Chromatic pairs: Difference between revisions

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== Terrain ==
== Terrain ==
{{Redirect|Terrain|the scale|Terrain (scale)}}
{{See also| Subgroup temperaments #Terrain }}
 
Terrain, the 6 & 21 temperament in the 2.9/5.9/7 subgroup, is related to [[domain (temperament)|domain]]. It is a remarkable temperament, in that while its complexity is low, it has no discernible error. The 1–7/5–9/5 and 1–9/7–9/5 chords are characteristic.
 
[[Subgroup]]: 2.9/5.9/7
 
[[Comma list]]: 250047/250000
 
{{Mapping|legend=2| 3 0 -4 | 0 1 2 }}
 
{{Mapping|legend=3| 3 10/9 -7/9 2/9 | 0 -2/3 -1/3 2/3 }}
 
: [[gencom]]: [63/50 10/9; 250047/250000]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~63/50 = 1\3, ~10/9 = 182.461
 
{{Optimal ET sequence|legend=1| 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558 }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.00844 cents


[[File:terrain_3558edo.png|right|alt=terrain_3558edo.png|Terrain in 3558edo]]
[[File:terrain_3558edo.png|right|alt=terrain_3558edo.png|Terrain in 3558edo]]
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== Petrtri ==
== Petrtri ==
Petrtri can be described as 3 & 5 temperament in the 2.11/5.13/5 subgroup.
{{See also| Subgroup temperaments #Petrtri }}
 
[[Subgroup]]: 2.11/5.13/5
 
[[Comma list]]: 2200/2197
 
{{Mapping|legend=2| 1 0 1| 0 3 1 }}
 
{{Mapping|legend=3| 1 0 -1/3 0 -1/3 2/3 | 0 0 -4/3 0 5/3 -1/3 }}
 
: [[gencom]]: [2 13/10; 2200/2197]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 455.012
 
{{Optimal ET sequence|legend=1| 21, 29, 153, 182, 211, 240, 269, 298, 327, 356, 385, 509, 741c, 1126c }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.0749 cents


[[File:petrtri_385edo.png|right|alt=petrtri_385edo.png|Petrtri in 385edo]]
[[File:petrtri_385edo.png|right|alt=petrtri_385edo.png|Petrtri in 385edo]]
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== Barton ==
== Barton ==
Barton may be described as the 11 &amp; 13 temperament in the 2.5.11.13 subgroup. It was named after [[Jacob Barton]] by [[Gene Ward Smith]] and [[Carl Lumma]] in 2006<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_14632.html Yahoo! Tuning Group | "father" variant?]</ref>.
{{Redirect|Barton|[[Jacob Barton]]'s scale|Barton (scale)}}
 
{{See also| The Jacobins #Barton }}
[[Subgroup]]: 2.5.11.13
 
[[Comma list]]: 2200/2197, 6656/6655
 
{{Mapping|legend=2| 1 6 3 6 | 0 -8 1 -5 }}
 
{{Mapping|legend=3| 1 0 6 0 3 6 | 0 0 -8 0 1 -5 }}
 
: gencom: [2 11/8; 2200/2197 6656/6655]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/8 = 551.699
 
{{Optimal ET sequence|legend=1| 11, 13, 24, 37, 50, 87, 298, 385, 472, 559, 1590cd }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.0822 cents


Scales:  
Scales:  
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* [[Barton11]] – 11-tone chromatic scale
* [[Barton11]] – 11-tone chromatic scale
* [[Barton13]] – 13-tone mega-chromatic scale
* [[Barton13]] – 13-tone mega-chromatic scale
== Voltage ==
Voltage is the 3 &amp; 7 temperament in the 2.7.13 subgroup.
[[Subgroup]]: 2.7.13
[[Comma list]]: 28672/28561
{{Mapping|legend=2| 1 4 4 | 0 -4 -1 }}
{{Mapping|legend=3| 1 0 0 4 0 4 | 0 0 0 -4 0 -1 }}
: [[gencom]]: [2, 16/13; 28672/28561]
[[Optimal tuning]]:
* [[POTE]]: ~2 = 1\1, ~16/13 = 357.677
* [[TOP tuning|POTT]]: ~2 = 1\1, ~16/13 = 357.794 (1200 - 300 log<sub>2</sub>(7))
{{Optimal ET sequence|legend=1| 3, 7, 10, 27, 37, 47, 57, 104 }}
[[Tp tuning #T2 tuning|RMS error]]: 0.1423


== Tridec ==
== Tridec ==
Tridec, the 5 &amp; 8 temperament in the 2.7/5.11/5.13/5 subgroup, extends [[petrtri]].
{{See also| Subgroup temperaments #Tridec }}
 
[[Subgroup]]: 2.7/5.11/5.13/5
 
[[Comma list]]: 847/845, 1001/1000
 
{{Mapping|legend=2| 1 2 0 1 | 0 -4 3 1 }}
 
{{Mapping|legend=3| 1 0 -3/4 5/4 -3/4 1/4 | 0 0 0 -4 3 1 }}
 
: [[gencom]]: [2 13/10; 847/845 1001/1000]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 454.556
 
{{Optimal ET sequence|legend=1| 5, 8, 21, 29, 37, 66, 169, 235, 404c, 639c, 953bc }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.1613 cents


[[File:tridec_235edo.png|right|alt=tridec_235edo.png|Tridec in 235edo]]
[[File:tridec_235edo.png|right|alt=tridec_235edo.png|Tridec in 235edo]]
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== Orgone ==
== Orgone ==
{{Main| Orgone }}
{{Main| Orgone }}
{{See also| Orgonia }}
{{See also| Orgonia #Orgone }}
 
Orgone, the 4 &amp; 7 temperament in the 2.7.11 subgroup, is related to [[superkleismic]].
 
