}}
{{main|Mohajira}}
Line 1,035: Line 1,034:
[[7-odd-limit|7]] and [[9-odd-limit|9-limit]] minimax 1/4 comma
[[7-odd-limit|7]] and [[9-odd-limit|9-limit]] minimax 1/4 comma


[|1 0 0 0&gt;, |1 0 1/4 0&gt;, |0 0 1 0&gt;, |6 0 -11/8 0&gt;]
[{{Monzo| 1 0 0 0 }}, {{Monzo| 1 0 1/4 0 }}, {{Monzo| 0 0 1 0 }}, {{Monzo| 6 0 -11/8 0 }}]


[[Eigenmonzo]]s: 2, 5
[[Eigenmonzo]]s: 2, 5
Line 1,055: Line 1,054:
[[Badness]]: 0.0557
[[Badness]]: 0.0557


==11-limit==
== 11-limit ==
Commas: 81/80, 121/120, 176/175
Commas: 81/80, 121/120, 176/175


[[11-odd-limit|11-limit]] minimax 1/4 comma
[[11-odd-limit|11-limit]] minimax 1/4 comma


[|1 0 0 0 0&gt;, |1 0 1/4 0 0&gt;, |0 0 1 0 0&gt;,
[{{Monzo| 1 0 0 0 0 }}, {{Monzo| 1 0 1/4 0 0 }}, {{Monzo| 0 0 1 0 0 }},
|6 0 -11/8 0 0&gt;, |2 0 5/8 0 0&gt;<nowiki>]</nowiki>
{{Monzo| 6 0 -11/8 0 0 }}, {{Monzo| 2 0 5/8 0 0 }}<nowiki>]</nowiki>


Eigenmonzos: 2, 5
Eigenmonzos: 2, 5
Line 1,077: Line 1,076:
Badness: 0.0261
Badness: 0.0261


==13-limit==
== 13-limit ==
Commas: 66/65, 81/80, 105/104, 121/120
Commas: 66/65, 81/80, 105/104, 121/120


Line 1,090: Line 1,089:
Badness: 0.0234
Badness: 0.0234


==17-limit==
== 17-limit ==
Commas: 66/65, 81/80, 105/104, 121/120, 154/153
Commas: 66/65, 81/80, 105/104, 121/120, 154/153


Line 1,103: Line 1,102:
Badness: 0.0206
Badness: 0.0206


==19-limit==
== 19-limit ==
Commas: 66/65, 77/76, 81/80, 96/95, 105/104, 153/152
Commas: 66/65, 77/76, 81/80, 96/95, 105/104, 153/152


Line 1,116: Line 1,115:
Badness: 0.0173
Badness: 0.0173


=Ptolemy=
= Ptolemy =
Commas: 81/80, 121/120, 525/512
Commas: 81/80, 121/120, 525/512


Line 1,127: Line 1,126:
Badness: 0.0588
Badness: 0.0588


==13-limit==
== 13-limit ==
Commas: 65/64, 81/80, 105/104, 121/120
Commas: 65/64, 81/80, 105/104, 121/120


Line 1,138: Line 1,137:
Badness: 0.0343
Badness: 0.0343


=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 article: [[maqamic|Maqamic]]
Main article: [[maqamic|Maqamic]]


[[Comma|Comma]]s: 81/80, 36/35, 121/120
[[Comma]]s: 81/80, 36/35, 121/120


Maqamic temperament is much like Mohajira, except in that it 36/35 vanishes instead of 176/175. It makes the most sense if viewed as an adaptive temperament, whereby 7/4 and 9/5 simply share an equivalence class in the resulting scales, but don't need to share a particular tempered "middle-of-the-road" intonation.
Maqamic temperament is much like Mohajira, except in that it 36/35 vanishes instead of 176/175. It makes the most sense if viewed as an adaptive temperament, whereby 7/4 and 9/5 simply share an equivalence class in the resulting scales, but don't need to share a particular tempered "middle-of-the-road" intonation.
Line 1,157: Line 1,156:
EDOs: [[7edo|7]], [[10edo|10c]], [[17edo|17c]], [[24edo|24d]], [[31edo|31d]]
EDOs: [[7edo|7]], [[10edo|10c]], [[17edo|17c]], [[24edo|24d]], [[31edo|31d]]


==13-limit==
== 13-limit ==
[[Comma|Comma]]s: 81/80, 36/35, 121/120, 144/143
[[Comma]]s: 81/80, 36/35, 121/120, 144/143


