Porwell temperaments: Difference between revisions

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This is a collection of [[regular temperament|temperaments]] that [[tempering out|~~tempers~~ out]] the porwell comma, {{monzo| 11 1 -3 -2 }} ([[6144/6125]]).

This is a collection of [[regular temperament|temperaments]] that [[tempering out|temper out]] the [[porwell comma]] ({{monzo|legend=1| 11 1 -3 -2 }}, [[ratio]]: [[6144/6125]]).

Temperaments discussed elsewhere are:

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* [[Porcupine]] (+64/63) → [[Porcupine family #Porcupine|Porcupine family]]

* ''[[Alphatrident]]'' (+14348907/14336000) → [[Alphatricot family #Alphatrident|Alphatricot family]]

* [[Shrutar]] (+245/243) → [[Diaschismic family #Shrutar|Diaschismic family]]

* ''[[Shrutar]]'' (+245/243) → [[Diaschismic family #Shrutar|Diaschismic family]]

* [[Amity]] (+4375/4374 or 5120/5103) → [[Amity family #Septimal amity|Amity family]]

* [[Orwell]] (+225/224) → [[Semicomma family #Orwell|Semicomma family]]

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* ''[[Decimaleap]]'' (+{{monzo| 15 -18 1 4 }}) → [[Quintaleap family #Decimaleap|Quintaleap family]]

* ''[[Hemikleismic]]'' (+4000/3969) → [[Kleismic family #Hemikleismic|Kleismic family]]

* ''[[Twothirdtonic]]'' (+686/675) → [[Sengic temperaments #Twothirdtonic|Sengic temperaments]]

* ''[[Bison]]'' (+78732/78125) → [[Sensipent family #Bison|Sensipent family]]

* ''[[Quinkee]]'' (+1029/1000) → [[~~Cloudy clan~~ #Quinkee|~~Cloudy clan~~]]

* ''[[Quinkee]]'' (+1029/1000) → [[Keegic temperaments #Quinkee|Keegic temperaments]]

* ''[[Hemiwürschmidt]]'' (+2401/2400 or 3136/3125) → [[Hemimean clan #Hemiwürschmidt|Hemimean clan]]

* ''[[Septisuperfourth]]'' (+118098/117649) → [[Escapade family #Septisuperfourth|Escapade family]]

* ''[[Semaja]]'' (+3125/3087) → [[Gariboh clan #Semaja|Gariboh clan]]

* ''[[Hemimabila]]'' (+117649/116640) → [[Mabila family #Hemimabila|Mabila family]]

* ''[[Countermiracle]]'' (+823543/819200) → [[Quince clan #Countermiracle|Quince clan]]

* ''[[Hemimaquila]]'' (+{{monzo| -5 10 5 -8 }}) → [[Maquila family #Hemimaquila|Maquila family]]

Considered below are hendecatonic, nessafof, ~~twothirdtonic~~, aufo, absurdity, polypyth, whoops, dodifo, and icositritonic, in the order of increasing [[badness]].

Considered below are hendecatonic, nessafof, grendel, aufo, absurdity, polypyth, whoops, dodifo, and icositritonic, in the order of increasing [[badness]].

== Hendecatonic ==

: ''For the 5-limit version, see [[~~11th~~-~~octave~~ temperaments #~~Hendecapent~~]].''

: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Hendecatonic]].''

The hendecatonic temperament has a period of 1/11 octave, which represents [[16/15]] and four times of which represent [[9/7]]. It tempers out 10976/10935, the [[hemimage comma]], and may be described as the {{nowrap| 22 & 99 }} temperament, with [[99edo]] giving an almost perfect tuning.

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[[Badness]] (Sintel): 1.04

=== ~~11-limit~~ ===

=== Hendecaton ===

Subgroup: 2.3.5.7.11

Comma list: 121/120, 176/175, 10976/10935

~~Mapping:~~ {{~~mapping~~| 11 0 43 -4 38 | 0 1 -1 2 0 }}

Optimal tunings:

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Line 70:

Comma list: 121/120, 176/175, 351/350, 4459/4455

~~Mapping:~~ {{~~mapping~~| 11 0 43 -4 38 93 | 0 1 -1 2 0 -3 }}

Optimal tunings:

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Comma list: 121/120, 154/153, 176/175, 273/272, 2025/2023

~~Mapping:~~ {{~~mapping~~| 11 0 43 -4 38 93 45 | 0 1 -1 2 0 -3 0 }}

Optimal tunings:

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Comma list: 540/539, 896/891, 4375/4356

~~Mapping:~~ {{~~mapping~~| 11 0 43 -4 73 | 0 1 -1 2 -2 }}

Optimal tunings:

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Line 115:

Comma list: 352/351, 364/363, 540/539, 625/624

~~Mapping:~~ {{~~mapping~~| 11 0 43 -4 73 128 | 0 1 -1 2 -2 -5 }}

Optimal tunings:

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Line 130:

Comma list: 256/255, 352/351, 364/363, 375/374, 540/539

~~Mapping:~~ {{~~mapping~~| 11 0 43 -4 73 128 45 | 0 1 -1 2 -2 -5 0 }}

Optimal tunings:

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Comma list: 3388/3375, 6144/6125, 9801/9800

~~Mapping:~~ {{~~mapping~~| 22 0 86 -8 111 | 0 1 -1 2 -1 }}

: mapping generators: ~33/32, ~3

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Comma list: 441/440, 1344/1331, 4375/4356

~~Mapping:~~ {{~~mapping~~| 3 2 5 10 10 | 0 7 5 -4 1 }}

Optimal tunings:

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Comma list: 144/143, 364/363, 441/440, 625/624

~~Mapping:~~ {{~~mapping~~| 3 2 5 10 10 6 | 0 7 5 -4 1 13 }}

Optimal tunings:

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Comma list: 121/120, 176/175, 250047/250000

~~Mapping:~~ {{~~mapping~~| 3 2 5 10 8 | 0 7 5 -4 6 }}

Optimal tunings:

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== Grendel ==

: ''For the 5-limit version, see [[Syntonic–31 equivalence continuum #Counterwürschmidt]].''