[[Subgroup]]: 2.7.11
 
[[Comma list]]: 65536/65219
 
{{Mapping|legend=2| 1 2 4 | 0 3 -2 }}
 
{{Mapping|legend=3| 1 0 0 2 4 | 0 0 0 3 -2 }}
 
: [[gencom]]: [2 77/64; 65536/65219]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~77/64 = 323.372
 
{{Optimal ET sequence|legend=1| 4, 7, 11, 15, 26, 89, 115, 141, 167, 308, 475bc, 783bc }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.1888 cents


[[File:orgone_308edo.jpg|right|alt=orgone_308edo.jpg|Orgone in 308edo]]
[[File:orgone_308edo.jpg|right|alt=orgone_308edo.jpg|Orgone in 308edo]]
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== Marveltwintri ==
== Marveltwintri ==
Marveltwintri can be described as the 3 &amp; 4 temperament in the 2.5/3.13/9 subgroup.
{{See also| Subgroup temperaments #Marveltwintri }}
 
[[Subgroup]]: 2.5/3.13/9
 
[[Comma list]]: 325/324
 
{{Mapping|legend=2| 1 0 2 | 0 1 -2 }}
 
{{Mapping|legend=3| 1 -1/6 5/6 0 0 -1/3 | 0 -1/2 -3/2 0 0 1 }}
 
: [[gencom]]: [2 6/5; 325/324]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~6/5 = 317.139
 
{{Optimal ET sequence|legend=1| 11, 15, 19, 34, 53, 87, 140, 185, 219, 253, 287b, 321b }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.2444 cents


[[File:marveltwintri_321edo.png|right|alt=marveltwintri_321edo.png|Marveltwintri in 321edo]]
[[File:marveltwintri_321edo.png|right|alt=marveltwintri_321edo.png|Marveltwintri in 321edo]]
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== Cata ==
== Cata ==
{{Main| Hanson and cata }}
{{Main| Kleismic }}
{{See also| Kleismic family #Cata }}
{{See also| Kleismic family #Cata }}


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== Bridgetown ==
== Bridgetown ==
Bridgetown, the 5 &amp; 24 temperament in the 2.3.11/5.13/5 subgroup, is related to [[haumea]] and [[barbados]].
{{See also| Subgroup temperaments #Bridgetown }}
 
[[Subgroup]]: 2.3.11/5.13/5
 
[[Comma list]]: 352/351, 676/675
 
{{Mapping|legend=2| 1 0 -6 -1 | 0 2 9 3 }}
 
{{Mapping|legend=3| 1 2 -5/3 0 4/3 1/3 | 0 -2 4 0 -5 1 }}
 
: [[gencom]]: [2 15/13; 352/351 676/675]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~15/13 = 248.399
 
{{Optimal ET sequence|legend=1| 5, 9, 14, 19, 24, 29, 169, 198, 227, 256, 285, 314 }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.2513 cents


[[File:bridgetown_29edo.png|right|alt=bridgetown_29edo.png|Bridgetown in 29edo]]
[[File:bridgetown_29edo.png|right|alt=bridgetown_29edo.png|Bridgetown in 29edo]]
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== Haumea ==
== Haumea ==
Related temperaments include [[bridgetown]], [[namaka]], [[hemigari]], [[barbados]], and [[parizekmic]].
{{See also| Subgroup temperaments #Haumea }}
 
[[Subgroup]]: 2.3.7/5.11/5.13/5
 
[[Comma list]]: 352/351, 676/675, 847/845
 
{{Mapping|legend=2| 1 0 10 -6 -1 | 0 2 -12 9 3 }}
 
{{Mapping|legend=3| 1 2 -3/4 -11/4 9/4 5/4 | 0 -2 0 12 -9 -3 }}
 
: [[gencom]]: [2 15/13; 352/351 676/675 847/845]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~15/13 = 248.491
 
{{Optimal ET sequence|legend=1| 24, 29, 111, 140, 169, 198, 565d, 763bd, 961bd }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.2668 cents


Scales:  
Scales:  
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== Huntington ==
== Huntington ==
Huntington may be described as the 10 &amp; 27 temperament in the 2.5.7.13 subgroup.
{{See also| No-threes subgroup temperaments #Huntington }}
 
[[Subgroup]]: 2.5.7.13
 
[[Comma list]]: 640/637, 10985/10976
 
{{Mapping|legend=2| 1 5 4 4 | 0 -9 -4 -1 }}
 
{{Mapping|legend=3| 1 0 5 4 0 4 | 0 0 -9 -4 0 -1 }}
 
: [[gencom]]: [2 16/13; 640/637 10985/10976]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~16/13 = 357.002
 
{{Optimal ET sequence|legend=1| 7, 10, 17, 27, 37, 84, 121, 279cd, 400cd }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.3452 cents


[[File:huntington_400edo.jpg|right|alt=huntington_400edo.jpg|Huntington in 400edo]]
[[File:huntington_400edo.jpg|right|alt=huntington_400edo.jpg|Huntington in 400edo]]
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== Tobago ==
== Tobago ==
Tobago, the 10 &amp; 14 temperament in the 2.3.11.13/5 subgroup, extends [[neutral]] and [[barbados]].
{{See also| Subgroup temperaments #Tobago }}
 
[[Subgroup]]: 2.3.11.13/5
 
[[Comma list]]: 243/242, 676/675
 
{{Mapping|legend=2| 2 0 -1 -2 | 0 2 5 3 }}
 
{{Mapping|legend=3| 2 4 -2 0 9 2 | 0 -2 3/2 0 -5 -3/2 }}
 
: [[gencom]]: [55/39 15/13; 243/242 676/675]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~55/39 = 1\2, ~15/13 = 249.312
 
{{Optimal ET sequence|legend=1| 10, 14, 24, 58, 82, 130 }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.3533 cents


Scales:  
Scales:  
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== Pepperoni ==
== Pepperoni ==
{{See also| Parapyth }}
{{See also| Parapyth }}
 
{{See also| Subgroup temperaments #Pepperoni }}
Pepperoni is generated by a fifth and can be described as the 5 &amp; 12 temperament in the 2.3.11/7.13/7. It is the single-chain retraction of [[parapyth]]. The [[Peppermint-24|Pepper fifth]], which is (40200 + 600 sqrt(5))/59 = 704.096 cents, is a good pepperoni generator, hence the name.
 
[[Subgroup]]: 2.3.11/7.13/7
 
[[Comma list]]: 352/351, 364/363
 
{{Mapping|legend=2| 1 0 7 12 | 0 1 -4 -7 }}
 
{{Mapping|legend=3| 1 1 0 -8/3 1/3 7/3 | 0 1 0 11/3 -1/3 -10/3 }}
 
: [[gencom]]: [2 3/2; 352/351 364/363]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~3/2 = 703.856
 
{{Optimal ET sequence|legend=1| 5, 7, 12, 17, 29, 46, 58, 75, 80, 87, 104, 121, 167, 196, 208, 271, 595bcd }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents


[[File:pepperoni_271edo.png|right|alt=pepperoni_271edo.png|Pepperoni in 271edo]]
[[File:pepperoni_271edo.png|right|alt=pepperoni_271edo.png|Pepperoni in 271edo]]
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== Wizz ==
== Wizz ==
Wizz, the 6 &amp; 16 temperament in the 2.5.11 subgroup, is related to [[wizard]].
{{See also| No-threes subgroup temperaments #Wizz }}
 
