Chromatic pairs: Difference between revisions
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[[Tp tuning #T2 tuning|RMS error]]: 0.00844 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.00844 cents | ||
[[File:terrain_3558edo.png|alt=terrain_3558edo.png| | [[File:terrain_3558edo.png|right|alt=terrain_3558edo.png|Terrain in 3558edo]] | ||
Scales: | Scales: | ||
| Line 31: | Line 31: | ||
; Music | ; Music | ||
[ | * ''5 5 1 mode of 33 equal'' (2013) by [[Chris Vaisvil]] – [https://www.chrisvaisvil.com/5-5-1-mode-of-33-equal-with-video/ blog] | [https://www.youtube.com/watch?v=2gYdUOPHXSQ YouTube] | [https://web.archive.org/web/20201127015117/http://micro.soonlabel.com/33edo/20130827_551of33.mp3 play] | ||
== Petrtri == | == Petrtri == | ||
| Line 52: | Line 52: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.0749 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.0749 cents | ||
[[File:petrtri_385edo.png|alt=petrtri_385edo.png| | [[File:petrtri_385edo.png|right|alt=petrtri_385edo.png|Petrtri in 385edo]] | ||
Scales: | |||
* [[petrtri5]] – 5-tone haplotonic scale | * [[petrtri5]] – 5-tone haplotonic scale | ||
* [[petrtri8]] – 8-tone albitonic scale | * [[petrtri8]] – 8-tone albitonic scale | ||
| Line 124: | Line 125: | ||
[[Tp tuning #T2 tuning|RMS error]]: 0.1613 cents | [[Tp tuning #T2 tuning|RMS error]]: 0.1613 cents | ||
[[File:tridec_235edo.png|alt=tridec_235edo.png| | [[File:tridec_235edo.png|right|alt=tridec_235edo.png|Tridec in 235edo]] | ||
* [[Tridec8]] – 8-tone albitonic scale | * [[Tridec8]] – 8-tone albitonic scale | ||
| Line 130: | Line 131: | ||
== Nestoria == | == Nestoria == | ||
{{See also| Schismatic family #Nestoria (2.3.5.19)}} | |||
[[File:nestoria_171edo.png|right|alt=nestoria_171edo.png|Nestoria in 171edo]] | |||
Scales: | |||
* [[nestoria7]] – 7-tone albitonic scale | |||
* [[nestoria12]] – 12-tone chromatic scale | |||
* [[nestoria17]] – 7-tone mega chromatic scale | |||
[[nestoria12 | |||
[[nestoria17 | |||
== Orgone == | == Orgone == | ||
{{Main| Orgone }} | |||
{{See also| Orgonia }} | |||
Orgone, the 4 & 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|alt=orgone_308edo.jpg| | [[File:orgone_308edo.jpg|right|alt=orgone_308edo.jpg|Orgone in 308edo]] | ||
[[orgone7 | Scales: | ||
* [[orgone7]] – 7-tone albitonic scale | |||
[[orgone11 | * [[orgone11]] – 11-tone chromatic scale | ||
* [[orgone15]] – 15-tone mega chromatic scale | |||
[[orgone15 | |||
== Marveltwintri == | == Marveltwintri == | ||
Marveltwintri can be described as the 3 & 4 temperament in the 2.5/3.13/9 subgroup. | |||
[[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]] ([[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|alt=marveltwintri_321edo.png| | [[File:marveltwintri_321edo.png|right|alt=marveltwintri_321edo.png|Marveltwintri in 321edo]] | ||
[[marveltwintri7 | Scales: | ||
* [[marveltwintri7]] – 7-tone albitonic scale | |||
[[marveltwintri11 | * [[marveltwintri11]] – 11-tone chromatic scale | ||
* [[marveltwintri15]] – 15-tone mega chromatic scale | |||
[[marveltwintri15 | |||
== Cata == | == Cata == | ||
| Line 227: | Line 208: | ||
== Bridgetown == | == Bridgetown == | ||
Bridgetown, the 5 & 24 temperament in the 2.3.11/5.13/5 subgroup, is related to [[haumea]] and [[barbados]]. | |||
[[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]] ([[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]] | ||
[[ | Scales: | ||
* [[bridgetown9]] – 9-tone albitonic scale | |||
* [[bridgetown14]] – 14-tone chromatic scale | |||
; Music | |||
* [https://web.archive.org/web/20201127014201/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/Paint%20in%20the%20Water%2029.mp3 ''Paint in the Water 29''] (archived 2020) by [[Igliashon Jones]] | |||
* [https://web.archive.org/web/20201127012744/http://micro.soonlabel.com/tuning-survey/daily20111026-bridgetown-14.mp3 ''Route 14 in Bridgetown''] (archived 2020) by [[Chris Vaisvil]] | |||
== Haumea == | == Haumea == | ||
Revision as of 08:20, 27 September 2024
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" redirects here. For the scale, see Terrain (scale).