Grendel tempers out 16875/16807, the [[mirkwai comma]], and may be described as the {{nowrap| 31 & 152 }} temperament. [[152edo]], [[183edo]] and especially [[335edo]] serve as good tunings.

[[Subgroup]]: 2.3.5.7

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Comma list: 540/539, 1375/1372, 5632/5625

~~Mapping:~~ {{~~mapping~~| 1 -14 3 -6 -25 | 0 23 -1 13 42 }}

Optimal tunings:

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Line 265:

Comma list: 352/351, 540/539, 625/624, 1375/1372

~~Mapping:~~ {{~~mapping~~| 1 -14 3 -6 -25 22 | 0 23 -1 13 42 -27 }}

Optimal tunings:

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Comma list: 256/255, 352/351, 625/624, 715/714, 1275/1274

~~Mapping:~~ {{~~mapping~~| 1 -14 3 -6 -25 22 19 | 0 23 -1 13 42 -27 -22 }}

{{Mapping|legend=0| 1 -14 3 -6 -25 22 19 | 0 23 -1 13 42 -27 -22 }}

Optimal tunings:

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Comma list: 256/255, 352/351, 375/374, 400/399, 456/455, 715/714

~~Mapping:~~ {{~~mapping~~| 1 -14 3 -6 -25 22 19 30 | 0 23 -1 13 42 -27 -22 -38 }}

{{Mapping|legend=0| 1 -14 3 -6 -25 22 19 30 | 0 23 -1 13 42 -27 -22 -38 }}

Optimal tunings:

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Badness (Sintel): 1.12

~~== Twothirdtonic ==~~

Twothirdtonic tempers out 686/675, the [[senga]], in addition to the porwell comma, and may be described as the {{nowrap| 37 & 46 }} temperament, generated by one third of a [[5/4|classical major third]] that represents [[15/14]], [[14/13]], and [[13/12]] in the [[13-limit]] interpretation. Note that in the data below, the generator is taken to be its [[octave complement]], thirteen of which [[octave reduction|octave reduced]] make the [[3/2|perfect fifth]]; it follows that the [[ploidacot]] for this temperament is 11-sheared 13-cot. [[46edo]] may be recommended as a tuning.

~~[[Subgroup]]: 2.3.5.7~~

~~[[Comma list]]: 686/675, 6144/6125~~

~~{{Mapping|legend=1| 1 -10 5 -7 | 0 13 -3 11 }}~~

~~: mapping generators: ~2, ~28/15~~

~~[[Optimal tuning]]s:~~

* [[WE]]: ~2 = 1199.3074{{c}}, ~28/15 = 1068.9820{{c}}

~~: [[error map]]: {{val| -0.693 +1.736 +3.278 -5.176 }}~~

* [[CWE]]: ~2 = 1200.0000{{c}}, ~28/15 = 1069.5746{{c}}

~~: error map: {{val| 0.000 +2.515 +4.962 -3.505 }}~~

~~{{Optimal ET sequence|legend=1| 9, 28b, 37, 46 }}~~

~~[[Badness]] (Sintel): 2.52~~

~~=== 11-limit ===~~

~~Subgroup: 2.3.5.7.11~~

~~Comma list: 121/120, 176/175, 686/675~~

~~Mapping: {{mapping| 1 -10 5 -7 -1 | 0 13 -3 11 5 }}~~

~~Optimal tunings:~~

* WE: ~2 = 1199.7068{{c}}, ~28/15 = 1069.3084{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~28/15 = 1069.5600{{c}}

~~{{Optimal ET sequence|legend=0| 9, 28b, 37, 46 }}~~

~~Badness (Sintel): 1.35~~

~~=== 13-limit ===~~

~~Subgroup: 2.3.5.7.11.13~~

~~Comma list: 91/90, 121/120, 169/168, 176/175~~

~~Mapping: {{mapping| 1 -10 5 -7 -1 -7 | 0 13 -3 11 5 12 }}~~

~~Optimal tunings:~~

* WE: ~2 = 1199.9531{{c}}, ~13/7 = 1069.5492{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~13/7 = 1069.5893{{c}}

~~{{Optimal ET sequence|legend=0| 9, 28b, 37, 46 }}~~

~~Badness (Sintel): 1.07~~

~~== Semaja ==~~

Cryptically named by [[Petr Pařízek]] in 2011, semaja adds the [[gariboh comma]] to the comma list, and may be described as the {{nowrap| 37 & 53 }} temperament. Its [[ploidacot]] is gamma-19-cot. The name actually refers to the fact that two of its ~[[8/7]] generator steps reach a ~[[13/10]]<ref name="petr's long post">[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>.

~~[[Subgroup]]: 2.3.5.7~~

~~[[Comma list]]: 3125/3087, 6144/6125~~

~~{{Mapping|legend=1| 1 -2 1 3 | 0 19 7 -1 }}~~

~~: mapping generators: ~2, ~8/7~~

~~[[Optimal tuning]]s:~~

* [[WE]]: ~2 = 1199.4860{{c}}, ~8/7 = 226.3864{{c}}

~~: [[error map]]: {{val| -0.514 +0.415 -2.123 +3.246 }}~~

* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 226.4697{{c}}

~~: error map: {{val| 0.000 +0.970 -1.026 +4.704 }}~~

~~{{Optimal ET sequence|legend=1| 16, 37, 53, 196d }}~~

~~[[Badness]] (Sintel): 2.71~~

~~=== 11-limit ===~~

~~Subgroup: 2.3.5.7.11~~

~~Comma list: 121/120, 176/175, 3125/3087~~

~~Mapping: {{mapping| 1 -2 1 3 1 | 0 19 7 -1 13 }}~~

~~Optimal tunings:~~

* WE: ~2 = 1199.9818{{c}}, ~8/7 = 226.4821{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 226.4851{{c}}

~~{{Optimal ET sequence|legend=0| 16, 37, 53 }}~~

~~Badness (Sintel): 1.98~~

~~=== 13-limit ===~~

~~Subgroup: 2.3.5.7.11.13~~

~~Comma list: 121/120, 169/168, 176/175, 275/273~~

~~Mapping: {{mapping| 1 -2 1 3 1 2 | 0 19 7 -1 13 9 }}~~

~~Optimal tunings:~~

* WE: ~2 = 1200.1020{{c}}, ~8/7 = 226.4987{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 226.4822{{c}}

~~{{Optimal ET sequence|legend=0| 16, 37, 53 }}~~

~~Badness (Sintel): 1.35~~

== Aufo ==

:''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Untriton]].''

