Meantone family: Difference between revisions

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<~~h2>IMPORTED REVISION FROM WIKISPACES</h2>~~

~~This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>~~

__FORCETOC__

~~: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2017-07-11 09:16:01 UTC</tt>.<br>~~

[[:de:mitteltönig Deutsch]]</span>

~~: The original revision id was <tt>615523693</tt>.<br>~~

~~: The revision comment was: <tt></tt><br>~~

The [[5-limit|5-limit]] parent [[Comma|comma]] of the [[Meantone|meantone]] family is the Didymus or [http://en.wikipedia.org/wiki/Syntonic_comma syntonic comma], 81/80. This is the one they all temper out. The [[Monzos_and_Interval_Space|monzo]] for 81/80 goes |-4 4 -1>, and that can be flipped around to the corresponding [[Wedgies_and_Multivals|wedgie]], <<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 revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>~~

~~<h4>Original Wikitext content:</h4>~~

[[POTE_tuning|POTE generator]]: ~3/2 = 696.239

<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]]~~

[[~~xenharmonie/~~mitteltönig|Deutsch]]

~~<~~/span~~>~~

The [[5-limit]] parent [[Comma|comma]] of the [[meantone]] family is the Didymus or [[http://en.wikipedia.org/wiki/Syntonic_comma|syntonic comma]], 81/80. This is the one they all temper out. The [[~~Monzos and Interval Space~~|monzo]] for 81/80 goes |-4 4 -1>, and that can be flipped around to the corresponding [[~~Wedgies and Multivals~~|wedgie]], <<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.

~~[[POTE tuning|POTE generator]]: ~3/2 = 696.239~~

Mapping generator: ~3

[[~~Tuning Ranges of Regular Temperaments~~|valid range]]: [685.714, 720.000] (7 to 5)

[[Tuning_Ranges_of_Regular_Temperaments|valid range]]: [685.714, 720.000] (7 to 5)

nice range: [694.786, 701.955] (1/3 comma to Pythagorean)

strict range: [694.786, 701.955]

[[Map]]: [<1 0 -4|, <0 1 4|]

[[Map|Map]]: [<1 0 -4|, <0 1 4|]

EDOs (patent val edo list is complete): [[5edo|5]], [[7edo|7]], [[12edo|12]], [[19edo|19]], [[24edo|24]], [[26edo|26]], [[31edo|31]], [[36edo|36]], [[38edo|38]], [[43edo|43]], [[45edo|45]], [[50edo|50]], [[55edo|55]], [[57edo|57]], [[62edo|62]], [[67edo|67]], [[69edo|69]], [[74edo|74]], [[76edo|76]], [[81edo|81]], [[86edo|86]], [[88edo|88]], [[93edo|93]], [[98edo|98]], [[100edo|100]], [[105edo|105]], [[117edo|117]], [[129edo|129]], [[212edo|212b]]

~~[[Badness]]: 0.00736~~

~~==Seven limit children==~~

[[Badness|Badness]]: 0.00736

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

=~~Septimal meantone~~=

==Seven limit children==

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

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

<~~/span~~>

[[~~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|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|7/5~~]], C-F#, the tritone. The [[Wedgies and Multivals|wedgie]] for septimal meantone is <<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.~~

=Septimal meantone=

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

[[Comma]]s: 81/80, 126/125

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

The comma |-13 10 0 -1> for septimal meantone tells us that the interval class for 7 is 10 generator steps up. Hence, the [[7/4|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|7/5]], C-F#, the tritone. The [[Wedgies_and_Multivals|wedgie]] for septimal meantone is <<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|31edo]] is a good tuning for it.

[[Comma|Comma]]s: 81/80, 126/125

7 and [[9-limit|9-limit]] minimax

~~7 and [[9-limit]] minimax~~

[|1 0 0 0>, |1 0 1/4 0>, |0 0 1 0>, |-3 0 5/2 0>]

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

[[~~Tuning Ranges of Regular Temperaments~~|valid range]]: [694.737, 700.000] (19 to 12)

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

[[Tuning_Ranges_of_Regular_Temperaments|valid range]]: [694.737, 700.000] (19 to 12)

nice range: [694.786, 701.955]

strict range: [694.786, 700.000]

[[~~POTE tuning~~|POTE generator]]: 696.495

[[POTE_tuning|POTE generator]]: 696.495

Mapping generator: ~3

Algebraic generator: Cybozem, the real root of 15x^3-10x^2-18, which comes to 503.4257 cents. The recurrence converges quickly.

[[Map]]: [<1 0 -4 -13|, <0 1 4 10|]

[[Map|Map]]: [<1 0 -4 -13|, <0 1 4 10|]

[[Generator]]s: 2, 3

[[Wedgie]]: <<1 4 10 4 13 12||

[[generator|Generator]]s: 2, 3

[[wedgie|Wedgie]]: <<1 4 10 4 13 12||

EDOs: [[12edo|12]], [[19edo|19]], [[31edo|31]], [[81edo|81]], [[143edo|143b]]

~~[[Badness]]: 0.0137~~

==Bimeantone==

[[Badness|Badness]]: 0.0137

==Bimeantone==

Commas: 81/80, 126/125, 245/242

[[~~POTE tuning~~|POTE generator]]: ~3/2 = 696.016

[[POTE_tuning|POTE generator]]: ~3/2 = 696.016

Map: [<2 0 -8 -26 -31|, <0 1 4 10 12|]

EDOs: 12, 38d, 50

Badness: 0.0381

===13-limit===

Commas: 81/80, 105/104, 126/125, 245/242

[[~~POTE tuning~~|POTE generator]]: ~3/2 = 695.836

[[POTE_tuning|POTE generator]]: ~3/2 = 695.836

Map: [<2 0 -8 -26 -31 -40|, <0 1 4 10 12 15|]

EDOs: 12f, 50

Badness: 0.0288

==Unidecimal meantone aka Huygens==

See also [[Meantone vs meanpop]]

See also [[Meantone_vs_meanpop|Meantone vs meanpop]]

[[Comma]]s: 81/80, 126/125, 385/384

[[Comma|Comma]]s: 81/80, 126/125, 385/384

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

~~[[11-limit]] [[minimax]] 1/4 comma~~

[|1 0 0 0 0>, |1 0 1/4 0 0>, |0 0 1 0 0>,

|-3 0 5/2 0 0>, |11 0 -13/4 0 0>]

[[Eigenmonzo]]s: 2, 5

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

valid range: [694.737, 696.774] (19 to 31)

nice range: [691.202, 701.955]

strict range: [694.737, 696.774]

[[~~POTE tuning~~|POTE generator]]: 696.434

[[POTE_tuning|POTE generator]]: 696.434

Mapping generator: ~3

[[Algebraic generator]]: Cybozem; or else Radieubiz, the real root of 3x^3+6x-19. Unlike Cybozem, the recurrence for Radieubiz does not converge.

[[Algebraic_generator|Algebraic generator]]: Cybozem; or else Radieubiz, the real root of 3x^3+6x-19. Unlike Cybozem, the recurrence for Radieubiz does not converge.

[[@http://soonlabel.com/xenharmonic/archives/607|Scott Joplin's "The Entertainer" tuned into meanpop]]

[http://soonlabel.com/xenharmonic/archives/607 Scott Joplin's "The Entertainer" tuned into meanpop]

Map: [<1 0 -4 -13 24|, <0 1 4 10 -13|]

[[Generator]]s: 2, 3

[[generator|Generator]]s: 2, 3

EDOs: [[12edo|12]], [[19edo|19]], [[31edo|31]], [[81edo|81]], [[112edo|112]]

~~[[Badness]]: 0.0215~~

[[~~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]]~~

[[Badness|Badness]]: 0.0215

===13-limit Meanpop===

[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]

[[Comma]]s: 81/80, 105/104, 144/143, 196/195

===13-limit Meanpop===

[[Comma|Comma]]s: 81/80, 105/104, 144/143, 196/195

valid range: [694.737, 696.774] (19 to 31)

nice range: [691.202, 701.955]

strict range: [694.737, 696.774]

POTE generator: ~3/2 = 696.211

Mapping generator: ~3

Map: [<1 0 -4 -13 24 -20|, <0 1 4 10 -13 15|]

EDOS: [[19edo|19]], [[31edo|31]], [[50edo|50]], [[81edo|81]], [[131edo|131bd]], [[212edo|212bdf]]

~~[[Badness]]: 0.0209~~

===Meanplop===

[[Badness|Badness]]: 0.0209

===Meanplop===

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

POTE generator: ~3/2 = 696.202

Mapping generator: ~3

Map: [<1 0 -4 -13 24 10|, <0 1 4 10 -13 -4|]

EDOs: 12e, 19, 31f, 50f

Badness: 0.0277

==Meanenneadecal==

[[Comma]]s: 45/44, 56/55, 81/80

[[Comma|Comma]]s: 45/44, 56/55, 81/80

[[POTE_tuning|POTE generator]]: ~3/2 = 696.250

~~[[POTE tuning|POTE generator]]: ~3/2 = 696.250~~

Mapping generator: ~3

Map: [<1 0 -4 -13 -6|, <0 1 4 10 6|]

EDOs: [[7edo|7]], [[12edo|12]], [[19edo|19]], [[31edo|31e]], [[50edo|50e]]

~~[[Badness]]: 0.0214~~

===13-limit===

[[Badness|Badness]]: 0.0214

[[Comma]]s: 45/44, 56/55, 78/77, 81/80

===13-limit===

[[Comma|Comma]]s: 45/44, 56/55, 78/77, 81/80

[[POTE_tuning|POTE generator]]: ~3/2 = 696.146

~~[[POTE tuning|POTE generator]]: ~3/2 = 696.146~~

Mapping generator: ~3

Map: [<1 0 -4 -13 -6 -20|, <0 1 4 10 6 15|]

EDOs: [[19edo|19]], [[31edo|31e]], [[50edo|50e]]]

~~[[Badness]]: 0.0212~~

===Vincenzo===

[[Badness|Badness]]: 0.0212

===Vincenzo===

Commas: 81/80 126/125 45/44 65/64 256/255 153/152 23/22

POTE generator: ~3/2

Mapping generator: ~3

Map: [<1 0 -4 -13 ... |, <0 1 4 10 6 -4 -5 -3 -6|]

EDOs: 12

Badness:

==Meanundeci==

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

POTE generator: ~3/2 = 694.689

Mapping generator: ~3

Map: [<1 0 -4 -13 5|, <0 1 4 10 -1|]

EDOs: 12e, 19e

Badness: 0.0315

===13-limit===

Commas: 33/32, 55/54, 77/75, 729/728

POTE generator: ~3/2 = 694.764

Mapping generator: ~3

Map: [<1 0 -4 -13 5 10|, <0 1 4 10 -1 -4|]

EDOs: 12e, 19e

Badness: 0.0263

==Meanundec==

Commas: 27/26, 40/39, 45/44, 56/55

POTE generator: ~3/2 = 697.254

Mapping generator: ~3

Map: [<1 0 -4 -13 -6 -1|, <0 1 4 10 6 3|]

EDOS: 12f, 19f, 31ef

Badness: 0.0242

=Flattone=

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

[[Comma|Comma]]s: 81/80, 525/512

The [[wedgie]] for flattone is <<1 4 -9 4 -17 -32||, which tells us among other things that 9 generator steps of 4/3 get to the interval class for 7, meaning that [[~~7_4~~|7/4]] is a diminished seventh interval. Other intervals are [[~~7_6~~|7/6]], a diminished third, and [[~~7_5~~|7/5]], a doubly diminshed fifth. Good tunings for flattone are [[26edo]], [[45edo]] and [[64edo]].

The [[wedgie|wedgie]] for flattone is <<1 4 -9 4 -17 -32||, which tells us among other things that 9 generator steps of 4/3 get to the interval class for 7, meaning that [[7/4|7/4]] is a diminished seventh interval. Other intervals are [[7/6|7/6]], a diminished third, and [[7/5|7/5]], a doubly diminshed fifth. Good tunings for flattone are [[26edo|26edo]], [[45edo|45edo]] and [[64edo|64edo]].

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

~~[[7-limit]] minimax~~

[|1 0 0 0>, |21/13 0 1/13 -1/13>,

|32/13 0 4/13 -4/13>, |32/13 0 -9/13 9/13>]

~~[[Eigenmonzo]]s: 2, 7/5~~

[[9-limit]] minimax

[[Eigenmonzo|Eigenmonzo]]s: 2, 7/5

[[9-limit|9-limit]] minimax

[|1 0 0 0>, |17/11 2/11 0 -1/11>,

|24/11 8/11 0 -4/11>, |34/11 -18/11 0 9/11>]

[[Eigenmonzo]]s: 2, 9/7

[[Eigenmonzo|Eigenmonzo]]s: 2, 9/7

valid range: [692.308, 694.737] (26 to 19)

nice range: [692.353, 701.955]

strict range: [692.353, 694.737]

[[~~POTE tuning~~|POTE generator]]: 693.779

[[POTE_tuning|POTE generator]]: 693.779

Mapping generator: ~3

Line 276:

Line 353:

Map: [<1 0 -4 17|, <0 1 4 -9|]

[[Wedgie]]: <<1 4 -9 4 -17 -32||

[[Generator]]s: 2, 3

[[wedgie|Wedgie]]: <<1 4 -9 4 -17 -32||

[[generator|Generator]]s: 2, 3

EDOs: [[7edo|7]], [[19edo|19]], [[45edo|45]], [[64edo|64]]

~~[[Badness]]: 0.0386~~

==11-limit==

[[Badness|Badness]]: 0.0386

==11-limit==

Commas: 45/44, 81/80, 385/384

valid range: [692.308, 694.737] (26 to 19)

nice range: [682.502, 701.955]

strict range: [692.308, 694.737]

POTE generator: ~3/2 = 693.126

Mapping generator: ~3

Map: [<1 0 -4 17 -6|, <0 1 4 -9 6|]

EDOs: 7, 19, 26, 45, 71bc, 116bcde

Badness: 0.0338

==13-limit==

45/44, 65/64, 78/77, 81/80

valid range: [692.308, 694.737] (26 to 19)

nice range: [682.502, 701.955]

strict range: [692.308, 694.737]

POTE generator: ~3/2 = 693.058

Mapping generator: ~3

Map: [<1 0 -4 17 -6 10|, <0 1 4 -9 6 -4|]

EDOs: 7, 19, 26, 45f, 71bcf, 116bcdef

Badness: 0.0223

=Dominant=

[[Comma]]s: 36/35, 64/63

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

The wedgie for dominant is <<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~~|3/2]] fifths, and with [[29edo]], [[41edo]], or [[53edo]].

The wedgie for dominant is <<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|12edo]], but it also works well with the Pythagorean tuning of pure [[3/2|3/2]] fifths, and with [[29edo|29edo]], [[41edo|41edo]], or [[53edo|53edo]].

valid range: [700.000, 720.000] (12 to 5)

nice range: [694.786, 715.587]

strict range: [700.000, 715.587]

[[~~POTE tuning~~|POTE generator]]: 701.573

[[POTE_tuning|POTE generator]]: 701.573

Mapping generator: ~3

Map: [<1 0 -4 6|, <0 1 4 -2|]

[[Wedgie]]: <<1 4 -2 4 -6 -16||

[[wedgie|Wedgie]]: <<1 4 -2 4 -6 -16||

EDOs: [[5edo|5]], [[7edo|7]], [[12edo|12]], [[53edo|53]], [[65edo|65]]

~~[[Badness]]: 0.0207~~

==11-limit==

[[Badness|Badness]]: 0.0207

==11-limit==

Commas: 36/35, 64/63, 56/55

valid range: [700.000, 705.882] (12 to 17)

nice range: [691.202, 715.587]

strict range: [700.000, 705.882]

POTE generator: ~3/2 = 703.254

Mapping generator: ~3

Map: [<1 0 -4 6 13|, <0 1 4 -2 -6|]

EDOs: 5, 12, 17c, 29cde

Badness: 0.0242

==13-limit==

Commas: 36/35, 56/55, 64/63, 66/65

valid range: 705.882 (17)

nice range: [691.202, 715.587]

strict range:705.882

Line 350:

Line 454:

Map: [<1 0 -4 6 13 18|, <0 1 4 -2 -6 -9|]

EDOs: 12f, 17c, 29cdef

Badness: 0.0241

==Dominion==

Commas: 26/25, 36/35, 56/55, 64/63

Line 359:

Line 465:

Map: [<1 0 -4 6 13 -9|, <0 1 4 -2 -6 8|]

EDOs: 5, 12, 17c, 46cde

Badness: 0.0273

==Domineering==

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

POTE generator: ~3/2 = 698.776

Mapping generator: ~3

Map: [<1 0 -4 6 -6|, <0 1 4 -2 6|]

EDOs: 7, 12, 43de

Badness: 0.0220

==Domination==

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

POTE generator: ~3/2 = 705.004

Mapping generator: ~3

Map: [<1 0 -4 6 -14|, <0 1 4 -2 11|]

EDOs: 17c, 46cd

Badness: 0.0366

===13-limit===

Commas: 26/25, 36/35, 64/63, 66/65

POTE generator: ~3/2 = 705.496

Mapping generator: ~3

Map: [<1 0 -4 6 -14 -9|, <0 1 4 -2 11 8|]

EDOs: 17c

Badness: 0.0274

==Twelve==

Commas: 81/80 64/63 45/44 65/64 256/255 153/152

POTE generator: ~3/2 = 696.217

Mapping generator: ~3

Map: [<1 0 -4 6 -6 10 12 9|, <0 1 4 -2 6 -4 -5 -3|]

EDOs: 7, 12, 19d, 31def

Badness: 0.0204

==Arnold==

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

POTE generator: ~3/2 = 698.491

Mapping generator: ~3

Map: [<1 0 -4 6 5|, <0 1 4 -2 -1|]

EDOs: 5, 7, 12e

Badness: 0.0261

==13-limit==

Commas: 22/21, 27/26, 33/32, 40/39

POTE generator: ~3/2 = 696.743

Mapping generator: ~3

Map: [<1 0 -4 6 5 -1|, <0 1 4 -2 -1 3|]

EDOs: 5, 7, 12ef, 19def, 31def

Badness: 0.0233

==Dominatrix==

Commas: 27/26 36/35 45/44 64/63

POTE generator: ~3/2 = 698.544

Mapping generator: ~3

Map: [<1 0 -4 6 -6 -1|, <0 1 4 -2 6 3|]

EDOs: 7, 12f

Badness: 0.0183

=Sharptone=

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

[[Comma|Comma]]s: 21/20, 28/27

Sharptone, with a wedgie <<1 4 3 4 2 -4||, 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]] tuning does sharptone about as well as such a thing can be done.

Sharptone, with a wedgie <<1 4 3 4 2 -4||, 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.

[[POTE_tuning|POTE generator]]: 700.140

~~[[POTE tuning|POTE generator]]: 700.140~~

Mapping generator: ~3

Map: [<1 0 -4 -2|, <0 1 4 3|]

[[Wedgie]]: <<1 4 3 4 2 -4||

[[wedgie|Wedgie]]: <<1 4 3 4 2 -4||

EDOs: [[5edo|5]], [[12edo|12]]

~~[[Badness]]: 0.0248~~

=Meansept=

[[Badness|Badness]]: 0.0248

=Meansept=

Commas: 15/14, 81/80

POTE generator: ~3/2 = 682.895

Mapping generator: ~3

Map: [<1 0 -4 -5|, <0 1 4 5|]

Wedgie: <<1 4 5 4 5 0||

EDOs: 7

Badness: 0.0453

==11-limit==

Commas: 15/14, 22/21, 125/121

POTE generator: ~3/2 = 685.234

Mapping generator: ~3

Map: [<1 0 -4 -5 -6|, <0 1 4 5 6|]

EDOs: 7

Badness: 0.0325

=Supermean=

Commas: 81/80, 672/625

Line 472:

Line 612:

Map: [<1 0 -4 -21|, <0 1 4 15|]

EDOs: 17c, 46c

Badness: 0.1342

==11-limit==

Commas: 56/55, 81/80, 132/125

Line 481:

Line 623:

Map: [<1 0 -4 -21 -14|, <0 1 4 15 11|]

EDOs: 17c, 46c

Badness: 0.0633

==13-limit==

Commas: 26/25, 56/55, 66/65, 81/80

Line 490:

Line 634:

Map: [<1 0 -4 -21 -14 -9|, <0 1 4 15 11 8|]

EDOs: 17c, 46c

=Injera=

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

[[Comma|Comma]]s: 50/49, 81/80

The wedgie for injera is <<2 8 8 8 7 -4||, which tells us it 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]], which is two parallel [[19edo]]s, is an excellent tuning for injera.

The wedgie for injera is <<2 8 8 8 7 -4||, which tells us it 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|19edo]]s, is an excellent tuning for injera.

[[http://tech.groups.yahoo.com/group/tuning-math/message/3091|Origin of the name]]

[http://tech.groups.yahoo.com/group/tuning-math/message/3091 Origin of the name]

valid range: [685.714, 700.000] (14c to 12)

nice range: [688.957, 701.955]

strict range: [688.957, 700.000]

[[~~POTE tuning~~|POTE generator]]: 694.375

[[POTE_tuning|POTE generator]]: 694.375

Mapping generator: ~3

Map: [<2 0 -8 -7|, <0 1 4 4|]

[[Wedgie]]: <<2 8 8 8 7 -4||

[[wedgie|Wedgie]]: <<2 8 8 8 7 -4||

EDOs: [[12edo|12]], [[26edo|26]], [[38edo|38]], [[102edo|102bcd]], [[140edo|140bcd]], [[178edo|178bcd]]

~~[[Badness]]: 0.0311~~

[[~~http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Two%20Pairs%20of%20Socks.mp3|Two Pairs of Socks]] (in [[26edo]]) by [[Igliashon Jones~~|~~Igliashon Calvin Jones-Coolidge~~]]

[[Badness|Badness]]: 0.0311

~~[[http~~:~~//micro.soonlabel~~.~~com/gene_ward_smith/Others/Curley/Zach%20Curley%20-%20Injera%20Jam.mp3|Injera Jam]] (in [[26edo]]) by [[Zach Curley]]~~

==11-limit==

[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Two%20Pairs%20of%20Socks.mp3 Two Pairs of Socks] (in [[26edo|26edo]]) by [[Igliashon_Jones|Igliashon Calvin Jones-Coolidge]]

[http://micro.soonlabel.com/gene_ward_smith/Others/Curley/Zach%20Curley%20-%20Injera%20Jam.mp3 Injera Jam] (in [[26edo|26edo]]) by [[Zach_Curley|Zach Curley]]

==11-limit==

Commas: 45/44, 50/49, 81/80

valid range: [685.714, 700.000] (14c to 12)

nice range: [682.458, 701.955]

strict range: [685.714, 700.000]

POTE generator: ~3/2 = 692.840

Mapping generator: ~3

Map: [<2 0 -8 -7 -12|, <0 1 4 4 6|]

EDOs: 12, 14c, 26. 90bce, 116bce

Badness: 0.0231

==13-limit==

Commas: 45/44, 50/49, 81/80, 78/77

valid range: 692.308 (26)

nice range: [682.458, 701.955]

strict range: 692.308 (26)

POTE generator: ~3/2 = 692.673

Mapping generator: ~3

Map: [<2 0 -8 -7 -12 -21|, <0 1 4 4 6 9|]

EDOs: 26, 104bcf

Badness: 0.0216

==Enjera==

Commas: 27/26, 40/39, 45/44, 99/98

POTE generator: ~3/2 = 694.121

Mapping generator: ~3

Map: [<2 0 -8 -7 -12 -2|, <0 1 4 4 6 3|]

EDOs: 12f, 26f, 38ef

Badness: 0.0265

==Injerous==

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

POTE generator: ~3/2 = 690.548

Mapping generator: ~3

Map: [<2 0 -8 -7 10|, <0 1 4 4 -1|]

EDOs: 12e, 14c, 26e, 40ce

Badness: 0.0386

==Lahoh==

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

POTE generator: ~3/2 = 699.001

Mapping generator: ~3

Map: [<2 0 -8 -7 7|, <0 1 4 4 0|]

EDOs: 12

Badness: 0.0431

=Godzilla=

~~<~~span style="display: block; text-align: right;"~~>~~[[~~xenharmonie/~~Semiphor, ~~Semaphor~~, ~~Godzilla|~~Deutsch]]

<span style="display: block; text-align: right;">[[:de:Semiphor,_Semaphor,_Godzilla Deutsch]]</span>

~~<~~/span~~>~~

Main article: [[Semaphore and Godzilla]]

Main article: [[Semaphore_and_Godzilla|Semaphore and Godzilla]]

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

Godzilla has wedgie <<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.

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

Godzilla has wedgie <<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|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.

valid range: [240.000, 257.143] (5 to 14c)

nice range: [231.174, 266.871]

strict range: [240.000, 257.143]

[[~~POTE tuning~~|POTE generator]]: ~8/7 = 252.635

[[POTE_tuning|POTE generator]]: ~8/7 = 252.635

Mapping generator: ~7/4

Map: [<1 0 -4 2|, <0 2 8 1|]

[[Wedgie]]: <<2 8 1 8 -4 -20||

[[wedgie|Wedgie]]: <<2 8 1 8 -4 -20||

EDOs: [[5edo|5]], [[9edo|9c]], [[14edo|14c]], [[19edo|19]], [[62edo|62d]], [[81edo|81d]], 143bd

~~[[Badness]]: 0.0267~~

==11-limit==

[[Badness|Badness]]: 0.0267

==11-limit==

Commas: 45/44, 49/48, 81/80

valid range: [252.632, 257.143] (19 to 14c)

nice range: [231.174, 266.871]

strict range: [252.632, 257.143]

POTE generator: ~8/7 = 254.027

Mapping generator: ~7/4

Map: [<1 0 -4 2 -6|, <0 2 8 1 12|]

EDOs: 14c, 19, 33cd, 52cd

Badness: 0.0290

==13-limit==

Commas: 45/44, 49/48, 78/77, 81/80

valid range: 694.737 (19)

nice range: [621.581, 737.652]

strict range: 694.737

POTE generator: ~8/7 = 253.603

Mapping generator: ~7/4

Map: [<1 0 -4 2 -6 -5|, <0 2 8 1 12 11|]

EDOs: 14cf, 19, 33cdf, 52cdf

Badness: 0.0225

==Semafour==

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

POTE generator: ~8/7 = 254.042

Mapping generator: ~7/4

Map: [<1 0 -4 2 5|, <0 2 8 1 -2|]

EDOs: 5, 14c, 19e, 33cde

Badness: 0.0285

==Varan==

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

POTE generator: ~8/7 = 251.079

Mapping generator: ~7/4

Map: [<1 0 -4 2 -10|, <0 2 8 1 17|]

EDOs: 19e, 24, 43de

Badness: 0.0396

===13-limit===

Commas: 49/48, 66/65, 77/75, 81/80

POTE generator: ~8/7 = 251.165

Mapping generator: ~7/4

Map: [<1 0 -4 2 -10 -5|, <0 2 8 1 17 11|]

EDOs: 19e, 24, 43de

Badness: 0.0257

==Baragon==

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

POTE generator: ~8/7 = 251.173

Mapping generator: ~7/4

Map: [<1 0 -4 2 9|, <0 2 8 1 -7|]

EDOs: 19, 24, 43d

Badness: 0.0357

==Music==

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

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

=Mohajira=

~~<~~span style="display: block; text-align: right;"~~>~~[[~~xenharmonie/~~Mohajira|Deutsch]]

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

~~<~~/span~~>~~

~~[[Comma]]s: 81/80, 6144/6125~~

Mohajira, with wedgie <<2 8 -11 8 -23 -48||, really makes more sense as an 11-limit temperament. It has a generator of a neutral third, two of which make up a fifth, and which can be taken to represent 128/105. Mohajira tempers out 6144/6125, the porwell comma. [[31edo]] makes for an excellent (7-limit) mohajira tuning, with generator 9/31. It has a 7-note MOS with three larger steps and four smaller ones, going sLsLsLs.

[[Comma|Comma]]s: 81/80, 6144/6125

Mohajira, with wedgie <<2 8 -11 8 -23 -48||, really makes more sense as an 11-limit temperament. It has a generator of a neutral third, two of which make up a fifth, and which can be taken to represent 128/105. Mohajira tempers out 6144/6125, the porwell comma. [[31edo|31edo]] makes for an excellent (7-limit) mohajira tuning, with generator 9/31. It has a 7-note MOS with three larger steps and four smaller ones, going sLsLsLs.

Mohajira can also be thought of, intuitively, as "meantone with quarter tones"; as is the 3/2 generator subdivided in half, so is the 25/24 chromatic semitone divided into two equal ~33/32 quarter tones (in the 11-limit). Within this paradigm, mohajira is the temperament that splits the 3/2 into two equal 11/9's, that splits the 6/5 into two equal 11/10's, that maps four 3/2's to 5/1, and that maps the interval one quarter tone flat of 16/9 to 7/4.

[[7-limit|7]] and [[9-limit]] minimax 1/4 comma

[[7-limit|7]] and [[9-limit|9-limit]] minimax 1/4 comma

[|1 0 0 0>, |1 0 1/4 0>, |0 0 1 0>, |6 0 -11/8 0>]

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

[[~~POTE tuning~~|POTE generator]]: ~128/105 = 348.415

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

[[POTE_tuning|POTE generator]]: ~128/105 = 348.415

Mapping generator: ~128/105

Line 683:

Line 887:

Map: [<1 1 0 6|, <0 2 8 -11|]

[[Generator]]s: 2, 128/105

[[Wedgie]]: <<2 8 -11 8 -23 -48||

[[generator|Generator]]s: 2, 128/105

[[wedgie|Wedgie]]: <<2 8 -11 8 -23 -48||

EDOs: [[7edo|7]], [[24edo|24]], [[31edo|31]]

~~[[Badness]]: 0.0557~~

==11-limit==

[[Badness|Badness]]: 0.0557

[[Comma]]s: 81/80, 121/120, 176/175

==11-limit==

[[Comma|Comma]]s: 81/80, 121/120, 176/175

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

~~[[11-limit]] minimax 1/4 comma~~

[|1 0 0 0 0>, |1 0 1/4 0 0>, |0 0 1 0 0>,

|6 0 -11/8 0 0>, |2 0 5/8 0 0>]

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

[[~~POTE tuning~~|POTE generator]]: ~11/9 = 348.477

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

[[POTE_tuning|POTE generator]]: ~11/9 = 348.477

Mapping generator: ~11/9

Map: [<1 1 0 6 2|, <0 2 8 -11 5|]

[[Generator]]s: 2, 11/9

[[generator|Generator]]s: 2, 11/9

EDOs: [[7edo|7]], [[24edo|24]], [[31edo|31]]

~~[[Badness]]: 0.0261~~

==13-limit==

[[Badness|Badness]]: 0.0261

==13-limit==

Commas: 81/80, 121/120, 105/104, 66/65

POTE generator: ~11/9 = 348.558

Mapping generator: ~11/9

Map: [<1 1 0 6 2 4|, <0 2 8 -11 5 -1|]

EDOs: 7, 24, 31, 117ef, 148bef

Badness: 0.0234

=Ptolemy=

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

Line 720:

Line 937:

Map: [<1 1 0 8 2|, <0 2 8 -18 5|]

EDOs: 7, 38d, 45e, 83bcde

Badness: 0.0588

==13-limit==

Commas: 65/64, 81/80, 105/104, 121/120

Line 729:

Line 948:

Map: [<1 1 0 8 2 6|, <0 2 8 -18 5 -8|]

EDOs: 7, 38df, 45ef, 83bcdef

Badness: 0.0343

=Maqamic=

~~<~~span style="display: block; text-align: right;"~~>~~[[~~xenharmonie/~~maqamisch|Deutsch]]

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

~~<~~/span~~>~~

Main article: [[Maqamic]]

Main article: [[maqamic|Maqamic]]

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

[[Comma|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.