[[POTE generator]]: ~11/9 = 350.816
[[POTE generator]]: ~11/9 = 350.816
Line 1,170: Line 1,169:
EDOs: [[7edo|7]], [[10edo|10c]], [[17edo|17c]], [[24edo|24d]],[[31edo| 31d]]
EDOs: [[7edo|7]], [[10edo|10c]], [[17edo|17c]], [[24edo|24d]],[[31edo| 31d]]


=Migration=
= Migration =
Commas: 81/80, 121/120, 126/125
Commas: 81/80, 121/120, 126/125


Line 1,183: Line 1,182:
Badness: 0.0255
Badness: 0.0255


==13-limit==
== 13-limit ==
Commas: 66/65, 81/80, 121/120, 126/125
Commas: 66/65, 81/80, 121/120, 126/125


Line 1,194: Line 1,193:
Badness: 0.0281
Badness: 0.0281


=Mohamaq=
= Mohamaq =
Commas: 81/80, 392/375
Commas: 81/80, 392/375


Line 1,207: Line 1,206:
Badness: 0.0777
Badness: 0.0777


==11-limit==
== 11-limit ==
Commas: 56/55, 77/75, 243/242
Commas: 56/55, 77/75, 243/242


Line 1,220: Line 1,219:
Badness: 0.0362
Badness: 0.0362


==13-limit==
== 13-limit ==
Commas: 56/55, 66/65, 77/75, 243/242
Commas: 56/55, 66/65, 77/75, 243/242


Line 1,233: Line 1,232:
Badness: 0.0287
Badness: 0.0287


=Orphic=
= Orphic =
Commas: 81/80, 5898240/5764801
Commas: 81/80, 5898240/5764801


Line 1,248: Line 1,247:
Badness: 0.2588
Badness: 0.2588


==11-limit==
== 11-limit ==
Commas: 81/80, 99/98, 73728/73205
Commas: 81/80, 99/98, 73728/73205


Line 1,261: Line 1,260:
Badness: 0.1015
Badness: 0.1015


==13-limit==
== 13-limit ==
Commas: 81/80, 99/98, 144/143, 2200/2197
Commas: 81/80, 99/98, 144/143, 2200/2197


Line 1,274: Line 1,273:
Badness: 0.0535
Badness: 0.0535


=Mothra=
= Mothra =
[[Comma]]s: 81/80, 1029/1024
[[Comma]]s: 81/80, 1029/1024


Line 1,283: Line 1,282:
[[7-odd-limit|7]] and [[9-odd-limit|9-limit]] minimax 1/4 comma
[[7-odd-limit|7]] and [[9-odd-limit|9-limit]] minimax 1/4 comma


[|1 0 0 0&gt;, |1 0 1/4 0&gt;, |0 0 1 0&gt;, |3 0 -1/12 0&gt;]
[{{Monzo| 1 0 0 0 }}, {{Monzo| 1 0 1/4 0 }}, {{Monzo| 0 0 1 0 }}, {{Monzo| 3 0 -1/12 0 }}]


[[Eigenmonzo]]s: 2, 5
[[Eigenmonzo]]s: 2, 5
Line 1,303: Line 1,302:
[[Badness]]: 0.0371
[[Badness]]: 0.0371


==11-limit==
== 11-limit ==
Commas: 81/80, 99/98, 385/384
Commas: 81/80, 99/98, 385/384


Line 1,329: Line 1,328:
Badness: 0.0240
Badness: 0.0240


==Cynder==
== Cynder ==
Commas: 45/44, 81/80, 1029/1024
Commas: 45/44, 81/80, 1029/1024


Line 1,342: Line 1,341:
Badness: 0.0557
Badness: 0.0557


===13-limit===
=== 13-limit ===
Commas: 45/44, 78/77, 81/80, 640/637
Commas: 45/44, 78/77, 81/80, 640/637


Line 1,355: Line 1,354:
Badness: 0.0341
Badness: 0.0341


==Mosura==
== Mosura ==
Commas: 81/80, 176/175, 540/539
Commas: 81/80, 176/175, 540/539


Line 1,368: Line 1,367:
Badness: 0.0313
Badness: 0.0313


===13-limit===
=== 13-limit ===
Commas: 81/80, 144/143, 176/175, 196/195
Commas: 81/80, 144/143, 176/175, 196/195


Line 1,381: Line 1,380:
Badness: 0.0369
Badness: 0.0369


=Squares=
= Squares =
[[Comma]]s: 81/80, 2401/2400
[[Comma]]s: 81/80, 2401/2400


Line 1,388: Line 1,387:
7 and 9 limit minimax 1/4 comma
7 and 9 limit minimax 1/4 comma