[[Subgroup]]: 2.5.11
 
[[Comma list]]: 15625/15488
 
{{Mapping|legend=2| 2 0 -7 | 0 1 3 }}
 
{{Mapping|legend=3| 2 0 4 0 5 | 0 0 1 0 3 }}
 
: [[gencom]]: [125/88 5/4; 15625/15488]
 
[[Optimal tuning]] ([[POTE]]): ~125/88 = 1\2, ~5/4 = 383.768
 
{{Optimal ET sequence|legend=1| 6, 16, 22, 28, 50, 122, 172, 222 }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.3997


Scales:  
Scales:  
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== Bossier ==
== Bossier ==
Bossier can be described as the 3 &amp; 17 in the 2.7.11.13 subgroup.
{{See also| No-threes subgroup temperaments #Bossier }}
 
[[Subgroup]]: 2.7.11.13
 
[[Comma list]]: 1573/1568, 15488/15379
 
{{Mapping|legend=2| 1 0 1 3 | 0 8 7 2 }}
 
{{Mapping|legend=3| 1 0 0 0 1 3 | 0 0 0 8 7 2 }}
 
: [[gencom]]: [2 14/11; 1573/1568 15488/15379]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~14/11 = 421.309
 
{{Optimal ET sequence|legend=1| 17, 20, 37, 57, 94, 225, 319cd, 413bcd }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.4043 cents


[[File:bossier_225edo.jpg|right|alt=bossier_225edo.jpg|Bossier in 225edo]]
[[File:bossier_225edo.jpg|right|alt=bossier_225edo.jpg|Bossier in 225edo]]
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== Bluebirds ==
== Bluebirds ==
[[Subgroup]]: 2.11.13
{{See also| No-threes subgroup temperaments #Bluebirds }}
 
[[Comma list]]: 265837/262144
 
{{Mapping|legend=2| 1 0 6 | 0 3 -2 }}
 
{{Mapping|legend=3| 1 0 0 0 3 4 | 0 0 0 0 3 -2 }}
 
: [[gencom]]: [2 143/128; 265837/262144]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~143/128 = 182.368
 
{{Optimal ET sequence|legend=1| 6, 7, 13, 33, 46, 79, 125c, 204bc, 329bc }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.4444 cents


Scales:  
Scales:  
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== Marveltri ==
== Marveltri ==
Marveltri, the 3 &amp; 13 temperament in the 2.5.9/7 subgroup, is related to [[marvel]], [[magic]], and the unnamed 22 &amp; 47 temperament.
{{See also| Subgroup temperaments #Marveltri }}
 
[[Subgroup]]: 2.5.9/7
 
[[Comma list]]: 225/224
 
{{Mapping|legend=2| 1 0 5 | 0 1 -2 }}
 
{{Mapping|legend=3| 1 2/5 2 -1/5 | 0 -4/5 1 2/5 }}
 
: [[gencom]]: [2 5/4; 225/224]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~5/4 = 383.638
 
{{Optimal ET sequence|legend=1| 13, 16, 19, 22, 25, 47, 69, 72, 97, 122, 269bc, 660bc }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.4801 cents


Scales:  
Scales:  
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== Edson ==
== Edson ==
Edson is related to [[pele]] and [[andromeda]].
{{See also| Subgroup temperaments #Edson }}
 
[[Subgroup]]: 2.3.7/5.11/5.13/5
 
[[Comma list]]: 196/195 = {{monzo| 2 -1 2 0 -1 }}, 352/351 = {{monzo| 5 -3 0 1 -1 }}, 364/363 = {{monzo| 2 -1 1 -2 1 }}
 
{{Mapping|legend=2| 1 0 10 17 22 | 0 1 -6 -10 -13 }}
 
: mapping generators: ~2, ~3
 
{{Mapping|legend=3| 1 1 -5 -1 2 4 | 0 1 29/4 5/4 -11/4 -23/4 }}
 
: [[gencom]]: [2 3/2; 196/195, 352/351, 364/363]
 
[[Optimal tuning]]s:
* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1\1, ~3/2 = 703.4398
* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1\1, ~3/2 = 703.414
 
{{Optimal ET sequence|legend=1| 12, 17, 29 }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.5102 cents


Scales:  
Scales:  
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== Silver ==
== Silver ==
Silver can be described as the 10 &amp; 27 temperament in the 2.5.7.13.17 subgroup.
{{See also | No-threes subgroup temperaments #Silver }}
 
[[Subgroup]]: 2.5.7.13.17
 
[[Comma list]]: 170/169, 640/637, 5525/5488
 
{{Mapping|legend=2| 1 5 4 4 2 | 0 -9 -4 -1 7 }}
 
{{Mapping|legend=3| 1 0 -4 0 0 3 9 | 0 0 9 4 0 1 -7 }}
 
: [[gencom]]: [2 13/8; 170/169 640/637 5525/5488]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~13/8 = 842.711
 
{{Optimal ET sequence|legend=1| 7, 10, 17, 27, 37, 47, 84, 131, 178e, 309cde, 487bcdee }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.5886 cents


[[File:silver_487edo.jpg|right|alt=silver_487edo.jpg|Silver in 487edo]]
[[File:silver_487edo.jpg|right|alt=silver_487edo.jpg|Silver in 487edo]]
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== Baldy ==
== Baldy ==
{{See also| Subgroup temperaments #Baldy }}
{{See also| Subgroup temperaments #Baldy }}
Baldy is every other step of [[garibaldi]], without the mapping of prime 11. It can be described as the 6 &amp; 35 temperament.
[[Subgroup]]: 2.9.5.7.13
[[Comma list]]: 225/224, 325/324, 640/637
{{Mapping|legend=2| 1 0 15 25 -28 | 0 1 -4 -7 10 }}
{{Mapping|legend=3| 1 3/2 3 4 0 2 | 0 1/2 -4 -7 0 10 }}
: [[gencom]]: [2 9/8; 225/224 325/324 640/637]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 204.090
{{Optimal ET sequence|legend=1| 6, 11, 17, 23, 29, 35, 41, 47, 100, 147, 488cd, 635cd }}
[[Tp tuning #T2 tuning|RMS error]]: 0.5999 cents


[[File:baldy_147edo.jpg|right|alt=baldy_147edo.jpg|Baldy in 147edo]]
[[File:baldy_147edo.jpg|right|alt=baldy_147edo.jpg|Baldy in 147edo]]
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* [[Baldy11]] – 11-tone albitonic scale
* [[Baldy11]] – 11-tone albitonic scale
* [[Baldy17]] – 17-tone chromatic scale
* [[Baldy17]] – 17-tone chromatic scale


