Chromatic pairs: Difference between revisions

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

See also: Subgroup temperaments § Terrain

Scales:

Terrain9 – 9-tone albitonic scale
Terrain15 – 15-tone chromatic scale

Music

5 5 1 mode of 33 equal (2013) by Chris Vaisvil – blog | YouTube | play

Petrtri

See also: Subgroup temperaments § Petrtri

Scales:

Petrtri5 – 5-tone haplotonic scale
Petrtri8 – 8-tone albitonic scale
Petrtri13 – 13-tone chromatic scale

Barton

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

See also: The Jacobins § Barton

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

See also: Subgroup temperaments § Tridec

Scales:

Tridec8 – 8-tone albitonic scale
Tridec13 – 13-tone chromatic scale

Nestoria

See also: Schismatic family § Nestoria (2.3.5.19)

Scales:

Nestoria7 – 7-tone albitonic scale
Nestoria12 – 12-tone chromatic scale
Nestoria17 – 17-tone mega chromatic scale

Orgone

Main article: Orgone

See also: Orgonia § Orgone

Scales:

Orgone7 – 7-tone albitonic scale
Orgone11 – 11-tone chromatic scale
Orgone15 – 15-tone mega-chromatic scale

Marveltwintri

See also: Subgroup temperaments § Marveltwintri

Scales:

Marveltwintri7 – 7-tone albitonic scale
Marveltwintri11 – 11-tone chromatic scale
Marveltwintri15 – 15-tone mega-chromatic scale

Cata

Main article: Kleismic

See also: Kleismic family § 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

See also: Subgroup temperaments § Bridgetown

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 (2011) by Chris Vaisvil – blog | play – in Bridgetown[14] for flute, bassoons, and contra-bassoon

Haumea

See also: Subgroup temperaments § Haumea

Scales:

Haumea5 – 5-tone haplotonic scale
Haumea9 – 9-tone albitonic scale
Haumea14 – 14-tone chromatic scale
Haumea19 – 19-tone mega-chromatic scale

Neutral

See also: Rastmic clan § 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], 24edo tuning

Slendric

Main article: Slendric

See also: Gamelismic clan #Slendric and No-fives subgroup temperaments #Slendric

Scales:

Slendric5 – 5-tone haplotonic scale
Slendric6 – 6-tone haplotonic scale
Slendric11 – 11-tone albitonic scale
Slendric16 – 16-tone chromatic scale

Huntington

See also: No-threes subgroup temperaments § Huntington

Scales:

Huntington7 – 7-tone haplotonic scale
Huntington10 – 10-tone albitonic scale
Huntington17 – 17-tone chromatic scale

Tobago

See also: Subgroup temperaments § Tobago

Scales:

Tobago6 – 6-tone haplotonic scale
Tobago10 – 10-tone albitonic scale
Tobago14 – 14-tone chromatic scale
Tobago24 – 24-tone quatertone scale

Pepperoni

See also: Parapyth

See also: Subgroup temperaments § Pepperoni

Scales:

Pepperoni7 – 7-tone albitonic scale
Pepperoni12 – 12-tone chromatic scale

Wizz

See also: No-threes subgroup temperaments § Wizz

Scales:

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

Bossier

See also: No-threes subgroup temperaments § Bossier

Scales:

Bossier8 – 8-tone albitonic scale
Bossier11 – 11-tone chromatic scale
Bossier14 – 14-tone mega-chromatic scale

Penta a.k.a. mechanism

See also: Subgroup temperaments § 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

See also: No-threes subgroup temperaments § Bluebirds

Scales:

Bluebirds6 – 6-tone haplotonic scale
Bluebirds7 – 7-tone albitonic scale
Bluebirds13 – 13-tone chromatic scale

Marveltri

See also: Subgroup temperaments § Marveltri

Scales:

Marveltri7 – 7-tone albitonic scale
Marveltri10 – 10-tone chromatic scale
Marveltri13 – 13-tone mega-chromatic scale