Terrain, the 6 & 21 temperament in the 2.9/5.9/7 subgroup, is related to 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
Sval mapping: [⟨3 0 -4], ⟨0 1 2]]
Gencom mapping: [⟨3 10/9 -7/9 2/9], ⟨0 -2/3 -1/3 2/3]]
- gencom: [63/50 10/9; 250047/250000]
Optimal tuning (POTE): ~63/50 = 1\3, ~10/9 = 182.461
Optimal ET sequence: 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558
RMS error: 0.00844 cents
Scales:
- Music
- 5 5 1 mode of 33 equal (2013) by Chris Vaisvil – blog | YouTube | play
Petrtri
Petrtri can be described as 3 & 5 temperament in the 2.11/5.13/5 subgroup.
Subgroup: 2.11/5.13/5
Comma list: 2200/2197
Sval mapping: [⟨1 0 1], ⟨0 3 1]]
Gencom mapping: [⟨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 (POTE): ~2 = 1\1, ~13/10 = 455.012
Optimal ET sequence: 21, 29, 153, 182, 211, 240, 269, 298, 327, 356, 385, 509, 741c, 1126c
RMS error: 0.0749 cents
Scales:
- petrtri5 – 5-tone haplotonic scale
- petrtri8 – 8-tone albitonic scale
- petrtri13 – 13-tone chromatic scale
Barton
Barton may be described as the 11 & 13 temperament in the 2.5.11.13 subgroup. It was named after Jacob Barton by Gene Ward Smith and Carl Lumma in 2006[1].
Subgroup: 2.5.11.13
Comma list: 2200/2197, 6656/6655
Sval mapping: [⟨1 6 3 6], ⟨0 -8 1 -5]]
Gencom mapping: [⟨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: 11, 13, 24, 37, 50, 87, 298, 385, 472, 559, 1590cd
RMS error: 0.0822 cents
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
Voltage
Voltage is the 3 & 7 temperament in the 2.7.13 subgroup.
Subgroup: 2.7.13
Comma list: 28672/28561
Sval mapping: [⟨1 4 4], ⟨0 -4 -1]]
Gencom mapping: [⟨1 0 0 4 0 4], ⟨0 0 0 -4 0 -1]]
- gencom: [2, 16/13; 28672/28561]
Optimal ET sequence: 3, 7, 10, 27, 37, 47, 57, 104
RMS error: 0.1423
Tridec
Tridec, the 5 & 8 temperament in the 2.7/5.11/5.13/5 subgroup, extends petrtri.
Subgroup: 2.7/5.11/5.13/5
Comma list: 847/845, 1001/1000
Sval mapping: [⟨1 2 0 1], ⟨0 -4 3 1]]
Gencom mapping: [⟨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 (POTE): ~2 = 1\1, ~13/10 = 454.556
Optimal ET sequence: 5, 8, 21, 29, 37, 66, 169, 235, 404c, 639c, 953bc
RMS error: 0.1613 cents
Nestoria
Scales:
- nestoria7 – 7-tone albitonic scale
- nestoria12 – 12-tone chromatic scale
- nestoria17 – 7-tone mega chromatic scale
Orgone
Orgone, the 4 & 7 temperament in the 2.7.11 subgroup, is related to superkleismic.
Subgroup: 2.7.11
Comma list: 65536/65219
Sval mapping: [⟨1 2 4], ⟨0 3 -2]]
Gencom mapping: [⟨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: 4, 7, 11, 15, 26, 89, 115, 141, 167, 308, 475bc, 783bc
RMS error: 0.1888 cents
Scales:
- orgone7 – 7-tone albitonic scale
- orgone11 – 11-tone chromatic scale
- orgone15 – 15-tone mega chromatic scale
Marveltwintri
Marveltwintri can be described as the 3 & 4 temperament in the 2.5/3.13/9 subgroup.
Subgroup: 2.5/3.13/9
Comma list: 325/324
Sval mapping: [⟨1 0 2], ⟨0 1 -2]]
Gencom mapping: [⟨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 (POTE): ~2 = 1\1, ~6/5 = 317.139
Optimal ET sequence: 11, 15, 19, 34, 53, 87, 140, 185, 219, 253, 287b, 321b
RMS error: 0.2444 cents
Scales:
- marveltwintri7 – 7-tone albitonic scale
- marveltwintri11 – 11-tone chromatic scale
- marveltwintri15 – 15-tone mega chromatic scale
Cata
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, the 5 & 24 temperament in the 2.3.11/5.13/5 subgroup, is related to haumea and barbados.