[[~~POTE tuning~~|POTE generator]]: ~11/9 = 350.934

[[POTE_tuning|POTE generator]]: ~11/9 = 350.934

Mapping generator: ~11/9

Map: [<1 1 0 4 2|, <0 2 8 -4 5|]

[[Generator]]s: 2, 11/9

[[generator|Generator]]s: 2, 11/9

==13-limit==

[[Comma]]s: 81/80, 36/35, 121/120, 144/143

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

[[POTE_tuning|POTE generator]]: ~11/9 = 350.816

~~[[POTE tuning|POTE generator]]: ~11/9 = 350.816~~

Mapping generator: ~11/9

Map: [<1 1 0 4 2 4|, <0 2 8 -4 5 -1|]

Generators: 2, 11/9

=Migration=

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

POTE generator: ~11/9 = 348.182

Mapping generator: ~11/9

Map: [<1 1 0 -3 2|, <0 2 8 20 5|]

EDOs: 31, 100de, 131bde, 162bde

Badness: 0.0255

=Mohamaq=

Commas: 81/80, 392/375

POTE generator: ~25/21 = 350.586

Mapping generator: ~25/21

Map: [<1 1 0 -1|, <0 2 8 13|]

EDOs: 17c, 24, 65c, 89cd

Badness: 0.0777

==11-limit==

Commas: 56/55, 77/75, 243/242

POTE generator: ~11/9 = 350.565

Mapping generator: ~11/9

Map: [<1 1 0 -1 2|, <0 2 8 13 5|]

EDOs: 17c, 24, 65c, 89cd

Badness: 0.0362

==13-limit==

Commas: 56/55, 66/65, 77/75, 243/242

POTE generator: ~11/9 = 350.745

Mapping generator: ~11/9

Map: [<1 1 0 -1 2 4|, <0 2 8 13 5 -1|]

EDOs: 17c, 24, 41c, 65c

Badness: 0.0287

=Orphic=

Commas: 81/80, 5898240/5764801

POTE generator: ~7/6 = 275.794

Mapping generator: ~343/288

Map: [<2 1 -4 4|, <0 4 16 3|]

Wedgie: <<8 32 6 32 -13 -76||

EDOs: 26, 74, 174bd, 248bd

Badness: 0.2588

==11-limit==

Commas: 81/80, 99/98, 73728/73205

POTE generator: ~7/6 = 275.762

Mapping generator: ~77/64

Map: [<2 1 -4 4 8|, <0 4 16 3 -2|]

EDOs: 26, 48c, 74, 248bd, 322bd

Badness: 0.1015

==13-limit==

Commas: 81/80, 99/98, 144/143, 2200/2197

POTE generator: ~7/6 = 275.774

Mapping generator: ~63/52

Map: [<2 1 -4 4 8 2|, <0 4 16 3 -2 10|]

EDOs: 26, 48c, 74, 174bd, 248bd, 322bd

Badness: 0.0535

=Mothra=

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

[[Comma|Comma]]s: 81/80, 1029/1024

Mothra, with wedgie <<3 12 -1 12 -10 -36||, 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-limit, mothra is identical to [[Slendric|slendric]].

Mothra, with wedgie <<3 12 -1 12 -10 -36||, 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]] 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-limit, mothra is identical to [[Slendric|slendric]].

Note that mothra can also be called cynder in the 7-limit, which can be a little confusing sometimes.

[[7-limit|7]] and [[9-limit]] minimax 1/4 comma

[[7-limit|7]] and [[9-limit|9-limit]] minimax 1/4 comma

[|1 0 0 0>, |1 0 1/4 0>, |0 0 1 0>, |3 0 -1/12 0>]

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

[[~~POTE tuning~~|POTE generator]]: ~8/7 = 232.193

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

[[POTE_tuning|POTE generator]]: ~8/7 = 232.193

Mapping generator: ~8/7

Line 844:

Line 1,098:

Map: [<1 1 0 3|, <0 3 12 -1|]

[[Generator]]s: 2, 8/7

[[Wedgie]]: <<3 12 -1 12 -10 -36||

[[generator|Generator]]s: 2, 8/7

[[wedgie|Wedgie]]: <<3 12 -1 12 -10 -36||

EDOs: [[5edo|5]], [[26edo|26]], [[31edo|31]]

~~[[Badness]]: 0.0371~~

==11-limit==

[[Badness|Badness]]: 0.0371

[[Comma]]s: 81/80, 99/98, 385/384

==11-limit==

[[Comma|Comma]]s: 81/80, 99/98, 385/384

POTE generator: ~8/7 = 232.031

Mapping generator: ~8/7

Map: [<1 1 0 3 5|, <0 3 12 -1 -8|]

EDOs: [[5edo|5]], [[26edo|26]], [[31edo|31]], [[88edo|88]], [[150edo|150]], [[181edo|181]]

~~[[Badness]]: 0.0256~~

==13-limit==

[[Badness|Badness]]: 0.0256

==13-limit==

Commas: 81/80, 99/98, 105/104, 144/143

POTE generator: ~8/7 = 231.811

Mapping generator: ~8/7

Map: [<1 1 0 3 5 1|, <0 3 12 -1 -8 14|]

EDOs: 5, 26, 31, 57, 88

Badness: 0.0240

==Cynder==

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

POTE generator: ~8/7 = 231.317

Mapping generator: ~8/7

Map: [<1 1 0 3 0|, <0 3 12 -1 18|]

EDOs: 26, 57e, 83bce

Badness: 0.0557

===13-limit===

Commas: 45/44, 78/77, 81/80, 640/637

POTE generator: ~8/7 = 231.293

Mapping generator: ~8/7

Map: [<1 1 0 3 0 1|, <0 3 12 -1 18 14|]

EDOs: 26, 57e, 83bce

Badness: 0.0341

==Mosura==

Commas: 81/80, 176/175, 1029/1024

POTE generator: ~8/7 = 232.419

Mapping generator: ~8/7

Map: [<1 1 0 3 -1|, <0 3 12 -1 23|]

EDOs: 31, 129, 136b, 148be, 160be, 191bce, 222bce, 253bce

Badness: 0.0313

===13-limit===

Commas: 81/80, 144/143, 176/175, 1029/1024

POTE generator: ~8/7 = 232.640

Mapping generator: ~8/7

Map: [<1 1 0 3 -1 7|, <0 3 12 -1 23 -17|]

EDOs: 31, 67, 98

Badness: 0.0369

=Squares=

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

[[Comma|Comma]]s: 81/80, 2401/2400

Squares, with wedgie <<4 16 9 16 3 -24||, splits the interval of an eleventh, or 8/3, into four supermajor third ([[~~9_7~~|9/7]]) intervals, and uses it for a generator. [[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, with wedgie <<4 16 9 16 3 -24||, splits the interval of an eleventh, or 8/3, into four supermajor third ([[9/7|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.

7 and 9 limit minimax 1/4 comma

[|1 0 0 0>, |1 0 1/4 0>, |0 0 1 0>, |3/2 0 9/16 0>]

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

[[~~POTE tuning~~|POTE generator]]: ~9/7 = 425.942

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

[[POTE_tuning|POTE generator]]: ~9/7 = 425.942

Mapping generator: ~9/7

Line 924:

Line 1,203:

Map: [<1 3 8 6|, <0 -4 -16 -9|]

[[Generator]]s: 2, 9/7

[[generator|Generator]]s: 2, 9/7

EDOs: [[14edo|14]], [[31edo|31]], [[262edo|262]], [[293edo|293]]

[[Badness]]: 0.0460

[[Badness|Badness]]: 0.0460

Music:

~~By [[Chris Vaisvil]]~~

~~[[http://clones.soonlabel.com/public/micro/tuning-survey/daily20100603-squares8piano.mp3|Square 8]]~~

==11-limit==

By [[Chris_Vaisvil|Chris Vaisvil]]

[http://clones.soonlabel.com/public/micro/tuning-survey/daily20100603-squares8piano.mp3 Square 8]

==11-limit==

Commas: 81/80, 99/98, 121/120

POTE generator: ~9/7 = 425.957

Mapping generator: ~9/7

Map: [<1 3 8 6 7|, <0 -4 -16 -9 -10|]

EDOs: [[5edo|5]], [[8edo|8]], [[11edo|11]], [[14edo|14]], [[17edo|17]], [[31edo|31]]

~~[[Badness]]: 0.0216~~

==13-limit==

[[Badness|Badness]]: 0.0216

==13-limit==

Commas: 81/80, 99/98, 121/120, 66/65

POTE generator: ~9/7 = 425.550

Mapping generator: ~9/7

Map: [<1 3 8 6 7 3|, <0 -4 -16 -9 -10 2|]

EDOs: 17c, 31, 79cf, 110cef, 141cef

~~[[Badness]]: 0.0255~~

==Agora==

[[Badness|Badness]]: 0.0255

==Agora==

Commas: 81/80, 99/98, 105/104, 121/120

POTE generator: ~9/7 = 426.276

Mapping generator: ~9/7

Map: [<1 3 8 6 7 14|, <0 -4 -16 -9 -10 -29|]

EDOs: 31, 45ef, 76e

Badness: 0.0245

=Cuboctahedra=

==11-limit==

[[Comma]]s: 81/80, 385/384, 1375/1372

==11-limit==

[[Comma|Comma]]s: 81/80, 385/384, 1375/1372

[[POTE_tuning|POTE generator]]: ~9/7 = 425.993

~~[[POTE tuning|POTE generator]]: ~9/7 = 425.993~~

Mapping generator: ~9/7

Map: [<1 3 8 6 -4|, <0 -4 -16 -9 21|]

EDOs: [[14edo|14]], [[31edo|31]], [[45edo|45]], [[200edo|200]]

~~[[Badness]]: 0.0568~~

=Liese=

[[Badness|Badness]]: 0.0568

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

~~<~~/span~~>~~

=Liese=

[[Comma]]s: 81/80, 686/675

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

[[Comma|Comma]]s: 81/80, 686/675

Liese, with wedgie <<3 12 11 12 9 -8||, splits the twelfth interval of 3/1 into three generators of 10/7, using the comma 1029/1000. It also tempers out 686/675, the senga. [[74edo]] makes for a good liese tuning, though [[19edo]] can be used. The tuning is well-supplied with MOS: 7, 9, 11, 13, 15, 17, 19, 36, 55.

Liese, with wedgie <<3 12 11 12 9 -8||, splits the twelfth interval of 3/1 into three generators of 10/7, using the comma 1029/1000. It also tempers out 686/675, the senga. [[74edo|74edo]] makes for a good liese tuning, though [[19edo|19edo]] can be used. The tuning is well-supplied with MOS: 7, 9, 11, 13, 15, 17, 19, 36, 55.

7 and 9 limit minimax 1/4 comma

[|1 0 0 0>, |1 0 1/4 0>, |0 0 1 0>, |2/3 0 11/12 0>]

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

[[~~POTE tuning~~|POTE generator]]: ~10/7 = 632.406

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

[[POTE_tuning|POTE generator]]: ~10/7 = 632.406

Mapping generator: ~10/7

Line 990:

Line 1,290:

Map: [<1 0 -4 -3|, <0 3 12 11|]

[[Generator]]s: 2, 10/7

[[generator|Generator]]s: 2, 10/7

EDOs: [[17edo|17]], [[19edo|19]], [[55edo|55]], [[74edo|74]]

~~[[Badness]]: 0.0467~~

==Liesel==

[[Badness|Badness]]: 0.0467

==Liesel==

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

POTE generator: ~10/7 = 633.073

Mapping generator: ~10/7

Map: [<1 0 -4 -3 4|, <0 3 12 11 -1|]

EDOs: 17c, 19, 36, 91ce

Badness: 0.0407

==13-limit==

Liesel is a very natural 13-limit tuning, given the generator is so near 13/9.

Line 1,010:

Line 1,316:

POTE generator: ~10/7 = ~13/9 = 633.042

Mapping generator: ~10/7

Map: [<1 0 -4 -3 4 0|, <0 3 12 11 -1 7|]

EDOs: 17c, 19, 36, 91cef

Badness: 0.0273

==Elisa==

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

POTE generator: ~10/7 = 633.061

Mapping generator: ~10/7

Map: [<1 0 -4 -3 -5|, <0 3 12 11 16|]

EDOs: 19e, 36e

Badness: 0.0416

==Lisa==

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

POTE generator: ~10/7 = 631.370

Mapping generator: ~10/7

Map: [<1 0 -4 -3 -6|, <0 3 12 11 18|]

EDOs: 19

Badness: 0.0548

==13-limit==

Commas: 45/44, 81/80, 91/88, 147/143

POTE generator: ~10/7 = 631.221

Mapping generator: ~10/7

Map: [<1 0 -4 -3 -6 0|, <0 3 12 11 18 7|]

EDOs: 19

Badness: 0.0361

=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.

Line 1,052:

Line 1,370:

POTE generator: ~54/49 = 139.343

Mapping generator: ~54/49

Map: [<1 1 0 2|, <0 5 20 7|]

Wedgie: <<5 30 7 20 -3 -40||

EDOs: 8, 9, 17, 26, 43, 112

Badness: 0.1087

==11-limit==

Commas: 81/80, 99/98, 864/847

POTE generator: ~12/11 = 139.428

Mapping generator: ~12/11

Map: [<1 1 0 2 3|, <0 5 20 7 4|]

EDOs: 8, 9, 17, 26, 43, 241

Badness: 0.0479

==13-limit==

Commas: 77/78, 81/80, 99/98, 144/143

POTE generator: ~13/12 = 139.387

Mapping generator: ~12/11

Map: [<1 1 0 2 3 3|, <0 5 20 7 4 6|]

EDOs: 8, 9, 17, 26, 43, 155, 198

Badness: 0.0293

==17-limit==

Commas: 78/77, 81/80, 99/98, 144/143, 189/187

POTE generator: ~13/12 = 139.362

Mapping generator: ~12/11

Map: [<1 1 0 2 3 3 2|, <0 5 20 7 4 6 18|]

EDOs: 8, 9, 17, 26, 43, 155

Badness: 0.0209

=Meanmag=

Commas: 81/80, 3125/3072

POTE generator: ~8/7 = 238.396

Mapping generator: ~7

Map: [<19 30 44 0|, <0 0 0 1|]

Wedgie: <<0 0 19 0 30 44||

EDOs: 19, 57, 76, 171bcd

Badness: 0.0770

=Undevigintone=

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

POTE generator: ~11/8 = 538.047

Mapping generator: ~11

Map: [<19 30 44 53 0|, <0 0 0 0 1|]

EDOs: 19, 38d

Badness: 0.0364

==13-limit==

Commas: 49/48, 65/64, 81/80, 126/125

Line 1,116:

Line 1,454:

Map: [<19 30 44 53 0 70|, <0 0 0 0 1 0|]

EDOs: 19, 38d

Badness: 0.0229~~</pre></div>~~

~~<h4>Original HTML content:</h4>~~

Badness: 0.0229

<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>Meantone family</title></head><body><span style="display: block; text-align: right;"><div id="toc"><h1 class="nopad">Table of Contents</h1><div style="margin-left: 2em;"><a href="#x-Seven limit children">Seven limit children</a></div>

[[Category:catalog]]

~~<div style="margin-left: 1em;"><a href="#Septimal meantone">Septimal meantone</a></div>~~

[[Category:family]]

~~<div style="margin-left: 2em;"><a href="#Septimal meantone-Bimeantone">Bimeantone</a></div>~~

[[Category:listen]]

<div style="margin-left: 3em;"><a href="#Septimal meantone-Bimeantone-13-limit">13-limit</a></div>

[[Category:meantone]]

<div style="margin-left: 2em;"><a href="#Septimal meantone-Unidecimal meantone aka Huygens">Unidecimal meantone aka Huygens</a></div>

[[Category:rank_2]]

<div style="margin-left: 3em;"><a href="#Septimal meantone-Unidecimal meantone aka Huygens-Tridecimal meantone">Tridecimal meantone</a></div>

[[Category:theory]]

<div style="margin-left: 3em;"><a href="#Septimal meantone-Unidecimal meantone aka Huygens-Grosstone">Grosstone</a></div>

<div style="margin-left: 3em;"><a href="#Septimal meantone-Unidecimal meantone aka Huygens-Meridetone">Meridetone</a></div>

<div style="margin-left: 3em;"><a href="#Septimal meantone-Unidecimal meantone aka Huygens-Hemimeantone">Hemimeantone</a></div>

~~<div style="margin-left: 2em;"><a href="#Septimal meantone-Meanpop">Meanpop</a></div>~~

<div style="margin-left: 3em;"><a href="#Septimal meantone-Meanpop-13-limit Meanpop">13-limit Meanpop</a></div>

<div style="margin-left: 3em;"><a href="#Septimal meantone-Meanpop-Meanplop">Meanplop</a></div>

<div style="margin-left: 2em;"><a href="#Septimal meantone-Meanenneadecal">Meanenneadecal</a></div>

<div style="margin-left: 3em;"><a href="#Septimal meantone-Meanenneadecal-13-limit">13-limit</a></div>

<div style="margin-left: 3em;"><a href="#Septimal meantone-Meanenneadecal-Vincenzo">Vincenzo</a></div>

~~<div style="margin-left: 2em;"><a href="#Septimal meantone-Meanundeci">Meanundeci</a></div>~~

<div style="margin-left: 3em;"><a href="#Septimal meantone-Meanundeci-13-limit">13-limit</a></div>

~~<div style="margin-left: 2em;"><a href="#Septimal meantone-Meanundec">Meanundec</a></div>~~

~~<div style="margin-left: 1em;"><a href="#Flattone">Flattone</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Flattone-11-limit">11-limit</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Flattone-13-limit">13-limit</a></div>~~

~~<div style="margin-left: 1em;"><a href="#Dominant">Dominant</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Dominant-11-limit">11-limit</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Dominant-13-limit">13-limit</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Dominant-Dominion">Dominion</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Dominant-Domineering">Domineering</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Dominant-Domination">Domination</a></div>~~

~~<div style="margin-left: 3em;"><a href="#Dominant-Domination-13-limit">13-limit</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Dominant-Twelve">Twelve</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Dominant-Arnold">Arnold</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Dominant-13-limit">13-limit</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Dominant-Dominatrix">Dominatrix</a></div>~~

~~<div style="margin-left: 1em;"><a href="#Sharptone">Sharptone</a></div>~~

~~<div style="margin-left: 1em;"><a href="#Meansept">Meansept</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Meansept-11-limit">11-limit</a></div>~~

~~<div style="margin-left: 1em;"><a href="#Supermean">Supermean</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Supermean-11-limit">11-limit</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Supermean-13-limit">13-limit</a></div>~~

~~<div style="margin-left: 1em;"><a href="#Injera">Injera</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Injera-11-limit">11-limit</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Injera-13-limit">13-limit</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Injera-Enjera">Enjera</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Injera-Injerous">Injerous</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Injera-Lahoh">Lahoh</a></div>~~

~~<div style="margin-left: 1em;"><a href="#Godzilla">Godzilla</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Godzilla-11-limit">11-limit</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Godzilla-13-limit">13-limit</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Godzilla-Semafour">Semafour</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Godzilla-Varan">Varan</a></div>~~

~~<div style="margin-left: 3em;"><a href="#Godzilla-Varan-13-limit">13-limit</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Godzilla-Baragon">Baragon</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Godzilla-Music">Music</a></div>~~

~~<div style="margin-left: 1em;"><a href="#Mohajira">Mohajira</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Mohajira-11-limit">11-limit</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Mohajira-13-limit">13-limit</a></div>~~

~~<div style="margin-left: 1em;"><a href="#Ptolemy">Ptolemy</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Ptolemy-13-limit">13-limit</a></div>~~

~~<div style="margin-left: 1em;"><a href="#Maqamic">Maqamic</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Maqamic-13-limit">13-limit</a></div>~~

~~<div style="margin-left: 1em;"><a href="#Migration">Migration</a></div>~~

~~<div style="margin-left: 1em;"><a href="#Mohamaq">Mohamaq</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Mohamaq-11-limit">11-limit</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Mohamaq-13-limit">13-limit</a></div>~~

~~<div style="margin-left: 1em;"><a href="#Orphic">Orphic</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Orphic-11-limit">11-limit</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Orphic-13-limit">13-limit</a></div>~~

~~<div style="margin-left: 1em;"><a href="#Mothra">Mothra</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Mothra-11-limit">11-limit</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Mothra-13-limit">13-limit</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Mothra-Cynder">Cynder</a></div>~~

~~<div style="margin-left: 3em;"><a href="#Mothra-Cynder-13-limit">13-limit</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Mothra-Mosura">Mosura</a></div>~~

~~<div style="margin-left: 3em;"><a href="#Mothra-Mosura-13-limit">13-limit</a></div>~~

~~<div style="margin-left: 1em;"><a href="#Squares">Squares</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Squares-11-limit">11-limit</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Squares-13-limit">13-limit</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Squares-Agora">Agora</a></div>~~

~~<div style="margin-left: 1em;"><a href="#Cuboctahedra">Cuboctahedra</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Cuboctahedra-11-limit">11-limit</a></div>~~

~~<div style="margin-left: 1em;"><a href="#Liese">Liese</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Liese-Liesel">Liesel</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Liese-13-limit">13-limit</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Liese-Elisa">Elisa</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Liese-Lisa">Lisa</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Liese-13-limit">13-limit</a></div>~~

~~<div style="margin-left: 1em;"><a href="#Jerome">Jerome</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Jerome-11-limit">11-limit</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Jerome-13-limit">13-limit</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Jerome-17-limit">17-limit</a></div>~~

~~<div style="margin-left: 1em;"><a href="#Meanmag">Meanmag</a></div>~~

~~<div style="margin-left: 1em;"><a href="#Undevigintone">Undevigintone</a></div>~~

~~<div style="margin-left: 2em;"><a href="#Undevigintone-13-limit">13-limit</a></div>~~

~~</div>~~

~~<br />~~

~~<a class="wiki_link" href="http://xenharmonie.wikispaces.com/mittelt%C3%B6nig">Deutsch</a><br />~~

~~</span><br />~~

The <a class="wiki_link" href="/5-limit">5-limit</a> parent <a class="wiki_link" href="/Comma">comma</a> of the <a class="wiki_link" href="/meantone">meantone</a> family is the Didymus or <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Syntonic_comma" rel="nofollow">syntonic comma</a>, 81/80. This is the one they all temper out. The <a class="wiki_link" href="/Monzos%20and%20Interval%20Space">monzo</a> for 81/80 goes |-4 4 -1&gt;, and that can be flipped around to the corresponding <a class="wiki_link" href="/Wedgies%20and%20Multivals">wedgie</a>, &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.<br />

~~<br />~~

~~<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~3/2 = 696.239<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~<a class="wiki_link" href="/Tuning%20Ranges%20of%20Regular%20Temperaments">valid range</a>:~~ [~~685.714, 720.000] (7 to 5)<br />~~

~~nice range:~~ [~~694.786, 701.955] (1/3 comma to Pythagorean)<br />~~

~~strict range~~: ~~[694.786, 701.955~~]~~<br />~~

~~<br />~~

~~<a class="wiki_link" href="/Map">Map</a>: [&lt;1 0 -4|, &lt;0 1 4|~~]~~<br />~~

EDOs (patent val edo list is complete): <a class="wiki_link" href="/5edo">5</a>, <a class="wiki_link" href="/7edo">7</a>, <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/24edo">24</a>, <a class="wiki_link" href="/26edo">26</a>, <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/36edo">36</a>, <a class="wiki_link" href="/38edo">38</a>, <a class="wiki_link" href="/43edo">43</a>, <a class="wiki_link" href="/45edo">45</a>, <a class="wiki_link" href="/50edo">50</a>, <a class="wiki_link" href="/55edo">55</a>, <a class="wiki_link" href="/57edo">57</a>, <a class="wiki_link" href="/62edo">62</a>, <a class="wiki_link" href="/67edo">67</a>, <a class="wiki_link" href="/69edo">69</a>, <a class="wiki_link" href="/74edo">74</a>, <a class="wiki_link" href="/76edo">76</a>, <a class="wiki_link" href="/81edo">81</a>, <a class="wiki_link" href="/86edo">86</a>, <a class="wiki_link" href="/88edo">88</a>, <a class="wiki_link" href="/93edo">93</a>, <a class="wiki_link" href="/98edo">98</a>, <a class="wiki_link" href="/100edo">100</a>, <a class="wiki_link" href="/105edo">105</a>, <a class="wiki_link" href="/117edo">117</a>, <a class="wiki_link" href="/129edo">129</a>, <a class="wiki_link" href="/212edo">212b</a><br />

~~<a class="wiki_link" href="/Badness">Badness</a>: 0.00736<br />~~

~~<br />~~

<h2 id="toc0"><a name="x-Seven limit children"></a>Seven limit children</h2>

The <a class="wiki_link" href="/7-limit">7-limit</a> 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;].<br />

~~<br />~~

~~<h1 id="toc1"><a name="Septimal meantone"></a>Septimal meantone</h1>~~

~~<span style="display: block; text-align: right;"><a class="wiki_link" href="http://xenharmonie.wikispaces.com/septimal-mittelt%C3%B6nig">Deutsch</a><br />~~

~~</span><br />~~

~~<a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Septimal_meantone_temperament" rel="nofollow">Wikipedia article</a><br />~~

~~<br />~~

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 <a class="wiki_link" href="/7_4">7/4</a> of septimal meantone is the augmented sixth, C-A#, and other septimal intervals are 7/6, C-D#, the augmented second, and <a class="wiki_link" href="/7_5">7/5</a>, C-F#, the tritone. The <a class="wiki_link" href="/Wedgies%20and%20Multivals">wedgie</a> 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 <a class="wiki_link" href="/31edo">31edo</a> is a good tuning for it.<br />

~~<br />~~

~~<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 126/125<br />~~

~~<br />~~

~~7 and <a class="wiki_link" href="/9-limit">9-limit</a> minimax<br />~~

~~[|1 0 0 0&gt;, |1 0 1/4 0&gt;, |0 0 1 0&gt;, |-3 0 5/2 0&gt;]<br />~~

~~<a class="wiki_link" href="/Eigenmonzo">Eigenmonzo</a>s: 2, 5<br />~~

~~<br />~~

~~<a class="wiki_link" href="/Tuning%20Ranges%20of%20Regular%20Temperaments">valid range</a>: [694.737, 700.000] (19 to 12)<br />~~

~~nice range: [694.786, 701.955]<br />~~

~~strict range: [694.786, 700.000]<br />~~

~~<br />~~

~~<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 696.495<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Algebraic generator: Cybozem, the real root of 15x^3-10x^2-18, which comes to 503.4257 cents. The recurrence converges quickly.<br />~~

~~<br />~~

~~<a class="wiki_link" href="/Map">Map</a>: [&lt;1 0 -4 -13|, &lt;0 1 4 10|]<br />~~

~~<a class="wiki_link" href="/Generator">Generator</a>s: 2, 3<br />~~

~~<a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;1 4 10 4 13 12||<br />~~

EDOs: <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/81edo">81</a>, <a class="wiki_link" href="/143edo">143b</a><br />

~~<a class="wiki_link" href="/Badness">Badness</a>: 0.0137<br />~~

~~<br />~~

<h2 id="toc2"><a name="Septimal meantone-Bimeantone"></a>Bimeantone</h2>

~~Commas: 81/80, 126/125, 245/242<br />~~

~~<br />~~

~~<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~3/2 = 696.016<br />~~

~~<br />~~

~~Map: [&lt;2 0 -8 -26 -31|, &lt;0 1 4 10 12|]<br />~~

~~EDOs: 12, 38d, 50<br />~~

~~Badness: 0.0381<br />~~

~~<br />~~

<h3 id="toc3"><a name="Septimal meantone-Bimeantone-13-limit"></a>13-limit</h3>

~~Commas: 81/80, 105/104, 126/125, 245/242<br />~~

~~<br />~~

~~<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~3/2 = 695.836<br />~~

~~<br />~~

~~Map: [&lt;2 0 -8 -26 -31 -40|, &lt;0 1 4 10 12 15|]<br />~~

~~EDOs: 12f, 50<br />~~

~~Badness: 0.0288<br />~~

~~<br />~~

<h2 id="toc4"><a name="Septimal meantone-Unidecimal meantone aka Huygens"></a>Unidecimal meantone aka Huygens</h2>

~~See also <a class="wiki_link" href="/Meantone%20vs%20meanpop">Meantone vs meanpop</a><br />~~

~~<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 126/125, 99/98<br />~~

~~<br />~~

~~<a class="wiki_link" href="/11-limit">11-limit</a> minimax<br />~~

~~[|1 0 0 0 0&gt;, |25/16 -1/8 0 0 1/16&gt;, |9/4 -1/2 0 0 1/4&gt;,<br />~~

~~|21/8 -5/4 0 0 5/8&gt;, |25/8 -9/4 0 0 9/8&gt;]<br />~~

~~<a class="wiki_link" href="/Eigenmonzo">Eigenmonzo</a>s: 2, 11/9<br />~~

~~<br />~~

~~valid range: [696.774, 700.000] (31 to 12)<br />~~

~~nice range: [691.202, 701.955]<br />~~

~~strict range: [696.774, 700.000]<br />~~

~~<br />~~

~~<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 696.967<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~<a class="wiki_link" href="/Algebraic%20generator">Algebraic generator</a>: Traverse, the positive real root of x^4+2x-13, or 696.9529 cents.<br />~~

~~<br />~~

~~<a class="wiki_link" href="/Map">Map</a>: [&lt;1 0 -4 -13 -25|, &lt;0 1 4 10 18|]<br />~~

~~<a class="wiki_link" href="/Generator">Generator</a>s: 2, 3<br />~~

EDOs: <a class="wiki_link" href="/7edo">7</a>, <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/105edo">105</a>, <a class="wiki_link" href="/198edo">198be</a><br />

~~<a class="wiki_link" href="/Badness">Badness</a>: 0.0170<br />~~

~~<br />~~

<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-74-edo.mp3" rel="nofollow">Twinkle canon – 74 edo</a> by <a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/archives/573" rel="nofollow">Claudi Meneghin</a><br />