== Guanyintet ==
== Guanyintet ==
Guanyintet, the 4 &amp; 9 temperament in the 2.5.7/3.11/3 subgroup, is related to [[guanyin]] as well as to [[orwell]].
{{See also | Subgroup temperaments #Guanyintet }}
 
[[Subgroup]]: 2.5.7/3.11/3
 
[[Comma list]]: 176/175, 540/539
 
{{Mapping|legend=2| 1 0 2 -2 | 0 3 -1 5 }}
 
{{Mapping|legend=3| 1 -4/3 3 -1/3 5/3 | 0 4/3 -3 7/3 -11/3 }}
 
: [[gencom]]: [2 7/6; 176/175 540/539]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~7/6 = 270.093
 
{{Optimal ET sequence|legend=1| 9, 31, 40, 49, 89, 191bc, 227bc, 231bc, 271bc, 311bc, 316bcd }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.6028 cents


Scales:  
Scales:  
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== Gariberttet ==
== Gariberttet ==
Gariberttet can be described as the 4 &amp; 29 temperament in the 2.5/3.7/3.13/11 subgroup.
{{See also | Subgroup temperaments #Gariberttet }}
 
[[Subgroup]]: 2.5/3.7/3.13/11
 
[[Comma list]]: 275/273, 847/845
 
{{Mapping|legend=2| 1 0 0 0 | 0 3 5 1 }}
 
{{Mapping|legend=3| 1 0 0 0 0 0 | 0 -8/3 1/3 7/3 -1/2 1/2 }}
 
: [[gencom]]: [2 13/11; 275/273 847/845]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/11 = 293.679
 
{{Optimal ET sequence|legend=1| 29, 33, 37, 41, 45, 49, 78, 94, 143d, 237bd, 380bd }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.6914 cents


Scales:  
Scales:  
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== Sentry ==
== Sentry ==
Sentry, the 3 &amp; 5 temperament in the 2.5/3.9/7 subgroup, is related to [[sensi]].
{{See also | Subgroup temperaments #Sentry }}
 
[[Subgroup]]: 2.5/3.9/7
 
[[Comma list]]: 245/243
 
{{Mapping|legend=2| 1 0 0 | 0 2 1 }}
 
{{Mapping|legend=3| 1 0 0 0 | 0 0 2 -1 }}
 
: [[gencom]]: [2 9/7; 245/243]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~9/7 = 440.902
 
{{Optimal ET sequence|legend=1| 8, 11, 19, 30, 41, 49, 52, 145b, 166c, 197bc, 215c, 264bc }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.7105 cents


Scales:  
Scales:  
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* [[Garibaldi17]] – 17-tone chromatic scale
* [[Garibaldi17]] – 17-tone chromatic scale


== Mabila ==
== Mabilic ==
Given below is the no-3 version of mabila, the 7 &amp; 9 temperament.
{{See also| No-threes subgroup temperaments #Mabilic }}
 
[[Subgroup]]: 2.5.7
 
[[Comma list]]: 1071875/1048576
 
{{Mapping|legend=2| 1 1 5 | 0 3 -5 }}
 
{{Mapping|legend=3| 1 0 1 5 | 0 0 3 -5 }}
 
: [[gencom]]: [2 175/128; 1071875/1048576]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~175/128 = 527.236
 
{{Optimal ET sequence|legend=1| 7, 9, 16, 25, 41, 66, 305bc }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.7729 cents


[[File:mabila_66edo.jpg|right|alt=mabila_66edo.jpg|Mabila in 66edo]]
[[File:mabila_66edo.jpg|right|alt=mabila_66edo.jpg|Mabilic in 66edo]]


Scales:  
Scales:  
* [[Mabila7]] – 7-tone haplotonic scale
* [[Mabilic7]] – 7-tone haplotonic scale
* [[Mabila9]] – 9-tone albitonic scale
* [[Mabilic9]] – 9-tone albitonic scale
* [[Mabila16]] – 16-tone chromatic scale
* [[Mabilic16]] – 16-tone chromatic scale


== Indium ==
== Indium ==
Indium can be described as the 8 &amp; 33 temperament in the 2.5/3.7/3.11/3 subgroup.
{{See also | Subgroup temperaments #Indium }}
 
[[Subgroup]]: 2.5/3.7/3.11/3
 
[[Comma list]]: 3025/3024, 3125/3087
 
{{Mapping|legend=2| 1 0 0 2 | 0 6 10 -1 }}
 
{{Mapping|legend=3| 1 -1/2 -1/2 -1/2 3/2 | 0 -15/4 9/4 25/4 -19/4 }}
 
: [[gencom]]: [2 12/11; 3025/3024 3125/3087]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~12/11 = 147.010
 
{{Optimal ET sequence|legend=1| 33, 41, 49, 57, 106, 204, 253 }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.7788 cents


[[File:indium_253edo.png|right|alt=indium_253edo.png|Indium in 253edo]]
[[File:indium_253edo.png|right|alt=indium_253edo.png|Indium in 253edo]]
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== Starlingtet ==
== Starlingtet ==
Starlingtet, the 4 &amp; 15 temperament in the 2.5/3.7/3 subgroup, is related to [[starling]] as well as to [[myna]].
{{See also | Subgroup temperaments #Starlingtet }}
 
[[Subgroup]]: 2.5/3.7/3
 
[[Comma list]]: 126/125
 
{{Mapping|legend=2| 1 0 -1 | 0 1 3 }}
 
{{Mapping|legend=3| 1 -1 0 1 | 0 4/3 1/3 -5/3 }}
 
: [[gencom]]: [2 6/5; 126/125]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~6/5 = 311.154
 
{{Optimal ET sequence|legend=1| 15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.8398 cents


Scales:  
Scales:  
Line 772: Line 360:


== Lovecraft ==
== Lovecraft ==
Lovecraft, the 4 & 13 temperament in the 2.11.13 subgroup, is generated by ~13/11. Two generator steps give ~11/8 and three generator steps give ~13/8.
{{See also | No-threes subgroup temperaments #Lovecraft }}
 
[[Subgroup]]: 2.11.13
 
[[Comma list]]: 1352/1331
 
{{Mapping|legend=2| 1 3 3 | 0 2 3 }}
 
{{Mapping|legend=3| 1 0 0 0 3 3 | 0 0 0 0 2 3 }}
 
: [[gencom]]: [2 13/11; 1352/1331]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~13/11 = 279.318
 
{{Optimal ET sequence|legend=1| 13, 30, 43, 73, 116b }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.8449 cents