Subgroup: 2.3.11/5.13/5
Comma list: 352/351, 676/675
Sval mapping: [⟨1 0 -6 -1], ⟨0 2 9 3]]
Gencom mapping: [⟨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 (POTE): ~2 = 1\1, ~15/13 = 248.399
Optimal ET sequence: 5, 9, 14, 19, 24, 29, 169, 198, 227, 256, 285, 314
RMS error: 0.2513 cents
Scales:
- bridgetown9 – 9-tone albitonic scale
- bridgetown14 – 14-tone chromatic scale
- Music
- Paint in the Water 29 (archived 2020) by Igliashon Jones
- Route 14 in Bridgetown (archived 2020) by Chris Vaisvil
Haumea
Subgroup: 2.3.7/5.11/5.13/5
Commas: 352/351, 676/675, 847/845
Related temperaments: bridgetown, namaka, hemigari, barbados, parizekmic
POT2 generator: ~15/13 = 248.491
Gencom: [2 15/13; 352/351 676/675 847/845]
Gencom mapping: [<1 2 -3/4 -11/4 9/4 5/4|, <0 -2 0 12 -9 -3|]
Mapping: [<1 0 10 -6 -1|, <0 2 -12 9 3|]
EDOs: 24, 29, 111, 140, 169, 198, 565d, 763bd, 961bd
RMS error: 0.2668 cents
Nineteen note mega chromatic scale
Neutral
Scales:
- neutral7 – 7-tone albitonic scale
- neutral10 – 10-tone chromatic scale
- neutral17 – 17-tone mega-chromatic scale
Music
Mo - Happy - Happy play by Jake Freivald in Neutral[7], 24et tuning
Slendric
Scales:
- Slendric5 – 5-tone haplotonic scale
- Slendric6 – 6-tone haplotonic scale
- Slendric11 – 11-tone albitonic scale
- Slendric16 – 16-tone chromatic scale
Huntington
Subgroup: 2.5.7.13
Commas: 640/637, 10985/10976
Sval name: 10&27
POT2 generator: ~16/13 = 357.002
Gencom: [2 16/13; 640/637 10985/10976]
Gencom mapping: [<1 0 5 4 0 4|, <0 0 -9 -4 0 -1|]
Mapping: [<1 5 4 4|, <0 -9 -4 -1|]
EDOs: 7, 10, 17, 27, 37, 84, 121, 279cd, 400cd
RMS error: 0.3452 cents
Seventeen note chromatic scale
Tobago
Subgroup: 2.3.11.13/5
Commas: 243/242, 676/675
Sval name: 10&14
Related temperaments: neutral, barbados
POT2 generator: ~15/13 = 249.312
Gencom: [55/39 15/13; 243/242 676/675]
Gencom mapping: [<2 4 -2 0 9 2|, <0 -2 3/2 0 -5 -3/2|]
Mapping: [<2 0 -1 -2], <0 2 5 3]]
RMS error: 0.3533 cents
Twentyfour note quatertone scale
Pepperoni
Subgroup: 2.3.11/7.13/7
Commas: 352/351, 364/363
Sval name: 5&12
Related temperament: The Pepper fifth, which is (40200 + 600 sqrt(5))/59 = 704.096 cents, is a good pepperoni generator, hence the name.
POT2 generator: ~3/2 = 703.856
Gencom: [2 3/2; 352/351 364/363]
Gencom mapping: [<1 1 0 -8/3 1/3 7/3|, <0 1 0 11/3 -1/3 -10/3|]
Mapping: [<1 0 7 12|, <0 1 -4 -7|]
EDOs: 5, 7, 12, 17, 29, 46, 58, 75, 80, 87, 104, 121, 167, 196, 208, 271, 595bcd
RMS error: 0.3789 cents
Wizz
Subgroup: 2.5.11
Commas: 15625/15488
Sval name: 6&16
Related temperaments: wizard
Generator: ~5/4 = 383.768
Gencom: [125/88 5/4; 15625/15488]
Gencom mapping: [<2 0 4 0 5| <0 0 1 0 3|]
Mapping: [<2 0 -7|, <0 1 3|]
EDOs: 6, 16, 22, 28, 50, 122, 172, 222
RMS error: 0.3997
Bossier
Subgroup: 2.7.11.13
Commas: 1573/1568, 15488/15379
Sval name: 3&17
POT2 generator: ~14/11 = 421.309
Gencom: [2 14/11; 1573/1568 15488/15379]
Gencom mapping: [<1 0 0 0 1 3|, <0 0 0 8 7 2|]
Mapping: [<1 0 1 3|, <0 8 7 2|]
EDOs: 17, 20, 37, 57, 94, 225, 319cd, 413bcd
RMS error: 0.4043 cents