~~<br />~~

<h3 id="toc5"><a name="Septimal meantone-Unidecimal meantone aka Huygens-Tridecimal meantone"></a>Tridecimal meantone</h3>

~~<a class="wiki_link" href="/Comma">Comma</a>s: 66/65, 81/80, 99/98, 105/104<br />~~

~~<br />~~

~~valid range: 697.674 (43)<br />~~

~~nice range: [691.202, 701.955]<br />~~

~~strict range: 697.674<br />~~

~~<br />~~

~~<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~3/2 = 696.642<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 -13 -25 -20|, &lt;0 1 4 10 18 15|]<br />~~

EDOs: <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/267edo">267</a>, <a class="wiki_link" href="/298edo">298</a><br />

~~<a class="wiki_link" href="/Badness">Badness</a>: 0.0180<br />~~

~~<br />~~

<h3 id="toc6"><a name="Septimal meantone-Unidecimal meantone aka Huygens-Grosstone"></a>Grosstone</h3>

~~Commas: 81/80, 99/98, 126/125, 144/143<br />~~

~~<br />~~

~~POTE generator: ~3/2 = 697.264<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 -13 -25 29|, &lt;0 1 4 10 18 -16|]<br />~~

~~EDOs: 12, 31, 43, 74<br />~~

~~Badness: 0.0259<br />~~

~~<br />~~

<h3 id="toc7"><a name="Septimal meantone-Unidecimal meantone aka Huygens-Meridetone"></a>Meridetone</h3>

~~Commas: 78/77, 81/80, 99/98, 126/125<br />~~

~~<br />~~

~~POTE generator: ~3/2 = 697.529<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 -13 -25 -39|, &lt;0 1 4 10 18 27|]<br />~~

~~EDOs: 43, 117df, 160bdf, 203bcdef<br />~~

~~Badness: 0.0264<br />~~

~~<br />~~

<h3 id="toc8"><a name="Septimal meantone-Unidecimal meantone aka Huygens-Hemimeantone"></a>Hemimeantone</h3>

~~Commas: 81/80, 99/98, 126/125, 169/168<br />~~

~~<br />~~

~~POTE generator: ~52/45 = 250.304<br />~~

~~Mapping generator: ~26/15<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 -13 -25 -5|, &lt;0 2 8 20 36 11|]<br />~~

~~EDOs: 43, 62, 167bef, 229bef<br />~~

~~Badness: 0.0314<br />~~

~~<br />~~

~~<h2 id="toc9"><a name="Septimal meantone-Meanpop"></a>Meanpop</h2>~~

~~See also <a class="wiki_link" href="/Meantone%20vs%20meanpop">Meantone vs meanpop</a><br />~~

~~<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 126/125, 385/384<br />~~

~~<br />~~

~~<a class="wiki_link" href="/11-limit">11-limit</a> <a class="wiki_link" href="/minimax">minimax</a> 1/4 comma<br />~~

~~[|1 0 0 0 0&gt;, |1 0 1/4 0 0&gt;, |0 0 1 0 0&gt;,<br />~~

~~|-3 0 5/2 0 0&gt;, |11 0 -13/4 0 0&gt;]<br />~~

~~<a class="wiki_link" href="/Eigenmonzo">Eigenmonzo</a>s: 2, 5<br />~~

~~<br />~~

~~valid range: [694.737, 696.774] (19 to 31)<br />~~

~~nice range: [691.202, 701.955~~]~~<br />~~

~~strict range: [694.737, 696.774~~]~~<br />~~

~~<br />~~

~~<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 696.434<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

<a class="wiki_link" href="/Algebraic%20generator">Algebraic generator</a>: Cybozem; or else Radieubiz, the real root of 3x^3+6x-19. Unlike Cybozem, the recurrence for Radieubiz does not converge.<br />

~~<br />~~

<a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/archives/607" rel="nofollow" target="_blank">Scott Joplin's &quot;The Entertainer&quot; tuned into meanpop</a><br />

~~<br />~~

~~Map: [&lt;1 0 -4 -13 24|, &lt;0 1 4 10 -13|]<br />~~

~~<a class="wiki_link" href="/Generator">Generator</a>s: 2, 3<br />~~

EDOs: <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/81edo">81</a>, <a class="wiki_link" href="/112edo">112</a><br />

~~<a class="wiki_link" href="/Badness">Badness</a>: 0.0215<br />~~

~~<br />~~

<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-50-edo.mp3" rel="nofollow">Twinkle canon – 50 edo</a> by <a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/archives/573" rel="nofollow">Claudi Meneghin</a><br />

~~<br />~~

<h3 id="toc10"><a name="Septimal meantone-Meanpop-13-limit Meanpop"></a>13-limit Meanpop</h3>

~~<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 105/104, 144/143, 196/195<br />~~

~~<br />~~

~~valid range: [694.737, 696.774] (19 to 31)<br />~~

~~nice range: [691.202, 701.955]<br />~~

~~strict range: [694.737, 696.774]<br />~~

~~<br />~~

~~POTE generator: ~3/2 = 696.211<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 -13 24 -20|, &lt;0 1 4 10 -13 15|]<br />~~

EDOS: <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/50edo">50</a>, <a class="wiki_link" href="/81edo">81</a>, <a class="wiki_link" href="/131edo">131bd</a>, <a class="wiki_link" href="/212edo">212bdf</a><br />

~~<a class="wiki_link" href="/Badness">Badness</a>: 0.0209<br />~~

~~<br />~~

<h3 id="toc11"><a name="Septimal meantone-Meanpop-Meanplop"></a>Meanplop</h3>

~~Commas: 65/64, 78/77, 81/80, 91/90<br />~~

~~<br />~~

~~POTE generator: ~3/2 = 696.202<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 -13 24 10|, &lt;0 1 4 10 -13 -4|]<br />~~

~~EDOs: 12e, 19, 31f, 50f<br />~~

~~Badness: 0.0277<br />~~

~~<br />~~

<h2 id="toc12"><a name="Septimal meantone-Meanenneadecal"></a>Meanenneadecal</h2>

~~<a class="wiki_link" href="/Comma">Comma</a>s: 45/44, 56/55, 81/80<br />~~

~~<br />~~

~~<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~3/2 = 696.250<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Map:~~ [~~&lt;1 0 -4 -13 -6|, &lt;0 1 4 10 6|]<br />~~

EDOs: <a class="wiki_link" href="/7edo">7</a>, <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/31edo">31e</a>, <a class="wiki_link" href="/50edo">50e</a><br />

~~<a class="wiki_link" href="/Badness">Badness</a>: 0.0214<br />~~

~~<br />~~

<h3 id="toc13"><a name="Septimal meantone-Meanenneadecal-13-limit"></a>13-limit</h3>

~~<a class="wiki_link" href="/Comma">Comma</a>s: 45/44, 56/55, 78/77, 81/80<br />~~

~~<br />~~

~~<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~3/2 = 696.146<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Map:~~ [~~&lt;1 0 -4 -13 -6 -20|, &lt;0 1 4 10 6 15|]<br />~~

~~EDOs~~: ~~<a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/31edo">31e</a>, <a class="wiki_link" href="/50edo">50e</a>~~]~~<br />~~

~~<a class="wiki_link" href="/Badness">Badness</a>: 0.0212<br />~~

~~<br />~~

<h3 id="toc14"><a name="Septimal meantone-Meanenneadecal-Vincenzo"></a>Vincenzo</h3>

~~Commas: 81/80 126/125 45/44 65/64 256/255 153/152 23/22<br />~~

~~<br />~~

~~POTE generator: ~3/2<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 -13 ... |, &lt;0 1 4 10 6 -4 -5 -3 -6|~~]~~<br />~~

~~EDOs: 12<br />~~

~~Badness:<br />~~

~~<br />~~

<h2 id="toc15"><a name="Septimal meantone-Meanundeci"></a>Meanundeci</h2>

~~Commas: 33/32, 55/54, 77/75<br />~~

~~<br />~~

~~POTE generator: ~3/2 = 694.689<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Map:~~ [~~&lt;1 0 -4 -13 5|, &lt;0 1 4 10 -1|]<br />~~

~~EDOs: 12e, 19e<br />~~

~~Badness: 0.0315<br />~~

~~<br />~~

<h3 id="toc16"><a name="Septimal meantone-Meanundeci-13-limit"></a>13-limit</h3>

~~Commas: 33/32, 55/54, 77/75, 729/728<br />~~

~~<br />~~

~~POTE generator: ~3/2 = 694.764<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Map:~~ [~~&lt;1 0 -4 -13 5 10|, &lt;0 1 4 10 -1 -4|]<br />~~

~~EDOs: 12e, 19e<br />~~

~~Badness: 0.0263<br />~~

~~<br />~~

~~<h2 id="toc17"><a name="Septimal~~ meantone~~-Meanundec"></a>Meanundec</h2>~~

~~Commas: 27/26, 40/39, 45/44, 56/55<br />~~

~~<br />~~

~~POTE generator: ~3/2 = 697.254<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 -13 -6 -1|, &lt;0 1 4 10 6 3|]<br />~~

~~EDOS: 12f, 19f, 31ef<br />~~

~~Badness: 0.0242<br />~~

~~<br />~~

~~<h1 id="toc18"><a name="Flattone"></a>Flattone</h1>~~

~~<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 525/512<br />~~

~~<br />~~

The <a class="wiki_link" href="/wedgie">wedgie</a> for flattone is &lt;&lt;1 4 -9 4 -17 -32||, which tells us among other things that 9 generator steps of 4/3 get to the interval class for 7, meaning that <a class="wiki_link" href="/7_4">7/4</a> is a diminished seventh interval. Other intervals are <a class="wiki_link" href="/7_6">7/6</a>, a diminished third, and <a class="wiki_link" href="/7_5">7/5</a>, a doubly diminshed fifth. Good tunings for flattone are <a class="wiki_link" href="/26edo">26edo</a>, <a class="wiki_link" href="/45edo">45edo</a> and <a class="wiki_link" href="/64edo">64edo</a>.<br />

~~<br />~~

~~<a class="wiki_link" href="/7-limit">7-limit</a> minimax<br />~~

~~[|1 0 0 0&gt;, |21/13 0 1/13 -1/13&gt;,<br />~~

~~|32/13 0 4/13 -4/13&gt;, |32/13 0 -9/13 9/13&gt;]<br />~~

~~<a class="wiki_link" href="/Eigenmonzo">Eigenmonzo</a>s: 2, 7/5<br />~~

~~<br />~~

~~<a class="wiki_link" href="/9-limit">9-limit</a> minimax<br />~~

~~[|1 0 0 0&gt;, |17/11 2/11 0 -1/11&gt;,<br />~~

~~|24/11 8/11 0 -4/11&gt;, |34/11 -18/11 0 9/11&gt;]<br />~~

~~<a class="wiki_link" href="/Eigenmonzo">Eigenmonzo</a>s: 2, 9/7<br />~~

~~<br />~~

~~valid range: [692.308, 694.737] (26 to 19)<br />~~

~~nice range: [692.353, 701.955]<br />~~

~~strict range: [692.353, 694.737]<br />~~

~~<br />~~

~~<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 693.779<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Algebraic generator: Squarto, the positive root of 8x^2-4x-9, at 506.3239 cents, equal to (1+sqrt(19))/4.<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 17|, &lt;0 1 4 -9|]<br />~~

~~<a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;1 4 -9 4 -17 -32||<br />~~

~~<a class="wiki_link" href="/Generator">Generator</a>s: 2, 3<br />~~

EDOs: <a class="wiki_link" href="/7edo">7</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/45edo">45</a>, <a class="wiki_link" href="/64edo">64</a><br />

~~<a class="wiki_link" href="/Badness">Badness</a>: 0.0386<br />~~

~~<br />~~

~~<h2 id="toc19"><a name="Flattone-11-limit"></a>11-limit</h2>~~

~~Commas: 45/44, 81/80, 385/384<br />~~

~~<br />~~

~~valid range: [692.308, 694.737] (26 to 19)<br />~~

~~nice range: [682.502, 701.955]<br />~~

~~strict range: [692.308, 694.737]<br />~~

~~<br />~~

~~POTE generator: ~3/2 = 693.126<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 17 -6|, &lt;0 1 4 -9 6|]<br />~~

~~EDOs: 7, 19, 26, 45, 71bc, 116bcde<br />~~

~~Badness: 0.0338<br />~~

~~<br />~~

~~<h2 id="toc20"><a name="Flattone-13-limit"></a>13-limit</h2>~~

~~45/44, 65/64, 78/77, 81/80<br />~~

~~<br />~~

~~valid range: [692.308, 694.737] (26 to 19)<br />~~

~~nice range: [682.502, 701.955]<br />~~

~~strict range: [692.308, 694.737]<br />~~

~~<br />~~

~~POTE generator: ~3/2 = 693.058<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 17 -6 10|, &lt;0 1 4 -9 6 -4|]<br />~~

~~EDOs: 7, 19, 26, 45f, 71bcf, 116bcdef<br />~~

~~Badness: 0.0223<br />~~

~~<br />~~

~~<h1 id="toc21"><a name="Dominant"></a>Dominant</h1>~~

~~<a class="wiki_link" href="/Comma">Comma</a>s: 36/35, 64/63<br />~~

~~<br />~~

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 <a class="wiki_link" href="/12edo">12edo</a>, but it also works well with the Pythagorean tuning of pure <a class="wiki_link" href="/3_2">3/2</a> fifths, and with <a class="wiki_link" href="/29edo">29edo</a>, <a class="wiki_link" href="/41edo">41edo</a>, or <a class="wiki_link" href="/53edo">53edo</a>.<br />

~~<br />~~

~~valid range: [700.000, 720.000] (12 to 5)<br />~~

~~nice range: [694.786, 715.587]<br />~~

~~strict range: [700.000, 715.587]<br />~~

~~<br />~~

~~<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 701.573<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 6|, &lt;0 1 4 -2|~~]~~<br />~~

~~<a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;1 4 -2 4 -6 -16||<br />~~

EDOs: <a class="wiki_link" href="/5edo">5</a>, <a class="wiki_link" href="/7edo">7</a>, <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/65edo">65</a><br />

~~<a class="wiki_link" href="/Badness">Badness</a>: 0.0207<br />~~

~~<br />~~

~~<h2 id="toc22"><a name="Dominant-11-limit"></a>11-limit</h2>~~

~~Commas: 36/35, 64/63, 56/55<br />~~

~~<br />~~

~~valid range: [700.000, 705.882~~] ~~(12 to 17)<br />~~

~~nice range:~~ [~~691.202, 715.587]<br />~~

~~strict range:~~ [~~700.000, 705.882]<br />~~

~~<br />~~

~~POTE generator~~: ~~~3/2 = 703.254<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 6 13|, &lt;0 1 4 -2 -6|~~]~~<br />~~

~~EDOs: 5, 12, 17c, 29cde<br />~~

~~Badness: 0.0242<br />~~

~~<br />~~

~~<h2 id="toc23"><a name="Dominant-13-limit"></a>13-limit</h2>~~

~~Commas: 36/35, 56/55, 64/63, 66/65<br />~~

~~<br />~~

~~valid range: 705.882 (17)<br />~~

~~nice range: [691.202, 715.587]<br />~~

~~strict range:705.882<br />~~

~~<br />~~

~~POTE generator: ~3/2 = 703.636<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 6 13 18|, &lt;0 1 4 -2 -6 -9|]<br />~~

~~EDOs: 12f, 17c, 29cdef<br />~~

~~Badness: 0.0241<br />~~

~~<br />~~

~~<h2 id="toc24"><a name="Dominant-Dominion"></a>Dominion</h2>~~

~~Commas: 26/25, 36/35, 56/55, 64/63<br />~~

~~<br />~~

~~POTE generator: ~3/2 = 704.905<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 6 13 -9|, &lt;0 1 4 -2 -6 8|]<br />~~

~~EDOs: 5, 12, 17c, 46cde<br />~~

~~Badness: 0.0273<br />~~

~~<br />~~

~~<h2 id="toc25"><a name="Dominant-Domineering"></a>Domineering</h2>~~

~~Commas: 36/35, 45/44, 64/63<br />~~

~~<br />~~

~~POTE generator: ~3/2 = 698.776<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 6 -6|, &lt;0 1 4 -2 6|~~]~~<br />~~

~~EDOs: 7, 12, 43de<br />~~

~~Badness: 0.0220<br />~~

~~<br />~~

~~<h2 id="toc26"><a name="Dominant-Domination"></a>Domination</h2>~~

~~Commas: 36/35, 64/63, 77/75<br />~~

~~<br />~~

~~POTE generator: ~3/2 = 705.004<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Map:~~ [~~&lt;1 0 -4 6 -14|, &lt;0 1 4 -2 11|]<br />~~

~~EDOs: 17c, 46cd<br />~~

~~Badness: 0.0366<br />~~

~~<br />~~

<h3 id="toc27"><a name="Dominant-Domination-13-limit"></a>13-limit</h3>

~~Commas: 26/25, 36/35, 64/63, 66/65<br />~~

~~<br />~~

~~POTE generator: ~3/2 = 705.496<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Map:~~ [~~&lt;1 0 -4 6 -14 -9|, &lt;0 1 4 -2 11 8|]<br />~~

~~EDOs: 17c<br />~~

~~Badness: 0.0274<br />~~

~~<br />~~

~~<h2 id="toc28"><a name="Dominant-Twelve"></a>Twelve</h2>~~

~~Commas: 81/80 64/63 45/44 65/64 256/255 153/152<br />~~

~~<br />~~

~~POTE generator: ~3/2 = 696.217<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 6 -6 10 12 9|, &lt;0 1 4 -2 6 -4 -5 -3|~~]~~<br />~~

~~EDOs: 7, 12, 19d, 31def<br />~~

~~Badness: 0.0204<br />~~

~~<br />~~

~~<h2 id="toc29"><a name="Dominant-Arnold"></a>Arnold</h2>~~

~~Commas: 22/21, 33/32, 36/35<br />~~

~~<br />~~

~~POTE generator: ~3/2 = 698.491<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 6 5|, &lt;0 1 4 -2 -1|~~]~~<br />~~

~~EDOs: 5, 7, 12e<br />~~

~~Badness: 0.0261<br />~~

~~<br />~~

~~<h2 id="toc30"><a name="Dominant-13-limit"></a>13-limit</h2>~~

~~Commas: 22/21, 27/26, 33/32, 40/39<br />~~

~~<br />~~

~~POTE generator: ~3/2 = 696.743<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 6 5 -1|, &lt;0 1 4 -2 -1 3|]<br />~~

~~EDOs: 5, 7, 12ef, 19def, 31def<br />~~

~~Badness: 0.0233<br />~~

~~<br />~~

~~<h2 id="toc31"><a name="Dominant-Dominatrix"></a>Dominatrix</h2>~~

~~Commas: 27/26 36/35 45/44 64/63<br />~~

~~<br />~~

~~POTE generator: ~3/2 = 698.544<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 6 -6 -1|, &lt;0 1 4 -2 6 3|]<br />~~

~~EDOs: 7, 12f<br />~~

~~Badness: 0.0183<br />~~

~~<br />~~

~~<h1 id="toc32"><a name="Sharptone"></a>Sharptone</h1>~~

~~<a class="wiki_link" href="/Comma">Comma</a>s: 21/20, 28/27<br />~~

~~<br />~~

Sharptone, with a wedgie &lt;&lt;1 4 3 4 2 -4||, 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. <a class="wiki_link" href="/12edo">12edo</a> tuning does sharptone about as well as such a thing can be done.<br />

~~<br />~~

~~<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 700.140<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 -2|, &lt;0 1 4 3|]<br />~~

~~<a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;1 4 3 4 2 -4||<br />~~

~~EDOs: <a class="wiki_link" href="/5edo">5</a>, <a class="wiki_link" href="/12edo">12</a><br />~~

~~<a class="wiki_link" href="/Badness">Badness</a>: 0.0248<br />~~

~~<br />~~

~~<h1 id="toc33"><a name="Meansept"></a>Meansept</h1>~~

~~Commas: 15/14, 81/80<br />~~

~~<br />~~

~~POTE generator: ~3/2 = 682.895<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 -5|, &lt;0 1 4 5|]<br />~~

~~Wedgie: &lt;&lt;1 4 5 4 5 0||<br />~~

~~EDOs: 7<br />~~

~~Badness: 0.0453<br />~~

~~<br />~~

~~<h2 id="toc34"><a name="Meansept-11-limit"></a>11-limit</h2>~~

~~Commas: 15/14, 22/21, 125/121<br />~~

~~<br />~~

~~POTE generator: ~3/2 = 685.234<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 -5 -6|, &lt;0 1 4 5 6|]<br />~~

~~EDOs: 7<br />~~

~~Badness: 0.0325<br />~~

~~<br />~~

~~<h1 id="toc35"><a name="Supermean"></a>Supermean</h1>~~

~~Commas: 81/80, 672/625<br />~~

~~<br />~~

~~POTE generator: ~3/2 = 704.889<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 -21|, &lt;0 1 4 15|]<br />~~

~~EDOs: 17c, 46c<br />~~

~~Badness: 0.1342<br />~~

~~<br />~~

~~<h2 id="toc36"><a name="Supermean-11-limit"></a>11-limit</h2>~~

~~Commas: 56/55, 81/80, 132/125<br />~~

~~<br />~~

~~POTE generator: ~3/2 = 705.096<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 -21 -14|, &lt;0 1 4 15 11|]<br />~~

~~EDOs: 17c, 46c<br />~~

~~Badness: 0.0633<br />~~

~~<br />~~

~~<h2 id="toc37"><a name="Supermean-13-limit"></a>13-limit</h2>~~

~~Commas: 26/25, 56/55, 66/65, 81/80<br />~~

~~<br />~~

~~POTE generator: ~3/2 = 705.094<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 -21 -14 -9|, &lt;0 1 4 15 11 8|]<br />~~

~~EDOs: 17c, 46c<br />~~

~~<br />~~

~~<h1 id="toc38"><a name="Injera"></a>Injera</h1>~~

~~<a class="wiki_link" href="/Comma">Comma</a>s: 50/49, 81/80<br />~~

~~<br />~~

The wedgie for injera is &lt;&lt;2 8 8 8 7 -4||, which tells us it 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. <a class="wiki_link" href="/38edo">38edo</a>, which is two parallel <a class="wiki_link" href="/19edo">19edo</a>s, is an excellent tuning for injera.<br />

~~<br />~~

~~<a class="wiki_link_ext" href="http://tech.groups.yahoo.com/group/tuning-math/message/3091" rel="nofollow">Origin of the name</a><br />~~

~~<br />~~

~~valid range: [685.714, 700.000] (14c to 12)<br />~~

~~nice range: [688.957, 701.955]<br />~~

~~strict range: [688.957, 700.000]<br />~~

~~<br />~~

~~<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 694.375<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Map: [&lt;2 0 -8 -7|, &lt;0 1 4 4|]<br />~~

~~<a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;2 8 8 8 7 -4||<br />~~

EDOs: <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/26edo">26</a>, <a class="wiki_link" href="/38edo">38</a>, <a class="wiki_link" href="/102edo">102bcd</a>, <a class="wiki_link" href="/140edo">140bcd</a>, <a class="wiki_link" href="/178edo">178bcd</a><br />

~~<a class="wiki_link" href="/Badness">Badness</a>: 0.0311<br />~~

~~<br />~~

<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Two%20Pairs%20of%20Socks.mp3" rel="nofollow">Two Pairs of Socks</a> (in <a class="wiki_link" href="/26edo">26edo</a>) by <a class="wiki_link" href="/Igliashon%20Jones">Igliashon Calvin Jones-Coolidge</a><br />

<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Curley/Zach%20Curley%20-%20Injera%20Jam.mp3" rel="nofollow">Injera Jam</a> (in <a class="wiki_link" href="/26edo">26edo</a>) by <a class="wiki_link" href="/Zach%20Curley">Zach Curley</a><br />

~~<br />~~

~~<h2 id="toc39"><a name="Injera-11-limit"></a>11-limit</h2>~~

~~Commas: 45/44, 50/49, 81/80<br />~~

~~<br />~~

~~valid range: [685.714, 700.000] (14c to 12)<br />~~

~~nice range: [682.458, 701.955]<br />~~

~~strict range: [685.714, 700.000]<br />~~

~~<br />~~

~~POTE generator: ~3/2 = 692.840<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Map: [&lt;2 0 -8 -7 -12|, &lt;0 1 4 4 6|]<br />~~

~~EDOs: 12, 14c, 26. 90bce, 116bce<br />~~

~~Badness: 0.0231<br />~~

~~<br />~~

~~<h2 id="toc40"><a name="Injera-13-limit"></a>13-limit</h2>~~

~~Commas: 45/44, 50/49, 81/80, 78/77<br />~~

~~<br />~~

~~valid range: 692.308 (26)<br />~~

~~nice range: [682.458, 701.955]<br />~~

~~strict range: 692.308 (26)<br />~~

~~<br />~~

~~POTE generator: ~3/2 = 692.673<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Map: [&lt;2 0 -8 -7 -12 -21|, &lt;0 1 4 4 6 9|]<br />~~

~~EDOs: 26, 104bcf<br />~~

~~Badness: 0.0216<br />~~

~~<br />~~

~~<h2 id="toc41"><a name="Injera-Enjera"></a>Enjera</h2>~~

~~Commas: 27/26, 40/39, 45/44, 99/98<br />~~

~~<br />~~

~~POTE generator: ~3/2 = 694.121<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Map: [&lt;2 0 -8 -7 -12 -2|, &lt;0 1 4 4 6 3|]<br />~~

~~EDOs: 12f, 26f, 38ef<br />~~

~~Badness: 0.0265<br />~~

~~<br />~~

~~<h2 id="toc42"><a name="Injera-Injerous"></a>Injerous</h2>~~

~~Commas: 33/32, 50/49, 55/54<br />~~

~~<br />~~

~~POTE generator: ~3/2 = 690.548<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Map: [&lt;2 0 -8 -7 10|, &lt;0 1 4 4 -1|]<br />~~

~~EDOs: 12e, 14c, 26e, 40ce<br />~~

~~Badness: 0.0386<br />~~

~~<br />~~

~~<h2 id="toc43"><a name="Injera-Lahoh"></a>Lahoh</h2>~~

~~Commas: 50/49, 56/55, 81/77<br />~~

~~<br />~~

~~POTE generator: ~3/2 = 699.001<br />~~

~~Mapping generator: ~3<br />~~

~~<br />~~

~~Map: [&lt;2 0 -8 -7 7|, &lt;0 1 4 4 0|]<br />~~

~~EDOs: 12<br />~~

~~Badness: 0.0431<br />~~

~~<br />~~

~~<h1 id="toc44"><a name="Godzilla"></a>Godzilla</h1>~~

~~<span style="display: block; text-align: right;"><a class="wiki_link" href="http://xenharmonie.wikispaces.com/Semiphor%2C%20Semaphor%2C%20Godzilla">Deutsch</a><br />~~

~~</span><br />~~

~~Main article: <a class="wiki_link" href="/Semaphore%20and%20Godzilla">Semaphore and Godzilla</a><br />~~

~~<a class="wiki_link" href="/Comma">Comma</a>s: 49/48, 81/80<br />~~

~~<br />~~

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. <a class="wiki_link" href="/19edo">19edo</a> 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.<br />

~~<br />~~

~~valid range: [240.000, 257.143] (5 to 14c)<br />~~

~~nice range: [231.174, 266.871]<br />~~

~~strict range: [240.000, 257.143]<br />~~

~~<br />~~

~~<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~8/7 = 252.635<br />~~

~~Mapping generator: ~7/4<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 2|, &lt;0 2 8 1|]<br />~~

~~<a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;2 8 1 8 -4 -20||<br />~~

EDOs: <a class="wiki_link" href="/5edo">5</a>, <a class="wiki_link" href="/9edo">9c</a>, <a class="wiki_link" href="/14edo">14c</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/62edo">62d</a>, <a class="wiki_link" href="/81edo">81d</a>, 143bd<br />

~~<a class="wiki_link" href="/Badness">Badness</a>: 0.0267<br />~~

~~<br />~~

~~<h2 id="toc45"><a name="Godzilla-11-limit"></a>11-limit</h2>~~

~~Commas: 45/44, 49/48, 81/80<br />~~

~~<br />~~

~~valid range: [252.632, 257.143] (19 to 14c)<br />~~

~~nice range: [231.174, 266.871]<br />~~

~~strict range: [252.632, 257.143]<br />~~

~~<br />~~

~~POTE generator: ~8/7 = 254.027<br />~~

~~Mapping generator: ~7/4<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 2 -6|, &lt;0 2 8 1 12|]<br />~~

~~EDOs: 14c, 19, 33cd, 52cd<br />~~

~~Badness: 0.0290<br />~~

~~<br />~~

~~<h2 id="toc46"><a name="Godzilla-13-limit"></a>13-limit</h2>~~

~~Commas: 45/44, 49/48, 78/77, 81/80<br />~~

~~<br />~~

~~valid range: 694.737 (19)<br />~~

~~nice range: [621.581, 737.652]<br />~~

~~strict range: 694.737<br />~~

~~<br />~~

~~POTE generator: ~8/7 = 253.603<br />~~

~~Mapping generator: ~7/4<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 2 -6 -5|, &lt;0 2 8 1 12 11|]<br />~~

~~EDOs: 14cf, 19, 33cdf, 52cdf<br />~~

~~Badness: 0.0225<br />~~

~~<br />~~

~~<h2 id="toc47"><a name="Godzilla-Semafour"></a>Semafour</h2>~~

~~Commas: 33/32, 49/48, 55/54<br />~~

~~<br />~~

~~POTE generator: ~8/7 = 254.042<br />~~

~~Mapping generator: ~7/4<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 2 5|, &lt;0 2 8 1 -2|]<br />~~

~~EDOs: 5, 14c, 19e, 33cde<br />~~

~~Badness: 0.0285<br />~~

~~<br />~~

~~<h2 id="toc48"><a name="Godzilla-Varan"></a>Varan</h2>~~

~~Commas: 49/48, 77/75, 81/80<br />~~

~~<br />~~

~~POTE generator: ~8/7 = 251.079<br />~~

~~Mapping generator: ~7/4<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 2 -10|, &lt;0 2 8 1 17|]<br />~~

~~EDOs: 19e, 24, 43de<br />~~

~~Badness: 0.0396<br />~~

~~<br />~~

~~<h3 id="toc49"><a name="Godzilla-Varan-13-limit"></a>13-limit</h3>~~

~~Commas: 49/48, 66/65, 77/75, 81/80<br />~~

~~<br />~~

~~POTE generator: ~8/7 = 251.165<br />~~

~~Mapping generator: ~7/4<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 2 -10 -5|, &lt;0 2 8 1 17 11|]<br />~~