Also named by [[Petr Pařízek]] in 2011, ''aufo'' refers to the augmented fourth, which is a generator of this temperament<ref name="petr's long post"/>. The functional generator however is the [[64/45]] diminished fifth, and like its [[untriton]] variant, nine generator steps give the [[interval class]] of [[3/1|3]]. The [[ploidacot]] for this temperament is delta-enneacot.

Also named by [[Petr Pařízek]] in 2011, ''aufo'' refers to the augmented fourth, which is a generator of this temperament<ref name="petr's long post">[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>. The functional generator however is the [[64/45]] diminished fifth, and like its [[untriton]] variant, nine generator steps give the [[interval class]] of [[3/1|3]]. The [[ploidacot]] for this temperament is delta-enneacot.

[[Subgroup]]: 2.3.5.7

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Comma list: 121/120, 176/175, 177147/175616

~~Mapping:~~ {{~~mapping~~| 1 -3 12 -14 6 | 0 9 -19 33 -5 }}

Optimal tunings:

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Comma list: 121/120, 176/175, 351/350, 58806/57967

~~Mapping:~~ {{~~mapping~~| 1 -3 12 -14 6 20 | 0 9 -19 33 -5 -32 }}

Optimal tunings:

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Comma list: 540/539, 5632/5625, 72171/71680

~~Mapping:~~ {{~~mapping~~| 1 -3 12 -14 33 | 0 9 -19 33 -58 }}

Optimal tunings:

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Comma list: 351/350, 540/539, 847/845, 4096/4095

~~Mapping:~~ {{~~mapping~~| 1 -3 12 -14 33 20 | 0 9 -19 33 -58 -32 }}

Optimal tunings:

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Comma list: 441/440, 6144/6125, 72171/71680

~~Mapping:~~ {{~~mapping~~| 7 0 -17 64 124 | 0 1 3 -4 -9 }}

Optimal tunings:

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Comma list: 351/350, 441/440, 1188/1183, 3584/3575

~~Mapping:~~ {{~~mapping~~| 7 0 -17 64 124 37 | 0 1 3 -4 -9 -1 }}

Optimal tunings:

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Comma list: 351/350, 441/440, 561/560, 1188/1183, 1632/1625

~~Mapping:~~ {{~~mapping~~| 7 0 -17 64 124 37 -49 | 0 1 3 -4 -9 -1 7 }}

Optimal tunings:

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Comma list: 324/323, 351/350, 441/440, 456/455, 476/475, 495/494

~~Mapping:~~ {{~~mapping~~| 7 0 -17 64 124 37 -49 63 | 0 1 3 -4 -9 -1 7 -3 }}

{{Mapping|legend=0| 7 0 -17 64 124 37 -49 63 | 0 1 3 -4 -9 -1 7 -3 }}

Optimal tunings:

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Comma list: 276/275, 324/323, 351/350, 441/440, 456/455, 476/475, 495/494

~~Mapping:~~ {{~~mapping~~| 7 0 -17 64 124 37 -49 63 76 | 0 1 3 -4 -9 -1 7 -3 -4 }}

{{Mapping|legend=0| 7 0 -17 64 124 37 -49 63 76 | 0 1 3 -4 -9 -1 7 -3 -4 }}

Optimal tunings:

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Comma list: 261/260, 276/275, 324/323, 351/350, 441/440, 456/455, 476/475, 495/494

~~Mapping:~~ {{~~mapping~~| 7 0 -17 64 124 37 -49 63 76 34 | 0 1 3 -4 -9 -1 7 -3 -4 0 }}

{{Mapping|legend=0| 7 0 -17 64 124 37 -49 63 76 34 | 0 1 3 -4 -9 -1 7 -3 -4 0 }}

Optimal tunings:

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: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Leapday]].''

Polypyth ~~(46 & 121)~~ tempers out the same 5-limit comma as the [[~~leapday~~]] ~~temperament (29 & 46)~~, but ~~with~~ the porwell (6144/6125) rather than the hemifamity (5120/5103) tempered out.

Polypyth tempers out the same 5-limit comma as [[leapday]], with which it shares the similarly sharp [[3/2|perfect-fifth]] generator, but the porwell comma (6144/6125) rather than the hemifamity comma (5120/5103) is tempered out here. It may be described as the {{nowrap| 46 & 121 }} temperament, and [[121edo]] and [[167edo]] make for good tunings.

[[Subgroup]]: 2.3.5.7

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Line 525:

Comma list: 896/891, 2200/2187, 6144/6125

~~Mapping:~~ {{~~mapping~~| 1 0 -31 52 59 | 0 1 21 -31 -35 }}

Optimal tunings:

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Line 540:

Comma list: 325/324, 352/351, 364/363, 1716/1715

~~Mapping:~~ {{~~mapping~~| 1 0 -31 52 59 64 | 0 1 21 -31 -35 -38 }}

Optimal tunings:

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Line 555:

Comma list: 256/255, 325/324, 352/351, 364/363, 1716/1715

~~Mapping:~~ {{~~mapping~~| 1 0 -31 52 59 64 39 | 0 1 21 -31 -35 -38 -22 }}

{{Mapping|legend=0| 1 0 -31 52 59 64 39 | 0 1 21 -31 -35 -38 -22 }}

Optimal tunings:

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Badness (Sintel): 0.971

== Majo ==

: ''For the 5-limit version, see [[Schismic–Mercator equivalence continuum #Maja (5-limit)]].''

Possibly named by [[Gene Ward Smith]] in 2012, majo may be described as {{nowrap| 53 & 167 }} and is a more complex alternative to [[maja]].