Fourteen note mega chromatic scale
Penta (aka Mechanism)
Subgroup: 2.9.7.11
Commas: 896/891, 26411/26244
Svalname: 8&11
POT2 generator: ~9/7 = 438.465
Gencom: [2 9/7; 896/891 26411/26244]
Gencom mapping: [<1 5/2 0 5 2|, <0 -5/2 0 -6 4|]
Mapping: [<1 0 -1 6|, <0 5 6 -4|]
RMS error: 0.4262 cents
Nineteen note mega chromatic scale
Bluebirds
Subgroup: 2.11.13
Comma: 265837/262144
POT2 generator: ~143/128 = 182.368
Gencom: [2 143/128; 265837/262144]
Gencom mapping: [<1 0 0 0 3 4|, <0 0 0 0 3 -2|]
Mapping: [<1 0 6|, <0 3 -2|]
EDOs: 6, 7, 13, 33, 46, 79, 125c, 204bc, 329bc
RMS error: 0.4444 cents
Marveltri
Subgroup: 2.5.9/7
Comma: 225/224
Sval name: 3&13
Related temperaments: marvel, 22&47, magic
POT2 generator: ~5/4 = 383.638
Gencom: [2 5/4; 225/224]
Gencom mapping: [<1 2/5 2 -1/5|, <0 -4/5 1 2/5|]
Mapping: [<1 0 5|, <0 1 -2|]
EDOs: 12, 13, 16, 19, 22, 25, 47, 69, 72, 97, 122, 269bc, 660bc
RMS error: 0.4801 cents
Thirteen note mega chromatic scale
Edson
Subgroup: 2.3.7/5.11/5.13/5
Comma list: 196/195 = [2 -1 2 0 -1⟩, 352/351 = [5 -3 0 1 -1⟩, 364/363 = [2 -1 1 -2 1⟩
Sval mapping: [⟨1 0 10 17 22], ⟨0 1 -6 -10 -13]]
- mapping generators: ~2, ~3
Gencom mapping: [⟨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 ET sequence: 12, 17, 29
RMS error: 0.5102 cents
Related temperaments: pele, cassandra
Scales:
- edson5 – 5-tone haplotonic scale
- edson7 – 7-tone albitonic scale
- edson12 – 12-tone chromatic scale
- edson17 – 17-tone mega-chromatic scale
Photia
Subgroup: 2.3.5.17.19
Commas: 171/170, 256/255, 324/323
Sval name: 12&41
Related temperament: schismatic
POT2 generator: ~3/2 = 701.470
Gencom: [2 3/2; 171/170 256/255 324/323]
Gencom mapping: [<1 1 7 0 0 0 0 6|, <0 1 -8 0 0 0 7 -3|]
Mapping: [<1 0 15 -7 9|, <0 1 -8 7 -3|]
EDOs: 7, 12, 17, 29, 41, 53, 65, 142d, 207d, 272d
RMS error: 0.5374 cents
Shoe
Subgroup: 2.5.7.11.13
Commas: 176/175, 640/637, 847/845
Sval name: 16&21
POT2 generator: ~8/7 = 227.108
Gencom: [2 8/7; 176/175 640/637 847/845]
Gencom mapping: [<1 0 1 3 1 2|, <0 0 7 -1 13 9|]
Mapping: [<1 1 3 1 2|, <0 7 -1 13 9|]
EDOs: 16, 21, 37, 206bce, 243bce, 280bce, 317bce, 354bce, 391bce
RMS error: 0.5433 cents
shoe5 - five note mini haplotonic scale
shoe6 - six note haplotonic scale
shoe11 - eleven note note albitonic scale
shoe16 - sixteen note chromatic scale
Roulette
Subgroup: 2.5.7.11.13
Commas: 176/175, 1375/1372, 640/637
Sval name: 6&25
Related temperament: Hemiwürschmidt
POT2 generator: ~28/25 = 194.594
Gencom: [2 28/25; 176/175 1375/1372 640/637]
Gencom mapping: [<1 0 2 2 2 5|, <0 0 2 5 9 -8|]
Mapping: [<1 0 -3 -7 13|, <0 2 5 9 -8|]
EDOs: 6, 7, 13, 19, 25, 31, 37
RMS error: 0.5567 cents
roulette6 - six note haplotonic scale
roulette7 - seven note albitonic scale
roulette13 - thirteen note chromatic scale
roulette19 - nineteen note mega chromatic scale
Silver
Subgroup: 2.5.7.13.17
Commas: 170/169, 640/637, 5525/5488
Sval name: 10&27
POT2 generator: ~13/8 = 842.711
Gencom: [2 13/8; 170/169 640/637 5525/5488]
Gencom mapping: [<1 0 -4 0 0 3 9|, <0 0 9 4 0 1 -7|]
Mapping: [<1 5 4 4 2|, <0 -9 -4 -1 7|]