~~EDOs: 19e, 24, 43de<br />~~

~~Badness: 0.0257<br />~~

~~<br />~~

~~<h2 id="toc50"><a name="Godzilla-Baragon"></a>Baragon</h2>~~

~~Commas: 49/48, 56/55, 81/80<br />~~

~~<br />~~

~~POTE generator: ~8/7 = 251.173<br />~~

~~Mapping generator: ~7/4<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 2 9|, &lt;0 2 8 1 -7|]<br />~~

~~EDOs: 19, 24, 43d<br />~~

~~Badness: 0.0357<br />~~

~~<br />~~

~~<h2 id="toc51"><a name="Godzilla-Music"></a>Music</h2>~~

<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Bobro/GodzillaExample.mp3" rel="nofollow">Godzilla Example</a> by <a class="wiki_link" href="/Cameron%20Bobro">Cameron Bobro</a><br />

<a class="wiki_link_ext" href="http://tinyurl.com/4uyumk9" rel="nofollow">&quot;Change is on the Wind&quot;</a> in Godzilla[9] by <a class="wiki_link" href="/Igliashon%20Jones">Igliashon Jones</a><br />

~~<br />~~

~~<h1 id="toc52"><a name="Mohajira"></a>Mohajira</h1>~~

~~<span style="display: block; text-align: right;"><a class="wiki_link" href="http://xenharmonie.wikispaces.com/Mohajira">Deutsch</a><br />~~

~~</span><br />~~

~~<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 6144/6125<br />~~

~~<br />~~

Mohajira, with wedgie &lt;&lt;2 8 -11 8 -23 -48||, really makes more sense as an 11-limit temperament. It has a generator of a neutral third, two of which make up a fifth, and which can be taken to represent 128/105. Mohajira tempers out 6144/6125, the porwell comma. <a class="wiki_link" href="/31edo">31edo</a> makes for an excellent (7-limit) mohajira tuning, with generator 9/31. It has a 7-note MOS with three larger steps and four smaller ones, going sLsLsLs.<br />

~~<br />~~

Mohajira can also be thought of, intuitively, as &quot;meantone with quarter tones&quot;; as is the 3/2 generator subdivided in half, so is the 25/24 chromatic semitone divided into two equal ~33/32 quarter tones (in the 11-limit). Within this paradigm, mohajira is the temperament that splits the 3/2 into two equal 11/9's, that splits the 6/5 into two equal 11/10's, that maps four 3/2's to 5/1, and that maps the interval one quarter tone flat of 16/9 to 7/4.<br />

~~<br />~~

~~<a class="wiki_link" href="/7-limit">7</a> and <a class="wiki_link" href="/9-limit">9-limit</a> minimax 1/4 comma<br />~~

~~[|1 0 0 0&gt;, |1 0 1/4 0&gt;, |0 0 1 0&gt;, |6 0 -11/8 0&gt;]<br />~~

~~<a class="wiki_link" href="/Eigenmonzo">Eigenmonzo</a>s: 2, 5<br />~~

~~<br />~~

~~<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~128/105 = 348.415<br />~~

~~Mapping generator: ~128/105<br />~~

~~<br />~~

~~Algebraic generator: Mohabis, real root of 3x^3-3x^2-1, 348.6067 cents. Corresponding recurrence converges quickly.<br />~~

~~<br />~~

~~Map: [&lt;1 1 0 6|, &lt;0 2 8 -11|]<br />~~

~~<a class="wiki_link" href="/Generator">Generator</a>s: 2, 128/105<br />~~

~~<a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;2 8 -11 8 -23 -48||<br />~~

~~EDOs: <a class="wiki_link" href="/7edo">7</a>, <a class="wiki_link" href="/24edo">24</a>, <a class="wiki_link" href="/31edo">31</a><br />~~

~~<a class="wiki_link" href="/Badness">Badness</a>: 0.0557<br />~~

~~<br />~~

~~<h2 id="toc53"><a name="Mohajira-11-limit"></a>11-limit</h2>~~

~~<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 121/120, 176/175<br />~~

~~<br />~~

~~<a class="wiki_link" href="/11-limit">11-limit</a> minimax 1/4 comma<br />~~

~~[|1 0 0 0 0&gt;, |1 0 1/4 0 0&gt;, |0 0 1 0 0&gt;,<br />~~

~~|6 0 -11/8 0 0&gt;, |2 0 5/8 0 0&gt;]<br />~~

~~<a class="wiki_link" href="/Eigenmonzo">Eigenmonzo</a>s: 2, 5<br />~~

~~<br />~~

~~<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~11/9 = 348.477<br />~~

~~Mapping generator: ~11/9<br />~~

~~<br />~~

~~Map: [&lt;1 1 0 6 2|, &lt;0 2 8 -11 5|]<br />~~

~~<a class="wiki_link" href="/Generator">Generator</a>s: 2, 11/9<br />~~

~~EDOs: <a class="wiki_link" href="/7edo">7</a>, <a class="wiki_link" href="/24edo">24</a>, <a class="wiki_link" href="/31edo">31</a><br />~~

~~<a class="wiki_link" href="/Badness">Badness</a>: 0.0261<br />~~

~~<br />~~

~~<h2 id="toc54"><a name="Mohajira-13-limit"></a>13-limit</h2>~~

~~Commas: 81/80, 121/120, 105/104, 66/65<br />~~

~~<br />~~

~~POTE generator: ~11/9 = 348.558<br />~~

~~Mapping generator: ~11/9<br />~~

~~<br />~~

~~Map: [&lt;1 1 0 6 2 4|, &lt;0 2 8 -11 5 -1|]<br />~~

~~EDOs: 7, 24, 31, 117ef, 148bef<br />~~

~~Badness: 0.0234<br />~~

~~<br />~~

~~<h1 id="toc55"><a name="Ptolemy"></a>Ptolemy</h1>~~

~~Commas: 81/80, 121/120, 525/512<br />~~

~~<br />~~

~~POTE generator: ~11/9 = 346.922<br />~~

~~<br />~~

~~Map: [&lt;1 1 0 8 2|, &lt;0 2 8 -18 5|]<br />~~

~~EDOs: 7, 38d, 45e, 83bcde<br />~~

~~Badness: 0.0588<br />~~

~~<br />~~

~~<h2 id="toc56"><a name="Ptolemy-13-limit"></a>13-limit</h2>~~

~~Commas: 65/64, 81/80, 105/104, 121/120<br />~~

~~<br />~~

~~POTE generator: ~11/9 = 346.910<br />~~

~~<br />~~

~~Map: [&lt;1 1 0 8 2 6|, &lt;0 2 8 -18 5 -8|]<br />~~

~~EDOs: 7, 38df, 45ef, 83bcdef<br />~~

~~Badness: 0.0343<br />~~

~~<br />~~

~~<h1 id="toc57"><a name="Maqamic"></a>Maqamic</h1>~~

~~<span style="display: block; text-align: right;"><a class="wiki_link" href="http://xenharmonie.wikispaces.com/maqamisch">Deutsch</a><br />~~

~~</span><br />~~

~~Main article: <a class="wiki_link" href="/Maqamic">Maqamic</a><br />~~

~~<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 36/35, 121/120<br />~~

~~<br />~~

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 &quot;middle-of-the-road&quot; intonation.<br />

~~<br />~~

~~<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~11/9 = 350.934<br />~~

~~Mapping generator: ~11/9<br />~~

~~<br />~~

~~Map: [&lt;1 1 0 4 2|, &lt;0 2 8 -4 5|]<br />~~

~~<a class="wiki_link" href="/Generator">Generator</a>s: 2, 11/9<br />~~

EDOs: <a class="wiki_link" href="/7edo">7</a>, <a class="wiki_link" href="/10edo">10c</a>, <a class="wiki_link" href="/17edo">17c</a>, <a class="wiki_link" href="/24edo">24d</a>, <a class="wiki_link" href="/31edo">31d</a><br />

~~<br />~~

~~<h2 id="toc58"><a name="Maqamic-13-limit"></a>13-limit</h2>~~

~~<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 36/35, 121/120, 144/143<br />~~

~~<br />~~

~~<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~11/9 = 350.816<br />~~

~~Mapping generator: ~11/9<br />~~

~~<br />~~

~~Map: [&lt;1 1 0 4 2 4|, &lt;0 2 8 -4 5 -1|]<br />~~

~~Generators: 2, 11/9<br />~~

EDOs: <a class="wiki_link" href="/7edo">7</a>, <a class="wiki_link" href="/10edo">10c</a>, <a class="wiki_link" href="/17edo">17c</a>, <a class="wiki_link" href="/24edo">24d</a>,<a class="wiki_link" href="/31edo"> 31d</a><br />

~~<br />~~

~~<h1 id="toc59"><a name="Migration"></a>Migration</h1>~~

~~Commas: 81/80, 121/120, 126/125<br />~~

~~<br />~~

~~POTE generator: ~11/9 = 348.182<br />~~

~~Mapping generator: ~11/9<br />~~

~~<br />~~

~~Map: [&lt;1 1 0 -3 2|, &lt;0 2 8 20 5|]<br />~~

~~EDOs: 31, 100de, 131bde, 162bde<br />~~

~~Badness: 0.0255<br />~~

~~<br />~~

~~<h1 id="toc60"><a name="Mohamaq"></a>Mohamaq</h1>~~

~~Commas: 81/80, 392/375<br />~~

~~<br />~~

~~POTE generator: ~25/21 = 350.586<br />~~

~~Mapping generator: ~25/21<br />~~

~~<br />~~

~~Map: [&lt;1 1 0 -1|, &lt;0 2 8 13|]<br />~~

~~EDOs: 17c, 24, 65c, 89cd<br />~~

~~Badness: 0.0777<br />~~

~~<br />~~

~~<h2 id="toc61"><a name="Mohamaq-11-limit"></a>11-limit</h2>~~

~~Commas: 56/55, 77/75, 243/242<br />~~

~~<br />~~

~~POTE generator: ~11/9 = 350.565<br />~~

~~Mapping generator: ~11/9<br />~~

~~<br />~~

~~Map: [&lt;1 1 0 -1 2|, &lt;0 2 8 13 5|]<br />~~

~~EDOs: 17c, 24, 65c, 89cd<br />~~

~~Badness: 0.0362<br />~~

~~<br />~~

~~<h2 id="toc62"><a name="Mohamaq-13-limit"></a>13-limit</h2>~~

~~Commas: 56/55, 66/65, 77/75, 243/242<br />~~

~~<br />~~

~~POTE generator: ~11/9 = 350.745<br />~~

~~Mapping generator: ~11/9<br />~~

~~<br />~~

~~Map: [&lt;1 1 0 -1 2 4|, &lt;0 2 8 13 5 -1|]<br />~~

~~EDOs: 17c, 24, 41c, 65c<br />~~

~~Badness: 0.0287<br />~~

~~<br />~~

~~<h1 id="toc63"><a name="Orphic"></a>Orphic</h1>~~

~~Commas: 81/80, 5898240/5764801<br />~~

~~<br />~~

~~POTE generator: ~7/6 = 275.794<br />~~

~~Mapping generator: ~343/288<br />~~

~~<br />~~

~~Map: [&lt;2 1 -4 4|, &lt;0 4 16 3|]<br />~~

~~Wedgie: &lt;&lt;8 32 6 32 -13 -76||<br />~~

~~EDOs: 26, 74, 174bd, 248bd<br />~~

~~Badness: 0.2588<br />~~

~~<br />~~

~~<h2 id="toc64"><a name="Orphic-11-limit"></a>11-limit</h2>~~

~~Commas: 81/80, 99/98, 73728/73205<br />~~

~~<br />~~

~~POTE generator: ~7/6 = 275.762<br />~~

~~Mapping generator: ~77/64<br />~~

~~<br />~~

~~Map: [&lt;2 1 -4 4 8|, &lt;0 4 16 3 -2|]<br />~~

~~EDOs: 26, 48c, 74, 248bd, 322bd<br />~~

~~Badness: 0.1015<br />~~

~~<br />~~

~~<h2 id="toc65"><a name="Orphic-13-limit"></a>13-limit</h2>~~

~~Commas: 81/80, 99/98, 144/143, 2200/2197<br />~~

~~<br />~~

~~POTE generator: ~7/6 = 275.774<br />~~

~~Mapping generator: ~63/52<br />~~

~~<br />~~

~~Map: [&lt;2 1 -4 4 8 2|, &lt;0 4 16 3 -2 10|]<br />~~

~~EDOs: 26, 48c, 74, 174bd, 248bd, 322bd<br />~~

~~Badness: 0.0535<br />~~

~~<br />~~

~~<h1 id="toc66"><a name="Mothra"></a>Mothra</h1>~~

~~<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 1029/1024<br />~~

~~<br />~~

Mothra, with wedgie &lt;&lt;3 12 -1 12 -10 -36||, 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 <a class="wiki_link" href="/31edo">31edo</a> 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-limit, mothra is identical to <a class="wiki_link" href="/Slendric">slendric</a>.<br />

~~Note that mothra can also be called cynder in the 7-limit, which can be a little confusing sometimes.<br />~~

~~<br />~~

~~<a class="wiki_link" href="/7-limit">7</a> and <a class="wiki_link" href="/9-limit">9-limit</a> minimax 1/4 comma<br />~~

~~[|1 0 0 0&gt;, |1 0 1/4 0&gt;, |0 0 1 0&gt;, |3 0 -1/12 0&gt;]<br />~~

~~<a class="wiki_link" href="/Eigenmonzo">Eigenmonzo</a>s: 2, 5<br />~~

~~<br />~~

~~<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~8/7 = 232.193<br />~~

~~Mapping generator: ~8/7<br />~~

~~<br />~~

~~Algebraic generator: Rabrindanath, largest real root of x^8-3x^2+1, or 232.0774 cents.<br />~~

~~<br />~~

~~Map: [&lt;1 1 0 3|, &lt;0 3 12 -1|]<br />~~

~~<a class="wiki_link" href="/Generator">Generator</a>s: 2, 8/7<br />~~

~~<a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;3 12 -1 12 -10 -36||<br />~~

~~EDOs: <a class="wiki_link" href="/5edo">5</a>, <a class="wiki_link" href="/26edo">26</a>, <a class="wiki_link" href="/31edo">31</a><br />~~

~~<a class="wiki_link" href="/Badness">Badness</a>: 0.0371<br />~~

~~<br />~~

~~<h2 id="toc67"><a name="Mothra-11-limit"></a>11-limit</h2>~~

~~<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 99/98, 385/384<br />~~

~~<br />~~

~~POTE generator: ~8/7 = 232.031<br />~~

~~Mapping generator: ~8/7<br />~~

~~<br />~~

~~Map: [&lt;1 1 0 3 5|, &lt;0 3 12 -1 -8|]<br />~~

EDOs: <a class="wiki_link" href="/5edo">5</a>, <a class="wiki_link" href="/26edo">26</a>, <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/88edo">88</a>, <a class="wiki_link" href="/150edo">150</a>, <a class="wiki_link" href="/181edo">181</a><br />

~~<a class="wiki_link" href="/Badness">Badness</a>: 0.0256<br />~~

~~<br />~~

~~<h2 id="toc68"><a name="Mothra-13-limit"></a>13-limit</h2>~~

~~Commas: 81/80, 99/98, 105/104, 144/143<br />~~

~~<br />~~

~~POTE generator: ~8/7 = 231.811<br />~~

~~Mapping generator: ~8/7<br />~~

~~<br />~~

~~Map: [&lt;1 1 0 3 5 1|, &lt;0 3 12 -1 -8 14|]<br />~~

~~EDOs: 5, 26, 31, 57, 88<br />~~

~~Badness: 0.0240<br />~~

~~<br />~~

~~<h2 id="toc69"><a name="Mothra-Cynder"></a>Cynder</h2>~~

~~Commas: 45/44, 81/80, 1029/1024<br />~~

~~<br />~~

~~POTE generator: ~8/7 = 231.317<br />~~

~~Mapping generator: ~8/7<br />~~

~~<br />~~

~~Map: [&lt;1 1 0 3 0|, &lt;0 3 12 -1 18|]<br />~~

~~EDOs: 26, 57e, 83bce<br />~~

~~Badness: 0.0557<br />~~

~~<br />~~

~~<h3 id="toc70"><a name="Mothra-Cynder-13-limit"></a>13-limit</h3>~~

~~Commas: 45/44, 78/77, 81/80, 640/637<br />~~

~~<br />~~

~~POTE generator: ~8/7 = 231.293<br />~~

~~Mapping generator: ~8/7<br />~~

~~<br />~~

~~Map: [&lt;1 1 0 3 0 1|, &lt;0 3 12 -1 18 14|]<br />~~

~~EDOs: 26, 57e, 83bce<br />~~

~~Badness: 0.0341<br />~~

~~<br />~~

~~<h2 id="toc71"><a name="Mothra-Mosura"></a>Mosura</h2>~~

~~Commas: 81/80, 176/175, 1029/1024<br />~~

~~<br />~~

~~POTE generator: ~8/7 = 232.419<br />~~

~~Mapping generator: ~8/7<br />~~

~~<br />~~

~~Map: [&lt;1 1 0 3 -1|, &lt;0 3 12 -1 23|]<br />~~

~~EDOs: 31, 129, 136b, 148be, 160be, 191bce, 222bce, 253bce<br />~~

~~Badness: 0.0313<br />~~

~~<br />~~

~~<h3 id="toc72"><a name="Mothra-Mosura-13-limit"></a>13-limit</h3>~~

~~Commas: 81/80, 144/143, 176/175, 1029/1024<br />~~

~~<br />~~

~~POTE generator: ~8/7 = 232.640<br />~~

~~Mapping generator: ~8/7<br />~~

~~<br />~~

~~Map: [&lt;1 1 0 3 -1 7|, &lt;0 3 12 -1 23 -17|]<br />~~

~~EDOs: 31, 67, 98<br />~~

~~Badness: 0.0369<br />~~

~~<br />~~

~~<h1 id="toc73"><a name="Squares"></a>Squares</h1>~~

~~<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 2401/2400<br />~~

~~<br />~~

Squares, with wedgie &lt;&lt;4 16 9 16 3 -24||, splits the interval of an eleventh, or 8/3, into four supermajor third (<a class="wiki_link" href="/9_7">9/7</a>) intervals, and uses it for a generator. <a class="wiki_link" href="/31edo">31edo</a>, 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.<br />

~~<br />~~

~~7 and 9 limit minimax 1/4 comma<br />~~

~~[|1 0 0 0&gt;, |1 0 1/4 0&gt;, |0 0 1 0&gt;, |3/2 0 9/16 0&gt;]<br />~~

~~<a class="wiki_link" href="/Eigenmonzo">Eigenmonzo</a>s: 2, 5<br />~~

~~<br />~~

~~<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~9/7 = 425.942<br />~~

~~Mapping generator: ~9/7<br />~~

~~<br />~~

~~Algebraic generator: Sceptre2, the positive root of 9x^2+x-16, or (sqrt(577)-1)/18, which is 425.9311 cents.<br />~~

~~<br />~~

~~Map: [&lt;1 3 8 6|, &lt;0 -4 -16 -9|]<br />~~

~~<a class="wiki_link" href="/Generator">Generator</a>s: 2, 9/7<br />~~

EDOs: <a class="wiki_link" href="/14edo">14</a>, <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/262edo">262</a>, <a class="wiki_link" href="/293edo">293</a><br />

~~<a class="wiki_link" href="/Badness">Badness</a>: 0.0460<br />~~

~~<br />~~

~~Music:<br />~~

~~By <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br />~~

~~<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/tuning-survey/daily20100603-squares8piano.mp3" rel="nofollow">Square 8</a><br />~~

~~<br />~~

~~<h2 id="toc74"><a name="Squares-11-limit"></a>11-limit</h2>~~

~~Commas: 81/80, 99/98, 121/120<br />~~

~~<br />~~

~~POTE generator: ~9/7 = 425.957<br />~~

~~Mapping generator: ~9/7<br />~~

~~<br />~~

~~Map: [&lt;1 3 8 6 7|, &lt;0 -4 -16 -9 -10|]<br />~~

EDOs: <a class="wiki_link" href="/5edo">5</a>, <a class="wiki_link" href="/8edo">8</a>, <a class="wiki_link" href="/11edo">11</a>, <a class="wiki_link" href="/14edo">14</a>, <a class="wiki_link" href="/17edo">17</a>, <a class="wiki_link" href="/31edo">31</a><br />

~~<a class="wiki_link" href="/Badness">Badness</a>: 0.0216<br />~~

~~<br />~~

~~<h2 id="toc75"><a name="Squares-13-limit"></a>13-limit</h2>~~

~~Commas: 81/80, 99/98, 121/120, 66/65<br />~~

~~<br />~~

~~POTE generator: ~9/7 = 425.550<br />~~

~~Mapping generator: ~9/7<br />~~

~~<br />~~

~~Map: [&lt;1 3 8 6 7 3|, &lt;0 -4 -16 -9 -10 2|]<br />~~

~~EDOs: 17c, 31, 79cf, 110cef, 141cef<br />~~

~~<a class="wiki_link" href="/Badness">Badness</a>: 0.0255<br />~~

~~<br />~~

~~<h2 id="toc76"><a name="Squares-Agora"></a>Agora</h2>~~

~~Commas: 81/80, 99/98, 105/104, 121/120<br />~~

~~<br />~~

~~POTE generator: ~9/7 = 426.276<br />~~

~~Mapping generator: ~9/7<br />~~

~~<br />~~

~~Map: [&lt;1 3 8 6 7 14|, &lt;0 -4 -16 -9 -10 -29|]<br />~~

~~EDOs: 31, 45ef, 76e<br />~~

~~Badness: 0.0245<br />~~

~~<br />~~

~~<h1 id="toc77"><a name="Cuboctahedra"></a>Cuboctahedra</h1>~~

~~<h2 id="toc78"><a name="Cuboctahedra-11-limit"></a>11-limit</h2>~~

~~<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 385/384, 1375/1372<br />~~

~~<br />~~

~~<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~9/7 = 425.993<br />~~

~~Mapping generator: ~9/7<br />~~

~~<br />~~

~~Map: [&lt;1 3 8 6 -4|, &lt;0 -4 -16 -9 21|]<br />~~

EDOs: <a class="wiki_link" href="/14edo">14</a>, <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/45edo">45</a>, <a class="wiki_link" href="/200edo">200</a><br />

~~<a class="wiki_link" href="/Badness">Badness</a>: 0.0568<br />~~

~~<br />~~

~~<h1 id="toc79"><a name="Liese"></a>Liese</h1>~~

~~<span style="display: block; text-align: right;"><a class="wiki_link" href="http://xenharmonie.wikispaces.com/Liese">Deutsch</a><br />~~

~~</span><br />~~

~~<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 686/675<br />~~

~~<br />~~

Liese, with wedgie &lt;&lt;3 12 11 12 9 -8||, splits the twelfth interval of 3/1 into three generators of 10/7, using the comma 1029/1000. It also tempers out 686/675, the senga. <a class="wiki_link" href="/74edo">74edo</a> makes for a good liese tuning, though <a class="wiki_link" href="/19edo">19edo</a> can be used. The tuning is well-supplied with MOS: 7, 9, 11, 13, 15, 17, 19, 36, 55.<br />

~~<br />~~

~~7 and 9 limit minimax 1/4 comma<br />~~

~~[|1 0 0 0&gt;, |1 0 1/4 0&gt;, |0 0 1 0&gt;, |2/3 0 11/12 0&gt;]<br />~~

~~<a class="wiki_link" href="/Eigenmonzo">Eigenmonzo</a>s: 2, 5<br />~~

~~<br />~~

~~<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~10/7 = 632.406<br />~~

~~Mapping generator: ~10/7<br />~~

~~<br />~~

~~Algebraic generator: Radix, the real root of x^5-2x^4+2x^3-2x^2+2x-2, also a root of x^6-x^5-2. The recurrence converges.<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 -3|, &lt;0 3 12 11|]<br />~~

~~<a class="wiki_link" href="/Generator">Generator</a>s: 2, 10/7<br />~~

EDOs: <a class="wiki_link" href="/17edo">17</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/55edo">55</a>, <a class="wiki_link" href="/74edo">74</a><br />

~~<a class="wiki_link" href="/Badness">Badness</a>: 0.0467<br />~~

~~<br />~~

~~<h2 id="toc80"><a name="Liese-Liesel"></a>Liesel</h2>~~

~~Commas: 56/55, 81/80, 540/539<br />~~

~~<br />~~

~~POTE generator: ~10/7 = 633.073<br />~~

~~Mapping generator: ~10/7<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 -3 4|, &lt;0 3 12 11 -1|]<br />~~

~~EDOs: 17c, 19, 36, 91ce<br />~~

~~Badness: 0.0407<br />~~

~~<br />~~

~~<h2 id="toc81"><a name="Liese-13-limit"></a>13-limit</h2>~~

~~Liesel is a very natural 13-limit tuning, given the generator is so near 13/9.<br />~~

~~<br />~~

~~Commas: 56/55, 78/77, 81/80, 91/90<br />~~

~~<br />~~

~~POTE generator: ~10/7 = ~13/9 = 633.042<br />~~

~~Mapping generator: ~10/7<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 -3 4 0|, &lt;0 3 12 11 -1 7|]<br />~~

~~EDOs: 17c, 19, 36, 91cef<br />~~

~~Badness: 0.0273<br />~~

~~<br />~~

~~<h2 id="toc82"><a name="Liese-Elisa"></a>Elisa</h2>~~

~~Commas: 77/75, 81/80, 99/98<br />~~

~~<br />~~

~~POTE generator: ~10/7 = 633.061<br />~~

~~Mapping generator: ~10/7<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 -3 -5|, &lt;0 3 12 11 16|]<br />~~

~~EDOs: 19e, 36e<br />~~

~~Badness: 0.0416<br />~~

~~<br />~~

~~<h2 id="toc83"><a name="Liese-Lisa"></a>Lisa</h2>~~

~~Commas: 45/44, 81/80, 343/330<br />~~

~~<br />~~

~~POTE generator: ~10/7 = 631.370<br />~~

~~Mapping generator: ~10/7<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 -3 -6|, &lt;0 3 12 11 18|]<br />~~

~~EDOs: 19<br />~~

~~Badness: 0.0548<br />~~

~~<br />~~

~~<h2 id="toc84"><a name="Liese-13-limit"></a>13-limit</h2>~~

~~Commas: 45/44, 81/80, 91/88, 147/143<br />~~

~~<br />~~

~~POTE generator: ~10/7 = 631.221<br />~~

~~Mapping generator: ~10/7<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 -3 -6 0|, &lt;0 3 12 11 18 7|]<br />~~

~~EDOs: 19<br />~~

~~Badness: 0.0361<br />~~

~~<br />~~

~~<h1 id="toc85"><a name="Jerome"></a>Jerome</h1>~~

Jerome is related to <a class="wiki_link" href="/20ed5">Hieronymus' tuning</a>; 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.<br />