[[File:lovecraft_116edo.png|right|alt=lovecraft_116edo.png|Lovecraft in 116edo]]
[[File:lovecraft_116edo.png|right|alt=lovecraft_116edo.png|Lovecraft in 116edo]]
Line 798: Line 370:


== Blackbirds ==
== Blackbirds ==
Blackbirds is a fairly straightforward temperament. It simply equates ~13/11 to 1/4 of the octave with a generator for prime 11 or 13.
{{See also | No-threes subgroup temperaments #Blackbirds }}
 
[[Subgroup]]: 2.11.13
 
[[Comma list]]: 29282/28561
 
{{Mapping|legend=2| 4 0 1 | 0 1 1 }}
 
{{Mapping|legend=3| 4 0 0 0 12 13 | 0 0 0 0 1 1 }}
 
: [[gencom]]: [13/11 11/8; 29282/28561]
 
[[Optimal tuning]] ([[POTE]]): ~13/11 = 1\4, ~11/8 = 546.660
 
{{Optimal ET sequence|legend=1| 4, 16, 20, 24, 44, 68, 112c, 180bc }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.8685 cents


Scales:  
Scales:  
Line 822: Line 378:


== Laz ==
== Laz ==
Laz is related to [[georgian]] as well as to [[winston]].
{{See also | Subgroup temperaments #Laz }}
 
[[Subgroup]]: 2.5.7/3.11/3.13/3
 
[[Comma list]]: 144/143, 176/175, 196/195
 
{{Mapping|legend=2| 1 0 2 -2 6 | 0 3 -1 5 -5 }}
 
{{Mapping|legend=3| 1 -5/4 3 -1/4 7/4 -1/4 | 0 -1/4 -3 3/4 -21/4 19/4 }}
 
: [[gencom]]: [2 7/6; 144/143 176/175 196/195]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~7/6 = 269.300
 
{{Optimal ET sequence|legend=1| 9, 31, 40, 49, 58, 156bde, 205bde }}
 
[[Tp tuning #T2 tuning|RMS error]]: 0.8790 cents


Scales:  
Scales:  
Line 857: Line 397:


== Greeley ==
== Greeley ==
Greeley is related to [[opossum]] as well as to [[nusecond]].
{{See also| Subgroup temperaments #Greeley }}
 
[[Subgroup]]: 2.5/3.7/3.11/3
 
[[Comma list]]: 121/120, 126/125
 
{{Mapping|legend=2| 1 1 2 2 | 0 -2 -6 -1}}
 
{{Mapping|legend=3| 1 -5/4 -1/4 3/4 3/4 | 0 9/4 1/4 -15/4 5/4 }}
 
: [[gencom]]: [2 11/10; 121/120 126/125]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~11/10 = 155.776
 
{{Optimal ET sequence|legend=1| 8, 15, 23, 54, 77, 100, 131d, 208bd }}
 
[[Tp tuning #T2 tuning|RMS error]]: 1.034 cents


[[File:greeley_100edo.png|right|alt=greeley_100edo.png|Greeley in 100edo]]
[[File:greeley_100edo.png|right|alt=greeley_100edo.png|Greeley in 100edo]]
Line 884: Line 408:
* ''A Greeley Steals Halloween'' by [[Chris Vaisvil]] (2011) – [https://www.chrisvaisvil.com/tuning-survey-october-26th-2011/ blog] | [https://web.archive.org/web/20201201174756/http://micro.soonlabel.com/tuning-survey/daily20111027-a-greely-steals-halloween.mp3 play] – in Greeley[15]
* ''A Greeley Steals Halloween'' by [[Chris Vaisvil]] (2011) – [https://www.chrisvaisvil.com/tuning-survey-october-26th-2011/ blog] | [https://web.archive.org/web/20201201174756/http://micro.soonlabel.com/tuning-survey/daily20111027-a-greely-steals-halloween.mp3 play] – in Greeley[15]


== Semidim ==
== Ammon ==
Semidim can be described as the 8 &amp; 29 temperament in the 2.5/3.7/3.11/3.13/3 subgroup.
{{See also| Subgroup temperaments #Ammon }}
 
[[Subgroup]]: 2.5/3.7/3.11/3.13/3
 
[[Comma list]]: 121/120, 169/168, 275/273
 
{{Mapping|legend=2| 1 3 5 3 4 | 0 -6 -10 -3 -5 }}
 
{{Mapping|legend=3| 1 -3 0 2 0 1 | 0 24/5 -6/5 -26/5 9/5 -1/5 }}
 
: [[gencom]]: [2 13/10; 121/120 169/168 275/273]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 453.242
 
{{Optimal ET sequence|legend=1| 5, 8, 13, 21, 29, 37, 44, 45, 188bde }}


[[Tp tuning #T2 tuning|RMS error]]: 1.052 cents
[[File:semidim_770edo.png|right|alt=semidim_770edo.png|Ammon in 770edo]]
 
[[File:semidim_770edo.png|right|alt=semidim_770edo.png|Semidim in 770edo]]


Scales:  
Scales:  
* [[Semidim8]] – 8-tone albitonic scale
* [[Ammon8]] – 8-tone albitonic scale
* [[Semidim13]] – 13-tone chromatic scale
* [[Ammon13]] – 13-tone chromatic scale


== Mothwelltri ==
== Mothwelltri ==
Mothwelltri, the 1 &amp; 4 temperament in the 2.7/3.11 subgroup, is related to [[orwell]].
{{See also| Subgroup temperaments #Mothwelltri }}
 
[[Subgroup]]: 2.7/3.11
 
[[Comma list]]: 99/98
 
{{Mapping|legend=2| 1 0 1 | 0 1 2 }}
 
{{Mapping|legend=3| 1 -1/2 0 1/2 3 | 0 -1/2 0 1/2 2 }}
 
: [[gencom]]: [2 7/6; 99/98]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~7/6 = 273.174
 
{{Optimal ET sequence|legend=1| 9, 22, 40, 49c, 58c, 67c, 76c, 79, 101b, 123bc }}
 
[[Tp tuning #T2 tuning|RMS error]]: 1.064 cents


Scales:  
Scales:  
Line 934: Line 426:


== Sulis ==
== Sulis ==
Sulis is related to [[minerva]] as well as to [[würschmidt]].
{{See also| Subgroup temperaments #Sulis }}
 
[[Subgroup]]: 2.5.9/7.11/9
 
[[Comma list]]: 99/98, 176/175
 
{{Mapping|legend=2| 1 0 5 -9 | 0 1 -2 4 }}
 
{{Mapping|legend=3| 1 4/9 2 -1/9 -1/9 | 0 -4/3 1 -2/3 4/3 }}
 
: [[gencom]]: [2 5/4; 99/98 176/175]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~5/4 = 386.558
 