EDOs: 7, 10, 17, 27, 37, 47, 84, 131, 178e, 309cde, 487bcdee
RMS error: 0.5886 cents
silver7 -seven note haplotonic scale
silver10 - ten note albitonic scale
silver17 - seventeen note chromatic scale
Baldy
Subgroup: 2.9.5.7.13
Commas: 225/224, 325/324, 640/637
Sval name: 6&35
Related temperament: Garibaldi
POT2 generator: ~9/8 = 204.090
Gencom: [2 9/8; 225/224 325/324 640/637]
Gencom mapping: [<1 3/2 3 4 0 2|, <0 1/2 -4 -7 0 10|]
Mapping: [<1 0 15 25 -28|, <0 1 -4 -7 10|]
EDOs: 6, 11, 17, 23, 29, 35, 41, 47, 100, 147, 488cd, 635cd
RMS error: 0.5999 cents
baldy6 - six note haplotonic scale
baldy11 - eleven note albitonic scale
baldy17 - seventeen note chromatic scale
Guanyintet
Subgroup: 2.5.7/3.11/3
Commas: 176/175, 540/539
Svalname: 4&9
Related temperaments: guanyin, orwell
POT2 generator: ~7/6 = 270.093
Gencom: [2 7/6; 176/175 540/539]
Gencom mapping: [<1 -4/3 3 -1/3 5/3|, <0 4/3 -3 7/3 -11/3|]
Mapping: [<1 0 2 -2|, <0 3 -1 5|]
EDOs: 9, 31, 40, 49, 89, 191bc, 227bc, 231bc, 271bc, 311bc, 316bcd
RMS error: 0.6028 cents
Radon
- Radon5 – 5-tone haplotonic scale
- Radon11 – 11-tone albitonic scale
- Radon16 – 16-tone chromatic scale
Gariberttet
Subgroup: 2.5/3.7/3.13/11
Commas: 275/273, 847/845
Svalname: 4&29
POT2 generator: ~13/11 = 293.679
Gencom: [2 13/11; 275/273 847/845]
Gencom mapping: [<1 0 0 0 0 0|, <0 -8/3 1/3 7/3 -1/2 1/2|]
Mapping: [<1 0 0 0|, <0 3 5 1|]
EDOs: 29, 33, 37, 41, 45, 49, 78, 94, 143d, 237bd, 380bd
RMS error: 0.6914 cents
Namo
Scales:
- namo7| – 7-tone haplotonic scale
- namo10 – 10-tone albitonic scale
- namo17 – 17-tone chromatic scale
Sentry
Subgroup: 2.5/3.9/7
Commas: 245/243
Svalname: 3&5
Related temperaments: sensi
POT2 generator: ~9/7 = 440.902
Gencom: [2 9/7; 245/243]
Gencom mapping: [<1 0 0 0|, <0 0 2 -1|]
Mapping: [<1 0 0|, <0 2 1|]
EDOs: 8, 11, 19, 30, 41, 49, 52, 145b, 166c, 197bc, 215c, 264bc
RMS error: 0.7105 cents
Eleven note note chromatic scale
Hemif
Subgroup: 2.3.7.11.13
Commas: 144/143, 243/242, 364/363
Related temperament: Hemififths, namo
POT2 generator: ~11/9 = 351.691
Gencom: [2 11/9; 144/143 243/242 364/363]
Gencom mapping: [<1 1 0 -1 2 4|, <0 2 0 13 5 -1|]
Mapping: [<1 1 -1 2 4|, <0 2 13 5 -1|]
RMS error: 0.7167 cents
Seventeen note chromatic scale
Garibaldi
Scales:
- Garibaldi12 – 12-tone albitonic scale
- Garibaldi17 – 17-tone chromatic scale
Mabila
Subgroup: 2.5.7
Comma: 1071875/1048576
Sval name: 7&9
POT2 generator: ~175/128 = 527.236
Gencom: [2 175/128; 1071875/1048576]
Gencom mapping: [<1 0 1 5}, <0, 0, 3, -5|]
Mapping: [<1 1 5|, <0 3 -5|]
EDOs: 7, 9, 16, 25, 41, 66, 305bc
RMS error: 0.7729 cents
Indium
Subgroup: 2.5/3.7/3.11/3
Commas: 3025/3024, 3125/3087
Sval name: 8&33
POT2 generator: ~12/11 = 147.010
Gencom: [2 12/11; 3025/3024 3125/3087]
Gencom mapping: [<1 -1/2 -1/2 -1/2 3/2|, <0 -15/4 9/4 25/4 -19/4|]
Mapping: [<1 0 0 2|, <0 6 10 -1|]
EDOs: 33, 41, 49, 57, 106, 204, 253
RMS error: 0.7788 cents
Seventeen note chromatic scale
Music
The Cry of Indium (in Indium 17) by Chris Vaisvil => details
Starlingtet
Subgroup: 2.5/3.7/3
Comma: 126/125