~~<br />~~

~~Commas: 81/80, 17280/16807<br />~~

~~<br />~~

~~POTE generator: ~54/49 = 139.343<br />~~

~~Mapping generator: ~54/49<br />~~

~~<br />~~

~~Map: [&lt;1 1 0 2|, &lt;0 5 20 7|]<br />~~

~~Wedgie: &lt;&lt;5 30 7 20 -3 -40||<br />~~

~~EDOs: 8, 9, 17, 26, 43, 112<br />~~

~~Badness: 0.1087<br />~~

~~<br />~~

~~<h2 id="toc86"><a name="Jerome-11-limit"></a>11-limit</h2>~~

~~Commas: 81/80, 99/98, 864/847<br />~~

~~<br />~~

~~POTE generator: ~12/11 = 139.428<br />~~

~~Mapping generator: ~12/11<br />~~

~~<br />~~

~~Map: [&lt;1 1 0 2 3|, &lt;0 5 20 7 4|]<br />~~

~~EDOs: 8, 9, 17, 26, 43, 241<br />~~

~~Badness: 0.0479<br />~~

~~<br />~~

~~<h2 id="toc87"><a name="Jerome-13-limit"></a>13-limit</h2>~~

~~Commas: 77/78, 81/80, 99/98, 144/143<br />~~

~~<br />~~

~~POTE generator: ~13/12 = 139.387<br />~~

~~Mapping generator: ~12/11<br />~~

~~<br />~~

~~Map: [&lt;1 1 0 2 3 3|, &lt;0 5 20 7 4 6|]<br />~~

~~EDOs: 8, 9, 17, 26, 43, 155, 198<br />~~

~~Badness: 0.0293<br />~~

~~<br />~~

~~<h2 id="toc88"><a name="Jerome-17-limit"></a>17-limit</h2>~~

~~Commas: 78/77, 81/80, 99/98, 144/143, 189/187<br />~~

~~<br />~~

~~POTE generator: ~13/12 = 139.362<br />~~

~~Mapping generator: ~12/11<br />~~

~~<br />~~

~~Map: [&lt;1 1 0 2 3 3 2|, &lt;0 5 20 7 4 6 18|]<br />~~

~~EDOs: 8, 9, 17, 26, 43, 155<br />~~

~~Badness: 0.0209<br />~~

~~<br />~~

~~<h1 id="toc89"><a name="Meanmag"></a>Meanmag</h1>~~

~~Commas: 81/80, 3125/3072<br />~~

~~<br />~~

~~POTE generator: ~8/7 = 238.396<br />~~

~~Mapping generator: ~7<br />~~

~~<br />~~

~~Map: [&lt;19 30 44 0|, &lt;0 0 0 1|]<br />~~

~~Wedgie: &lt;&lt;0 0 19 0 30 44||<br />~~

~~EDOs: 19, 57, 76, 171bcd<br />~~

~~Badness: 0.0770<br />~~

~~<br />~~

~~<h1 id="toc90"><a name="Undevigintone"></a>Undevigintone</h1>~~

~~Commas: 49/48, 81/80, 126/125<br />~~

~~<br />~~

~~POTE generator: ~11/8 = 538.047<br />~~

~~Mapping generator: ~11<br />~~

~~<br />~~

~~Map: [&lt;19 30 44 53 0|, &lt;0 0 0 0 1|]<br />~~

~~EDOs: 19, 38d<br />~~

~~Badness: 0.0364<br />~~

~~<br />~~

~~<h2 id="toc91"><a name="Undevigintone-13-limit"></a>13-limit</h2>~~

~~Commas: 49/48, 65/64, 81/80, 126/125<br />~~

~~<br />~~

~~POTE generator: ~11/8 = 537.061<br />~~

~~<br />~~

~~Map: [&lt;19 30 44 53 0 70|, &lt;0 0 0 0 1 0|]<br />~~

~~EDOs: 19, 38d<br />~~

~~Badness: 0.0229</body></html></pre></div>~~

@@ Line 1: / Line 1: @@
-<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:hstraub|hstraub]] and made on <tt>2017-07-11 09:16:01 UTC</tt>.<br>
+[[:de:mitteltönig Deutsch]]</span>
-: The original revision id was <tt>615523693</tt>.<br>
-: The revision comment was: <tt></tt><br>
+The [[5-limit|5-limit]] parent [[Comma|comma]] of the [[Meantone|meantone]] family is the Didymus or [http://en.wikipedia.org/wiki/Syntonic_comma syntonic comma], 81/80. This is the one they all temper out. The [[Monzos_and_Interval_Space|monzo]] for 81/80 goes |-4 4 -1&gt;, 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 revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
-<h4>Original Wikitext content:</h4>
+[[POTE_tuning|POTE generator]]: ~3/2 = 696.239
-<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">&lt;span style="display: block; text-align: right;"&gt;[[toc]]
-[[xenharmonie/mitteltönig|Deutsch]]
-&lt;/span&gt;
-The [[5-limit]] parent [[Comma|comma]] of the [[meantone]] family is the Didymus or [[http://en.wikipedia.org/wiki/Syntonic_comma|syntonic comma]], 81/80. This is the one they all temper out. The [[Monzos and Interval Space|monzo]] for 81/80 goes |-4 4 -1&gt;, 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.
-[[POTE tuning|POTE generator]]: ~3/2 = 696.239
 Mapping generator: ~3
-[[Tuning Ranges of Regular Temperaments|valid range]]: [685.714, 720.000] (7 to 5)
+[[Tuning_Ranges_of_Regular_Temperaments|valid range]]: [685.714, 720.000] (7 to 5)
 nice range: [694.786, 701.955] (1/3 comma to Pythagorean)
 strict range: [694.786, 701.955]
-[[Map]]: [&lt;1 0 -4|, &lt;0 1 4|]
+[[Map|Map]]: [&lt;1 0 -4|, &lt;0 1 4|]
 EDOs (patent val edo list is complete): [[5edo|5]], [[7edo|7]], [[12edo|12]], [[19edo|19]], [[24edo|24]], [[26edo|26]], [[31edo|31]], [[36edo|36]], [[38edo|38]], [[43edo|43]], [[45edo|45]], [[50edo|50]], [[55edo|55]], [[57edo|57]], [[62edo|62]], [[67edo|67]], [[69edo|69]], [[74edo|74]], [[76edo|76]], [[81edo|81]], [[86edo|86]], [[88edo|88]], [[93edo|93]], [[98edo|98]], [[100edo|100]], [[105edo|105]], [[117edo|117]], [[129edo|129]], [[212edo|212b]]
-[[Badness]]: 0.00736
-==Seven limit children==
+[[Badness|Badness]]: 0.00736
-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;].
-=Septimal meantone=
+==Seven limit children==
-&lt;span style="display: block; text-align: right;"&gt;[[xenharmonie/septimal-mitteltönig|Deutsch]]
+The [[7-limit|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;].
-&lt;/span&gt;
-[[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|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|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.
+=Septimal meantone=
+<span style="display: block; text-align: right;">[[:de:septimal-mitteltönig Deutsch]]</span>
-[[Comma]]s: 81/80, 126/125
+[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|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|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|31edo]] is a good tuning for it.
+[[Comma|Comma]]s: 81/80, 126/125
+and [[9-limit|9-limit]] minimax
-and [[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;]
-[[Eigenmonzo]]s: 2, 5
-[[Tuning Ranges of Regular Temperaments|valid range]]: [694.737, 700.000] (19 to 12)
+[[Eigenmonzo|Eigenmonzo]]s: 2, 5
+[[Tuning_Ranges_of_Regular_Temperaments|valid range]]: [694.737, 700.000] (19 to 12)
 nice range: [694.786, 701.955]
 strict range: [694.786, 700.000]
-[[POTE tuning|POTE generator]]: 696.495
+[[POTE_tuning|POTE generator]]: 696.495
 Mapping generator: ~3
 Algebraic generator: Cybozem, the real root of 15x^3-10x^2-18, which comes to 503.4257 cents. The recurrence converges quickly.
-[[Map]]: [&lt;1 0 -4 -13|, &lt;0 1 4 10|]
+[[Map|Map]]: [&lt;1 0 -4 -13|, &lt;0 1 4 10|]
-[[Generator]]s: 2, 3
-[[Wedgie]]: &lt;&lt;1 4 10 4 13 12||
+[[generator|Generator]]s: 2, 3
+[[wedgie|Wedgie]]: &lt;&lt;1 4 10 4 13 12||
 EDOs: [[12edo|12]], [[19edo|19]], [[31edo|31]], [[81edo|81]], [[143edo|143b]]
-[[Badness]]: 0.0137
-==Bimeantone==
+[[Badness|Badness]]: 0.0137
+==Bimeantone==
 Commas: 81/80, 126/125, 245/242
-[[POTE tuning|POTE generator]]: ~3/2 = 696.016
+[[POTE_tuning|POTE generator]]: ~3/2 = 696.016
 Map: [&lt;2 0 -8 -26 -31|, &lt;0 1 4 10 12|]
 EDOs: 12, 38d, 50
 Badness: 0.0381
 ===13-limit===
 Commas: 81/80, 105/104, 126/125, 245/242
-[[POTE tuning|POTE generator]]: ~3/2 = 695.836
+[[POTE_tuning|POTE generator]]: ~3/2 = 695.836
 Map: [&lt;2 0 -8 -26 -31 -40|, &lt;0 1 4 10 12 15|]
 EDOs: 12f, 50
 Badness: 0.0288
 ==Unidecimal meantone aka Huygens==
-See also [[Meantone vs meanpop]]
+See also [[Meantone_vs_meanpop|Meantone vs meanpop]]
-[[Comma]]s: 81/80, 126/125, 99/98
+[[Comma|Comma]]s: 81/80, 126/125, 99/98
+[[11-limit|11-limit]] minimax
-[[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;,
 |21/8 -5/4 0 0 5/8&gt;, |25/8 -9/4 0 0 9/8&gt;]
-[[Eigenmonzo]]s: 2, 11/9
+[[Eigenmonzo|Eigenmonzo]]s: 2, 11/9
 valid range: [696.774, 700.000] (31 to 12)
 nice range: [691.202, 701.955]
 strict range: [696.774, 700.000]
-[[POTE tuning|POTE generator]]: 696.967
+[[POTE_tuning|POTE generator]]: 696.967
 Mapping generator: ~3
-[[Algebraic generator]]: Traverse, the positive real root of x^4+2x-13, or 696.9529 cents.
+[[Algebraic_generator|Algebraic generator]]: Traverse, the positive real root of x^4+2x-13, or 696.9529 cents.
+[[Map|Map]]: [&lt;1 0 -4 -13 -25|, &lt;0 1 4 10 18|]
+[[generator|Generator]]s: 2, 3
-[[Map]]: [&lt;1 0 -4 -13 -25|, &lt;0 1 4 10 18|]
-[[Generator]]s: 2, 3
 EDOs: [[7edo|7]], [[12edo|12]], [[31edo|31]], [[105edo|105]], [[198edo|198be]]
-[[Badness]]: 0.0170
-[[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]]
+[[Badness|Badness]]: 0.0170
-===Tridecimal meantone===
+[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]
-[[Comma]]s: 66/65, 81/80, 99/98, 105/104
+===Tridecimal meantone===
+[[Comma|Comma]]s: 66/65, 81/80, 99/98, 105/104
 valid range: 697.674 (43)
 nice range: [691.202, 701.955]
 strict range: 697.674
-[[POTE tuning|POTE generator]]: ~3/2 = 696.642
+[[POTE_tuning|POTE generator]]: ~3/2 = 696.642
 Mapping generator: ~3
 Map: [&lt;1 0 -4 -13 -25 -20|, &lt;0 1 4 10 18 15|]
 EDOs: [[12edo|12]], [[19edo|19]], [[31edo|31]], [[267edo|267]], [[298edo|298]]
-[[Badness]]: 0.0180
-===Grosstone===
+[[Badness|Badness]]: 0.0180
+===Grosstone===
 Commas: 81/80, 99/98, 126/125, 144/143
 POTE generator: ~3/2 = 697.264
 Mapping generator: ~3
 Map: [&lt;1 0 -4 -13 -25 29|, &lt;0 1 4 10 18 -16|]
 EDOs: 12, 31, 43, 74
 Badness: 0.0259
 ===Meridetone===
 Commas: 78/77, 81/80, 99/98, 126/125
 POTE generator: ~3/2 = 697.529
 Mapping generator: ~3
 Map: [&lt;1 0 -4 -13 -25 -39|, &lt;0 1 4 10 18 27|]
 EDOs: 43, 117df, 160bdf, 203bcdef
 Badness: 0.0264
 ===Hemimeantone===
 Commas: 81/80, 99/98, 126/125, 169/168
 POTE generator: ~52/45 = 250.304
 Mapping generator: ~26/15
 Map: [&lt;1 0 -4 -13 -25 -5|, &lt;0 2 8 20 36 11|]
 EDOs: 43, 62, 167bef, 229bef
 Badness: 0.0314
 ==Meanpop==
-See also [[Meantone vs meanpop]]
+See also [[Meantone_vs_meanpop|Meantone vs meanpop]]
-[[Comma]]s: 81/80, 126/125, 385/384
+[[Comma|Comma]]s: 81/80, 126/125, 385/384
+[[11-limit|11-limit]] [[minimax|minimax]] 1/4 comma
-[[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;,
 |-3 0 5/2 0 0&gt;, |11 0 -13/4 0 0&gt;]
-[[Eigenmonzo]]s: 2, 5
+[[Eigenmonzo|Eigenmonzo]]s: 2, 5
 valid range: [694.737, 696.774] (19 to 31)
 nice range: [691.202, 701.955]
 strict range: [694.737, 696.774]
-[[POTE tuning|POTE generator]]: 696.434
+[[POTE_tuning|POTE generator]]: 696.434
 Mapping generator: ~3
-[[Algebraic generator]]: Cybozem; or else Radieubiz, the real root of 3x^3+6x-19. Unlike Cybozem, the recurrence for Radieubiz does not converge.
+[[Algebraic_generator|Algebraic generator]]: Cybozem; or else Radieubiz, the real root of 3x^3+6x-19. Unlike Cybozem, the recurrence for Radieubiz does not converge.
-[[@http://soonlabel.com/xenharmonic/archives/607|Scott Joplin's "The Entertainer" tuned into meanpop]]
+[http://soonlabel.com/xenharmonic/archives/607 Scott Joplin's "The Entertainer" tuned into meanpop]
 Map: [&lt;1 0 -4 -13 24|, &lt;0 1 4 10 -13|]
-[[Generator]]s: 2, 3
+[[generator|Generator]]s: 2, 3
 EDOs: [[12edo|12]], [[19edo|19]], [[31edo|31]], [[81edo|81]], [[112edo|112]]
-[[Badness]]: 0.0215
-[[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]]
+[[Badness|Badness]]: 0.0215
-===13-limit Meanpop===
+[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]
-[[Comma]]s: 81/80, 105/104, 144/143, 196/195
+===13-limit Meanpop===
+[[Comma|Comma]]s: 81/80, 105/104, 144/143, 196/195
 valid range: [694.737, 696.774] (19 to 31)
 nice range: [691.202, 701.955]
 strict range: [694.737, 696.774]
 POTE generator: ~3/2 = 696.211
 Mapping generator: ~3
 Map: [&lt;1 0 -4 -13 24 -20|, &lt;0 1 4 10 -13 15|]
 EDOS: [[19edo|19]], [[31edo|31]], [[50edo|50]], [[81edo|81]], [[131edo|131bd]], [[212edo|212bdf]]
-[[Badness]]: 0.0209
-===Meanplop===
+[[Badness|Badness]]: 0.0209
+===Meanplop===
 Commas: 65/64, 78/77, 81/80, 91/90
 POTE generator: ~3/2 = 696.202
 Mapping generator: ~3
 Map: [&lt;1 0 -4 -13 24 10|, &lt;0 1 4 10 -13 -4|]
 EDOs: 12e, 19, 31f, 50f
 Badness: 0.0277
 ==Meanenneadecal==
-[[Comma]]s: 45/44, 56/55, 81/80
+[[Comma|Comma]]s: 45/44, 56/55, 81/80
+[[POTE_tuning|POTE generator]]: ~3/2 = 696.250
-[[POTE tuning|POTE generator]]: ~3/2 = 696.250
 Mapping generator: ~3
 Map: [&lt;1 0 -4 -13 -6|, &lt;0 1 4 10 6|]
 EDOs: [[7edo|7]], [[12edo|12]], [[19edo|19]], [[31edo|31e]], [[50edo|50e]]
-[[Badness]]: 0.0214
-===13-limit===
+[[Badness|Badness]]: 0.0214
-[[Comma]]s: 45/44, 56/55, 78/77, 81/80
+===13-limit===
+[[Comma|Comma]]s: 45/44, 56/55, 78/77, 81/80
+[[POTE_tuning|POTE generator]]: ~3/2 = 696.146
-[[POTE tuning|POTE generator]]: ~3/2 = 696.146
 Mapping generator: ~3
 Map: [&lt;1 0 -4 -13 -6 -20|, &lt;0 1 4 10 6 15|]
 EDOs: [[19edo|19]], [[31edo|31e]], [[50edo|50e]]]
-[[Badness]]: 0.0212
-===Vincenzo===
+[[Badness|Badness]]: 0.0212
+===Vincenzo===
 Commas: 81/80 126/125 45/44 65/64 256/255 153/152 23/22
 POTE generator: ~3/2
 Mapping generator: ~3
 Map: [&lt;1 0 -4 -13 ... |, &lt;0 1 4 10 6 -4 -5 -3 -6|]
 EDOs: 12
 Badness:
 ==Meanundeci==
 Commas: 33/32, 55/54, 77/75
 POTE generator: ~3/2 = 694.689
 Mapping generator: ~3
 Map: [&lt;1 0 -4 -13 5|, &lt;0 1 4 10 -1|]
 EDOs: 12e, 19e
 Badness: 0.0315
 ===13-limit===
 Commas: 33/32, 55/54, 77/75, 729/728
 POTE generator: ~3/2 = 694.764
 Mapping generator: ~3
 Map: [&lt;1 0 -4 -13 5 10|, &lt;0 1 4 10 -1 -4|]
 EDOs: 12e, 19e
 Badness: 0.0263
 ==Meanundec==
 Commas: 27/26, 40/39, 45/44, 56/55
 POTE generator: ~3/2 = 697.254
 Mapping generator: ~3
 Map: [&lt;1 0 -4 -13 -6 -1|, &lt;0 1 4 10 6 3|]
 EDOS: 12f, 19f, 31ef
 Badness: 0.0242
 =Flattone=
-[[Comma]]s: 81/80, 525/512
+[[Comma|Comma]]s: 81/80, 525/512
-The [[wedgie]] for flattone is &lt;&lt;1 4 -9 4 -17 -32||, which tells us among other things that 9 generator steps of 4/3 get to the interval class for 7, meaning that [[7_4|7/4]] is a diminished seventh interval. Other intervals are [[7_6|7/6]], a diminished third, and [[7_5|7/5]], a doubly diminshed fifth. Good tunings for flattone are [[26edo]], [[45edo]] and [[64edo]].
+The [[wedgie|wedgie]] for flattone is &lt;&lt;1 4 -9 4 -17 -32||, which tells us among other things that 9 generator steps of 4/3 get to the interval class for 7, meaning that [[7/4|7/4]] is a diminished seventh interval. Other intervals are [[7/6|7/6]], a diminished third, and [[7/5|7/5]], a doubly diminshed fifth. Good tunings for flattone are [[26edo|26edo]], [[45edo|45edo]] and [[64edo|64edo]].
+[[7-limit|7-limit]] minimax
-[[7-limit]] minimax
 [|1 0 0 0&gt;, |21/13 0 1/13 -1/13&gt;,
 |32/13 0 4/13 -4/13&gt;, |32/13 0 -9/13 9/13&gt;]
-[[Eigenmonzo]]s: 2, 7/5
-[[9-limit]] minimax
+[[Eigenmonzo|Eigenmonzo]]s: 2, 7/5
+[[9-limit|9-limit]] minimax
 [|1 0 0 0&gt;, |17/11 2/11 0 -1/11&gt;,
 |24/11 8/11 0 -4/11&gt;, |34/11 -18/11 0 9/11&gt;]
-[[Eigenmonzo]]s: 2, 9/7
+[[Eigenmonzo|Eigenmonzo]]s: 2, 9/7
 valid range: [692.308, 694.737] (26 to 19)
 nice range: [692.353, 701.955]
 strict range: [692.353, 694.737]
-[[POTE tuning|POTE generator]]: 693.779
+[[POTE_tuning|POTE generator]]: 693.779
 Mapping generator: ~3
@@ Line 276: / Line 353: @@
 Map: [&lt;1 0 -4 17|, &lt;0 1 4 -9|]
-[[Wedgie]]: &lt;&lt;1 4 -9 4 -17 -32||
-[[Generator]]s: 2, 3
+[[wedgie|Wedgie]]: &lt;&lt;1 4 -9 4 -17 -32||
+[[generator|Generator]]s: 2, 3
 EDOs: [[7edo|7]], [[19edo|19]], [[45edo|45]], [[64edo|64]]
-[[Badness]]: 0.0386
-==11-limit==
+[[Badness|Badness]]: 0.0386
+==11-limit==
 Commas: 45/44, 81/80, 385/384
 valid range: [692.308, 694.737] (26 to 19)
 nice range: [682.502, 701.955]
 strict range: [692.308, 694.737]
 POTE generator: ~3/2 = 693.126
 Mapping generator: ~3
 Map: [&lt;1 0 -4 17 -6|, &lt;0 1 4 -9 6|]
 EDOs: 7, 19, 26, 45, 71bc, 116bcde
 Badness: 0.0338
 ==13-limit==
 /44, 65/64, 78/77, 81/80
 valid range: [692.308, 694.737] (26 to 19)
 nice range: [682.502, 701.955]
 strict range: [692.308, 694.737]
 POTE generator: ~3/2 = 693.058
 Mapping generator: ~3
 Map: [&lt;1 0 -4 17 -6 10|, &lt;0 1 4 -9 6 -4|]
 EDOs: 7, 19, 26, 45f, 71bcf, 116bcdef
 Badness: 0.0223
 =Dominant=
-[[Comma]]s: 36/35, 64/63
+[[Comma|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|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|12edo]], but it also works well with the Pythagorean tuning of pure [[3/2|3/2]] fifths, and with [[29edo|29edo]], [[41edo|41edo]], or [[53edo|53edo]].
 valid range: [700.000, 720.000] (12 to 5)
 nice range: [694.786, 715.587]
 strict range: [700.000, 715.587]
-[[POTE tuning|POTE generator]]: 701.573
+[[POTE_tuning|POTE generator]]: 701.573
 Mapping generator: ~3
 Map: [&lt;1 0 -4 6|, &lt;0 1 4 -2|]
-[[Wedgie]]: &lt;&lt;1 4 -2 4 -6 -16||
+[[wedgie|Wedgie]]: &lt;&lt;1 4 -2 4 -6 -16||
 EDOs: [[5edo|5]], [[7edo|7]], [[12edo|12]], [[53edo|53]], [[65edo|65]]
-[[Badness]]: 0.0207
-==11-limit==
+[[Badness|Badness]]: 0.0207
+==11-limit==
 Commas: 36/35, 64/63, 56/55
 valid range: [700.000, 705.882] (12 to 17)
 nice range: [691.202, 715.587]
 strict range: [700.000, 705.882]
 POTE generator: ~3/2 = 703.254
 Mapping generator: ~3
 Map: [&lt;1 0 -4 6 13|, &lt;0 1 4 -2 -6|]
 EDOs: 5, 12, 17c, 29cde
 Badness: 0.0242
 ==13-limit==
 Commas: 36/35, 56/55, 64/63, 66/65
 valid range: 705.882 (17)
 nice range: [691.202, 715.587]
 strict range:705.882
@@ Line 350: / Line 454: @@
 Map: [&lt;1 0 -4 6 13 18|, &lt;0 1 4 -2 -6 -9|]
 EDOs: 12f, 17c, 29cdef
 Badness: 0.0241
 ==Dominion==
 Commas: 26/25, 36/35, 56/55, 64/63
@@ Line 359: / Line 465: @@
 Map: [&lt;1 0 -4 6 13 -9|, &lt;0 1 4 -2 -6 8|]
 EDOs: 5, 12, 17c, 46cde
 Badness: 0.0273
 ==Domineering==
 Commas: 36/35, 45/44, 64/63
 POTE generator: ~3/2 = 698.776
 Mapping generator: ~3
 Map: [&lt;1 0 -4 6 -6|, &lt;0 1 4 -2 6|]
 EDOs: 7, 12, 43de
 Badness: 0.0220
 ==Domination==
 Commas: 36/35, 64/63, 77/75
 POTE generator: ~3/2 = 705.004
 Mapping generator: ~3
 Map: [&lt;1 0 -4 6 -14|, &lt;0 1 4 -2 11|]
 EDOs: 17c, 46cd
 Badness: 0.0366
 ===13-limit===
 Commas: 26/25, 36/35, 64/63, 66/65
 POTE generator: ~3/2 = 705.496
 Mapping generator: ~3
 Map: [&lt;1 0 -4 6 -14 -9|, &lt;0 1 4 -2 11 8|]
 EDOs: 17c
 Badness: 0.0274
 ==Twelve==
 Commas: 81/80 64/63 45/44 65/64 256/255 153/152
 POTE generator: ~3/2 = 696.217
 Mapping generator: ~3
 Map: [&lt;1 0 -4 6 -6 10 12 9|, &lt;0 1 4 -2 6 -4 -5 -3|]
 EDOs: 7, 12, 19d, 31def
 Badness: 0.0204
 ==Arnold==
 Commas: 22/21, 33/32, 36/35
 POTE generator: ~3/2 = 698.491
 Mapping generator: ~3
 Map: [&lt;1 0 -4 6 5|, &lt;0 1 4 -2 -1|]
 EDOs: 5, 7, 12e
 Badness: 0.0261
 ==13-limit==
 Commas: 22/21, 27/26, 33/32, 40/39
 POTE generator: ~3/2 = 696.743
 Mapping generator: ~3
 Map: [&lt;1 0 -4 6 5 -1|, &lt;0 1 4 -2 -1 3|]
 EDOs: 5, 7, 12ef, 19def, 31def
 Badness: 0.0233
 ==Dominatrix==
 Commas: 27/26 36/35 45/44 64/63
 POTE generator: ~3/2 = 698.544
 Mapping generator: ~3
 Map: [&lt;1 0 -4 6 -6 -1|, &lt;0 1 4 -2 6 3|]
 EDOs: 7, 12f
 Badness: 0.0183
 =Sharptone=
-[[Comma]]s: 21/20, 28/27
+[[Comma|Comma]]s: 21/20, 28/27
-Sharptone, with a wedgie &lt;&lt;1 4 3 4 2 -4||, 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]] tuning does sharptone about as well as such a thing can be done.
+Sharptone, with a wedgie &lt;&lt;1 4 3 4 2 -4||, 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.
+[[POTE_tuning|POTE generator]]: 700.140
-[[POTE tuning|POTE generator]]: 700.140
 Mapping generator: ~3
 Map: [&lt;1 0 -4 -2|, &lt;0 1 4 3|]
-[[Wedgie]]: &lt;&lt;1 4 3 4 2 -4||
+[[wedgie|Wedgie]]: &lt;&lt;1 4 3 4 2 -4||
 EDOs: [[5edo|5]], [[12edo|12]]
-[[Badness]]: 0.0248
-=Meansept=
+[[Badness|Badness]]: 0.0248
+=Meansept=
 Commas: 15/14, 81/80
 POTE generator: ~3/2 = 682.895
 Mapping generator: ~3
 Map: [&lt;1 0 -4 -5|, &lt;0 1 4 5|]
 Wedgie: &lt;&lt;1 4 5 4 5 0||
 EDOs: 7
 Badness: 0.0453
 ==11-limit==
 Commas: 15/14, 22/21, 125/121
 POTE generator: ~3/2 = 685.234
 Mapping generator: ~3
 Map: [&lt;1 0 -4 -5 -6|, &lt;0 1 4 5 6|]
 EDOs: 7
 Badness: 0.0325
 =Supermean=
 Commas: 81/80, 672/625
@@ Line 472: / Line 612: @@
 Map: [&lt;1 0 -4 -21|, &lt;0 1 4 15|]
 EDOs: 17c, 46c
 Badness: 0.1342
 ==11-limit==
 Commas: 56/55, 81/80, 132/125
@@ Line 481: / Line 623: @@
 Map: [&lt;1 0 -4 -21 -14|, &lt;0 1 4 15 11|]
 EDOs: 17c, 46c
 Badness: 0.0633
 ==13-limit==
 Commas: 26/25, 56/55, 66/65, 81/80
@@ Line 490: / Line 634: @@
 Map: [&lt;1 0 -4 -21 -14 -9|, &lt;0 1 4 15 11 8|]
 EDOs: 17c, 46c
 =Injera=
-[[Comma]]s: 50/49, 81/80
+[[Comma|Comma]]s: 50/49, 81/80
-The wedgie for injera is &lt;&lt;2 8 8 8 7 -4||, which tells us it 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]], which is two parallel [[19edo]]s, is an excellent tuning for injera.
+The wedgie for injera is &lt;&lt;2 8 8 8 7 -4||, which tells us it 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|19edo]]s, is an excellent tuning for injera.
-[[http://tech.groups.yahoo.com/group/tuning-math/message/3091|Origin of the name]]
+[http://tech.groups.yahoo.com/group/tuning-math/message/3091 Origin of the name]
 valid range: [685.714, 700.000] (14c to 12)
 nice range: [688.957, 701.955]
 strict range: [688.957, 700.000]
-[[POTE tuning|POTE generator]]: 694.375
+[[POTE_tuning|POTE generator]]: 694.375
 Mapping generator: ~3
 Map: [&lt;2 0 -8 -7|, &lt;0 1 4 4|]
-[[Wedgie]]: &lt;&lt;2 8 8 8 7 -4||
+[[wedgie|Wedgie]]: &lt;&lt;2 8 8 8 7 -4||
 EDOs: [[12edo|12]], [[26edo|26]], [[38edo|38]], [[102edo|102bcd]], [[140edo|140bcd]], [[178edo|178bcd]]
-[[Badness]]: 0.0311
-[[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Two%20Pairs%20of%20Socks.mp3|Two Pairs of Socks]] (in [[26edo]]) by [[Igliashon Jones|Igliashon Calvin Jones-Coolidge]]
+[[Badness|Badness]]: 0.0311
-[[http://micro.soonlabel.com/gene_ward_smith/Others/Curley/Zach%20Curley%20-%20Injera%20Jam.mp3|Injera Jam]] (in [[26edo]]) by [[Zach Curley]]
-==11-limit==
+[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Two%20Pairs%20of%20Socks.mp3 Two Pairs of Socks] (in [[26edo|26edo]]) by [[Igliashon_Jones|Igliashon Calvin Jones-Coolidge]]
+[http://micro.soonlabel.com/gene_ward_smith/Others/Curley/Zach%20Curley%20-%20Injera%20Jam.mp3 Injera Jam] (in [[26edo|26edo]]) by [[Zach_Curley|Zach Curley]]
+==11-limit==
 Commas: 45/44, 50/49, 81/80
 valid range: [685.714, 700.000] (14c to 12)
 nice range: [682.458, 701.955]
 strict range: [685.714, 700.000]
 POTE generator: ~3/2 = 692.840
 Mapping generator: ~3
 Map: [&lt;2 0 -8 -7 -12|, &lt;0 1 4 4 6|]
 EDOs: 12, 14c, 26. 90bce, 116bce
 Badness: 0.0231
 ==13-limit==
 Commas: 45/44, 50/49, 81/80, 78/77
 valid range: 692.308 (26)
 nice range: [682.458, 701.955]
 strict range: 692.308 (26)
 POTE generator: ~3/2 = 692.673
 Mapping generator: ~3
 Map: [&lt;2 0 -8 -7 -12 -21|, &lt;0 1 4 4 6 9|]
 EDOs: 26, 104bcf
 Badness: 0.0216
 ==Enjera==
 Commas: 27/26, 40/39, 45/44, 99/98
 POTE generator: ~3/2 = 694.121
 Mapping generator: ~3
 Map: [&lt;2 0 -8 -7 -12 -2|, &lt;0 1 4 4 6 3|]
 EDOs: 12f, 26f, 38ef
 Badness: 0.0265
 ==Injerous==
 Commas: 33/32, 50/49, 55/54
 POTE generator: ~3/2 = 690.548
 Mapping generator: ~3
 Map: [&lt;2 0 -8 -7 10|, &lt;0 1 4 4 -1|]
 EDOs: 12e, 14c, 26e, 40ce
 Badness: 0.0386
 ==Lahoh==
 Commas: 50/49, 56/55, 81/77
 POTE generator: ~3/2 = 699.001
 Mapping generator: ~3
 Map: [&lt;2 0 -8 -7 7|, &lt;0 1 4 4 0|]
 EDOs: 12
 Badness: 0.0431
 =Godzilla=
-&lt;span style="display: block; text-align: right;"&gt;[[xenharmonie/Semiphor, Semaphor, Godzilla|Deutsch]]
+<span style="display: block; text-align: right;">[[:de:Semiphor,_Semaphor,_Godzilla Deutsch]]</span>
-&lt;/span&gt;
-Main article: [[Semaphore and Godzilla]]
+Main article: [[Semaphore_and_Godzilla|Semaphore and Godzilla]]
-[[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.
+[[Comma|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|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.
 valid range: [240.000, 257.143] (5 to 14c)
 nice range: [231.174, 266.871]
 strict range: [240.000, 257.143]
-[[POTE tuning|POTE generator]]: ~8/7 = 252.635
+[[POTE_tuning|POTE generator]]: ~8/7 = 252.635
 Mapping generator: ~7/4
 Map: [&lt;1 0 -4 2|, &lt;0 2 8 1|]
-[[Wedgie]]: &lt;&lt;2 8 1 8 -4 -20||
+[[wedgie|Wedgie]]: &lt;&lt;2 8 1 8 -4 -20||
 EDOs: [[5edo|5]], [[9edo|9c]], [[14edo|14c]], [[19edo|19]], [[62edo|62d]], [[81edo|81d]], 143bd
-[[Badness]]: 0.0267
-==11-limit==
+[[Badness|Badness]]: 0.0267
+==11-limit==
 Commas: 45/44, 49/48, 81/80
 valid range: [252.632, 257.143] (19 to 14c)
 nice range: [231.174, 266.871]
 strict range: [252.632, 257.143]
 POTE generator: ~8/7 = 254.027
 Mapping generator: ~7/4
 Map: [&lt;1 0 -4 2 -6|, &lt;0 2 8 1 12|]
 EDOs: 14c, 19, 33cd, 52cd
 Badness: 0.0290
 ==13-limit==
 Commas: 45/44, 49/48, 78/77, 81/80
 valid range: 694.737 (19)
 nice range: [621.581, 737.652]
 strict range: 694.737
 POTE generator: ~8/7 = 253.603
 Mapping generator: ~7/4
 Map: [&lt;1 0 -4 2 -6 -5|, &lt;0 2 8 1 12 11|]
 EDOs: 14cf, 19, 33cdf, 52cdf
 Badness: 0.0225
 ==Semafour==
 Commas: 33/32, 49/48, 55/54
 POTE generator: ~8/7 = 254.042
 Mapping generator: ~7/4
 Map: [&lt;1 0 -4 2 5|, &lt;0 2 8 1 -2|]
 EDOs: 5, 14c, 19e, 33cde
 Badness: 0.0285
 ==Varan==
 Commas: 49/48, 77/75, 81/80
 POTE generator: ~8/7 = 251.079
 Mapping generator: ~7/4
 Map: [&lt;1 0 -4 2 -10|, &lt;0 2 8 1 17|]
 EDOs: 19e, 24, 43de
 Badness: 0.0396
 ===13-limit===
 Commas: 49/48, 66/65, 77/75, 81/80
 POTE generator: ~8/7 = 251.165
 Mapping generator: ~7/4
 Map: [&lt;1 0 -4 2 -10 -5|, &lt;0 2 8 1 17 11|]
 EDOs: 19e, 24, 43de
 Badness: 0.0257
 ==Baragon==
 Commas: 49/48, 56/55, 81/80
 POTE generator: ~8/7 = 251.173
 Mapping generator: ~7/4
 Map: [&lt;1 0 -4 2 9|, &lt;0 2 8 1 -7|]
 EDOs: 19, 24, 43d
 Badness: 0.0357
 ==Music==
-[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Bobro/GodzillaExample.mp3|Godzilla Example]] by [[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]]
+[http://tinyurl.com/4uyumk9 "Change is on the Wind"] in Godzilla[9] by [[Igliashon_Jones|Igliashon Jones]]
 =Mohajira=
-&lt;span style="display: block; text-align: right;"&gt;[[xenharmonie/Mohajira|Deutsch]]
+<span style="display: block; text-align: right;">[[:de:Mohajira Deutsch]]</span>
-&lt;/span&gt;
-[[Comma]]s: 81/80, 6144/6125
-Mohajira, with wedgie &lt;&lt;2 8 -11 8 -23 -48||, really makes more sense as an 11-limit temperament. It has a generator of a neutral third, two of which make up a fifth, and which can be taken to represent 128/105. Mohajira tempers out 6144/6125, the porwell comma. [[31edo]] makes for an excellent (7-limit) mohajira tuning, with generator 9/31. It has a 7-note MOS with three larger steps and four smaller ones, going sLsLsLs.
+[[Comma|Comma]]s: 81/80, 6144/6125
+Mohajira, with wedgie &lt;&lt;2 8 -11 8 -23 -48||, really makes more sense as an 11-limit temperament. It has a generator of a neutral third, two of which make up a fifth, and which can be taken to represent 128/105. Mohajira tempers out 6144/6125, the porwell comma. [[31edo|31edo]] makes for an excellent (7-limit) mohajira tuning, with generator 9/31. It has a 7-note MOS with three larger steps and four smaller ones, going sLsLsLs.
 Mohajira can also be thought of, intuitively, as "meantone with quarter tones"; as is the 3/2 generator subdivided in half, so is the 25/24 chromatic semitone divided into two equal ~33/32 quarter tones (in the 11-limit). Within this paradigm, mohajira is the temperament that splits the 3/2 into two equal 11/9's, that splits the 6/5 into two equal 11/10's, that maps four 3/2's to 5/1, and that maps the interval one quarter tone flat of 16/9 to 7/4.
-[[7-limit|7]] and [[9-limit]] minimax 1/4 comma
+[[7-limit|7]] and [[9-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;]
-[[Eigenmonzo]]s: 2, 5
-[[POTE tuning|POTE generator]]: ~128/105 = 348.415
+[[Eigenmonzo|Eigenmonzo]]s: 2, 5
+[[POTE_tuning|POTE generator]]: ~128/105 = 348.415
 Mapping generator: ~128/105
@@ Line 683: / Line 887: @@
 Map: [&lt;1 1 0 6|, &lt;0 2 8 -11|]
-[[Generator]]s: 2, 128/105
-[[Wedgie]]: &lt;&lt;2 8 -11 8 -23 -48||
+[[generator|Generator]]s: 2, 128/105
+[[wedgie|Wedgie]]: &lt;&lt;2 8 -11 8 -23 -48||
 EDOs: [[7edo|7]], [[24edo|24]], [[31edo|31]]
-[[Badness]]: 0.0557
-==11-limit==
+[[Badness|Badness]]: 0.0557
-[[Comma]]s: 81/80, 121/120, 176/175
+==11-limit==
+[[Comma|Comma]]s: 81/80, 121/120, 176/175
+[[11-limit|11-limit]] minimax 1/4 comma
-[[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;,
 |6 0 -11/8 0 0&gt;, |2 0 5/8 0 0&gt;]
-[[Eigenmonzo]]s: 2, 5
-[[POTE tuning|POTE generator]]: ~11/9 = 348.477
+[[Eigenmonzo|Eigenmonzo]]s: 2, 5
+[[POTE_tuning|POTE generator]]: ~11/9 = 348.477
 Mapping generator: ~11/9
 Map: [&lt;1 1 0 6 2|, &lt;0 2 8 -11 5|]
-[[Generator]]s: 2, 11/9
+[[generator|Generator]]s: 2, 11/9
 EDOs: [[7edo|7]], [[24edo|24]], [[31edo|31]]