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 6144/6125, 1250000/1240029

: mapping generators: ~2, ~125/81

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.4701{{c}}, ~125/81 = 746.9341{{c}}

: [[error map]]: {{val| -0.530 +0.694 -0.470 +0.819 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~125/81 = 747.2751{{c}}

: error map: {{val| 0.000 +1.721 +1.013 +2.022 }}

[[Badness]] (Sintel): 3.56

=== 11-limit ===

Subgroup: 2.3.5.7.11

Comma list: 2200/2187, 3388/3375, 6144/6125

Optimal tunings:

* WE: ~2 = 1199.4882{{c}}, ~77/50 = 746.9681{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~77/50 = 747.2776{{c}}

Badness (Sintel): 2.71

=== 13-limit ===

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 352/351, 1001/1000, 2704/2695

Optimal tunings:

* WE: ~2 = 1199.5860{{c}}, ~20/13 = 747.0285{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 747.2789{{c}}

Badness (Sintel): 1.78

== Whoops ==

: ''For the 5-limit version, see [[Very high accuracy temperaments #Whoosh]].''

Also named by [[Petr Pařízek]] in 2011, ''whoops'' is a relatively simple extension to the otherwise very accurate microtemperament known as ''whoosh''<ref name="petr's long post"/>.

Also named by [[Petr Pařízek]] in 2011, whoops is a relatively simple extension to the otherwise very accurate microtemperament known as ''whoosh''<ref name="petr's long post"/>.

[[Subgroup]]: 2.3.5.7

Line 688:

Line 644:

Comma list: 3025/3024, 4000/3993, 6144/6125

~~Mapping:~~ {{~~mapping~~| 1 -16 -11 14 -4 | 0 33 25 -21 14 }}

Optimal tunings:

Line 725:

Line 681:

Comma list: 1375/1372, 2560/2541, 4375/4356

~~Mapping:~~ {{~~mapping~~| 1 -23 -4 0 14 | 0 35 9 4 -15 }}

Optimal tunings:

Line 740:

Line 696:

Comma list: 364/363, 625/624, 640/637, 1375/1372

~~Mapping:~~ {{~~mapping~~| 1 12 5 4 -1 4 | 0 -35 -9 -4 15 -1 }}

Optimal tunings:

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~~The icositritonic temperament (46 & 161)~~ has a period of 1/23 octave, so six period represents [[6/5]] and nine period represents [[21/16]].

Icositritonic has a period of 1/23 octave, so six period represents [[6/5]] and nine period represents [[21/16]]. It may be described as {{nowrap| 46 & 161 }}. It was named by [[Xenllium]] in 2019 for its number of periods per octave.

[[Subgroup]]: 2.3.5.7

Line 777:

Line 733:

Comma list: 441/440, 6144/6125, 35937/35840

~~Mapping:~~ {{~~mapping~~| 23 0 17 101 116 | 0 1 1 -1 -1 }}

Optimal tunings:

Line 792:

Line 748:

Comma list: 351/350, 441/440, 847/845, 3584/3575

~~Mapping:~~ {{~~mapping~~| 23 0 17 101 116 158 | 0 1 1 -1 -1 -2 }}

Optimal tunings:

Line 807:

Line 763:

Comma list: 351/350, 441/440, 561/560, 847/845, 1089/1088

~~Mapping:~~ {{~~mapping~~| 23 0 17 101 116 158 94 | 0 1 1 -1 -1 -2 0 }}

Optimal tunings:

Line 822:

Line 778:

Comma list: 351/350, 441/440, 456/455, 476/475, 513/512, 847/845

~~Mapping:~~ {{~~mapping~~| 23 0 17 101 116 158 94 207 | 0 1 1 -1 -1 -2 0 -3 }}

{{Mapping|legend=0| 23 0 17 101 116 158 94 207 | 0 1 1 -1 -1 -2 0 -3 }}

Optimal tunings:

Line 837:

Line 793:

Comma list: 276/275, 351/350, 391/390, 441/440, 456/455, 476/475, 847/845

~~Mapping:~~ {{~~mapping~~| 23 0 17 101 116 158 94 207 104 | 0 1 1 -1 -1 -2 0 -3 0 }}

{{Mapping|legend=0| 23 0 17 101 116 158 94 207 104 | 0 1 1 -1 -1 -2 0 -3 0 }}

Optimal tunings:

Line 849:

Line 805:

== References ==

[[Category:Porwell temperaments| ]]

[[Category:Temperament collections]]

[[Category:~~Porwell temperaments| ]] <!~~-~~- main article -->~~

[[Category:Catalogs of rank-2 temperaments]]

~~[[Category:Rank~~ 2]]