Edson

See also: Subgroup temperaments § Edson

Scales:

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

Photia

See also: Schismatic family § Photia (2.3.5.17)

Scales:

Photia7 – 7-tone albitonic scale
Photia12 – 12-tone chromatic scale

Shoe a.k.a. llywelyn

See also: Llywelynsmic clan § Llywelyn a.k.a. shoe

Scales:

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

Roulette

See also: Hemimean clan § Roulette

Scales:

Roulette6 – 6-tone haplotonic scale
Roulette7 – 7-tone albitonic scale
Roulette13 – 13-tone chromatic scale
Roulette19 – 19-tone mega-chromatic scale

Silver

See also: No-threes subgroup temperaments § Silver

Scales:

Silver7 – 7-tone haplotonic scale
Silver10 – 10-tone albitonic scale
Silver17 – 17-tone chromatic scale

Baldy

See also: Subgroup temperaments § Baldy

Scales

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

Guanyintet

See also: Subgroup temperaments § Guanyintet

Scales:

Guanyintet5 – 5-tone haplotonic scale
Guanyintet9 – 9-tone albitonic scale
Guanyintet13 – 13-tone chromatic scale

Radon

See also: Gamelismic clan § Radon

Radon5 – 5-tone haplotonic scale
Radon11 – 11-tone albitonic scale
Radon16 – 16-tone chromatic scale

Gariberttet

See also: Subgroup temperaments § Gariberttet

Scales:

Gariberttet5 – 5-tone haplotonic scale
Gariberttet9 – 9-tone albitonic scale
Gariberttet13 – 13-tone chromatic scale

Namo

See also: Rastmic clan § Namo

Scales:

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

Sentry

See also: Subgroup temperaments § Sentry

Scales:

Sentry5 – 5-tone haplotonic scale
Sentry8 – 8-tone albitonic scale
Sentry11 – 11-tone chromatic scale

Hemif

See also: No-fives subgroup temperaments § Hemif

Scales:

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

Garibaldi

Main article: Garibaldi temperament

See also: Schismatic family § Garibaldi

Scales:

Garibaldi12 – 12-tone albitonic scale
Garibaldi17 – 17-tone chromatic scale

Mabilic

See also: No-threes subgroup temperaments § Mabilic

Scales:

Mabilic7 – 7-tone haplotonic scale
Mabilic9 – 9-tone albitonic scale
Mabilic16 – 16-tone chromatic scale

Indium

See also: Subgroup temperaments § Indium

Scales:

Indium8 – 8-tone albitonic scale
Indium17 – 17-tone chromatic scale

Music

The Cry of Indium (2011) by Chris Vaisvil – blog | play – in Indium[17]

Starlingtet

See also: Subgroup temperaments § Starlingtet

Scales:

Starlingtet4 – 4-tone haplotonic scale
Starlingtet7 – 7-tone albitonic scale
Starlingtet11 – 11-tone chromatic scale

Lovecraft

See also: No-threes subgroup temperaments § Lovecraft

Scales:

Lovecraft5 – 5-tone haplotonic scale
Lovecraft9 – 9-tone albitonic scale
Lovecraft13 – 13-tone chromatic scale

Blackbirds

See also: No-threes subgroup temperaments § Blackbirds

Scales:

Blackbirds8 – 8-tone albitonic scale
Blackbirds12 – 12-tone chromatic scale
Blackbirds16 – 16-tone mega-chromatic scale

Laz

See also: Subgroup temperaments § Laz

Scales:

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

Myna

Main article: Myna

See also: Starling temperaments § Myna

Scales:

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

Greeley

See also: Subgroup temperaments § Greeley

Scales:

Greeley8 – 8-tone albitonic scale
Greeley15 – 15-tone chromatic scale

Music

A Greeley Steals Halloween by Chris Vaisvil (2011) – blog | play – in Greeley[15]