-[[Badness]]: 0.0261
-==13-limit==
+[[Badness|Badness]]: 0.0261
+==13-limit==
 Commas: 81/80, 121/120, 105/104, 66/65
 POTE generator: ~11/9 = 348.558
 Mapping generator: ~11/9
 Map: [&lt;1 1 0 6 2 4|, &lt;0 2 8 -11 5 -1|]
 EDOs: 7, 24, 31, 117ef, 148bef
 Badness: 0.0234
 =Ptolemy=
 Commas: 81/80, 121/120, 525/512
@@ Line 720: / Line 937: @@
 Map: [&lt;1 1 0 8 2|, &lt;0 2 8 -18 5|]
 EDOs: 7, 38d, 45e, 83bcde
 Badness: 0.0588
 ==13-limit==
 Commas: 65/64, 81/80, 105/104, 121/120
@@ Line 729: / Line 948: @@
 Map: [&lt;1 1 0 8 2 6|, &lt;0 2 8 -18 5 -8|]
 EDOs: 7, 38df, 45ef, 83bcdef
 Badness: 0.0343
 =Maqamic=
-&lt;span style="display: block; text-align: right;"&gt;[[xenharmonie/maqamisch|Deutsch]]
+<span style="display: block; text-align: right;">[[:de:maqamisch Deutsch]]</span>
-&lt;/span&gt;
-Main article: [[Maqamic]]
+Main article: [[maqamic|Maqamic]]
-[[Comma]]s: 81/80, 36/35, 121/120
+[[Comma|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.
-[[POTE tuning|POTE generator]]: ~11/9 = 350.934
+[[POTE_tuning|POTE generator]]: ~11/9 = 350.934
 Mapping generator: ~11/9
 Map: [&lt;1 1 0 4 2|, &lt;0 2 8 -4 5|]
-[[Generator]]s: 2, 11/9
+[[generator|Generator]]s: 2, 11/9
 EDOs: [[7edo|7]], [[10edo|10c]], [[17edo|17c]], [[24edo|24d]], [[31edo|31d]]
 ==13-limit==
-[[Comma]]s: 81/80, 36/35, 121/120, 144/143
+[[Comma|Comma]]s: 81/80, 36/35, 121/120, 144/143
+[[POTE_tuning|POTE generator]]: ~11/9 = 350.816
-[[POTE tuning|POTE generator]]: ~11/9 = 350.816
 Mapping generator: ~11/9
 Map: [&lt;1 1 0 4 2 4|, &lt;0 2 8 -4 5 -1|]
 Generators: 2, 11/9
 EDOs: [[7edo|7]], [[10edo|10c]], [[17edo|17c]], [[24edo|24d]],[[31edo| 31d]]
 =Migration=
 Commas: 81/80, 121/120, 126/125
 POTE generator: ~11/9 = 348.182
 Mapping generator: ~11/9
 Map: [&lt;1 1 0 -3 2|, &lt;0 2 8 20 5|]
 EDOs: 31, 100de, 131bde, 162bde
 Badness: 0.0255
 =Mohamaq=
 Commas: 81/80, 392/375
 POTE generator: ~25/21 = 350.586
 Mapping generator: ~25/21
 Map: [&lt;1 1 0 -1|, &lt;0 2 8 13|]
 EDOs: 17c, 24, 65c, 89cd
 Badness: 0.0777
 ==11-limit==
 Commas: 56/55, 77/75, 243/242
 POTE generator: ~11/9 = 350.565
 Mapping generator: ~11/9
 Map: [&lt;1 1 0 -1 2|, &lt;0 2 8 13 5|]
 EDOs: 17c, 24, 65c, 89cd
 Badness: 0.0362
 ==13-limit==
 Commas: 56/55, 66/65, 77/75, 243/242
 POTE generator: ~11/9 = 350.745
 Mapping generator: ~11/9
 Map: [&lt;1 1 0 -1 2 4|, &lt;0 2 8 13 5 -1|]
 EDOs: 17c, 24, 41c, 65c
 Badness: 0.0287
 =Orphic=
 Commas: 81/80, 5898240/5764801
 POTE generator: ~7/6 = 275.794
 Mapping generator: ~343/288
 Map: [&lt;2 1 -4 4|, &lt;0 4 16 3|]
 Wedgie: &lt;&lt;8 32 6 32 -13 -76||
 EDOs: 26, 74, 174bd, 248bd
 Badness: 0.2588
 ==11-limit==
 Commas: 81/80, 99/98, 73728/73205
 POTE generator: ~7/6 = 275.762
 Mapping generator: ~77/64
 Map: [&lt;2 1 -4 4 8|, &lt;0 4 16 3 -2|]
 EDOs: 26, 48c, 74, 248bd, 322bd
 Badness: 0.1015
 ==13-limit==
 Commas: 81/80, 99/98, 144/143, 2200/2197
 POTE generator: ~7/6 = 275.774
 Mapping generator: ~63/52
 Map: [&lt;2 1 -4 4 8 2|, &lt;0 4 16 3 -2 10|]
 EDOs: 26, 48c, 74, 174bd, 248bd, 322bd
 Badness: 0.0535
 =Mothra=
-[[Comma]]s: 81/80, 1029/1024
+[[Comma|Comma]]s: 81/80, 1029/1024
+Mothra, with wedgie &lt;&lt;3 12 -1 12 -10 -36||, 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-limit, mothra is identical to [[Slendric|slendric]].
-Mothra, with wedgie &lt;&lt;3 12 -1 12 -10 -36||, 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]] 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-limit, mothra is identical to [[Slendric|slendric]].
 Note that mothra can also be called cynder in the 7-limit, which can be a little confusing sometimes.
-[[7-limit|7]] and [[9-limit]] minimax 1/4 comma
+[[7-limit|7]] and [[9-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;]
-[[Eigenmonzo]]s: 2, 5
-[[POTE tuning|POTE generator]]: ~8/7 = 232.193
+[[Eigenmonzo|Eigenmonzo]]s: 2, 5
+[[POTE_tuning|POTE generator]]: ~8/7 = 232.193
 Mapping generator: ~8/7
@@ Line 844: / Line 1,098: @@
 Map: [&lt;1 1 0 3|, &lt;0 3 12 -1|]
-[[Generator]]s: 2, 8/7
-[[Wedgie]]: &lt;&lt;3 12 -1 12 -10 -36||
+[[generator|Generator]]s: 2, 8/7
+[[wedgie|Wedgie]]: &lt;&lt;3 12 -1 12 -10 -36||
 EDOs: [[5edo|5]], [[26edo|26]], [[31edo|31]]
-[[Badness]]: 0.0371
-==11-limit==
+[[Badness|Badness]]: 0.0371
-[[Comma]]s: 81/80, 99/98, 385/384
+==11-limit==
+[[Comma|Comma]]s: 81/80, 99/98, 385/384
 POTE generator: ~8/7 = 232.031
 Mapping generator: ~8/7
 Map: [&lt;1 1 0 3 5|, &lt;0 3 12 -1 -8|]
 EDOs: [[5edo|5]], [[26edo|26]], [[31edo|31]], [[88edo|88]], [[150edo|150]], [[181edo|181]]
-[[Badness]]: 0.0256
-==13-limit==
+[[Badness|Badness]]: 0.0256
+==13-limit==
 Commas: 81/80, 99/98, 105/104, 144/143
 POTE generator: ~8/7 = 231.811
 Mapping generator: ~8/7
 Map: [&lt;1 1 0 3 5 1|, &lt;0 3 12 -1 -8 14|]
 EDOs: 5, 26, 31, 57, 88
 Badness: 0.0240
 ==Cynder==
 Commas: 45/44, 81/80, 1029/1024
 POTE generator: ~8/7 = 231.317
 Mapping generator: ~8/7
 Map: [&lt;1 1 0 3 0|, &lt;0 3 12 -1 18|]
 EDOs: 26, 57e, 83bce
 Badness: 0.0557
 ===13-limit===
 Commas: 45/44, 78/77, 81/80, 640/637
 POTE generator: ~8/7 = 231.293
 Mapping generator: ~8/7
 Map: [&lt;1 1 0 3 0 1|, &lt;0 3 12 -1 18 14|]
 EDOs: 26, 57e, 83bce
 Badness: 0.0341
 ==Mosura==
 Commas: 81/80, 176/175, 1029/1024
 POTE generator: ~8/7 = 232.419
 Mapping generator: ~8/7
 Map: [&lt;1 1 0 3 -1|, &lt;0 3 12 -1 23|]
 EDOs: 31, 129, 136b, 148be, 160be, 191bce, 222bce, 253bce
 Badness: 0.0313
 ===13-limit===
 Commas: 81/80, 144/143, 176/175, 1029/1024
 POTE generator: ~8/7 = 232.640
 Mapping generator: ~8/7
 Map: [&lt;1 1 0 3 -1 7|, &lt;0 3 12 -1 23 -17|]
 EDOs: 31, 67, 98
 Badness: 0.0369
 =Squares=
-[[Comma]]s: 81/80, 2401/2400
+[[Comma|Comma]]s: 81/80, 2401/2400
-Squares, with wedgie &lt;&lt;4 16 9 16 3 -24||, splits the interval of an eleventh, or 8/3, into four supermajor third ([[9_7|9/7]]) intervals, and uses it for a generator. [[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, with wedgie &lt;&lt;4 16 9 16 3 -24||, splits the interval of an eleventh, or 8/3, into four supermajor third ([[9/7|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.
 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;]
-[[Eigenmonzo]]s: 2, 5
-[[POTE tuning|POTE generator]]: ~9/7 = 425.942
+[[Eigenmonzo|Eigenmonzo]]s: 2, 5
+[[POTE_tuning|POTE generator]]: ~9/7 = 425.942
 Mapping generator: ~9/7
@@ Line 924: / Line 1,203: @@
 Map: [&lt;1 3 8 6|, &lt;0 -4 -16 -9|]
-[[Generator]]s: 2, 9/7
+[[generator|Generator]]s: 2, 9/7
 EDOs: [[14edo|14]], [[31edo|31]], [[262edo|262]], [[293edo|293]]
-[[Badness]]: 0.0460
+[[Badness|Badness]]: 0.0460
 Music:
-By [[Chris Vaisvil]]
-[[http://clones.soonlabel.com/public/micro/tuning-survey/daily20100603-squares8piano.mp3|Square 8]]
-==11-limit==
+By [[Chris_Vaisvil|Chris Vaisvil]]
+[http://clones.soonlabel.com/public/micro/tuning-survey/daily20100603-squares8piano.mp3 Square 8]
+==11-limit==
 Commas: 81/80, 99/98, 121/120
 POTE generator: ~9/7 = 425.957
 Mapping generator: ~9/7
 Map: [&lt;1 3 8 6 7|, &lt;0 -4 -16 -9 -10|]
 EDOs: [[5edo|5]], [[8edo|8]], [[11edo|11]], [[14edo|14]], [[17edo|17]], [[31edo|31]]
-[[Badness]]: 0.0216
-==13-limit==
+[[Badness|Badness]]: 0.0216
+==13-limit==
 Commas: 81/80, 99/98, 121/120, 66/65
 POTE generator: ~9/7 = 425.550
 Mapping generator: ~9/7
 Map: [&lt;1 3 8 6 7 3|, &lt;0 -4 -16 -9 -10 2|]
 EDOs: 17c, 31, 79cf, 110cef, 141cef
-[[Badness]]: 0.0255
-==Agora==
+[[Badness|Badness]]: 0.0255
+==Agora==
 Commas: 81/80, 99/98, 105/104, 121/120
 POTE generator: ~9/7 = 426.276
 Mapping generator: ~9/7
 Map: [&lt;1 3 8 6 7 14|, &lt;0 -4 -16 -9 -10 -29|]
 EDOs: 31, 45ef, 76e
 Badness: 0.0245
 =Cuboctahedra=
-==11-limit==
-[[Comma]]s: 81/80, 385/384, 1375/1372
+==11-limit==
+[[Comma|Comma]]s: 81/80, 385/384, 1375/1372
+[[POTE_tuning|POTE generator]]: ~9/7 = 425.993
-[[POTE tuning|POTE generator]]: ~9/7 = 425.993
 Mapping generator: ~9/7
 Map: [&lt;1 3 8 6 -4|, &lt;0 -4 -16 -9 21|]
 EDOs: [[14edo|14]], [[31edo|31]], [[45edo|45]], [[200edo|200]]
-[[Badness]]: 0.0568
-=Liese=
+[[Badness|Badness]]: 0.0568
-&lt;span style="display: block; text-align: right;"&gt;[[xenharmonie/Liese|Deutsch]]
-&lt;/span&gt;
+=Liese=
-[[Comma]]s: 81/80, 686/675
+<span style="display: block; text-align: right;">[[:de:Liese Deutsch]]</span>
+[[Comma|Comma]]s: 81/80, 686/675
-Liese, with wedgie &lt;&lt;3 12 11 12 9 -8||, splits the twelfth interval of 3/1 into three generators of 10/7, using the comma 1029/1000. It also tempers out 686/675, the senga. [[74edo]] makes for a good liese tuning, though [[19edo]] can be used. The tuning is well-supplied with MOS: 7, 9, 11, 13, 15, 17, 19, 36, 55.
+Liese, with wedgie &lt;&lt;3 12 11 12 9 -8||, splits the twelfth interval of 3/1 into three generators of 10/7, using the comma 1029/1000. It also tempers out 686/675, the senga. [[74edo|74edo]] makes for a good liese tuning, though [[19edo|19edo]] can be used. The tuning is well-supplied with MOS: 7, 9, 11, 13, 15, 17, 19, 36, 55.
 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;]
-[[Eigenmonzo]]s: 2, 5
-[[POTE tuning|POTE generator]]: ~10/7 = 632.406
+[[Eigenmonzo|Eigenmonzo]]s: 2, 5
+[[POTE_tuning|POTE generator]]: ~10/7 = 632.406
 Mapping generator: ~10/7
@@ Line 990: / Line 1,290: @@
 Map: [&lt;1 0 -4 -3|, &lt;0 3 12 11|]
-[[Generator]]s: 2, 10/7
+[[generator|Generator]]s: 2, 10/7
 EDOs: [[17edo|17]], [[19edo|19]], [[55edo|55]], [[74edo|74]]
-[[Badness]]: 0.0467
-==Liesel==
+[[Badness|Badness]]: 0.0467
+==Liesel==
 Commas: 56/55, 81/80, 540/539
 POTE generator: ~10/7 = 633.073
 Mapping generator: ~10/7
 Map: [&lt;1 0 -4 -3 4|, &lt;0 3 12 11 -1|]
 EDOs: 17c, 19, 36, 91ce
 Badness: 0.0407
 ==13-limit==
 Liesel is a very natural 13-limit tuning, given the generator is so near 13/9.
@@ Line 1,010: / Line 1,316: @@
 POTE generator: ~10/7 = ~13/9 = 633.042
 Mapping generator: ~10/7
 Map: [&lt;1 0 -4 -3 4 0|, &lt;0 3 12 11 -1 7|]
 EDOs: 17c, 19, 36, 91cef
 Badness: 0.0273
 ==Elisa==
 Commas: 77/75, 81/80, 99/98
 POTE generator: ~10/7 = 633.061
 Mapping generator: ~10/7
 Map: [&lt;1 0 -4 -3 -5|, &lt;0 3 12 11 16|]
 EDOs: 19e, 36e
 Badness: 0.0416
 ==Lisa==
 Commas: 45/44, 81/80, 343/330
 POTE generator: ~10/7 = 631.370
 Mapping generator: ~10/7
 Map: [&lt;1 0 -4 -3 -6|, &lt;0 3 12 11 18|]
 EDOs: 19
 Badness: 0.0548
 ==13-limit==
 Commas: 45/44, 81/80, 91/88, 147/143
 POTE generator: ~10/7 = 631.221
 Mapping generator: ~10/7
 Map: [&lt;1 0 -4 -3 -6 0|, &lt;0 3 12 11 18 7|]
 EDOs: 19
 Badness: 0.0361
 =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.
@@ Line 1,052: / Line 1,370: @@
 POTE generator: ~54/49 = 139.343
 Mapping generator: ~54/49
 Map: [&lt;1 1 0 2|, &lt;0 5 20 7|]
 Wedgie: &lt;&lt;5 30 7 20 -3 -40||
 EDOs: 8, 9, 17, 26, 43, 112
 Badness: 0.1087
 ==11-limit==
 Commas: 81/80, 99/98, 864/847
 POTE generator: ~12/11 = 139.428
 Mapping generator: ~12/11
 Map: [&lt;1 1 0 2 3|, &lt;0 5 20 7 4|]
 EDOs: 8, 9, 17, 26, 43, 241
 Badness: 0.0479
 ==13-limit==
 Commas: 77/78, 81/80, 99/98, 144/143
 POTE generator: ~13/12 = 139.387
 Mapping generator: ~12/11
 Map: [&lt;1 1 0 2 3 3|, &lt;0 5 20 7 4 6|]
 EDOs: 8, 9, 17, 26, 43, 155, 198
 Badness: 0.0293
 ==17-limit==
 Commas: 78/77, 81/80, 99/98, 144/143, 189/187
 POTE generator: ~13/12 = 139.362
 Mapping generator: ~12/11
 Map: [&lt;1 1 0 2 3 3 2|, &lt;0 5 20 7 4 6 18|]
 EDOs: 8, 9, 17, 26, 43, 155
 Badness: 0.0209
 =Meanmag=
 Commas: 81/80, 3125/3072
 POTE generator: ~8/7 = 238.396
 Mapping generator: ~7
 Map: [&lt;19 30 44 0|, &lt;0 0 0 1|]
 Wedgie: &lt;&lt;0 0 19 0 30 44||
 EDOs: 19, 57, 76, 171bcd
 Badness: 0.0770
 =Undevigintone=
 Commas: 49/48, 81/80, 126/125
 POTE generator: ~11/8 = 538.047
 Mapping generator: ~11
 Map: [&lt;19 30 44 53 0|, &lt;0 0 0 0 1|]
 EDOs: 19, 38d
 Badness: 0.0364
 ==13-limit==
 Commas: 49/48, 65/64, 81/80, 126/125
@@ Line 1,116: / Line 1,454: @@
 Map: [&lt;19 30 44 53 0 70|, &lt;0 0 0 0 1 0|]
 EDOs: 19, 38d
-Badness: 0.0229</pre></div>
-<h4>Original HTML content:</h4>
+Badness: 0.0229
-<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Meantone family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="display: block; text-align: right;"&gt;&lt;!-- ws:start:WikiTextTocRule:184:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:184 --&gt;&lt;!-- ws:start:WikiTextTocRule:185: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#x-Seven limit children"&gt;Seven limit children&lt;/a&gt;&lt;/div&gt;
+[[Category:catalog]]
-&lt;!-- ws:end:WikiTextTocRule:185 --&gt;&lt;!-- ws:start:WikiTextTocRule:186: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Septimal meantone"&gt;Septimal meantone&lt;/a&gt;&lt;/div&gt;
+[[Category:family]]
-&lt;!-- ws:end:WikiTextTocRule:186 --&gt;&lt;!-- ws:start:WikiTextTocRule:187: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Septimal meantone-Bimeantone"&gt;Bimeantone&lt;/a&gt;&lt;/div&gt;
+[[Category:listen]]
-&lt;!-- ws:end:WikiTextTocRule:187 --&gt;&lt;!-- ws:start:WikiTextTocRule:188: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Septimal meantone-Bimeantone-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
+[[Category:meantone]]
-&lt;!-- ws:end:WikiTextTocRule:188 --&gt;&lt;!-- ws:start:WikiTextTocRule:189: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Septimal meantone-Unidecimal meantone aka Huygens"&gt;Unidecimal meantone aka Huygens&lt;/a&gt;&lt;/div&gt;
+[[Category:rank_2]]
-&lt;!-- ws:end:WikiTextTocRule:189 --&gt;&lt;!-- ws:start:WikiTextTocRule:190: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Septimal meantone-Unidecimal meantone aka Huygens-Tridecimal meantone"&gt;Tridecimal meantone&lt;/a&gt;&lt;/div&gt;
+[[Category:theory]]
-&lt;!-- ws:end:WikiTextTocRule:190 --&gt;&lt;!-- ws:start:WikiTextTocRule:191: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Septimal meantone-Unidecimal meantone aka Huygens-Grosstone"&gt;Grosstone&lt;/a&gt;&lt;/div&gt;
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-&lt;!-- ws:end:WikiTextTocRule:193 --&gt;&lt;!-- ws:start:WikiTextTocRule:194: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Septimal meantone-Meanpop"&gt;Meanpop&lt;/a&gt;&lt;/div&gt;
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-&lt;!-- ws:end:WikiTextTocRule:202 --&gt;&lt;!-- ws:start:WikiTextTocRule:203: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Flattone"&gt;Flattone&lt;/a&gt;&lt;/div&gt;
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-&lt;!-- ws:end:WikiTextTocRule:273 --&gt;&lt;!-- ws:start:WikiTextTocRule:274: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Meanmag"&gt;Meanmag&lt;/a&gt;&lt;/div&gt;
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-&lt;!-- ws:end:WikiTextTocRule:277 --&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="http://xenharmonie.wikispaces.com/mittelt%C3%B6nig"&gt;Deutsch&lt;/a&gt;&lt;br /&gt;
-&lt;/span&gt;&lt;br /&gt;
-The &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; parent &lt;a class="wiki_link" href="/Comma"&gt;comma&lt;/a&gt; of the &lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt; family is the Didymus or &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Syntonic_comma" rel="nofollow"&gt;syntonic comma&lt;/a&gt;, 81/80. This is the one they all temper out. The &lt;a class="wiki_link" href="/Monzos%20and%20Interval%20Space"&gt;monzo&lt;/a&gt; for 81/80 goes |-4 4 -1&amp;gt;, and that can be flipped around to the corresponding &lt;a class="wiki_link" href="/Wedgies%20and%20Multivals"&gt;wedgie&lt;/a&gt;, &amp;lt;&amp;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.&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~3/2 = 696.239&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/Tuning%20Ranges%20of%20Regular%20Temperaments"&gt;valid range&lt;/a&gt;: [685.714, 720.000] (7 to 5)&lt;br /&gt;
-nice range: [694.786, 701.955] (1/3 comma to Pythagorean)&lt;br /&gt;
-strict range: [694.786, 701.955]&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/Map"&gt;Map&lt;/a&gt;: [&amp;lt;1 0 -4|, &amp;lt;0 1 4|]&lt;br /&gt;
-EDOs (patent val edo list is complete): &lt;a class="wiki_link" href="/5edo"&gt;5&lt;/a&gt;, &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/24edo"&gt;24&lt;/a&gt;, &lt;a class="wiki_link" href="/26edo"&gt;26&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/36edo"&gt;36&lt;/a&gt;, &lt;a class="wiki_link" href="/38edo"&gt;38&lt;/a&gt;, &lt;a class="wiki_link" href="/43edo"&gt;43&lt;/a&gt;, &lt;a class="wiki_link" href="/45edo"&gt;45&lt;/a&gt;, &lt;a class="wiki_link" href="/50edo"&gt;50&lt;/a&gt;, &lt;a class="wiki_link" href="/55edo"&gt;55&lt;/a&gt;, &lt;a class="wiki_link" href="/57edo"&gt;57&lt;/a&gt;, &lt;a class="wiki_link" href="/62edo"&gt;62&lt;/a&gt;, &lt;a class="wiki_link" href="/67edo"&gt;67&lt;/a&gt;, &lt;a class="wiki_link" href="/69edo"&gt;69&lt;/a&gt;, &lt;a class="wiki_link" href="/74edo"&gt;74&lt;/a&gt;, &lt;a class="wiki_link" href="/76edo"&gt;76&lt;/a&gt;, &lt;a class="wiki_link" href="/81edo"&gt;81&lt;/a&gt;, &lt;a class="wiki_link" href="/86edo"&gt;86&lt;/a&gt;, &lt;a class="wiki_link" href="/88edo"&gt;88&lt;/a&gt;, &lt;a class="wiki_link" href="/93edo"&gt;93&lt;/a&gt;, &lt;a class="wiki_link" href="/98edo"&gt;98&lt;/a&gt;, &lt;a class="wiki_link" href="/100edo"&gt;100&lt;/a&gt;, &lt;a class="wiki_link" href="/105edo"&gt;105&lt;/a&gt;, &lt;a class="wiki_link" href="/117edo"&gt;117&lt;/a&gt;, &lt;a class="wiki_link" href="/129edo"&gt;129&lt;/a&gt;, &lt;a class="wiki_link" href="/212edo"&gt;212b&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.00736&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Seven limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Seven limit children&lt;/h2&gt;
- The &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; children of 81/80 are septimal meantone, with normal comma list [|-4 4 -1&amp;gt;, |-13 10 0 -1&amp;gt;], flattone, with normal list [|-4 4 -1&amp;gt;, |-17 9 0 1&amp;gt;], dominant, with normal list [|-4 4 -1&amp;gt;, |6 -2 0 -1&amp;gt;], sharptone, with normal list [|-4 4 -1&amp;gt;, |2 -3 0 1&amp;gt;], injera, with normal list [|-4 4 -1&amp;gt;, |-7 8 0 -2&amp;gt;], mohajira, with normal list [|-4 4 -1&amp;gt;, |-23 11 0 2&amp;gt;], godzilla, with normal list [|-4 4 -1&amp;gt;, |-4 -1 0 2&amp;gt;], mothra, with normal list [|-4 4 -1&amp;gt;, |-10 1 0 3&amp;gt;], squares, with normal list [|-4 4 -1&amp;gt;, |-3 9 0 -4&amp;gt;], and liese, with normal list [|-4 4 -1&amp;gt;, |-9 11 0 -3&amp;gt;].&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Septimal meantone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Septimal meantone&lt;/h1&gt;
- &lt;span style="display: block; text-align: right;"&gt;&lt;a class="wiki_link" href="http://xenharmonie.wikispaces.com/septimal-mittelt%C3%B6nig"&gt;Deutsch&lt;/a&gt;&lt;br /&gt;
-&lt;/span&gt;&lt;br /&gt;
-&lt;a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Septimal_meantone_temperament" rel="nofollow"&gt;Wikipedia article&lt;/a&gt;&lt;br /&gt;
-&lt;br /&gt;
-The comma |-13 10 0 -1&amp;gt; for septimal meantone tells us that the interval class for 7 is 10 generator steps up. Hence, the &lt;a class="wiki_link" href="/7_4"&gt;7/4&lt;/a&gt; of septimal meantone is the augmented sixth, C-A#, and other septimal intervals are 7/6, C-D#, the augmented second, and &lt;a class="wiki_link" href="/7_5"&gt;7/5&lt;/a&gt;, C-F#, the tritone. The &lt;a class="wiki_link" href="/Wedgies%20and%20Multivals"&gt;wedgie&lt;/a&gt; for septimal meantone is &amp;lt;&amp;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 &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; is a good tuning for it.&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 81/80, 126/125&lt;br /&gt;
-&lt;br /&gt;
-and &lt;a class="wiki_link" href="/9-limit"&gt;9-limit&lt;/a&gt; minimax&lt;br /&gt;
-[|1 0 0 0&amp;gt;, |1 0 1/4 0&amp;gt;, |0 0 1 0&amp;gt;, |-3 0 5/2 0&amp;gt;]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzo&lt;/a&gt;s: 2, 5&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/Tuning%20Ranges%20of%20Regular%20Temperaments"&gt;valid range&lt;/a&gt;: [694.737, 700.000] (19 to 12)&lt;br /&gt;
-nice range: [694.786, 701.955]&lt;br /&gt;
-strict range: [694.786, 700.000]&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 696.495&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Algebraic generator: Cybozem, the real root of 15x^3-10x^2-18, which comes to 503.4257 cents. The recurrence converges quickly.&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/Map"&gt;Map&lt;/a&gt;: [&amp;lt;1 0 -4 -13|, &amp;lt;0 1 4 10|]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Generator"&gt;Generator&lt;/a&gt;s: 2, 3&lt;br /&gt;
-&lt;a class="wiki_link" href="/Wedgie"&gt;Wedgie&lt;/a&gt;: &amp;lt;&amp;lt;1 4 10 4 13 12||&lt;br /&gt;
-EDOs: &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/81edo"&gt;81&lt;/a&gt;, &lt;a class="wiki_link" href="/143edo"&gt;143b&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0137&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Septimal meantone-Bimeantone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Bimeantone&lt;/h2&gt;
- Commas: 81/80, 126/125, 245/242&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~3/2 = 696.016&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;2 0 -8 -26 -31|, &amp;lt;0 1 4 10 12|]&lt;br /&gt;
-EDOs: 12, 38d, 50&lt;br /&gt;
-Badness: 0.0381&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="Septimal meantone-Bimeantone-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h3&gt;
- Commas: 81/80, 105/104, 126/125, 245/242&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~3/2 = 695.836&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;2 0 -8 -26 -31 -40|, &amp;lt;0 1 4 10 12 15|]&lt;br /&gt;
-EDOs: 12f, 50&lt;br /&gt;
-Badness: 0.0288&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Septimal meantone-Unidecimal meantone aka Huygens"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Unidecimal meantone aka Huygens&lt;/h2&gt;
- See also &lt;a class="wiki_link" href="/Meantone%20vs%20meanpop"&gt;Meantone vs meanpop&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 81/80, 126/125, 99/98&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; minimax&lt;br /&gt;
-[|1 0 0 0 0&amp;gt;, |25/16 -1/8 0 0 1/16&amp;gt;, |9/4 -1/2 0 0 1/4&amp;gt;,&lt;br /&gt;
-|21/8 -5/4 0 0 5/8&amp;gt;, |25/8 -9/4 0 0 9/8&amp;gt;]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzo&lt;/a&gt;s: 2, 11/9&lt;br /&gt;
-&lt;br /&gt;
-valid range: [696.774, 700.000] (31 to 12)&lt;br /&gt;
-nice range: [691.202, 701.955]&lt;br /&gt;
-strict range: [696.774, 700.000]&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 696.967&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/Algebraic%20generator"&gt;Algebraic generator&lt;/a&gt;: Traverse, the positive real root of x^4+2x-13, or 696.9529 cents.&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/Map"&gt;Map&lt;/a&gt;: [&amp;lt;1 0 -4 -13 -25|, &amp;lt;0 1 4 10 18|]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Generator"&gt;Generator&lt;/a&gt;s: 2, 3&lt;br /&gt;
-EDOs: &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/105edo"&gt;105&lt;/a&gt;, &lt;a class="wiki_link" href="/198edo"&gt;198be&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0170&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-74-edo.mp3" rel="nofollow"&gt;Twinkle canon – 74 edo&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/archives/573" rel="nofollow"&gt;Claudi Meneghin&lt;/a&gt;&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="Septimal meantone-Unidecimal meantone aka Huygens-Tridecimal meantone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Tridecimal meantone&lt;/h3&gt;
- &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 66/65, 81/80, 99/98, 105/104&lt;br /&gt;
-&lt;br /&gt;
-valid range: 697.674 (43)&lt;br /&gt;
-nice range: [691.202, 701.955]&lt;br /&gt;
-strict range: 697.674&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~3/2 = 696.642&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 -13 -25 -20|, &amp;lt;0 1 4 10 18 15|]&lt;br /&gt;
-EDOs: &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/267edo"&gt;267&lt;/a&gt;, &lt;a class="wiki_link" href="/298edo"&gt;298&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0180&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc6"&gt;&lt;a name="Septimal meantone-Unidecimal meantone aka Huygens-Grosstone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Grosstone&lt;/h3&gt;
- Commas: 81/80, 99/98, 126/125, 144/143&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 = 697.264&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 -13 -25 29|, &amp;lt;0 1 4 10 18 -16|]&lt;br /&gt;
-EDOs: 12, 31, 43, 74&lt;br /&gt;
-Badness: 0.0259&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="Septimal meantone-Unidecimal meantone aka Huygens-Meridetone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Meridetone&lt;/h3&gt;
- Commas: 78/77, 81/80, 99/98, 126/125&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 = 697.529&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 -13 -25 -39|, &amp;lt;0 1 4 10 18 27|]&lt;br /&gt;
-EDOs: 43, 117df, 160bdf, 203bcdef&lt;br /&gt;
-Badness: 0.0264&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc8"&gt;&lt;a name="Septimal meantone-Unidecimal meantone aka Huygens-Hemimeantone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Hemimeantone&lt;/h3&gt;
- Commas: 81/80, 99/98, 126/125, 169/168&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~52/45 = 250.304&lt;br /&gt;
-Mapping generator: ~26/15&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 -13 -25 -5|, &amp;lt;0 2 8 20 36 11|]&lt;br /&gt;
-EDOs: 43, 62, 167bef, 229bef&lt;br /&gt;
-Badness: 0.0314&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Septimal meantone-Meanpop"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Meanpop&lt;/h2&gt;
- See also &lt;a class="wiki_link" href="/Meantone%20vs%20meanpop"&gt;Meantone vs meanpop&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 81/80, 126/125, 385/384&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; &lt;a class="wiki_link" href="/minimax"&gt;minimax&lt;/a&gt; 1/4 comma&lt;br /&gt;
-[|1 0 0 0 0&amp;gt;, |1 0 1/4 0 0&amp;gt;, |0 0 1 0 0&amp;gt;,&lt;br /&gt;
-|-3 0 5/2 0 0&amp;gt;, |11 0 -13/4 0 0&amp;gt;]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzo&lt;/a&gt;s: 2, 5&lt;br /&gt;
-&lt;br /&gt;
-valid range: [694.737, 696.774] (19 to 31)&lt;br /&gt;
-nice range: [691.202, 701.955]&lt;br /&gt;
-strict range: [694.737, 696.774]&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 696.434&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/Algebraic%20generator"&gt;Algebraic generator&lt;/a&gt;: Cybozem; or else Radieubiz, the real root of 3x^3+6x-19. Unlike Cybozem, the recurrence for Radieubiz does not converge.&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/archives/607" rel="nofollow" target="_blank"&gt;Scott Joplin's &amp;quot;The Entertainer&amp;quot; tuned into meanpop&lt;/a&gt;&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 -13 24|, &amp;lt;0 1 4 10 -13|]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Generator"&gt;Generator&lt;/a&gt;s: 2, 3&lt;br /&gt;
-EDOs: &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/81edo"&gt;81&lt;/a&gt;, &lt;a class="wiki_link" href="/112edo"&gt;112&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0215&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-50-edo.mp3" rel="nofollow"&gt;Twinkle canon – 50 edo&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/archives/573" rel="nofollow"&gt;Claudi Meneghin&lt;/a&gt;&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc10"&gt;&lt;a name="Septimal meantone-Meanpop-13-limit Meanpop"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;13-limit Meanpop&lt;/h3&gt;
- &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 81/80, 105/104, 144/143, 196/195&lt;br /&gt;
-&lt;br /&gt;
-valid range: [694.737, 696.774] (19 to 31)&lt;br /&gt;
-nice range: [691.202, 701.955]&lt;br /&gt;
-strict range: [694.737, 696.774]&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 = 696.211&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 -13 24 -20|, &amp;lt;0 1 4 10 -13 15|]&lt;br /&gt;