@@ Line 1: / Line 1: @@
 {{Technical data page}}
-This is a collection of [[regular temperament|temperaments]] that [[tempering out|tempers out]] the porwell comma, {{monzo| 11 1 -3 -2 }} ([[6144/6125]]).
+This is a collection of [[regular temperament|temperaments]] that [[tempering out|temper out]] the [[porwell comma]] ({{monzo|legend=1| 11 1 -3 -2 }}, [[ratio]]: [[6144/6125]]).
 Temperaments discussed elsewhere are:
@@ Line 8: / Line 8: @@
 * [[Porcupine]] (+64/63) → [[Porcupine family #Porcupine|Porcupine family]]
 * ''[[Alphatrident]]'' (+14348907/14336000) → [[Alphatricot family #Alphatrident|Alphatricot family]]
-* [[Shrutar]] (+245/243) → [[Diaschismic family #Shrutar|Diaschismic family]]
+* ''[[Shrutar]]'' (+245/243) → [[Diaschismic family #Shrutar|Diaschismic family]]
 * [[Amity]] (+4375/4374 or 5120/5103) → [[Amity family #Septimal amity|Amity family]]
 * [[Orwell]] (+225/224) → [[Semicomma family #Orwell|Semicomma family]]
@@ Line 16: / Line 16: @@
 * ''[[Decimaleap]]'' (+{{monzo| 15 -18 1 4 }}) → [[Quintaleap family #Decimaleap|Quintaleap family]]
 * ''[[Hemikleismic]]'' (+4000/3969) → [[Kleismic family #Hemikleismic|Kleismic family]]
+* ''[[Twothirdtonic]]'' (+686/675) → [[Sengic temperaments #Twothirdtonic|Sengic temperaments]]
 * ''[[Bison]]'' (+78732/78125) → [[Sensipent family #Bison|Sensipent family]]
-* ''[[Quinkee]]'' (+1029/1000) → [[Cloudy clan #Quinkee|Cloudy clan]]
+* ''[[Quinkee]]'' (+1029/1000) → [[Keegic temperaments #Quinkee|Keegic temperaments]]
 * ''[[Hemiwürschmidt]]'' (+2401/2400 or 3136/3125) → [[Hemimean clan #Hemiwürschmidt|Hemimean clan]]
 * ''[[Septisuperfourth]]'' (+118098/117649) → [[Escapade family #Septisuperfourth|Escapade family]]
+* ''[[Semaja]]'' (+3125/3087) → [[Gariboh clan #Semaja|Gariboh clan]]
 * ''[[Hemimabila]]'' (+117649/116640) → [[Mabila family #Hemimabila|Mabila family]]
 * ''[[Countermiracle]]'' (+823543/819200) → [[Quince clan #Countermiracle|Quince clan]]
 * ''[[Hemimaquila]]'' (+{{monzo| -5 10 5 -8 }}) → [[Maquila family #Hemimaquila|Maquila family]]
-Considered below are hendecatonic, nessafof, twothirdtonic, aufo, absurdity, polypyth, whoops, dodifo, and icositritonic, in the order of increasing [[badness]].
+Considered below are hendecatonic, nessafof, grendel, aufo, absurdity, polypyth, whoops, dodifo, and icositritonic, in the order of increasing [[badness]].
 == Hendecatonic ==
-: ''For the 5-limit version, see [[11th-octave temperaments #Hendecapent]].''
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Hendecatonic]].''
 The hendecatonic temperament has a period of 1/11 octave, which represents [[16/15]] and four times of which represent [[9/7]]. It tempers out 10976/10935, the [[hemimage comma]], and may be described as the {{nowrap| 22 & 99 }} temperament, with [[99edo]] giving an almost perfect tuning.
@@ Line 48: / Line 50: @@
 [[Badness]] (Sintel): 1.04
-=== 11-limit ===
+=== Hendecaton ===
 Subgroup: 2.3.5.7.11
 Comma list: 121/120, 176/175, 10976/10935
-Mapping: {{mapping| 11 0 43 -4 38 | 0 1 -1 2 0 }}
+{{Mapping|legend=0| 11 0 43 -4 38 | 0 1 -1 2 0 }}
 Optimal tunings:
@@ Line 68: / Line 70: @@
 Comma list: 121/120, 176/175, 351/350, 4459/4455
-Mapping: {{mapping| 11 0 43 -4 38 93 | 0 1 -1 2 0 -3 }}
+{{Mapping|legend=0| 11 0 43 -4 38 93 | 0 1 -1 2 0 -3 }}
 Optimal tunings:
@@ Line 83: / Line 85: @@
 Comma list: 121/120, 154/153, 176/175, 273/272, 2025/2023
-Mapping: {{mapping| 11 0 43 -4 38 93 45 | 0 1 -1 2 0 -3 0 }}
+{{Mapping|legend=0| 11 0 43 -4 38 93 45 | 0 1 -1 2 0 -3 0 }}
 Optimal tunings:
@@ Line 98: / Line 100: @@
 Comma list: 540/539, 896/891, 4375/4356
-Mapping: {{mapping| 11 0 43 -4 73 | 0 1 -1 2 -2 }}
+{{Mapping|legend=0| 11 0 43 -4 73 | 0 1 -1 2 -2 }}
 Optimal tunings:
@@ Line 113: / Line 115: @@
 Comma list: 352/351, 364/363, 540/539, 625/624
-Mapping: {{mapping| 11 0 43 -4 73 128 | 0 1 -1 2 -2 -5 }}
+{{Mapping|legend=0| 11 0 43 -4 73 128 | 0 1 -1 2 -2 -5 }}
 Optimal tunings:
@@ Line 128: / Line 130: @@
 Comma list: 256/255, 352/351, 364/363, 375/374, 540/539
-Mapping: {{mapping| 11 0 43 -4 73 128 45 | 0 1 -1 2 -2 -5 0 }}
+{{Mapping|legend=0| 11 0 43 -4 73 128 45 | 0 1 -1 2 -2 -5 0 }}
 Optimal tunings:
@@ Line 143: / Line 145: @@
 Comma list: 3388/3375, 6144/6125, 9801/9800
-Mapping: {{mapping| 22 0 86 -8 111 | 0 1 -1 2 -1 }}
+{{Mapping|legend=0| 22 0 86 -8 111 | 0 1 -1 2 -1 }}
 : mapping generators: ~33/32, ~3
@@ Line 181: / Line 183: @@
 Comma list: 441/440, 1344/1331, 4375/4356
-Mapping: {{mapping| 3 2 5 10 10 | 0 7 5 -4 1 }}
+{{Mapping|legend=0| 3 2 5 10 10 | 0 7 5 -4 1 }}
 Optimal tunings:
@@ Line 196: / Line 198: @@
 Comma list: 144/143, 364/363, 441/440, 625/624
-Mapping: {{mapping| 3 2 5 10 10 6 | 0 7 5 -4 1 13 }}