Svalname: 4&15
Related temperaments: starling; becomes myna
POT2 generator: ~6/5 = 311.154
Gencom: [2 6/5; 126/125]
Gencom mapping: [<1 -1 0 1|, <0 4/3 1/3 -5/3|]
Mapping: [<1 0 -1|, <0 1 3|]
EDOs: 15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b
RMS error: 0.8398 cents
Lovecraft
Subgroup: 2.11.13
Commas: 1352/1331
POT2 generator: ~13/11 = 279.318
Gencom: [2 13/11; 1352/1331]
Gencom mapping: [<1 0 0 0 3 3|, <0 0 0 0 2 3|]
Mapping: [<1 1 0|, <0 2 3|]
RMS error: 0.8449 cents
Blackbirds
Subgroup: 2.11.13
Comma: 29282/28561
POT2 generator: ~11/8 = 546.660
Gencom: [13/11 11/8; 29282/28561]
Gencom mapping: [<4 0 0 0 12 13|, <0 0 0 0 1 1|]
Mapping: [<4 0 1|, <0 1 1|]
EDOs: 4, 16, 20, 24, 44, 68, 112c, 180bc
RMS error: 0.8685 cents
Sixteen note mega chromatic scale
Laz
Subgroup: 2.5.7/3.11/3.13/3
Commas: 144/143, 176/175, 196/195
Related temperaments: georgian, winston
POT2 generator: ~7/6 = 269.300
Gencom: [2 7/6; 144/143 176/175 196/195]
Gencom mapping: [<1 -5/4 3 -1/4 7/4 -1/4|, <0 -1/4 -3 3/4 -21/4 19/4|]
Mapping: [<1 0 2 -2 6|, <0 3 -1 5 -5|]
EDOs: 9, 31, 40, 49, 58, 156bde, 205bde
RMS error: 0.8790 cents
Myna
Scales:
- Myna7 – 7-tone haplotonic scale
- Myna11 – 11-tone albitonic scale
- Myna15 – 15-tone chromatic scale
Greeley
Subgroup: 2.5/3.7/3.11/3
Commas: 121/120, 126/125
Related temperament: Opossum, Nusecond
POT2 generator: ~11/10 = 155.776
Gencom: [2 11/10; 121/120 126/125]
Gencom mapping: <1 -5/4 -1/4 3/4 3/4|, <0 9/4 1/4 -15/4 5/4|]
Mapping: [<1 1 2 2|, <0 -2 -6 -1|]
EDOs: 8, 15, 23, 54, 77, 100, 131d, 208bd
RMS error: 1.034 cents
Music
A Greeley Steals Halloween by Chris Vaisvil in Greeley 15
Semidim
Subgroup: 2.5/3.7/3.11/3.13/3
Commas: 121/120, 169/168, 275/273
Sval name: 8&29
POT2 generator: ~13/10 = 453.242
Gencom: [2 13/10; 121/120 169/168 275/273]
Gencom mapping: [<1 -3 0 2 0 1|, <0 24/5 -6/5 -26/5 9/5 -1/5|]
Mapping: [<1 3 5 3 4|, <0 -6 -10 -3 -5|]
EDOs: 5, 8, 13, 21, 29, 37, 44, 45, 188bde
RMS error: 1.052 cents
Mothwelltri
Subgroup: 2.7/3.11
Comma: 99/98
Svalname: 1&4
Related temperament: Orwell
POT2 generator: ~7/6 = 273.174
Gencom: [2 7/6; 99/98]
Gencom mapping: [<1 -1/2 0 1/2 3|, <0 -1/2 0 1/2 2|]
Mapping: [<1 0 1|, <0 1 2|]
EDOs: 9, 22, 40, 49c, 58c, 67c, 76c, 79, 101b, 123bc
RMS error: 1.064 cents
Sulis
Subgroup: 2.5.9/7.11/9
Commas: 99/98, 176/175
Related temperament: minerva, würschmidt
POT2 generator: ~5/4 = 386.558
Gencom: [2 5/4; 99/98 176/175]
Gencom mapping: [<1 4/9 2 -1/9 -1/9|, <0 -4/3 1 -2/3 4/3|]
Mapping: [<1 0 5 -9|, <0 1 -2 4|]
EDOs: 22, 25, 28, 31, 59, 90c, 149c
RMS error: 1.074 cents
Skwares
Subgroup: 2.3.7.11
Commas: 99/98, 243/242
Related temperament: squares
POT2 generator: ~9/7 = 425.244
Gencom: [2 9/7; 99/98 243/242]
Gencom mapping: [<1 3 0 6 7|, <0 -4 0 -9 -10|]
Mapping: [<1 3 6 7|, <0 -4 -9 -10|]
EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, 206bcd
RMS error: 1.099 cents
Eleven note mega albitonic scale
Orwell
Scales:
- Orwell5 – 5-tone haplotonic scale
- Orwell9 – 9-tone albitonic scale
- Orwell13 – 13-tone chromatic scale
Magicaltet