-EDOS: &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/50edo"&gt;50&lt;/a&gt;, &lt;a class="wiki_link" href="/81edo"&gt;81&lt;/a&gt;, &lt;a class="wiki_link" href="/131edo"&gt;131bd&lt;/a&gt;, &lt;a class="wiki_link" href="/212edo"&gt;212bdf&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0209&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc11"&gt;&lt;a name="Septimal meantone-Meanpop-Meanplop"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Meanplop&lt;/h3&gt;
- Commas: 65/64, 78/77, 81/80, 91/90&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 = 696.202&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 -13 24 10|, &amp;lt;0 1 4 10 -13 -4|]&lt;br /&gt;
-EDOs: 12e, 19, 31f, 50f&lt;br /&gt;
-Badness: 0.0277&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="Septimal meantone-Meanenneadecal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Meanenneadecal&lt;/h2&gt;
- &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 45/44, 56/55, 81/80&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~3/2 = 696.250&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 -13 -6|, &amp;lt;0 1 4 10 6|]&lt;br /&gt;
-EDOs: &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31e&lt;/a&gt;, &lt;a class="wiki_link" href="/50edo"&gt;50e&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0214&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc13"&gt;&lt;a name="Septimal meantone-Meanenneadecal-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;13-limit&lt;/h3&gt;
- &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 45/44, 56/55, 78/77, 81/80&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~3/2 = 696.146&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 -13 -6 -20|, &amp;lt;0 1 4 10 6 15|]&lt;br /&gt;
-EDOs: &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31e&lt;/a&gt;, &lt;a class="wiki_link" href="/50edo"&gt;50e&lt;/a&gt;]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0212&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc14"&gt;&lt;a name="Septimal meantone-Meanenneadecal-Vincenzo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Vincenzo&lt;/h3&gt;
- Commas: 81/80 126/125 45/44 65/64 256/255 153/152 23/22&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 -13 ... |, &amp;lt;0 1 4 10 6 -4 -5 -3 -6|]&lt;br /&gt;
-EDOs: 12&lt;br /&gt;
-Badness:&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="Septimal meantone-Meanundeci"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Meanundeci&lt;/h2&gt;
- Commas: 33/32, 55/54, 77/75&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 = 694.689&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 -13 5|, &amp;lt;0 1 4 10 -1|]&lt;br /&gt;
-EDOs: 12e, 19e&lt;br /&gt;
-Badness: 0.0315&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc16"&gt;&lt;a name="Septimal meantone-Meanundeci-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;13-limit&lt;/h3&gt;
- Commas: 33/32, 55/54, 77/75, 729/728&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 = 694.764&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 -13 5 10|, &amp;lt;0 1 4 10 -1 -4|]&lt;br /&gt;
-EDOs: 12e, 19e&lt;br /&gt;
-Badness: 0.0263&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Septimal meantone-Meanundec"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Meanundec&lt;/h2&gt;
- Commas: 27/26, 40/39, 45/44, 56/55&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 = 697.254&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 -13 -6 -1|, &amp;lt;0 1 4 10 6 3|]&lt;br /&gt;
-EDOS: 12f, 19f, 31ef&lt;br /&gt;
-Badness: 0.0242&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc18"&gt;&lt;a name="Flattone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Flattone&lt;/h1&gt;
- &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 81/80, 525/512&lt;br /&gt;
-&lt;br /&gt;
-The &lt;a class="wiki_link" href="/wedgie"&gt;wedgie&lt;/a&gt; for flattone is &amp;lt;&amp;lt;1 4 -9 4 -17 -32||, which tells us among other things that 9 generator steps of 4/3 get to the interval class for 7, meaning that &lt;a class="wiki_link" href="/7_4"&gt;7/4&lt;/a&gt; is a diminished seventh interval. Other intervals are &lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt;, a diminished third, and &lt;a class="wiki_link" href="/7_5"&gt;7/5&lt;/a&gt;, a doubly diminshed fifth. Good tunings for flattone are &lt;a class="wiki_link" href="/26edo"&gt;26edo&lt;/a&gt;, &lt;a class="wiki_link" href="/45edo"&gt;45edo&lt;/a&gt; and &lt;a class="wiki_link" href="/64edo"&gt;64edo&lt;/a&gt;.&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; minimax&lt;br /&gt;
-[|1 0 0 0&amp;gt;, |21/13 0 1/13 -1/13&amp;gt;,&lt;br /&gt;
-|32/13 0 4/13 -4/13&amp;gt;, |32/13 0 -9/13 9/13&amp;gt;]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzo&lt;/a&gt;s: 2, 7/5&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/9-limit"&gt;9-limit&lt;/a&gt; minimax&lt;br /&gt;
-[|1 0 0 0&amp;gt;, |17/11 2/11 0 -1/11&amp;gt;,&lt;br /&gt;
-|24/11 8/11 0 -4/11&amp;gt;, |34/11 -18/11 0 9/11&amp;gt;]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzo&lt;/a&gt;s: 2, 9/7&lt;br /&gt;
-&lt;br /&gt;
-valid range: [692.308, 694.737] (26 to 19)&lt;br /&gt;
-nice range: [692.353, 701.955]&lt;br /&gt;
-strict range: [692.353, 694.737]&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 693.779&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Algebraic generator: Squarto, the positive root of 8x^2-4x-9, at 506.3239 cents, equal to (1+sqrt(19))/4.&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 17|, &amp;lt;0 1 4 -9|]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Wedgie"&gt;Wedgie&lt;/a&gt;: &amp;lt;&amp;lt;1 4 -9 4 -17 -32||&lt;br /&gt;
-&lt;a class="wiki_link" href="/Generator"&gt;Generator&lt;/a&gt;s: 2, 3&lt;br /&gt;
-EDOs: &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/45edo"&gt;45&lt;/a&gt;, &lt;a class="wiki_link" href="/64edo"&gt;64&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0386&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="Flattone-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;11-limit&lt;/h2&gt;
- Commas: 45/44, 81/80, 385/384&lt;br /&gt;
-&lt;br /&gt;
-valid range: [692.308, 694.737] (26 to 19)&lt;br /&gt;
-nice range: [682.502, 701.955]&lt;br /&gt;
-strict range: [692.308, 694.737]&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 = 693.126&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 17 -6|, &amp;lt;0 1 4 -9 6|]&lt;br /&gt;
-EDOs: 7, 19, 26, 45, 71bc, 116bcde&lt;br /&gt;
-Badness: 0.0338&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="Flattone-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;13-limit&lt;/h2&gt;
-/44, 65/64, 78/77, 81/80&lt;br /&gt;
-&lt;br /&gt;
-valid range: [692.308, 694.737] (26 to 19)&lt;br /&gt;
-nice range: [682.502, 701.955]&lt;br /&gt;
-strict range: [692.308, 694.737]&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 = 693.058&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 17 -6 10|, &amp;lt;0 1 4 -9 6 -4|]&lt;br /&gt;
-EDOs: 7, 19, 26, 45f, 71bcf, 116bcdef&lt;br /&gt;
-Badness: 0.0223&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc21"&gt;&lt;a name="Dominant"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;Dominant&lt;/h1&gt;
- &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 36/35, 64/63&lt;br /&gt;
-&lt;br /&gt;
-The wedgie for dominant is &amp;lt;&amp;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 &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, but it also works well with the Pythagorean tuning of pure &lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt; fifths, and with &lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt;, &lt;a class="wiki_link" href="/41edo"&gt;41edo&lt;/a&gt;, or &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt;.&lt;br /&gt;
-&lt;br /&gt;
-valid range: [700.000, 720.000] (12 to 5)&lt;br /&gt;
-nice range: [694.786, 715.587]&lt;br /&gt;
-strict range: [700.000, 715.587]&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 701.573&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 6|, &amp;lt;0 1 4 -2|]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Wedgie"&gt;Wedgie&lt;/a&gt;: &amp;lt;&amp;lt;1 4 -2 4 -6 -16||&lt;br /&gt;
-EDOs: &lt;a class="wiki_link" href="/5edo"&gt;5&lt;/a&gt;, &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53&lt;/a&gt;, &lt;a class="wiki_link" href="/65edo"&gt;65&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0207&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc22"&gt;&lt;a name="Dominant-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;11-limit&lt;/h2&gt;
- Commas: 36/35, 64/63, 56/55&lt;br /&gt;
-&lt;br /&gt;
-valid range: [700.000, 705.882] (12 to 17)&lt;br /&gt;
-nice range: [691.202, 715.587]&lt;br /&gt;
-strict range: [700.000, 705.882]&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 = 703.254&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 6 13|, &amp;lt;0 1 4 -2 -6|]&lt;br /&gt;
-EDOs: 5, 12, 17c, 29cde&lt;br /&gt;
-Badness: 0.0242&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc23"&gt;&lt;a name="Dominant-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;13-limit&lt;/h2&gt;
- Commas: 36/35, 56/55, 64/63, 66/65&lt;br /&gt;
-&lt;br /&gt;
-valid range: 705.882 (17)&lt;br /&gt;
-nice range: [691.202, 715.587]&lt;br /&gt;
-strict range:705.882&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 = 703.636&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 6 13 18|, &amp;lt;0 1 4 -2 -6 -9|]&lt;br /&gt;
-EDOs: 12f, 17c, 29cdef&lt;br /&gt;
-Badness: 0.0241&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc24"&gt;&lt;a name="Dominant-Dominion"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;Dominion&lt;/h2&gt;
- Commas: 26/25, 36/35, 56/55, 64/63&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 = 704.905&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 6 13 -9|, &amp;lt;0 1 4 -2 -6 8|]&lt;br /&gt;
-EDOs: 5, 12, 17c, 46cde&lt;br /&gt;
-Badness: 0.0273&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc25"&gt;&lt;a name="Dominant-Domineering"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;Domineering&lt;/h2&gt;
- Commas: 36/35, 45/44, 64/63&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 = 698.776&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 6 -6|, &amp;lt;0 1 4 -2 6|]&lt;br /&gt;
-EDOs: 7, 12, 43de&lt;br /&gt;
-Badness: 0.0220&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc26"&gt;&lt;a name="Dominant-Domination"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;Domination&lt;/h2&gt;
- Commas: 36/35, 64/63, 77/75&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 = 705.004&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 6 -14|, &amp;lt;0 1 4 -2 11|]&lt;br /&gt;
-EDOs: 17c, 46cd&lt;br /&gt;
-Badness: 0.0366&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc27"&gt;&lt;a name="Dominant-Domination-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;13-limit&lt;/h3&gt;
- Commas: 26/25, 36/35, 64/63, 66/65&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 = 705.496&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 6 -14 -9|, &amp;lt;0 1 4 -2 11 8|]&lt;br /&gt;
-EDOs: 17c&lt;br /&gt;
-Badness: 0.0274&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc28"&gt;&lt;a name="Dominant-Twelve"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;Twelve&lt;/h2&gt;
- Commas: 81/80 64/63 45/44 65/64 256/255 153/152&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 = 696.217&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 6 -6 10 12 9|, &amp;lt;0 1 4 -2 6 -4 -5 -3|]&lt;br /&gt;
-EDOs: 7, 12, 19d, 31def&lt;br /&gt;
-Badness: 0.0204&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc29"&gt;&lt;a name="Dominant-Arnold"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;Arnold&lt;/h2&gt;
- Commas: 22/21, 33/32, 36/35&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 = 698.491&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 6 5|, &amp;lt;0 1 4 -2 -1|]&lt;br /&gt;
-EDOs: 5, 7, 12e&lt;br /&gt;
-Badness: 0.0261&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:60:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc30"&gt;&lt;a name="Dominant-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;13-limit&lt;/h2&gt;
- Commas: 22/21, 27/26, 33/32, 40/39&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 = 696.743&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 6 5 -1|, &amp;lt;0 1 4 -2 -1 3|]&lt;br /&gt;
-EDOs: 5, 7, 12ef, 19def, 31def&lt;br /&gt;
-Badness: 0.0233&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:62:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc31"&gt;&lt;a name="Dominant-Dominatrix"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:62 --&gt;Dominatrix&lt;/h2&gt;
- Commas: 27/26 36/35 45/44 64/63&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 = 698.544&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 6 -6 -1|, &amp;lt;0 1 4 -2 6 3|]&lt;br /&gt;
-EDOs: 7, 12f&lt;br /&gt;
-Badness: 0.0183&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:64:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc32"&gt;&lt;a name="Sharptone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:64 --&gt;Sharptone&lt;/h1&gt;
- &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 21/20, 28/27&lt;br /&gt;
-&lt;br /&gt;
-Sharptone, with a wedgie &amp;lt;&amp;lt;1 4 3 4 2 -4||, 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. &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; tuning does sharptone about as well as such a thing can be done.&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 700.140&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 -2|, &amp;lt;0 1 4 3|]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Wedgie"&gt;Wedgie&lt;/a&gt;: &amp;lt;&amp;lt;1 4 3 4 2 -4||&lt;br /&gt;
-EDOs: &lt;a class="wiki_link" href="/5edo"&gt;5&lt;/a&gt;, &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0248&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:66:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc33"&gt;&lt;a name="Meansept"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:66 --&gt;Meansept&lt;/h1&gt;
- Commas: 15/14, 81/80&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 = 682.895&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 -5|, &amp;lt;0 1 4 5|]&lt;br /&gt;
-Wedgie: &amp;lt;&amp;lt;1 4 5 4 5 0||&lt;br /&gt;
-EDOs: 7&lt;br /&gt;
-Badness: 0.0453&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:68:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc34"&gt;&lt;a name="Meansept-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:68 --&gt;11-limit&lt;/h2&gt;
- Commas: 15/14, 22/21, 125/121&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 = 685.234&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 -5 -6|, &amp;lt;0 1 4 5 6|]&lt;br /&gt;
-EDOs: 7&lt;br /&gt;
-Badness: 0.0325&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:70:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc35"&gt;&lt;a name="Supermean"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:70 --&gt;Supermean&lt;/h1&gt;
- Commas: 81/80, 672/625&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 = 704.889&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 -21|, &amp;lt;0 1 4 15|]&lt;br /&gt;
-EDOs: 17c, 46c&lt;br /&gt;
-Badness: 0.1342&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:72:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc36"&gt;&lt;a name="Supermean-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:72 --&gt;11-limit&lt;/h2&gt;
- Commas: 56/55, 81/80, 132/125&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 = 705.096&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 -21 -14|, &amp;lt;0 1 4 15 11|]&lt;br /&gt;
-EDOs: 17c, 46c&lt;br /&gt;
-Badness: 0.0633&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:74:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc37"&gt;&lt;a name="Supermean-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:74 --&gt;13-limit&lt;/h2&gt;
- Commas: 26/25, 56/55, 66/65, 81/80&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 = 705.094&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 -21 -14 -9|, &amp;lt;0 1 4 15 11 8|]&lt;br /&gt;
-EDOs: 17c, 46c&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:76:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc38"&gt;&lt;a name="Injera"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:76 --&gt;Injera&lt;/h1&gt;
- &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 50/49, 81/80&lt;br /&gt;
-&lt;br /&gt;
-The wedgie for injera is &amp;lt;&amp;lt;2 8 8 8 7 -4||, which tells us it 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. &lt;a class="wiki_link" href="/38edo"&gt;38edo&lt;/a&gt;, which is two parallel &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;s, is an excellent tuning for injera.&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link_ext" href="http://tech.groups.yahoo.com/group/tuning-math/message/3091" rel="nofollow"&gt;Origin of the name&lt;/a&gt;&lt;br /&gt;
-&lt;br /&gt;
-valid range: [685.714, 700.000] (14c to 12)&lt;br /&gt;
-nice range: [688.957, 701.955]&lt;br /&gt;
-strict range: [688.957, 700.000]&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 694.375&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;2 0 -8 -7|, &amp;lt;0 1 4 4|]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Wedgie"&gt;Wedgie&lt;/a&gt;: &amp;lt;&amp;lt;2 8 8 8 7 -4||&lt;br /&gt;
-EDOs: &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/26edo"&gt;26&lt;/a&gt;, &lt;a class="wiki_link" href="/38edo"&gt;38&lt;/a&gt;, &lt;a class="wiki_link" href="/102edo"&gt;102bcd&lt;/a&gt;, &lt;a class="wiki_link" href="/140edo"&gt;140bcd&lt;/a&gt;, &lt;a class="wiki_link" href="/178edo"&gt;178bcd&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0311&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Two%20Pairs%20of%20Socks.mp3" rel="nofollow"&gt;Two Pairs of Socks&lt;/a&gt; (in &lt;a class="wiki_link" href="/26edo"&gt;26edo&lt;/a&gt;) by &lt;a class="wiki_link" href="/Igliashon%20Jones"&gt;Igliashon Calvin Jones-Coolidge&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Curley/Zach%20Curley%20-%20Injera%20Jam.mp3" rel="nofollow"&gt;Injera Jam&lt;/a&gt; (in &lt;a class="wiki_link" href="/26edo"&gt;26edo&lt;/a&gt;) by &lt;a class="wiki_link" href="/Zach%20Curley"&gt;Zach Curley&lt;/a&gt;&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:78:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc39"&gt;&lt;a name="Injera-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:78 --&gt;11-limit&lt;/h2&gt;
- Commas: 45/44, 50/49, 81/80&lt;br /&gt;
-&lt;br /&gt;
-valid range: [685.714, 700.000] (14c to 12)&lt;br /&gt;
-nice range: [682.458, 701.955]&lt;br /&gt;
-strict range: [685.714, 700.000]&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 = 692.840&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;2 0 -8 -7 -12|, &amp;lt;0 1 4 4 6|]&lt;br /&gt;
-EDOs: 12, 14c, 26. 90bce, 116bce&lt;br /&gt;
-Badness: 0.0231&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:80:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc40"&gt;&lt;a name="Injera-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:80 --&gt;13-limit&lt;/h2&gt;
- Commas: 45/44, 50/49, 81/80, 78/77&lt;br /&gt;
-&lt;br /&gt;
-valid range: 692.308 (26)&lt;br /&gt;
-nice range: [682.458, 701.955]&lt;br /&gt;
-strict range: 692.308 (26)&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 = 692.673&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;2 0 -8 -7 -12 -21|, &amp;lt;0 1 4 4 6 9|]&lt;br /&gt;
-EDOs: 26, 104bcf&lt;br /&gt;
-Badness: 0.0216&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:82:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc41"&gt;&lt;a name="Injera-Enjera"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:82 --&gt;Enjera&lt;/h2&gt;
- Commas: 27/26, 40/39, 45/44, 99/98&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 = 694.121&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;2 0 -8 -7 -12 -2|, &amp;lt;0 1 4 4 6 3|]&lt;br /&gt;
-EDOs: 12f, 26f, 38ef&lt;br /&gt;
-Badness: 0.0265&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:84:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc42"&gt;&lt;a name="Injera-Injerous"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:84 --&gt;Injerous&lt;/h2&gt;
- Commas: 33/32, 50/49, 55/54&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 = 690.548&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;2 0 -8 -7 10|, &amp;lt;0 1 4 4 -1|]&lt;br /&gt;
-EDOs: 12e, 14c, 26e, 40ce&lt;br /&gt;
-Badness: 0.0386&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:86:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc43"&gt;&lt;a name="Injera-Lahoh"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:86 --&gt;Lahoh&lt;/h2&gt;
- Commas: 50/49, 56/55, 81/77&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 = 699.001&lt;br /&gt;
-Mapping generator: ~3&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;2 0 -8 -7 7|, &amp;lt;0 1 4 4 0|]&lt;br /&gt;
-EDOs: 12&lt;br /&gt;
-Badness: 0.0431&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:88:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc44"&gt;&lt;a name="Godzilla"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:88 --&gt;Godzilla&lt;/h1&gt;
- &lt;span style="display: block; text-align: right;"&gt;&lt;a class="wiki_link" href="http://xenharmonie.wikispaces.com/Semiphor%2C%20Semaphor%2C%20Godzilla"&gt;Deutsch&lt;/a&gt;&lt;br /&gt;
-&lt;/span&gt;&lt;br /&gt;
-Main article: &lt;a class="wiki_link" href="/Semaphore%20and%20Godzilla"&gt;Semaphore and Godzilla&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 49/48, 81/80&lt;br /&gt;
-&lt;br /&gt;
-Godzilla has wedgie &amp;lt;&amp;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. &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; 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.&lt;br /&gt;
-&lt;br /&gt;
-valid range: [240.000, 257.143] (5 to 14c)&lt;br /&gt;
-nice range: [231.174, 266.871]&lt;br /&gt;
-strict range: [240.000, 257.143]&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~8/7 = 252.635&lt;br /&gt;
-Mapping generator: ~7/4&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 2|, &amp;lt;0 2 8 1|]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Wedgie"&gt;Wedgie&lt;/a&gt;: &amp;lt;&amp;lt;2 8 1 8 -4 -20||&lt;br /&gt;
-EDOs: &lt;a class="wiki_link" href="/5edo"&gt;5&lt;/a&gt;, &lt;a class="wiki_link" href="/9edo"&gt;9c&lt;/a&gt;, &lt;a class="wiki_link" href="/14edo"&gt;14c&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/62edo"&gt;62d&lt;/a&gt;, &lt;a class="wiki_link" href="/81edo"&gt;81d&lt;/a&gt;, 143bd&lt;br /&gt;
-&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0267&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:90:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc45"&gt;&lt;a name="Godzilla-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:90 --&gt;11-limit&lt;/h2&gt;
- Commas: 45/44, 49/48, 81/80&lt;br /&gt;
-&lt;br /&gt;
-valid range: [252.632, 257.143] (19 to 14c)&lt;br /&gt;
-nice range: [231.174, 266.871]&lt;br /&gt;
-strict range: [252.632, 257.143]&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~8/7 = 254.027&lt;br /&gt;
-Mapping generator: ~7/4&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 2 -6|, &amp;lt;0 2 8 1 12|]&lt;br /&gt;
-EDOs: 14c, 19, 33cd, 52cd&lt;br /&gt;
-Badness: 0.0290&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:92:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc46"&gt;&lt;a name="Godzilla-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:92 --&gt;13-limit&lt;/h2&gt;
- Commas: 45/44, 49/48, 78/77, 81/80&lt;br /&gt;
-&lt;br /&gt;
-valid range: 694.737 (19)&lt;br /&gt;
-nice range: [621.581, 737.652]&lt;br /&gt;
-strict range: 694.737&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~8/7 = 253.603&lt;br /&gt;
-Mapping generator: ~7/4&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 2 -6 -5|, &amp;lt;0 2 8 1 12 11|]&lt;br /&gt;
-EDOs: 14cf, 19, 33cdf, 52cdf&lt;br /&gt;
-Badness: 0.0225&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:94:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc47"&gt;&lt;a name="Godzilla-Semafour"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:94 --&gt;Semafour&lt;/h2&gt;
- Commas: 33/32, 49/48, 55/54&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~8/7 = 254.042&lt;br /&gt;
-Mapping generator: ~7/4&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 2 5|, &amp;lt;0 2 8 1 -2|]&lt;br /&gt;
-EDOs: 5, 14c, 19e, 33cde&lt;br /&gt;
-Badness: 0.0285&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:96:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc48"&gt;&lt;a name="Godzilla-Varan"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:96 --&gt;Varan&lt;/h2&gt;
- Commas: 49/48, 77/75, 81/80&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~8/7 = 251.079&lt;br /&gt;
-Mapping generator: ~7/4&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 2 -10|, &amp;lt;0 2 8 1 17|]&lt;br /&gt;
-EDOs: 19e, 24, 43de&lt;br /&gt;
-Badness: 0.0396&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:98:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc49"&gt;&lt;a name="Godzilla-Varan-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:98 --&gt;13-limit&lt;/h3&gt;
- Commas: 49/48, 66/65, 77/75, 81/80&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~8/7 = 251.165&lt;br /&gt;
-Mapping generator: ~7/4&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 2 -10 -5|, &amp;lt;0 2 8 1 17 11|]&lt;br /&gt;
-EDOs: 19e, 24, 43de&lt;br /&gt;
-Badness: 0.0257&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:100:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc50"&gt;&lt;a name="Godzilla-Baragon"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:100 --&gt;Baragon&lt;/h2&gt;
- Commas: 49/48, 56/55, 81/80&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~8/7 = 251.173&lt;br /&gt;
-Mapping generator: ~7/4&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 2 9|, &amp;lt;0 2 8 1 -7|]&lt;br /&gt;
-EDOs: 19, 24, 43d&lt;br /&gt;
-Badness: 0.0357&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:102:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc51"&gt;&lt;a name="Godzilla-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:102 --&gt;Music&lt;/h2&gt;
- &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Bobro/GodzillaExample.mp3" rel="nofollow"&gt;Godzilla Example&lt;/a&gt; by &lt;a class="wiki_link" href="/Cameron%20Bobro"&gt;Cameron Bobro&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link_ext" href="http://tinyurl.com/4uyumk9" rel="nofollow"&gt;&amp;quot;Change is on the Wind&amp;quot;&lt;/a&gt; in Godzilla[9] by &lt;a class="wiki_link" href="/Igliashon%20Jones"&gt;Igliashon Jones&lt;/a&gt;&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:104:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc52"&gt;&lt;a name="Mohajira"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:104 --&gt;Mohajira&lt;/h1&gt;
- &lt;span style="display: block; text-align: right;"&gt;&lt;a class="wiki_link" href="http://xenharmonie.wikispaces.com/Mohajira"&gt;Deutsch&lt;/a&gt;&lt;br /&gt;
-&lt;/span&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 81/80, 6144/6125&lt;br /&gt;
-&lt;br /&gt;
-Mohajira, with wedgie &amp;lt;&amp;lt;2 8 -11 8 -23 -48||, really makes more sense as an 11-limit temperament. It has a generator of a neutral third, two of which make up a fifth, and which can be taken to represent 128/105. Mohajira tempers out 6144/6125, the porwell comma. &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; makes for an excellent (7-limit) mohajira tuning, with generator 9/31. It has a 7-note MOS with three larger steps and four smaller ones, going sLsLsLs.&lt;br /&gt;
-&lt;br /&gt;