+{{Mapping|legend=0| 3 2 5 10 10 6 | 0 7 5 -4 1 13 }}
 Optimal tunings:
@@ Line 211: / Line 213: @@
 Comma list: 121/120, 176/175, 250047/250000
-Mapping: {{mapping| 3 2 5 10 8 | 0 7 5 -4 6 }}
+{{Mapping|legend=0| 3 2 5 10 8 | 0 7 5 -4 6 }}
 Optimal tunings:
@@ Line 223: / Line 225: @@
 == Grendel ==
 : ''For the 5-limit version, see [[Syntonic–31 equivalence continuum #Counterwürschmidt]].''
+Grendel tempers out 16875/16807, the [[mirkwai comma]], and may be described as the {{nowrap| 31 & 152 }} temperament. [[152edo]], [[183edo]] and especially [[335edo]] serve as good tunings.
 [[Subgroup]]: 2.3.5.7
@@ Line 246: / Line 250: @@
 Comma list: 540/539, 1375/1372, 5632/5625
-Mapping: {{mapping| 1 -14 3 -6 -25 | 0 23 -1 13 42 }}
+{{Mapping|legend=0| 1 -14 3 -6 -25 | 0 23 -1 13 42 }}
 Optimal tunings:
@@ Line 261: / Line 265: @@
 Comma list: 352/351, 540/539, 625/624, 1375/1372
-Mapping: {{mapping| 1 -14 3 -6 -25 22 | 0 23 -1 13 42 -27 }}
+{{Mapping|legend=0| 1 -14 3 -6 -25 22 | 0 23 -1 13 42 -27 }}
 Optimal tunings:
@@ Line 276: / Line 280: @@
 Comma list: 256/255, 352/351, 625/624, 715/714, 1275/1274
-Mapping: {{mapping| 1 -14 3 -6 -25 22 19 | 0 23 -1 13 42 -27 -22 }}
+{{Mapping|legend=0| 1 -14 3 -6 -25 22 19 | 0 23 -1 13 42 -27 -22 }}
 Optimal tunings:
@@ Line 291: / Line 295: @@
 Comma list: 256/255, 352/351, 375/374, 400/399, 456/455, 715/714
-Mapping: {{mapping| 1 -14 3 -6 -25 22 19 30 | 0 23 -1 13 42 -27 -22 -38 }}
+{{Mapping|legend=0| 1 -14 3 -6 -25 22 19 30 | 0 23 -1 13 42 -27 -22 -38 }}
 Optimal tunings:
@@ Line 300: / Line 304: @@
 Badness (Sintel): 1.12
-== Twothirdtonic ==
-Twothirdtonic tempers out 686/675, the [[senga]], in addition to the porwell comma, and may be described as the {{nowrap| 37 & 46 }} temperament, generated by one third of a [[5/4|classical major third]] that represents [[15/14]], [[14/13]], and [[13/12]] in the [[13-limit]] interpretation. Note that in the data below, the generator is taken to be its [[octave complement]], thirteen of which [[octave reduction|octave reduced]] make the [[3/2|perfect fifth]]; it follows that the [[ploidacot]] for this temperament is 11-sheared 13-cot. [[46edo]] may be recommended as a tuning.
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 686/675, 6144/6125
-{{Mapping|legend=1| 1 -10 5 -7 | 0 13 -3 11 }}
-: mapping generators: ~2, ~28/15
-[[Optimal tuning]]s:
-* [[WE]]: ~2 = 1199.3074{{c}}, ~28/15 = 1068.9820{{c}}
-: [[error map]]: {{val| -0.693 +1.736 +3.278 -5.176 }}
-* [[CWE]]: ~2 = 1200.0000{{c}}, ~28/15 = 1069.5746{{c}}
-: error map: {{val| 0.000 +2.515 +4.962 -3.505 }}
-{{Optimal ET sequence|legend=1| 9, 28b, 37, 46 }}
-[[Badness]] (Sintel): 2.52
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 121/120, 176/175, 686/675
-Mapping: {{mapping| 1 -10 5 -7 -1 | 0 13 -3 11 5 }}
-Optimal tunings:
-* WE: ~2 = 1199.7068{{c}}, ~28/15 = 1069.3084{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~28/15 = 1069.5600{{c}}
-{{Optimal ET sequence|legend=0| 9, 28b, 37, 46 }}
-Badness (Sintel): 1.35
-=== 13-limit ===
-Subgroup: 2.3.5.7.11.13
-Comma list: 91/90, 121/120, 169/168, 176/175
-Mapping: {{mapping| 1 -10 5 -7 -1 -7 | 0 13 -3 11 5 12 }}
-Optimal tunings:
-* WE: ~2 = 1199.9531{{c}}, ~13/7 = 1069.5492{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~13/7 = 1069.5893{{c}}
-{{Optimal ET sequence|legend=0| 9, 28b, 37, 46 }}
-Badness (Sintel): 1.07
-== Semaja ==
-Cryptically named by [[Petr Pařízek]] in 2011, semaja adds the [[gariboh comma]] to the comma list, and may be described as the {{nowrap| 37 & 53 }} temperament. Its [[ploidacot]] is gamma-19-cot. The name actually refers to the fact that two of its ~[[8/7]] generator steps reach a ~[[13/10]]<ref name="petr's long post">[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>.
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 3125/3087, 6144/6125
-{{Mapping|legend=1| 1 -2 1 3 | 0 19 7 -1 }}
-: mapping generators: ~2, ~8/7
-[[Optimal tuning]]s:
-* [[WE]]: ~2 = 1199.4860{{c}}, ~8/7 = 226.3864{{c}}
-: [[error map]]: {{val| -0.514 +0.415 -2.123 +3.246 }}
-* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 226.4697{{c}}
-: error map: {{val| 0.000 +0.970 -1.026 +4.704 }}
-{{Optimal ET sequence|legend=1| 16, 37, 53, 196d }}
-[[Badness]] (Sintel): 2.71
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 121/120, 176/175, 3125/3087
-Mapping: {{mapping| 1 -2 1 3 1 | 0 19 7 -1 13 }}
-Optimal tunings:
-* WE: ~2 = 1199.9818{{c}}, ~8/7 = 226.4821{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 226.4851{{c}}
-{{Optimal ET sequence|legend=0| 16, 37, 53 }}
-Badness (Sintel): 1.98
-=== 13-limit ===
-Subgroup: 2.3.5.7.11.13
-Comma list: 121/120, 169/168, 176/175, 275/273
-Mapping: {{mapping| 1 -2 1 3 1 2 | 0 19 7 -1 13 9 }}