Ammon

See also: Subgroup temperaments § Ammon

Scales:

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

Mothwelltri

See also: Subgroup temperaments § Mothwelltri

Scales:

Mothwelltri5 – 5-tone haplotonic scale
Mothwelltri9 – 9-tone albitonic scale
Mothwelltri13 – 13-tone chromatic scale

Sulis

See also: Subgroup temperaments § Sulis

Scales:

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

Skwares

Main article: Squares

See also: No-fives subgroup temperaments § Skwares

Scales:

Skwares8 – 8-tone albitonic scale
Skwares11 – 11-tone mega-albitonic scale
Skwares14 – 14-tone chromatic scale

Orwell

Main article: Orwell

See also: Semicomma family § Orwell

Scales:

Orwell5 – 5-tone haplotonic scale
Orwell9 – 9-tone albitonic scale
Orwell13 – 13-tone chromatic scale

Magicaltet

See also: Subgroup temperaments § Magicaltet

Scales:

Magicaltet7 – 7-tone albitonic scale
Magicaltet11 – 11-tone chromatic scale
Magicaltet15 – 15-tone mega-chromatic scale

Magic

Main article: Magic

See also: Magic family § Magic

Scales:

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

Kiribati

See also: Subgroup temperaments § Kiribati

Scales:

Kiribati13 – 13-tone chromatic scale
Kiribati14 – 14-tone chromatic scale

Score

See also: No-threes subgroup temperaments § Score

Scales:

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

Sensi

Main article: Sensi

See also: Sensipent family § Sensi

Scales:

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

Sensation

Main article: Sensi

See also: Sensipent family § Sensi

Scales:

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

Meantone

Main article: Meantone

See also: Meantone family § Meantone

Scales:

Meantone5 – 5-tone haplotonic scale
Meantone7 – 7-tone albitonic scale
Meantone12 – 12-tone chromatic scale

Mohaha

See also: Rastmic clan § Mohaha

Scales:

Mohaha7 – 7-tone albitonic scale
Mohaha10 – 10-tone chromatic scale

Music:

Billy Stiltner

Mohaha10ping2^{[dead link]}

Mohoho

See also: Rastmic clan § Mohoho

Joan

See also: Subgroup temperaments § Joan

Scales:

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

Tutone

See also: Hemimean clan § Tutone

Scales:

Tutone6 – 6-tone haplotonic scale
Tutone7 – 7-tone albitonic scale
Tutone13 – 13-tone chromatic scale

Stacks

See also: Subgroup temperaments § Stacks (a.k.a. 2magic)

Scales:

Stacks5 – 5-tone haplotonic scale
Stacks8 – 8-tone albitonic scale
Stacks11 – 11-tone chromatic scale
Stacks19 – 19-tone mega-chromatic scale

Bleu

See also: No-fives subgroup temperaments § Bleu

Scales:

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

Sephiroth

See also: No-threes subgroup temperaments § Sephiroth

Scales:

Sephiroth7 – 7-tone haplotonic scale
Sephiroth10 – 10-tone albitonic scale
Sephiroth13 – 13-tone chromatic scale
Sephiroth16 – 16-tone mega-chromatic scale

Archy

Main article: Superpyth

See also: Archytas clan § Archy

Scales:

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

Supra

Main article: Superpyth

See also: Archytas clan § Supra

Scales:

Supra7 – 7-tone albitonic scale
Supra12 – 12-tone chromatic scale

Supraphon

Main article: Superpyth

See also: Archytas clan § Supraphon

Suhajira

See also: Archytas clan § Suhajira

Scales:

Suhajira7 – 7-tone haplotonic scale
Suhajira10 – 10-tone albitonic scale
Suhajira17 – 17-tone chromatic scale

Machine

See also: Subgroup temperaments § Machine

Scales:

Machine5 – 5-tone haplotonic scale
Machine6 – 6-tone albitonic scale
Machine11 – 11-tone chromatic scale