-Mohajira can also be thought of, intuitively, as &amp;quot;meantone with quarter tones&amp;quot;; as is the 3/2 generator subdivided in half, so is the 25/24 chromatic semitone divided into two equal ~33/32 quarter tones (in the 11-limit). Within this paradigm, mohajira is the temperament that splits the 3/2 into two equal 11/9's, that splits the 6/5 into two equal 11/10's, that maps four 3/2's to 5/1, and that maps the interval one quarter tone flat of 16/9 to 7/4.&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/7-limit"&gt;7&lt;/a&gt; and &lt;a class="wiki_link" href="/9-limit"&gt;9-limit&lt;/a&gt; minimax 1/4 comma&lt;br /&gt;
-[|1 0 0 0&amp;gt;, |1 0 1/4 0&amp;gt;, |0 0 1 0&amp;gt;, |6 0 -11/8 0&amp;gt;]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzo&lt;/a&gt;s: 2, 5&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~128/105 = 348.415&lt;br /&gt;
-Mapping generator: ~128/105&lt;br /&gt;
-&lt;br /&gt;
-Algebraic generator: Mohabis, real root of 3x^3-3x^2-1, 348.6067 cents. Corresponding recurrence converges quickly.&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 0 6|, &amp;lt;0 2 8 -11|]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Generator"&gt;Generator&lt;/a&gt;s: 2, 128/105&lt;br /&gt;
-&lt;a class="wiki_link" href="/Wedgie"&gt;Wedgie&lt;/a&gt;: &amp;lt;&amp;lt;2 8 -11 8 -23 -48||&lt;br /&gt;
-EDOs: &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, &lt;a class="wiki_link" href="/24edo"&gt;24&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0557&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:106:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc53"&gt;&lt;a name="Mohajira-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:106 --&gt;11-limit&lt;/h2&gt;
- &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 81/80, 121/120, 176/175&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; minimax 1/4 comma&lt;br /&gt;
-[|1 0 0 0 0&amp;gt;, |1 0 1/4 0 0&amp;gt;, |0 0 1 0 0&amp;gt;,&lt;br /&gt;
-|6 0 -11/8 0 0&amp;gt;, |2 0 5/8 0 0&amp;gt;]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzo&lt;/a&gt;s: 2, 5&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~11/9 = 348.477&lt;br /&gt;
-Mapping generator: ~11/9&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 0 6 2|, &amp;lt;0 2 8 -11 5|]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Generator"&gt;Generator&lt;/a&gt;s: 2, 11/9&lt;br /&gt;
-EDOs: &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, &lt;a class="wiki_link" href="/24edo"&gt;24&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0261&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:108:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc54"&gt;&lt;a name="Mohajira-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:108 --&gt;13-limit&lt;/h2&gt;
- Commas: 81/80, 121/120, 105/104, 66/65&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~11/9 = 348.558&lt;br /&gt;
-Mapping generator: ~11/9&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 0 6 2 4|, &amp;lt;0 2 8 -11 5 -1|]&lt;br /&gt;
-EDOs: 7, 24, 31, 117ef, 148bef&lt;br /&gt;
-Badness: 0.0234&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:110:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc55"&gt;&lt;a name="Ptolemy"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:110 --&gt;Ptolemy&lt;/h1&gt;
- Commas: 81/80, 121/120, 525/512&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~11/9 = 346.922&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 0 8 2|, &amp;lt;0 2 8 -18 5|]&lt;br /&gt;
-EDOs: 7, 38d, 45e, 83bcde&lt;br /&gt;
-Badness: 0.0588&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:112:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc56"&gt;&lt;a name="Ptolemy-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:112 --&gt;13-limit&lt;/h2&gt;
- Commas: 65/64, 81/80, 105/104, 121/120&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~11/9 = 346.910&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 0 8 2 6|, &amp;lt;0 2 8 -18 5 -8|]&lt;br /&gt;
-EDOs: 7, 38df, 45ef, 83bcdef&lt;br /&gt;
-Badness: 0.0343&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:114:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc57"&gt;&lt;a name="Maqamic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:114 --&gt;Maqamic&lt;/h1&gt;
- &lt;span style="display: block; text-align: right;"&gt;&lt;a class="wiki_link" href="http://xenharmonie.wikispaces.com/maqamisch"&gt;Deutsch&lt;/a&gt;&lt;br /&gt;
-&lt;/span&gt;&lt;br /&gt;
-Main article: &lt;a class="wiki_link" href="/Maqamic"&gt;Maqamic&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 81/80, 36/35, 121/120&lt;br /&gt;
-&lt;br /&gt;
-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 &amp;quot;middle-of-the-road&amp;quot; intonation.&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~11/9 = 350.934&lt;br /&gt;
-Mapping generator: ~11/9&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 0 4 2|, &amp;lt;0 2 8 -4 5|]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Generator"&gt;Generator&lt;/a&gt;s: 2, 11/9&lt;br /&gt;
-EDOs: &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, &lt;a class="wiki_link" href="/10edo"&gt;10c&lt;/a&gt;, &lt;a class="wiki_link" href="/17edo"&gt;17c&lt;/a&gt;, &lt;a class="wiki_link" href="/24edo"&gt;24d&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31d&lt;/a&gt;&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:116:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc58"&gt;&lt;a name="Maqamic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:116 --&gt;13-limit&lt;/h2&gt;
- &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 81/80, 36/35, 121/120, 144/143&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~11/9 = 350.816&lt;br /&gt;
-Mapping generator: ~11/9&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 0 4 2 4|, &amp;lt;0 2 8 -4 5 -1|]&lt;br /&gt;
-Generators: 2, 11/9&lt;br /&gt;
-EDOs: &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, &lt;a class="wiki_link" href="/10edo"&gt;10c&lt;/a&gt;, &lt;a class="wiki_link" href="/17edo"&gt;17c&lt;/a&gt;, &lt;a class="wiki_link" href="/24edo"&gt;24d&lt;/a&gt;,&lt;a class="wiki_link" href="/31edo"&gt; 31d&lt;/a&gt;&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:118:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc59"&gt;&lt;a name="Migration"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:118 --&gt;Migration&lt;/h1&gt;
- Commas: 81/80, 121/120, 126/125&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~11/9 = 348.182&lt;br /&gt;
-Mapping generator: ~11/9&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 0 -3 2|, &amp;lt;0 2 8 20 5|]&lt;br /&gt;
-EDOs: 31, 100de, 131bde, 162bde&lt;br /&gt;
-Badness: 0.0255&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:120:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc60"&gt;&lt;a name="Mohamaq"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:120 --&gt;Mohamaq&lt;/h1&gt;
- Commas: 81/80, 392/375&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~25/21 = 350.586&lt;br /&gt;
-Mapping generator: ~25/21&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 0 -1|, &amp;lt;0 2 8 13|]&lt;br /&gt;
-EDOs: 17c, 24, 65c, 89cd&lt;br /&gt;
-Badness: 0.0777&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:122:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc61"&gt;&lt;a name="Mohamaq-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:122 --&gt;11-limit&lt;/h2&gt;
- Commas: 56/55, 77/75, 243/242&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~11/9 = 350.565&lt;br /&gt;
-Mapping generator: ~11/9&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 0 -1 2|, &amp;lt;0 2 8 13 5|]&lt;br /&gt;
-EDOs: 17c, 24, 65c, 89cd&lt;br /&gt;
-Badness: 0.0362&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:124:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc62"&gt;&lt;a name="Mohamaq-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:124 --&gt;13-limit&lt;/h2&gt;
- Commas: 56/55, 66/65, 77/75, 243/242&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~11/9 = 350.745&lt;br /&gt;
-Mapping generator: ~11/9&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 0 -1 2 4|, &amp;lt;0 2 8 13 5 -1|]&lt;br /&gt;
-EDOs: 17c, 24, 41c, 65c&lt;br /&gt;
-Badness: 0.0287&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:126:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc63"&gt;&lt;a name="Orphic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:126 --&gt;Orphic&lt;/h1&gt;
- Commas: 81/80, 5898240/5764801&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~7/6 = 275.794&lt;br /&gt;
-Mapping generator: ~343/288&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;2 1 -4 4|, &amp;lt;0 4 16 3|]&lt;br /&gt;
-Wedgie: &amp;lt;&amp;lt;8 32 6 32 -13 -76||&lt;br /&gt;
-EDOs: 26, 74, 174bd, 248bd&lt;br /&gt;
-Badness: 0.2588&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:128:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc64"&gt;&lt;a name="Orphic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:128 --&gt;11-limit&lt;/h2&gt;
- Commas: 81/80, 99/98, 73728/73205&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~7/6 = 275.762&lt;br /&gt;
-Mapping generator: ~77/64&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;2 1 -4 4 8|, &amp;lt;0 4 16 3 -2|]&lt;br /&gt;
-EDOs: 26, 48c, 74, 248bd, 322bd&lt;br /&gt;
-Badness: 0.1015&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:130:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc65"&gt;&lt;a name="Orphic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:130 --&gt;13-limit&lt;/h2&gt;
- Commas: 81/80, 99/98, 144/143, 2200/2197&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~7/6 = 275.774&lt;br /&gt;
-Mapping generator: ~63/52&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;2 1 -4 4 8 2|, &amp;lt;0 4 16 3 -2 10|]&lt;br /&gt;
-EDOs: 26, 48c, 74, 174bd, 248bd, 322bd&lt;br /&gt;
-Badness: 0.0535&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:132:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc66"&gt;&lt;a name="Mothra"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:132 --&gt;Mothra&lt;/h1&gt;
- &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 81/80, 1029/1024&lt;br /&gt;
-&lt;br /&gt;
-Mothra, with wedgie &amp;lt;&amp;lt;3 12 -1 12 -10 -36||, 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 &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; 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-limit, mothra is identical to &lt;a class="wiki_link" href="/Slendric"&gt;slendric&lt;/a&gt;.&lt;br /&gt;
-Note that mothra can also be called cynder in the 7-limit, which can be a little confusing sometimes.&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/7-limit"&gt;7&lt;/a&gt; and &lt;a class="wiki_link" href="/9-limit"&gt;9-limit&lt;/a&gt; minimax 1/4 comma&lt;br /&gt;
-[|1 0 0 0&amp;gt;, |1 0 1/4 0&amp;gt;, |0 0 1 0&amp;gt;, |3 0 -1/12 0&amp;gt;]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzo&lt;/a&gt;s: 2, 5&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~8/7 = 232.193&lt;br /&gt;
-Mapping generator: ~8/7&lt;br /&gt;
-&lt;br /&gt;
-Algebraic generator: Rabrindanath, largest real root of x^8-3x^2+1, or 232.0774 cents.&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 0 3|, &amp;lt;0 3 12 -1|]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Generator"&gt;Generator&lt;/a&gt;s: 2, 8/7&lt;br /&gt;
-&lt;a class="wiki_link" href="/Wedgie"&gt;Wedgie&lt;/a&gt;: &amp;lt;&amp;lt;3 12 -1 12 -10 -36||&lt;br /&gt;
-EDOs: &lt;a class="wiki_link" href="/5edo"&gt;5&lt;/a&gt;, &lt;a class="wiki_link" href="/26edo"&gt;26&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0371&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:134:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc67"&gt;&lt;a name="Mothra-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:134 --&gt;11-limit&lt;/h2&gt;
- &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 81/80, 99/98, 385/384&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~8/7 = 232.031&lt;br /&gt;
-Mapping generator: ~8/7&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 0 3 5|, &amp;lt;0 3 12 -1 -8|]&lt;br /&gt;
-EDOs: &lt;a class="wiki_link" href="/5edo"&gt;5&lt;/a&gt;, &lt;a class="wiki_link" href="/26edo"&gt;26&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/88edo"&gt;88&lt;/a&gt;, &lt;a class="wiki_link" href="/150edo"&gt;150&lt;/a&gt;, &lt;a class="wiki_link" href="/181edo"&gt;181&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0256&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:136:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc68"&gt;&lt;a name="Mothra-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:136 --&gt;13-limit&lt;/h2&gt;
- Commas: 81/80, 99/98, 105/104, 144/143&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~8/7 = 231.811&lt;br /&gt;
-Mapping generator: ~8/7&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 0 3 5 1|, &amp;lt;0 3 12 -1 -8 14|]&lt;br /&gt;
-EDOs: 5, 26, 31, 57, 88&lt;br /&gt;
-Badness: 0.0240&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:138:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc69"&gt;&lt;a name="Mothra-Cynder"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:138 --&gt;Cynder&lt;/h2&gt;
- Commas: 45/44, 81/80, 1029/1024&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~8/7 = 231.317&lt;br /&gt;
-Mapping generator: ~8/7&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 0 3 0|, &amp;lt;0 3 12 -1 18|]&lt;br /&gt;
-EDOs: 26, 57e, 83bce&lt;br /&gt;
-Badness: 0.0557&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:140:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc70"&gt;&lt;a name="Mothra-Cynder-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:140 --&gt;13-limit&lt;/h3&gt;
- Commas: 45/44, 78/77, 81/80, 640/637&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~8/7 = 231.293&lt;br /&gt;
-Mapping generator: ~8/7&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 0 3 0 1|, &amp;lt;0 3 12 -1 18 14|]&lt;br /&gt;
-EDOs: 26, 57e, 83bce&lt;br /&gt;
-Badness: 0.0341&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:142:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc71"&gt;&lt;a name="Mothra-Mosura"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:142 --&gt;Mosura&lt;/h2&gt;
- Commas: 81/80, 176/175, 1029/1024&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~8/7 = 232.419&lt;br /&gt;
-Mapping generator: ~8/7&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 0 3 -1|, &amp;lt;0 3 12 -1 23|]&lt;br /&gt;
-EDOs: 31, 129, 136b, 148be, 160be, 191bce, 222bce, 253bce&lt;br /&gt;
-Badness: 0.0313&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:144:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc72"&gt;&lt;a name="Mothra-Mosura-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:144 --&gt;13-limit&lt;/h3&gt;
- Commas: 81/80, 144/143, 176/175, 1029/1024&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~8/7 = 232.640&lt;br /&gt;
-Mapping generator: ~8/7&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 0 3 -1 7|, &amp;lt;0 3 12 -1 23 -17|]&lt;br /&gt;
-EDOs: 31, 67, 98&lt;br /&gt;
-Badness: 0.0369&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:146:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc73"&gt;&lt;a name="Squares"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:146 --&gt;Squares&lt;/h1&gt;
- &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 81/80, 2401/2400&lt;br /&gt;
-&lt;br /&gt;
-Squares, with wedgie &amp;lt;&amp;lt;4 16 9 16 3 -24||, splits the interval of an eleventh, or 8/3, into four supermajor third (&lt;a class="wiki_link" href="/9_7"&gt;9/7&lt;/a&gt;) intervals, and uses it for a generator. &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;, 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.&lt;br /&gt;
-&lt;br /&gt;
-and 9 limit minimax 1/4 comma&lt;br /&gt;
-[|1 0 0 0&amp;gt;, |1 0 1/4 0&amp;gt;, |0 0 1 0&amp;gt;, |3/2 0 9/16 0&amp;gt;]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzo&lt;/a&gt;s: 2, 5&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~9/7 = 425.942&lt;br /&gt;
-Mapping generator: ~9/7&lt;br /&gt;
-&lt;br /&gt;
-Algebraic generator: Sceptre2, the positive root of 9x^2+x-16, or (sqrt(577)-1)/18, which is 425.9311 cents.&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 3 8 6|, &amp;lt;0 -4 -16 -9|]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Generator"&gt;Generator&lt;/a&gt;s: 2, 9/7&lt;br /&gt;
-EDOs: &lt;a class="wiki_link" href="/14edo"&gt;14&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/262edo"&gt;262&lt;/a&gt;, &lt;a class="wiki_link" href="/293edo"&gt;293&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0460&lt;br /&gt;
-&lt;br /&gt;
-Music:&lt;br /&gt;
-By &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/tuning-survey/daily20100603-squares8piano.mp3" rel="nofollow"&gt;Square 8&lt;/a&gt;&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:148:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc74"&gt;&lt;a name="Squares-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:148 --&gt;11-limit&lt;/h2&gt;
- Commas: 81/80, 99/98, 121/120&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~9/7 = 425.957&lt;br /&gt;
-Mapping generator: ~9/7&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 3 8 6 7|, &amp;lt;0 -4 -16 -9 -10|]&lt;br /&gt;
-EDOs: &lt;a class="wiki_link" href="/5edo"&gt;5&lt;/a&gt;, &lt;a class="wiki_link" href="/8edo"&gt;8&lt;/a&gt;, &lt;a class="wiki_link" href="/11edo"&gt;11&lt;/a&gt;, &lt;a class="wiki_link" href="/14edo"&gt;14&lt;/a&gt;, &lt;a class="wiki_link" href="/17edo"&gt;17&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0216&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:150:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc75"&gt;&lt;a name="Squares-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:150 --&gt;13-limit&lt;/h2&gt;
- Commas: 81/80, 99/98, 121/120, 66/65&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~9/7 = 425.550&lt;br /&gt;
-Mapping generator: ~9/7&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 3 8 6 7 3|, &amp;lt;0 -4 -16 -9 -10 2|]&lt;br /&gt;
-EDOs: 17c, 31, 79cf, 110cef, 141cef&lt;br /&gt;
-&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0255&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:152:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc76"&gt;&lt;a name="Squares-Agora"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:152 --&gt;Agora&lt;/h2&gt;
- Commas: 81/80, 99/98, 105/104, 121/120&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~9/7 = 426.276&lt;br /&gt;
-Mapping generator: ~9/7&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 3 8 6 7 14|, &amp;lt;0 -4 -16 -9 -10 -29|]&lt;br /&gt;
-EDOs: 31, 45ef, 76e&lt;br /&gt;
-Badness: 0.0245&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:154:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc77"&gt;&lt;a name="Cuboctahedra"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:154 --&gt;Cuboctahedra&lt;/h1&gt;
- &lt;!-- ws:start:WikiTextHeadingRule:156:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc78"&gt;&lt;a name="Cuboctahedra-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:156 --&gt;11-limit&lt;/h2&gt;
- &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 81/80, 385/384, 1375/1372&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~9/7 = 425.993&lt;br /&gt;
-Mapping generator: ~9/7&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 3 8 6 -4|, &amp;lt;0 -4 -16 -9 21|]&lt;br /&gt;
-EDOs: &lt;a class="wiki_link" href="/14edo"&gt;14&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/45edo"&gt;45&lt;/a&gt;, &lt;a class="wiki_link" href="/200edo"&gt;200&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0568&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:158:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc79"&gt;&lt;a name="Liese"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:158 --&gt;Liese&lt;/h1&gt;
- &lt;span style="display: block; text-align: right;"&gt;&lt;a class="wiki_link" href="http://xenharmonie.wikispaces.com/Liese"&gt;Deutsch&lt;/a&gt;&lt;br /&gt;
-&lt;/span&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 81/80, 686/675&lt;br /&gt;
-&lt;br /&gt;
-Liese, with wedgie &amp;lt;&amp;lt;3 12 11 12 9 -8||, splits the twelfth interval of 3/1 into three generators of 10/7, using the comma 1029/1000. It also tempers out 686/675, the senga. &lt;a class="wiki_link" href="/74edo"&gt;74edo&lt;/a&gt; makes for a good liese tuning, though &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; can be used. The tuning is well-supplied with MOS: 7, 9, 11, 13, 15, 17, 19, 36, 55.&lt;br /&gt;
-&lt;br /&gt;
-and 9 limit minimax 1/4 comma&lt;br /&gt;
-[|1 0 0 0&amp;gt;, |1 0 1/4 0&amp;gt;, |0 0 1 0&amp;gt;, |2/3 0 11/12 0&amp;gt;]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzo&lt;/a&gt;s: 2, 5&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~10/7 = 632.406&lt;br /&gt;
-Mapping generator: ~10/7&lt;br /&gt;
-&lt;br /&gt;
-Algebraic generator: Radix, the real root of x^5-2x^4+2x^3-2x^2+2x-2, also a root of x^6-x^5-2. The recurrence converges.&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 -3|, &amp;lt;0 3 12 11|]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Generator"&gt;Generator&lt;/a&gt;s: 2, 10/7&lt;br /&gt;
-EDOs: &lt;a class="wiki_link" href="/17edo"&gt;17&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/55edo"&gt;55&lt;/a&gt;, &lt;a class="wiki_link" href="/74edo"&gt;74&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0467&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:160:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc80"&gt;&lt;a name="Liese-Liesel"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:160 --&gt;Liesel&lt;/h2&gt;
- Commas: 56/55, 81/80, 540/539&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~10/7 = 633.073&lt;br /&gt;
-Mapping generator: ~10/7&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 -3 4|, &amp;lt;0 3 12 11 -1|]&lt;br /&gt;
-EDOs: 17c, 19, 36, 91ce&lt;br /&gt;
-Badness: 0.0407&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:162:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc81"&gt;&lt;a name="Liese-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:162 --&gt;13-limit&lt;/h2&gt;
- Liesel is a very natural 13-limit tuning, given the generator is so near 13/9.&lt;br /&gt;
-&lt;br /&gt;
-Commas: 56/55, 78/77, 81/80, 91/90&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~10/7 = ~13/9 = 633.042&lt;br /&gt;
-Mapping generator: ~10/7&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 -3 4 0|, &amp;lt;0 3 12 11 -1 7|]&lt;br /&gt;
-EDOs: 17c, 19, 36, 91cef&lt;br /&gt;
-Badness: 0.0273&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:164:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc82"&gt;&lt;a name="Liese-Elisa"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:164 --&gt;Elisa&lt;/h2&gt;
- Commas: 77/75, 81/80, 99/98&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~10/7 = 633.061&lt;br /&gt;
-Mapping generator: ~10/7&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 -3 -5|, &amp;lt;0 3 12 11 16|]&lt;br /&gt;
-EDOs: 19e, 36e&lt;br /&gt;
-Badness: 0.0416&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:166:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc83"&gt;&lt;a name="Liese-Lisa"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:166 --&gt;Lisa&lt;/h2&gt;
- Commas: 45/44, 81/80, 343/330&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~10/7 = 631.370&lt;br /&gt;
-Mapping generator: ~10/7&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 -3 -6|, &amp;lt;0 3 12 11 18|]&lt;br /&gt;
-EDOs: 19&lt;br /&gt;
-Badness: 0.0548&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:168:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc84"&gt;&lt;a name="Liese-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:168 --&gt;13-limit&lt;/h2&gt;
- Commas: 45/44, 81/80, 91/88, 147/143&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~10/7 = 631.221&lt;br /&gt;
-Mapping generator: ~10/7&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 -3 -6 0|, &amp;lt;0 3 12 11 18 7|]&lt;br /&gt;
-EDOs: 19&lt;br /&gt;
-Badness: 0.0361&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:170:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc85"&gt;&lt;a name="Jerome"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:170 --&gt;Jerome&lt;/h1&gt;
- Jerome is related to &lt;a class="wiki_link" href="/20ed5"&gt;Hieronymus' tuning&lt;/a&gt;; 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.&lt;br /&gt;
-&lt;br /&gt;
-Commas: 81/80, 17280/16807&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~54/49 = 139.343&lt;br /&gt;
-Mapping generator: ~54/49&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 0 2|, &amp;lt;0 5 20 7|]&lt;br /&gt;
-Wedgie: &amp;lt;&amp;lt;5 30 7 20 -3 -40||&lt;br /&gt;
-EDOs: 8, 9, 17, 26, 43, 112&lt;br /&gt;
-Badness: 0.1087&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:172:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc86"&gt;&lt;a name="Jerome-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:172 --&gt;11-limit&lt;/h2&gt;
- Commas: 81/80, 99/98, 864/847&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~12/11 = 139.428&lt;br /&gt;
-Mapping generator: ~12/11&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 0 2 3|, &amp;lt;0 5 20 7 4|]&lt;br /&gt;
-EDOs: 8, 9, 17, 26, 43, 241&lt;br /&gt;
-Badness: 0.0479&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:174:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc87"&gt;&lt;a name="Jerome-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:174 --&gt;13-limit&lt;/h2&gt;
- Commas: 77/78, 81/80, 99/98, 144/143&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~13/12 = 139.387&lt;br /&gt;
-Mapping generator: ~12/11&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 0 2 3 3|, &amp;lt;0 5 20 7 4 6|]&lt;br /&gt;
-EDOs: 8, 9, 17, 26, 43, 155, 198&lt;br /&gt;
-Badness: 0.0293&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:176:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc88"&gt;&lt;a name="Jerome-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:176 --&gt;17-limit&lt;/h2&gt;
- Commas: 78/77, 81/80, 99/98, 144/143, 189/187&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~13/12 = 139.362&lt;br /&gt;
-Mapping generator: ~12/11&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 0 2 3 3 2|, &amp;lt;0 5 20 7 4 6 18|]&lt;br /&gt;
-EDOs: 8, 9, 17, 26, 43, 155&lt;br /&gt;
-Badness: 0.0209&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:178:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc89"&gt;&lt;a name="Meanmag"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:178 --&gt;Meanmag&lt;/h1&gt;
- Commas: 81/80, 3125/3072&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~8/7 = 238.396&lt;br /&gt;
-Mapping generator: ~7&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;19 30 44 0|, &amp;lt;0 0 0 1|]&lt;br /&gt;
-Wedgie: &amp;lt;&amp;lt;0 0 19 0 30 44||&lt;br /&gt;
-EDOs: 19, 57, 76, 171bcd&lt;br /&gt;
-Badness: 0.0770&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:180:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc90"&gt;&lt;a name="Undevigintone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:180 --&gt;Undevigintone&lt;/h1&gt;
- Commas: 49/48, 81/80, 126/125&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~11/8 = 538.047&lt;br /&gt;
-Mapping generator: ~11&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;19 30 44 53 0|, &amp;lt;0 0 0 0 1|]&lt;br /&gt;
-EDOs: 19, 38d&lt;br /&gt;
-Badness: 0.0364&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:182:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc91"&gt;&lt;a name="Undevigintone-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:182 --&gt;13-limit&lt;/h2&gt;
- Commas: 49/48, 65/64, 81/80, 126/125&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~11/8 = 537.061&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;19 30 44 53 0 70|, &amp;lt;0 0 0 0 1 0|]&lt;br /&gt;
-EDOs: 19, 38d&lt;br /&gt;
-Badness: 0.0229&lt;/body&gt;&lt;/html&gt;</pre></div>