-Optimal tunings:
-* WE: ~2 = 1200.1020{{c}}, ~8/7 = 226.4987{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 226.4822{{c}}
-{{Optimal ET sequence|legend=0| 16, 37, 53 }}
-Badness (Sintel): 1.35
 == Aufo ==
 :''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Untriton]].''
-Also named by [[Petr Pařízek]] in 2011, ''aufo'' refers to the augmented fourth, which is a generator of this temperament<ref name="petr's long post"/>. The functional generator however is the [[64/45]] diminished fifth, and like its [[untriton]] variant, nine generator steps give the [[interval class]] of [[3/1|3]]. The [[ploidacot]] for this temperament is delta-enneacot.
+Also named by [[Petr Pařízek]] in 2011, ''aufo'' refers to the augmented fourth, which is a generator of this temperament<ref name="petr's long post">[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>. The functional generator however is the [[64/45]] diminished fifth, and like its [[untriton]] variant, nine generator steps give the [[interval class]] of [[3/1|3]]. The [[ploidacot]] for this temperament is delta-enneacot.
 [[Subgroup]]: 2.3.5.7
@@ Line 428: / Line 332: @@
 Comma list: 121/120, 176/175, 177147/175616
-Mapping: {{mapping| 1 -3 12 -14 6 | 0 9 -19 33 -5 }}
+{{Mapping|legend=0| 1 -3 12 -14 6 | 0 9 -19 33 -5 }}
 Optimal tunings:
@@ Line 443: / Line 347: @@
 Comma list: 121/120, 176/175, 351/350, 58806/57967
-Mapping: {{mapping| 1 -3 12 -14 6 20 | 0 9 -19 33 -5 -32 }}
+{{Mapping|legend=0| 1 -3 12 -14 6 20 | 0 9 -19 33 -5 -32 }}
 Optimal tunings:
@@ Line 458: / Line 362: @@
 Comma list: 540/539, 5632/5625, 72171/71680
-Mapping: {{mapping| 1 -3 12 -14 33 | 0 9 -19 33 -58 }}
+{{Mapping|legend=0| 1 -3 12 -14 33 | 0 9 -19 33 -58 }}
 Optimal tunings:
@@ Line 473: / Line 377: @@
 Comma list: 351/350, 540/539, 847/845, 4096/4095
-Mapping: {{mapping| 1 -3 12 -14 33 20 | 0 9 -19 33 -58 -32 }}
+{{Mapping|legend=0| 1 -3 12 -14 33 20 | 0 9 -19 33 -58 -32 }}
 Optimal tunings:
@@ Line 509: / Line 413: @@
 Comma list: 441/440, 6144/6125, 72171/71680
-Mapping: {{mapping| 7 0 -17 64 124 | 0 1 3 -4 -9 }}
+{{Mapping|legend=0| 7 0 -17 64 124 | 0 1 3 -4 -9 }}
 Optimal tunings:
@@ Line 524: / Line 428: @@
 Comma list: 351/350, 441/440, 1188/1183, 3584/3575
-Mapping: {{mapping| 7 0 -17 64 124 37 | 0 1 3 -4 -9 -1 }}
+{{Mapping|legend=0| 7 0 -17 64 124 37 | 0 1 3 -4 -9 -1 }}
 Optimal tunings:
@@ Line 539: / Line 443: @@
 Comma list: 351/350, 441/440, 561/560, 1188/1183, 1632/1625
-Mapping: {{mapping| 7 0 -17 64 124 37 -49 | 0 1 3 -4 -9 -1 7 }}
+{{Mapping|legend=0| 7 0 -17 64 124 37 -49 | 0 1 3 -4 -9 -1 7 }}
 Optimal tunings:
@@ Line 554: / Line 458: @@
 Comma list: 324/323, 351/350, 441/440, 456/455, 476/475, 495/494
-Mapping: {{mapping| 7 0 -17 64 124 37 -49 63 | 0 1 3 -4 -9 -1 7 -3 }}
+{{Mapping|legend=0| 7 0 -17 64 124 37 -49 63 | 0 1 3 -4 -9 -1 7 -3 }}
 Optimal tunings:
@@ Line 569: / Line 473: @@
 Comma list: 276/275, 324/323, 351/350, 441/440, 456/455, 476/475, 495/494
-Mapping: {{mapping| 7 0 -17 64 124 37 -49 63 76 | 0 1 3 -4 -9 -1 7 -3 -4 }}
+{{Mapping|legend=0| 7 0 -17 64 124 37 -49 63 76 | 0 1 3 -4 -9 -1 7 -3 -4 }}
 Optimal tunings:
@@ Line 584: / Line 488: @@
 Comma list: 261/260, 276/275, 324/323, 351/350, 441/440, 456/455, 476/475, 495/494
-Mapping: {{mapping| 7 0 -17 64 124 37 -49 63 76 34 | 0 1 3 -4 -9 -1 7 -3 -4 0 }}
+{{Mapping|legend=0| 7 0 -17 64 124 37 -49 63 76 34 | 0 1 3 -4 -9 -1 7 -3 -4 0 }}
 Optimal tunings:
@@ Line 597: / Line 501: @@
 : ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Leapday]].''
-Polypyth (46 & 121) tempers out the same 5-limit comma as the [[leapday]] temperament (29 & 46), but with the porwell (6144/6125) rather than the hemifamity (5120/5103) tempered out.
+Polypyth tempers out the same 5-limit comma as [[leapday]], with which it shares the similarly sharp [[3/2|perfect-fifth]] generator, but the porwell comma (6144/6125) rather than the hemifamity comma (5120/5103) is tempered out here. It may be described as the {{nowrap| 46 & 121 }} temperament, and [[121edo]] and [[167edo]] make for good tunings.
 [[Subgroup]]: 2.3.5.7
@@ Line 621: / Line 525: @@
 Comma list: 896/891, 2200/2187, 6144/6125
-Mapping: {{mapping| 1 0 -31 52 59 | 0 1 21 -31 -35 }}
+{{Mapping|legend=0| 1 0 -31 52 59 | 0 1 21 -31 -35 }}
 Optimal tunings:
@@ Line 636: / Line 540: @@
 Comma list: 325/324, 352/351, 364/363, 1716/1715
-Mapping: {{mapping| 1 0 -31 52 59 64 | 0 1 21 -31 -35 -38 }}
+{{Mapping|legend=0| 1 0 -31 52 59 64 | 0 1 21 -31 -35 -38 }}
 Optimal tunings:
@@ Line 651: / Line 555: @@
 Comma list: 256/255, 325/324, 352/351, 364/363, 1716/1715
-Mapping: {{mapping| 1 0 -31 52 59 64 39 | 0 1 21 -31 -35 -38 -22 }}
+{{Mapping|legend=0| 1 0 -31 52 59 64 39 | 0 1 21 -31 -35 -38 -22 }}