Subgroup: 2.5/3.7.11
Comma list: 100/99 = [2 2 0 -1⟩, 385/384 = [-7 1 1 1⟩
Sval mapping: [⟨1 0 5 2], ⟨0 1 -3 2]]
- mapping generators: ~2, ~5/3
Gencom mapping: [⟨1 -1/2 1/2 2 4], ⟨0 1/2 -1/2 3 -2]]
- gencom: [2 6/5; 100/99 385/384]
Optimal ET sequence: 4, 7, 11, 15, 26, 67, 93*
* wart for 5/3
RMS error: 1.206 cents
Related temperaments: supermagic, superkleismic, magic
Scales:
- magicaltet7 – 7-tone albitonic scale
- magicaltet11 – 11-tone chromatic scale
- magicaltet15 – 15-tone mega-chromatic scale
Magic
Scales:
- Magic7 – 7-tone haplotonic scale
- Magic10 – 10-tone albitonic scale
- Magic13 – 13-tone chromatic scale
- Magic16 – 16-tone mega-chromatic scale
Kiribati
Subgroup: 2.9/5.7/3.11/9
Commas: 100/99, 245/242
Related temperament: nakika, octacot
POT2 generator: ~21/20 = 87.892
Gencom: [2 21/20; 100/99 245/242]
Gencom mapping: [<1 1/10 -4/5 11/10 1/5|, <0 -3/2 -1 3/2 1|]
Mapping: [<1 1 1 0|, <0 -2 3 4|]
EDOs: 13, 14, 27, 41, 55, 191bd, 232bcd, 273bcd
RMS error: 1.245 cents
Score
Subgroup: 2.7.11.13
Commas: 343/338, 847/832
POT2 generator: ~11/8 = 540.099
Gencom: [2 11/8; 343/338 847/832]
Gencom mapping: [<1 0 0 1 3 1|, <0 0 0 4 1 6|]
Mapping: [<1 1 3 1|, <0 4 1 6|]
RMS error: 1.282 cents
Nine note mega albitonic scale
Sensi
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
Scales:
- Meantone5 – 5-tone haplotonic scale
- Meantone7 – 7-tone albitonic scale
- Meantone12 – 12-tone chromatic scale
Mohaha
Scales:
- Mohaha7 – 7-tone albitonic scale
- Mohaha10 – 10-tone chromatic scale
Music:
Mohoho
Joan
Subgroup: 2.9.7.11
Commas: 99/98, 9317/9216
Related temperaments: casablanca, orwell
POT2 generator: ~11/8 = 542.672 cents
Gencom: [2 11/8; 99/98 9317/9216]
Gencom mapping: [<1 0 0 1 3|, <0 7/2 0 4 1|]
Mapping: [<1 0 1 3|, <0 7 4 1|]
EDOs: 11, 20, 31, 42, 115bd, 157bd
RMS error: 1.424 cents
Nine note mega albitonic scale
Tutone
Scales:
- Tutone6 – 6-tone haplotonic scale
- Tutone7 – 7-tone albitonic scale
- Tutone13 – 13-tone chromatic scale
Stacks
Subgroup: 2.9.15.7.11.13
Commas: 100/99, 105/104, 144/143, 196/195
Related temperament: magic
Svalname: 11&30
POT2 generator: ~9/7 = 439.146
Gencom: [2 9/7; 100/99 105/104 144/143 196/195]
Gencom mapping: [<1 5/2 5/2 5 2 7|, <0 -5/2 -1/2 -6 4 -9|]
Mapping: [<1 0 2 -1 6 -2|, <0 5 3 6 -4 9|]
EDOs: 11, 30, 41, 153cdef, 194cdef, 235cdef
RMS error: 1.540 cents
Eleven note note chromatic scale
Nineteen note note mega chromatic scale
Bleu
Subgroup: 2.3.7.11.13
Commas: 78/77, 99/98, 144/143
Sval name: 9&17
POL2 generator: ~13/12 = 139.990
Gencom: [2 13/12; 78/77 99/98 144/143]
Gencom mapping: [<1 1 0 2 3 3|, <0 5 0 7 4 6|]
Mapping: [<1 1 2 3 3|, <0 5 7 4 6|]
RMS error: 1.752 cents
bleu8 - Eight note haplotonic scale
bleu9 - Nine note albitonic scale
bleu17 - Seventeen note chromatic scale
On a Well Worn Riff (Bleu 17) by Chris Vaisvil
Sephiroth
Subgroup: 2.5.11.13.17
Commas: 65/64, 170/169, 221/220
Related temperament: Muggles
POT2 generator: ~5/4 = 372.236
Gencom: [2 5/4; 65/64 170/169 221/220]
Gencom mapping: [<1 0 2 0 5 4 5|, <0 0 1 0 -5 -1 -3|]