Deutone

See also: Hemimean clan § Deutone

Scales:

Deutone6 – 6-tone haplotonic scale
Deutone7 – 7-tone albitonic scale
Deutone13 – 13-tone chromatic scale

Negra

Main article: Negri

See also: Marvel temperaments § Negri

Porkypine

Main article: Porcupine

See also: Porcupine family § Porcupine

Scales:

Porkypine7 – 7-tone haplotonic scale
Porkypine8 – 8-tone albitonic scale
Porkypine15 – 15-tone chromatic scale

Skateboard

See also: Subgroup temperaments § Skateboard

Scales:

Skateboard7 – 7-tone haplotonic scale
Skateboard11 – 11-tone albitonic scale
Skateboard15 – 15-tone chromatic scale

Augment

See also: No-threes subgroup temperaments § Augment

Scales:

Augment6 – 6-tone haplotonic scale
Augment9 – 9-tone albitonic scale
Augment12 – 12-tone chromatic scale

Semaphore

Main article: Semaphore and godzilla

See also: Semaphoresmic clan § Semaphore

Scales:

Semaphore5 – 5-tone haplotonic scale
Semaphore9 – 9-tone albitonic scale
Semaphore14 – 14-tone chromatic scale

Kryptonite

See also: Subgroup temperaments § Kryptonite

Scales:

Kryptonite9 – 9-tone albitonic scale
Kryptonite10 – 10-tone albitonic scale
Kryptonite19 – 19-tone mega-chromatic scale

Oregon

See also: Orgonia § Oregon

Scales:

Oregon7 – 7-tone haplotonic scale
Oregon11 – 11-tone albitonic scale
Oregon15 – 15-tone chromatic scale

Antikythera

See also: Jubilismic clan § Antikythera

Scales:

Antikythera6 – 6-tone haplotonic scale
Antikythera10 – 10-tone albitonic scale
Antikythera16 – 16-tone chromatic scale

Glacial

See also: Subgroup temperaments § Glacial

Scales:

Glacial6 – 6-tone haplotonic scale
Glacial7 – 7-tone albitonic scale
Glacial13 – 13-tone chromatic scale

Leantone

See also: Hemimean clan § Leantone

Scales:

Leantone6 – 6-tone haplotonic scale
Leantone7 – 7-tone albitonic scale
Leantone13 – 13-tone chromatic scale