 Optimal tunings:
@@ Line 660: / Line 564: @@
 Badness (Sintel): 0.971
+== Majo ==
+: ''For the 5-limit version, see [[Schismic–Mercator equivalence continuum #Maja (5-limit)]].''
+Possibly named by [[Gene Ward Smith]] in 2012, majo may be described as {{nowrap| 53 & 167 }} and is a more complex alternative to [[maja]].
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 6144/6125, 1250000/1240029
+{{Mapping|legend=1| 1 -9 -12 19 | 0 17 23 -26 }}
+: mapping generators: ~2, ~125/81
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.4701{{c}}, ~125/81 = 746.9341{{c}}
+: [[error map]]: {{val| -0.530 +0.694 -0.470 +0.819 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~125/81 = 747.2751{{c}}
+: error map: {{val| 0.000 +1.721 +1.013 +2.022 }}
+{{Optimal ET sequence|legend=1| 53, 167, 220, 493bd, 713bdd }}
+[[Badness]] (Sintel): 3.56
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 2200/2187, 3388/3375, 6144/6125
+{{Mapping|legend=0| 1 -9 -12 19 -42 | 0 17 23 -26 73 }}
+Optimal tunings:
+* WE: ~2 = 1199.4882{{c}}, ~77/50 = 746.9681{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~77/50 = 747.2776{{c}}
+{{Optimal ET sequence|legend=0| 53, 114e, 167, 220, 387bd }}
+Badness (Sintel): 2.71
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 325/324, 352/351, 1001/1000, 2704/2695
+{{Mapping|legend=0| 1 -9 -12 19 -42 -10 | 0 17 23 -26 73 22 }}
+Optimal tunings:
+* WE: ~2 = 1199.5860{{c}}, ~20/13 = 747.0285{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 747.2789{{c}}
+{{Optimal ET sequence|legend=0| 53, 114e, 167, 220, 387bd }}
+Badness (Sintel): 1.78
 == Whoops ==
 : ''For the 5-limit version, see [[Very high accuracy temperaments #Whoosh]].''
-Also named by [[Petr Pařízek]] in 2011, ''whoops'' is a relatively simple extension to the otherwise very accurate microtemperament known as ''whoosh''<ref name="petr's long post"/>.
+Also named by [[Petr Pařízek]] in 2011, whoops is a relatively simple extension to the otherwise very accurate microtemperament known as ''whoosh''<ref name="petr's long post"/>.
 [[Subgroup]]: 2.3.5.7
@@ Line 688: / Line 644: @@
 Comma list: 3025/3024, 4000/3993, 6144/6125
-Mapping: {{mapping| 1 -16 -11 14 -4 | 0 33 25 -21 14 }}
+{{Mapping|legend=0| 1 -16 -11 14 -4 | 0 33 25 -21 14 }}
 Optimal tunings:
@@ Line 725: / Line 681: @@
 Comma list: 1375/1372, 2560/2541, 4375/4356
-Mapping: {{mapping| 1 -23 -4 0 14 | 0 35 9 4 -15 }}
+{{Mapping|legend=0| 1 -23 -4 0 14 | 0 35 9 4 -15 }}
 Optimal tunings:
@@ Line 740: / Line 696: @@
 Comma list: 364/363, 625/624, 640/637, 1375/1372
-Mapping: {{mapping| 1 12 5 4 -1 4 | 0 -35 -9 -4 15 -1 }}
+{{Mapping|legend=0| 1 12 5 4 -1 4 | 0 -35 -9 -4 15 -1 }}
 Optimal tunings:
@@ Line 753: / Line 709: @@
 {{See also| 23rd-octave temperaments }}
-The icositritonic temperament (46 & 161) has a period of 1/23 octave, so six period represents [[6/5]] and nine period represents [[21/16]].
+Icositritonic has a period of 1/23 octave, so six period represents [[6/5]] and nine period represents [[21/16]]. It may be described as {{nowrap| 46 & 161 }}. It was named by [[Xenllium]] in 2019 for its number of periods per octave.
 [[Subgroup]]: 2.3.5.7
@@ Line 777: / Line 733: @@
 Comma list: 441/440, 6144/6125, 35937/35840
-Mapping: {{mapping| 23 0 17 101 116 | 0 1 1 -1 -1 }}
+{{Mapping|legend=0| 23 0 17 101 116 | 0 1 1 -1 -1 }}
 Optimal tunings:
@@ Line 792: / Line 748: @@
 Comma list: 351/350, 441/440, 847/845, 3584/3575
-Mapping: {{mapping| 23 0 17 101 116 158 | 0 1 1 -1 -1 -2 }}
+{{Mapping|legend=0| 23 0 17 101 116 158 | 0 1 1 -1 -1 -2 }}
 Optimal tunings:
@@ Line 807: / Line 763: @@
 Comma list: 351/350, 441/440, 561/560, 847/845, 1089/1088
-Mapping: {{mapping| 23 0 17 101 116 158 94 | 0 1 1 -1 -1 -2 0 }}
+{{Mapping|legend=0| 23 0 17 101 116 158 94 | 0 1 1 -1 -1 -2 0 }}
 Optimal tunings:
@@ Line 822: / Line 778: @@
 Comma list: 351/350, 441/440, 456/455, 476/475, 513/512, 847/845
-Mapping: {{mapping| 23 0 17 101 116 158 94 207 | 0 1 1 -1 -1 -2 0 -3 }}
+{{Mapping|legend=0| 23 0 17 101 116 158 94 207 | 0 1 1 -1 -1 -2 0 -3 }}
 Optimal tunings:
@@ Line 837: / Line 793: @@
 Comma list: 276/275, 351/350, 391/390, 441/440, 456/455, 476/475, 847/845
-Mapping: {{mapping| 23 0 17 101 116 158 94 207 104 | 0 1 1 -1 -1 -2 0 -3 0 }}
+{{Mapping|legend=0| 23 0 17 101 116 158 94 207 104 | 0 1 1 -1 -1 -2 0 -3 0 }}
 Optimal tunings:
@@ Line 849: / Line 805: @@
 == References ==
+[[Category:Porwell temperaments| ]] <!-- main article -->
 [[Category:Temperament collections]]
-[[Category:Porwell temperaments| ]] <!-- main article -->
+[[Category:Catalogs of rank-2 temperaments]]
-[[Category:Rank 2]]

Porwell temperaments: Difference between revisions

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