Mapping: [<1 0 15 6 11|, <0 1 -5 -1 -3|]
RMS error: 1.774 cents
Sixteen note mega chromatic scale
Archy
Scales:
Supra
Scales:
- Supra7 – 7-tone albitonic scale
- Supra12 – 12-tone chromatic scale
Supraphon
Suhajira
Scales:
- Suhajira7 – 7-tone haplotonic scale
- Suhajira10 – 10-tone albitonic scale
- Suhajira17 – 17-tone chromatic scale
Machine
Subgroup: 2.9.7.11
Commas: 64/63, 99/98
POT2 generator: ~9/8 = 214.384
Gencom: [2 9/8; 64/63 99/98]
Gencom mapping: [<1 3/2 0 3 4|, <0 1/2 0 -1 -3|]
Mapping: [<1 0 6 13|, <0 1 -1 -3|]
RMS error: 1.977 cents
Deutone
Subgroup: 2.9.5.7.13
Commas: 65/64, 81/80, 91/90
Related temperament: meanpop
POT2 generator: ~9/8 = 191.059
Gencom: [2 9/8; 65/64 81/80 91/90]
Gencom mapping: [<1 3/2 2 2 0 4|, <0 1/2 2 5 0 -2|]
Mapping: [<1 0 -4 -13 10|, <0 1 2 5 -2|]
RMS error: 2.003 cents
Negra
Porkypine
Scales:
- Porkypine7 – 7-tone haplotonic scale
- Porkypine8 – 8-tone albitonic scale
- Porkypine15 – 15-tone chromatic scale
Skateboard
Subgroup: 2.5/3.7/3.11.13/9
Commas: 56/55, 91/90, 100/99
Related temperament: thrasher
POT2 generator: ~6/5 = 313.842
Gencom: [2 6/5; 56/55 91/90 100/99]
Gencom mapping: [<1 -3/7 4/7 11/7 4 -6/7|, <0 0 -1 -3 -2 2|]
Mapping: [<1 0 -1 2 2|, <0 1 3 2 -2|]
EDOs: 11, 15, 19, 23, 42d, 65d
RMS error: 2.396 cents
Augment
Subgroup: 2.5.7.11
Commas: 56/55, 128/125
Related temperament: augmented
POT2 generator: ~8/7 = 228.275
Gencom: [5/4 8/7; 56/55 128/125]
Gencom mapping: [<3 0 7 9 11|, <0 0 0 -1 -1|]
Mapping: [<3 7 0 2|, <0 0 1 1|]
RMS error: 2.422 cents
Semaphore
Scales:
- Semaphore5 – 5-tone haplotonic scale
- Semaphore9 – 9-tone albitonic scale
- Semaphore14 – 14-tone chromatic scale
Kryptonite
Subgroup: 2.5.7/3.11/3.13/3
Commas: 56/55, 78/77, 91/90
Related temperaments: krypton
POT2 generator: ~13/12 = 132.428
Gencom: [2 13/12; 56/55 78/77 91/90]
Gencom mapping: [<1 -5/4 2 -1/4 3/4 3/4|, <0 -1/2 3 3/2 -3/2 1/2|]
Mapping: [<1 2 1 2 2|, <0 -3 -2 1 -1|]
RMS error: 2.545 cents
Nineteen note mega chromatic scale
Oregon
Subgroup: 2.9.15.7.11
Commas: 55/54, 64/63, 100/99
POT2 generator: ~6/5 = 325.495
Gencom: [2 6/5; 55/54 64/63 100/99]
Gencom mapping: [<1 2 3 2 4|, <0 -3/2 -5/2 3 -2|]
Mapping: [<1 1 1 5 2|, <0 3 4 -3 2|]
RMS error: 2.550 cents
Antikythera
Subgroup: 2.9.5.7
Commas: 50/49, 64/63
Related temperament: pajara
POT2 generator: ~8/7 = 214.095
Gencom: [7/5 8/7; 50/49 64/63]
Gencom mapping: [<2 3 5 6|, <0 1/2 -1 -1|]
Mapping: [<2 0 11 12|, <0 1 -1 -1|]
RMS error: 2.572 cents
Glacial
Subgroup: 2.9.5.11.13
Commas: 45/44, 65/64, 81/80
POT2 generator: ~9/8 = 186.151
Gencom: [2 9/8; 45/44 65/64 81/80]
Gencom mapping: [<1 3/2 2 0 3 4|, <0 1/2 2 0 3 -2|]
Mapping: [<1 0 -4 -6 10|, <0 1 2 3 -2|]
EDOs: 6, 13, 45be, 58bce, 71bce, 84bce
RMS error: 2.887 cents
Leantone
Subgroup: 2.9.5.7.11
Commas: 45/44, 56/55, 81/80
Related temperament: meanenneadecal
POT2 generator: ~9/8 = 192.500
Gencom: [2 9/8; 45/44 56/55 81/80]
Gencom mapping: [<1 3/2 2 2 3|, <0 1/2 2 5 3|]
Mapping: [<1 0 -4 -13 -6|, <0 1 2 5 3|]
EDOs: 6, 7, 13, 19, 25, 31, 56, 81
RMS error: 3.882 cents