[|1 0 0 0&gt;, |1 0 1/4 0&gt;, |0 0 1 0&gt;, |3/2 0 9/16 0&gt;]
[{{Monzo| 1 0 0 0 }}, {{Monzo| 1 0 1/4 0 }}, {{Monzo| 0 0 1 0 }}, {{Monzo| 3/2 0 9/16 0 }}]


[[Eigenmonzo]]s: 2, 5
[[Eigenmonzo]]s: 2, 5
Line 1,412: Line 1,411:
[http://clones.soonlabel.com/public/micro/tuning-survey/daily20100603-squares8piano.mp3 Square 8]
[http://clones.soonlabel.com/public/micro/tuning-survey/daily20100603-squares8piano.mp3 Square 8]


==11-limit==
== 11-limit ==
Commas: 81/80, 99/98, 121/120
Commas: 81/80, 99/98, 121/120


Line 1,486: Line 1,485:
[[Badness]]: 0.0568
[[Badness]]: 0.0568


=Liese=
= Liese =
<span style="display: block; text-align: right;">[[:de:Liese|Deutsch]]</span>
<span style="display: block; text-align: right;">[[:de:Liese|Deutsch]]</span>


Line 1,495: Line 1,494:
7 and 9 limit minimax 1/4 comma
7 and 9 limit minimax 1/4 comma


[|1 0 0 0&gt;, |1 0 1/4 0&gt;, |0 0 1 0&gt;, |2/3 0 11/12 0&gt;]
[{{Monzo| 1 0 0 0 }}, {{Monzo| 1 0 1/4 0 }}, {{Monzo| 0 0 1 0 }}, {{Monzo| 2/3 0 11/12 0 }}]


[[Eigenmonzo]]s: 2, 5
[[Eigenmonzo]]s: 2, 5
Line 1,513: Line 1,512:
[[Badness]]: 0.0467
[[Badness]]: 0.0467


==Liesel==
== Liesel ==
Commas: 56/55, 81/80, 540/539
Commas: 56/55, 81/80, 540/539


Line 1,526: Line 1,525:
Badness: 0.0407
Badness: 0.0407


===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.


Line 1,541: Line 1,540:
Badness: 0.0273
Badness: 0.0273


==Elisa==
== Elisa ==
Commas: 77/75, 81/80, 99/98
Commas: 77/75, 81/80, 99/98


Line 1,554: Line 1,553:
Badness: 0.0416
Badness: 0.0416


==Lisa==
== Lisa ==
Commas: 45/44, 81/80, 343/330
Commas: 45/44, 81/80, 343/330


Line 1,567: Line 1,566:
Badness: 0.0548
Badness: 0.0548


===13-limit===
=== 13-limit ===
Commas: 45/44, 81/80, 91/88, 147/143
Commas: 45/44, 81/80, 91/88, 147/143


Line 1,578: Line 1,577:
Badness: 0.0361
Badness: 0.0361


=Jerome=
= Jerome =
Jerome is related to [[20ed5|Hieronymus' tuning]]; the Hieronymus generator is 5^(1/20), 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^(1/20), 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.


Line 1,595: Line 1,594:
Badness: 0.1087
Badness: 0.1087


==11-limit==
== 11-limit ==
Commas: 81/80, 99/98, 864/847
Commas: 81/80, 99/98, 864/847


Line 1,608: Line 1,607:
Badness: 0.0479
Badness: 0.0479


==13-limit==
== 13-limit ==
Commas: 78/77, 81/80, 99/98, 144/143
Commas: 78/77, 81/80, 99/98, 144/143


Line 1,621: Line 1,620:
Badness: 0.0293
Badness: 0.0293


==17-limit==
== 17-limit ==
Commas: 78/77, 81/80, 99/98, 144/143, 189/187
Commas: 78/77, 81/80, 99/98, 144/143, 189/187


Line 1,634: Line 1,633:
Badness: 0.0209
Badness: 0.0209


==19-limit==
== 19-limit ==
Commas: 78/77, 81/80, 99/98, 120/119, 135/133, 144/143
Commas: 78/77, 81/80, 99/98, 120/119, 135/133, 144/143


Line 1,647: Line 1,646:
Badness: 0.0182
Badness: 0.0182


=Meanmag=
= Meanmag =
Commas: 81/80, 3125/3072
Commas: 81/80, 3125/3072


Line 1,662: Line 1,661:
Badness: 0.0770
Badness: 0.0770


=Undevigintone=
= Undevigintone =
Commas: 49/48, 81/80, 126/125
Commas: 49/48, 81/80, 126/125


Line 1,675: Line 1,674:
Badness: 0.0364
Badness: 0.0364


==13-limit==
== 13-limit ==
Commas: 49/48, 65/64, 81/80, 126/125
Commas: 49/48, 65/64, 81/80, 126/125


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