{{Optimal ET sequence|legend=1| 22, 25, 28, 31, 59, 90c, 149c }}
 
[[Tp tuning #T2 tuning|RMS error]]: 1.074 cents


Scales:  
Scales:  
Line 980: Line 456:


== Magicaltet ==
== Magicaltet ==
Magicaltet is related to [[supermagic]], [[superkleismic]], and [[magic]].
{{See also| Subgroup temperaments #Magicaltet }}
 
[[Subgroup]]: 2.5/3.7.11
 
[[Comma list]]: 100/99 = {{monzo| 2 2 0 -1 }}, 385/384 = {{monzo| -7 1 1 1 }}
 
{{Mapping|legend=2| 1 0 5 2 | 0 1 -3 2 }}
 
: mapping generators: ~2, ~5/3
 
{{Mapping|legend=3| 1 -1/2 1/2 2 4 | 0 1/2 -1/2 3 -2 }}
 
: [[gencom]]: [2 6/5; 100/99 385/384]
 
[[Optimal tuning]]s:
* [[Tp tuning|subgroup]] [[CTE]]: ~2 = 1\1, ~5/3 = 877.3426
* [[Tp tuning|subgroup]] [[POTE]]: ~2 = 1\1, ~5/3 = 877.351
 
{{Optimal ET sequence|legend=1| 4, 7, 11, 15, 26, 67, 93* }}
 
<nowiki>*</nowiki> wart for 5/3
 
[[Tp tuning #T2 tuning|RMS error]]: 1.206 cents


Scales:  
Scales:  
Line 1,022: Line 476:


== Kiribati ==
== Kiribati ==
Kiribati is related to [[nakika]] as well as to [[octacot]].
{{See also| Subgroup temperaments #Kiribati }}
 
[[Subgroup]]: 2.9/5.7/3.11/9
 
[[Comma list]]: 100/99, 245/242
 
{{Mapping|legend=2| 1 1 1 0 | 0 -2 3 4 }}
 
{{Mapping|legend=3| 1 1/10 -4/5 11/10 1/5 | 0 -3/2 -1 3/2 1 }}
 
: [[gencom]]: [2 21/20; 100/99 245/242]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~21/20 = 87.892
 
{{Optimal ET sequence|legend=1| 13, 14, 27, 41, 55, 191bd, 232bcd, 273bcd }}
 
[[Tp tuning #T2 tuning|RMS error]]: 1.245 cents


Scales:  
Scales:  
Line 1,045: Line 483:


== Score ==
== Score ==
[[Subgroup]]: 2.7.11.13
{{See also|No-threes subgroup temperaments #Score }}
 
[[Comma list]]: 343/338, 847/832
 
{{Mapping|legend=2| 1 1 3 1 | 0 4 1 6 }}
 
{{Mapping|legend=3| 1 0 0 1 3 1| 0 0 0 4 1 6 }}
 
: [[gencom]]: [2 11/8; 343/338 847/832]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/8 = 540.099
 
{{Optimal ET sequence|legend=1| 5, 7, 9, 11, 20 }}
 
[[Tp tuning #T2 tuning|RMS error]]: 1.282 cents


[[File:score_20edo.jpg|right|alt=score_20edo.jpg|Score in 20edo]]
[[File:score_20edo.jpg|right|alt=score_20edo.jpg|Score in 20edo]]
Line 1,119: Line 543:


== Joan ==
== Joan ==
Joan is related to [[casablanca]] as well as to [[orwell]].
{{See also| Subgroup temperaments #Joan }}
 
[[Subgroup]]: 2.9.7.11
 
[[Comma list]]: 99/98, 9317/9216
 
{{Mapping|legend=2| 1 0 1 3 | 0 7 4 1 }}
 
{{Mapping|legend=3| 1 0 0 1 3 | 0 7/2 0 4 1 }}
 
: [[gencom]]: [2 11/8; 99/98 9317/9216]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/8 = 542.672 cents
 
{{Optimal ET sequence|legend=1| 11, 20, 31, 42, 115bd, 157bd }}
 
[[Tp tuning #T2 tuning|RMS error]]: 1.424 cents


Scales:  
Scales:  
Line 1,171: Line 579:


== Sephiroth ==
== Sephiroth ==
Sephiroth is the no-7 restriction of [[muggles]].
{{See also| No-threes subgroup temperaments #Sephiroth }}
 
[[Subgroup]]: 2.5.11.13.17
 
[[Comma list]]: 65/64, 170/169, 221/220
 
{{Mapping|legend=2| 1 0 15 6 11 | 0 1 -5 -1 -3 }}
 
{{Mapping|legend=3| 1 0 2 0 5 4 5 | 0 0 1 0 -5 -1 -3 }}
 
: [[gencom]]: [2 5/4; 65/64 170/169 221/220]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~5/4 = 372.236
 
{{Optimal ET sequence|legend=1| 10, 13, 16, 29 }}
 
[[Tp tuning #T2 tuning|RMS error]]: 1.774 cents


Scales:  
Scales:  
Line 1,260: Line 652:


== Skateboard ==
== Skateboard ==
Skateboard is related to [[thrasher]].
{{See also| Subgroup temperaments #Skateboard }}
 
[[Subgroup]]: 2.5/3.7/3.11.13/9
 
[[Comma list]]: 56/55, 91/90, 100/99
 
{{Mapping|legend=2| 1 0 -1 2 2 | 0 1 3 2 -2 }}
 
{{Mapping|legend=3| 1 -3/7 4/7 11/7 4 -6/7 | 0 0 -1 -3 -2 2 }}
 
: [[gencom]]: [2 6/5; 56/55 91/90 100/99]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~6/5 = 313.842
 
{{Optimal ET sequence|legend=1| 11, 15, 19, 23, 42d, 65d }}
 
[[Tp tuning #T2 tuning|RMS error]]: 2.396 cents


Scales:  
Scales:  
Line 1,284: Line 660:


== Augment ==
== Augment ==
Augment is related to [[augmented]].
{{See also| No-threes subgroup temperaments #Augment }}
 
[[Subgroup]]: 2.5.7.11
 
[[Comma list]]: 56/55, 128/125
 
{{Mapping|legend=2| 3 7 0 2 | 0 0 1 1 }}
 
{{Mapping|legend=3| 3 0 7 9 11| 0 0 0 -1 -1 }}
 
: [[gencom]]: [5/4 8/7; 56/55 128/125]
 