Notes

@@ Line 4: / Line 4: @@
 == Terrain ==
-{{Redirect|Terrain|the scale|Terrain (scale)}}
 {{See also| Subgroup temperaments #Terrain }}
@@ Line 17: / Line 16: @@
 == Petrtri ==
-Petrtri can be described as 3 &amp; 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]]
@@ Line 44: / Line 27: @@
 == Barton ==
 {{Redirect|Barton|[[Jacob Barton]]'s scale|Barton (scale)}}
+{{See also| The Jacobins #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>.
-[[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:
@@ Line 69: / Line 35: @@
 * [[Barton11]] – 11-tone 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, 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]]
@@ Line 128: / Line 57: @@
 == 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]]
@@ Line 156: / Line 67: @@
 == 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]]
@@ Line 182: / Line 77: @@
 == Cata ==
-{{Main| Hanson and cata }}
+{{Main| Kleismic }}
 {{See also| Kleismic family #Cata }}
@@ Line 194: / Line 89: @@
 == 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]]
@@ Line 223: / Line 102: @@
 == 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:
@@ Line 273: / Line 136: @@
 == 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]]
@@ Line 299: / Line 146: @@
 == 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:
@@ Line 325: / Line 156: @@
 == Pepperoni ==
 {{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]]
@@ Line 351: / Line 165: @@
 == 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:
@@ Line 375: / Line 173: @@
 == 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]]
@@ Line 410: / Line 192: @@
 == 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:
@@ Line 432: / Line 200: @@
 == 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:
@@ Line 456: / Line 208: @@
 == 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:
@@ Line 516: / Line 248: @@
 == 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]]
@@ Line 543: / Line 259: @@
 == 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]]
@@ Line 568: / Line 266: @@
 * [[Baldy11]] – 11-tone albitonic scale
 * [[Baldy17]] – 17-tone chromatic scale
 == 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:
@@ Line 603: / Line 286: @@
 == 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:
@@ Line 635: / Line 302: @@
 == 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:
@@ Line 679: / Line 330: @@
 == Mabilic ==
-Given below is the no-three version of [[Mabila family#Semabila|semabila]], or equivalently the no-threes version of [[Magic family#Trismegistus|trismegistus]]. It is the 7 &amp; 9 temperament in the [[2.5.7 subgroup]], and tempers out [[1071875/1048576]], the mabilisma.
+{{See also| No-threes subgroup temperaments #Mabilic }}
-[[Subgroup]]: 2.5.7
+[[File:mabila_66edo.jpg|right|alt=mabila_66edo.jpg|Mabilic in 66edo]]
-[[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]]
 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 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]]
@@ Line 733: / Line 352: @@
 == 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:
@@ Line 757: / Line 360: @@
 == 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]]
@@ Line 783: / Line 370: @@
 == 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:
@@ Line 807: / Line 378: @@
 == 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:
@@ Line 842: / Line 397: @@
 == 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]]
@@ Line 869: / 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]
-== 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]
+[[File:semidim_770edo.png|right|alt=semidim_770edo.png|Ammon in 770edo]]
-[[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|Semidim in 770edo]]
 Scales:
-* [[Semidim8]] – 8-tone albitonic scale
+* [[Ammon8]] – 8-tone albitonic scale
-* [[Semidim13]] – 13-tone chromatic scale
+* [[Ammon13]] – 13-tone chromatic scale
 == 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:
@@ Line 919: / Line 426: @@
 == 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:
@@ Line 965: / Line 456: @@
 == 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:
@@ Line 1,007: / Line 476: @@
 == 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:
@@ Line 1,030: / Line 483: @@
 == 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]]
@@ Line 1,104: / Line 543: @@
 == 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:
@@ Line 1,156: / Line 579: @@
 == 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:
@@ Line 1,245: / Line 652: @@
 == 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:
@@ Line 1,269: / Line 660: @@
 == 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]]
@@ Line 1,306: / Line 681: @@
 == 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:
@@ Line 1,330: / Line 689: @@
 == 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:
@@ Line 1,362: / Line 707: @@
 == 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:
@@ Line 1,399: / Line 730: @@
 [[Category:Listen]]
 [[Category:Rank 2]]
 {{todo|cleanup}}

Chromatic pairs: Difference between revisions

Latest revision as of 00:23, 24 June 2025

Terrain

Petrtri

Barton

Tridec

Nestoria

Orgone

Marveltwintri

Cata

Bridgetown

Haumea

Neutral

Slendric

Huntington

Tobago

Pepperoni

Wizz

Bossier

Penta a.k.a. mechanism

Bluebirds

Marveltri

Edson

Photia

Shoe a.k.a. llywelyn

Roulette

Silver

Baldy

Guanyintet

Radon

Gariberttet

Namo

Sentry

Hemif

Garibaldi

Mabilic

Indium

Starlingtet

Lovecraft

Blackbirds

Laz

Myna

Greeley

Ammon

Mothwelltri

Sulis

Skwares

Orwell

Magicaltet

Magic

Kiribati

Score

Sensi

Sensation

Meantone

Mohaha

Mohoho

Joan

Tutone

Stacks

Bleu

Sephiroth

Archy

Supra

Supraphon

Suhajira

Machine

Deutone

Negra

Porkypine

Skateboard

Augment

Semaphore

Kryptonite

Oregon

Antikythera

Glacial

Leantone

Notes

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