[[Optimal tuning]] ([[POTE]]): ~5/4 = 1\3, ~8/7 = 228.275
 
{{Optimal ET sequence|legend=1| 3, 6, 9, 15, 21 }}
 
[[Tp tuning #T2 tuning|RMS error]]: 2.422 cents


[[File:augment_21edo.png|right|alt=augment_21edo.png|Augment in 21edo]]
[[File:augment_21edo.png|right|alt=augment_21edo.png|Augment in 21edo]]
Line 1,321: Line 681:


== Kryptonite ==
== Kryptonite ==
Kryptonite is related to [[krypton]].
{{See also| Subgroup temperaments #Kryptonite }}
 
[[Subgroup]]: 2.5.7/3.11/3.13/3
 
[[Comma list]]: 56/55, 78/77, 91/90
 
{{Mapping|legend=2| 1 2 1 2 2 | 0 -3 -2 1 -1 }}
 
{{Mapping|legend=3| 1 -5/4 2 -1/4 3/4 3/4 | 0 -1/2 3 3/2 -3/2 1/2 }}
 
: [[gencom]]: [2 13/12; 56/55 78/77 91/90]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/12 = 132.428
 
{{Optimal ET sequence|legend=1| 9, 63, 82bd, 91bde }}
 
[[Tp tuning #T2 tuning|RMS error]]: 2.545 cents


Scales:  
Scales:  
Line 1,345: Line 689:


== Oregon ==
== Oregon ==
[[Subgroup]]: 2.9.15.7.11
{{See also| Orgonia #Oregon }}
 
[[Comma list]]: 55/54, 64/63, 100/99
 
{{Mapping|legend=2| 1 1 1 5 2 | 0 3 4 -3 2 }}
 
{{Mapping|legend=3| 1 2 3 2 4 | 0 -3/2 -5/2 3 -2 }}
 
: [[gencom]]: [2 6/5; 55/54 64/63 100/99]
 
[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~6/5 = 325.495
 
{{Optimal ET sequence|legend=1| 7, 11, 37b, 48b, 59b }}
 
[[Tp tuning #T2 tuning|RMS error]]: 2.550 cents


Scales:  
Scales:  
Line 1,377: Line 707:


== Glacial ==
== Glacial ==
[[Subgroup]]: 2.9.5.11.13
{{See also| Subgroup temperaments #Glacial }}
 
[[Comma list]]: 45/44, 65/64, 81/80
 
{{Mapping|legend=2| 1 0 -4 -6 10 | 0 1 2 3 -2 }}
 
{{Mapping|legend=3| 1 3/2 2 0 3 4 | 0 1/2 2 0 3 -2 }}
 
: [[gencom]]: [2 9/8; 45/44 65/64 81/80]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 186.151
 
{{Optimal ET sequence|legend=1| 6, 13, 45be, 58bce, 71bce, 84bce }}
 
[[Tp tuning #T2 tuning|RMS error]]: 2.887 cents


Scales:  
Scales:  
Line 1,399: Line 715:


== Leantone ==
== Leantone ==
Leantone is every other step of [[meanenneadecal]].
{{See also| Hemimean clan #Leantone }}
 
[[Subgroup]]: 2.9.5.7.11
 
[[Comma list]]: 45/44, 56/55, 81/80
 
{{Mapping|legend=2| 1 0 -4 -13 -6 | 0 1 2 5 3 }}
 
{{Mapping|legend=3| 1 3/2 2 2 3 | 0 1/2 2 5 3 }}
 
: [[gencom]]: [2 9/8; 45/44 56/55 81/80]
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/8 = 192.500
 
{{Optimal ET sequence|legend=1| 6, 7, 13, 19, 25, 31, 56, 81 }}
 
[[Tp tuning #T2 tuning|RMS error]]: 3.882 cents


[[File:leantone_81edo.png|right|alt=leantone_81edo.png|Leantone in 81edo]]
[[File:leantone_81edo.png|right|alt=leantone_81edo.png|Leantone in 81edo]]
Line 1,430: Line 730:
[[Category:Listen]]
[[Category:Listen]]
[[Category:Rank 2]]
[[Category:Rank 2]]
{{todo|cleanup}}
{{todo|cleanup}}

Latest revision as of 00:23, 24 June 2025

A chromatic pair is a pair of mos scales in some rank-2 temperament (either a full p-limit temperament or a subgroup temperament) that are analogous to the familiar diatonic and chromatic scales of standard tuning. The smaller scale is an albitonic scale (from Latin albus, "white"), named such since the diatonic scale can be played using the white keys of a piano, and the larger of the two is a chromatic scale, analogous to the chromatic scale of standard tuning. Other related scales can be associated to chromatic pairs, namely a haplotonic scale (from Greek haplóos, "single, simple"), analogous to the pentatonic scale of standard tuning and played using the black keys of a piano.

In the sections below, the pair temperaments are listed in order of increasing RMS error, which is an appropriate error measure for subgroups as well as full p-limit groups.

Terrain

terrain_3558edo.png
Terrain in 3558edo

Scales:

Music

Petrtri

petrtri_385edo.png
Petrtri in 385edo

Scales:

Barton

"Barton" redirects here. For Jacob Barton's scale, see Barton (scale).

Scales:

  • Barton5 – 5-tone haplotonic scale
  • Barton7 – 7-tone albitonic scale
  • Barton9 – 9-tone mega-albitonic scale
  • Barton11 – 11-tone chromatic scale
  • Barton13 – 13-tone mega-chromatic scale

Tridec

tridec_235edo.png
Tridec in 235edo

Scales:

Nestoria

nestoria_171edo.png
Nestoria in 171edo

Scales:

Orgone

orgone_308edo.jpg
Orgone in 308edo

Scales:

Marveltwintri

marveltwintri_321edo.png
Marveltwintri in 321edo

Scales:

Cata

cata_246edo.jpg
Cata in 246edo

Scales:

  • Cata7 – 7-tone albitonic scale
  • Cata11 – 11-tone mega-albitonic scale
  • Cata15 – 15-tone chromatic scale
  • Cata19 – 19-tone mega-chromatic scale

Bridgetown

bridgetown_29edo.png
Bridgetown in 29edo

Scales:

Music

Haumea

Scales:

Neutral

neutral_380edo.png
Neutral in 380edo

Scales:

Music

Slendric

See also: Gamelismic clan #Slendric and No-fives subgroup temperaments #Slendric
slendric_190edo.jpg
Slendric in 190edo

Scales:

Huntington

huntington_400edo.jpg
Huntington in 400edo

Scales:

Tobago

Scales:

Pepperoni

pepperoni_271edo.png
Pepperoni in 271edo

Scales:

Wizz

Scales:

  • Wizz6 – 6-tone haplotonic scale
  • Wizz10 – 10-tone albitonic scale
  • Wizz16 – 16-tone chromatic scale

Bossier

bossier_225edo.jpg
Bossier in 225edo

Scales:

Penta a.k.a. mechanism

Scales:

  • Penta5 – 5-tone haplotonic scale
  • Penta8 – 8-tone albitonic scale
  • Penta11 – 11-tone chromatic scale
  • Penta19 – 19-tone mega-chromatic scale

Bluebirds

Scales:

Marveltri

Scales:

Edson

Scales:

  • Edson5 – 5-tone haplotonic scale
  • Edson7 – 7-tone albitonic scale
  • Edson12 – 12-tone chromatic scale
  • Edson17 – 17-tone mega-chromatic scale

Photia

photia_65edo.png
Photia in 65edo

Scales:

Shoe a.k.a. llywelyn

shoe_37edo.jpg
Shoe in 37edo

Scales:

  • Shoe5 – 5-tone mini-haplotonic scale
  • Shoe6 – 6-tone haplotonic scale
  • Shoe11 – 11-tone albitonic scale
  • Shoe16 – 16-tone chromatic scale

Roulette

roulette_37edo.jpg
Roulette in 37edo

Scales:

Silver

silver_487edo.jpg
Silver in 487edo

Scales:

Baldy

baldy_147edo.jpg
Baldy in 147edo

Scales

  • Baldy6 – 6-tone haplotonic scale
  • Baldy11 – 11-tone albitonic scale
  • Baldy17 – 17-tone chromatic scale


Guanyintet

Scales:

Radon

radon_128edo.jpg
Radon in 128edo
  • Radon5 – 5-tone haplotonic scale
  • Radon11 – 11-tone albitonic scale
  • Radon16 – 16-tone chromatic scale

Gariberttet

Scales:

Namo

Scales:

  • Namo7 – 7-tone haplotonic scale
  • Namo10 – 10-tone albitonic scale
  • Namo17 – 17-tone chromatic scale

Sentry

Scales:

Hemif

hemif_58edo.jpg
Hemif in 58edo

Scales:

  • Hemif7 – 7-tone haplotonic scale
  • Hemif10 – 10-tone albitonic scale
  • Hemif17 – 17-tone chromatic scale

Garibaldi

garibaldi_94edo.png
Garibaldi in 94edo

Scales:

Mabilic

mabila_66edo.jpg
Mabilic in 66edo

Scales:

Indium

indium_253edo.png
Indium in 253edo

Scales:

Music

Starlingtet

Scales:

Lovecraft

lovecraft_116edo.png
Lovecraft in 116edo

Scales:

Blackbirds

Scales:

Laz

Scales:

  • Laz5 – 5-tone haplotonic scale
  • Laz9 – 9-tone albitonic scale
  • Laz13 – 13-tone chromatic scale

Myna

myna_89edo.jpg
Myna in 89edo

Scales:

  • Myna7 – 7-tone haplotonic scale
  • Myna11 – 11-tone albitonic scale
  • Myna15 – 15-tone chromatic scale

Greeley

greeley_100edo.png
Greeley in 100edo

Scales:

Music

Ammon

semidim_770edo.png
Ammon in 770edo

Scales:

  • Ammon8 – 8-tone albitonic scale
  • Ammon13 – 13-tone chromatic scale

Mothwelltri

Scales:

Sulis

Scales:

  • Sulis7 – 7-tone haplotonic scale
  • Sulis10 – 10-tone albitonic scale
  • Sulis13 – 13-tone chromatic scale

Skwares

skwares_206edo.png
Skwares in 206edo

Scales:

Orwell

orwell_84edo.png
Orwell in 84edo

Scales:

Magicaltet

Scales:

Magic

magic_145edo.jpg
Magic in 145edo

Scales:

  • Magic7 – 7-tone haplotonic scale
  • Magic10 – 10-tone albitonic scale
  • Magic13 – 13-tone chromatic scale
  • Magic16 – 16-tone mega-chromatic scale

Kiribati

Scales:

Score

score_20edo.jpg
Score in 20edo

Scales:

  • Score5 – 5-tone haplotonic scale
  • Score7 – 7-tone albitonic scale
  • Score9 – 9-tone mega-albitonic scale
  • Score11 – 11-tone chromatic scale

Sensi

sensi_46edo.jpg
Sensi in 46edo

Scales:

  • Sensi5 – 5-tone haplotonic scale
  • Sensi8 – 8-tone albitonic scale
  • Sensi11 – 11-tone mega-albitonic scale
  • Sensi19 – 19-tone chromatic scale

Sensation

Scales:

  • Sensi5 – 5-tone haplotonic scale
  • Sensi8 – 8-tone albitonic scale
  • Sensi11 – 11-tone mega-albitonic scale
  • Sensi19 – 19-tone chromatic scale

Meantone

meantone_31edo.jpg
Meantone in 31edo

Scales:

Mohaha

mohaha_131edo.png
Mohaha in 131edo

Scales:

Music:

Billy Stiltner

Mohoho

Joan

Scales:

  • Joan5 – 5-tone haplotonic scale
  • Joan7 – 7-tone albitonic scale
  • Joan9 – 9-tone mega-albitonic scale
  • Joan11 – 11-tone chromatic scale

Tutone

tutone_99edo.png
Tutone in 99edo

Scales:

Stacks

Scales:

Bleu

Scales:

  • Bleu8 – 8-tone haplotonic scale
  • Bleu9 – 9-tone albitonic scale
  • Bleu17 – 17-tone chromatic scale

Sephiroth

Scales:

Archy

Scales:

  • Archy5 – 5-tone haplotonic scale
  • Archy7 – 7-tone albitonic scale
  • Archy12 – 12-tone chromatic scale

Supra

supra_56edo.png
Supra in 56edo

Scales:

Supraphon

Suhajira

Scales:

Machine

machine_28edo.png
Machine in 28edo

Scales:

Deutone

deutone_44edo.png
Deutone in 44edo

Scales:

Negra

Porkypine

Scales:

Skateboard

Scales:

Augment

augment_21edo.png
Augment in 21edo

Scales:

Semaphore

semaphore_24edo.png
Semaphore in 24edo

Scales:

Kryptonite

Scales:

Oregon

Scales:

Antikythera

antikythera_28edo.png
Antikythera in 28edo

Scales:

Glacial

Scales:

Leantone

leantone_81edo.png
Leantone in 81edo

Scales:

Notes