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A '''chromatic pair''' is a pair of [[mos scale]]s in some [[rank-2 temperament]] (either a full [[Harmonic limit|''p''-limit]] temperament or a [[subgroup temperament]]) that are analogous to the familiar [[5L 2s|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.


The phrase ''chromatic pair'' refers to a pair of [[MOS scale|moment-of-symmetry scales]] in some rank-2 temperament (or [[Just intonation subgroups|subgroup temperament]]) that are analogous to the familiar diatonic and chromatic scales of standard tuning. The smaller scale is referred to as "albitonic" (from the Latin word for "white"), named such since the diatonic scale can be played using the white keys of a piano, and the larger of the two is "chromatic", analogous to the chromatic scale of standard tuning. A third type of related scale are "haplotonic" scales (from the Greek word for "single" or "simple"), analogous to the pentatonic scale of standard tuning and played using the black keys of a piano. The pair temperaments are listed in order of increasing [[Tp_tuning#T2 tuning|RMS error]], which is an appropriate error measure for subgroups as well as full p-limit groups.
In the sections below, the pair temperaments are listed in order of increasing [[Tp tuning#T2 tuning|RMS error]], which is an appropriate error measure for subgroups as well as full ''p''-limit groups.


== Terrain ==
== Terrain ==
Subgroup: 2.9/5.9/7
{{See also| Subgroup temperaments #Terrain }}


Commas: 250047/250000
[[File:terrain_3558edo.png|right|alt=terrain_3558edo.png|Terrain in 3558edo]]


Sval name: 6&21
Scales:  
* [[Terrain9]] – 9-tone albitonic scale
* [[Terrain15]] – 15-tone chromatic scale


Related temperament: [[Minortonic_family#Domain|domain]]
; 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]
[[Tp_tuning|POT2 generator]]: ~10/9 = 182.461
 
[[Gencom|Gencom]]: [63/50 10/9; 250047/250000]
 
Gencom mapping: [<3 10/9 -7/9 2/9|, <0 -2/3 -1/3 2/3|]
 
Mapping: [<3 0 -4|, <0 1 2|]
 
EDOs: 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
 
Terrain 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.
 
[[File:terrain_3558edo.png|alt=terrain_3558edo.png|terrain_3558edo.png]]
 
[[terrain9|Nine note albitonic scale]]
 
[[terrain15|Fifteen note chromatic scale]]
 
[http://chrisvaisvil.com/5-5-1-mode-of-33-equal-with-video/ 5 5 1 mode of 33 equal (with video)] [http://micro.soonlabel.com/33edo/20130827_551of33.mp3 play] by [[Chris_Vaisvil|Chris Vaisvil]]


== Petrtri ==
== Petrtri ==
Subgroup: 2.11/5.13/5
{{See also| Subgroup temperaments #Petrtri }}


Comma: 2200/2197
[[File:petrtri_385edo.png|right|alt=petrtri_385edo.png|Petrtri in 385edo]]


Svalname: 3&5
Scales:  
 
* [[Petrtri5]] – 5-tone haplotonic scale
[[Tp_tuning|POT2 generator]]: ~13/10 = 455.012
* [[Petrtri8]] – 8-tone albitonic scale
 
* [[Petrtri13]] – 13-tone chromatic scale
[[Gencom|Gencom]]: [2 13/10; 2200/2197]
 
Gencom mapping: [<1 0 -1/3 0 -1/3 2/3|, <0 0 -4/3 0 5/3 -1/3|]
 
Mapping: [<1 0 1|, <0 3 1|]
 
EDOs: 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|alt=petrtri_385edo.png|petrtri_385edo.png]]
 
[[petrtri5|Five note haplotonic scale]]
 
[[petrtri8|Eight note albitonic scale]]
 
[[petrtri13|Thirteen note chromatic scale]]


== Barton ==
== Barton ==
Subgroup: 2.5.11.13
{{Redirect|Barton|[[Jacob Barton]]'s scale|Barton (scale)}}
 
{{See also| The Jacobins #Barton }}
Commas: 2200/2197, 6656/6655
 
Svalname: 11&13


[[Tp_tuning|POT2 generator]]: ~11/8 = 551.699
Scales:
 
* [[Barton5]] – 5-tone haplotonic scale
Gencom: [2 11/8; 2200/2197 6656/6655]
* [[Barton7]] – 7-tone albitonic scale
 
* [[Barton9]] – 9-tone mega-albitonic scale
Gencom mapping: [<1 0 6 0 3 6|, <0 0 -8 0 1 -5|]
* [[Barton11]] – 11-tone chromatic scale
 
* [[Barton13]] – 13-tone mega-chromatic scale
Mapping: [<1 6 3 6|, <0 -8 1 -5|]
 
EDOs: 11, 13, 24, 37, 50, 87, 298, 385, 472, 559, 1590cd
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.0822 cents
 
[[barton5|Five note haplotonic scale]]
 
[[barton7|Seven note albitonic scale]]
 
[[barton9|Nine note mega albitonic scale]]
 
[[barton11|Eleven note chromatic scale]]
 
[[barton13|Thirteen note mega chromatic scale]]
 
== Voltage ==
Subgroup: 2.7.13
 
Comma: 28672/28561
 
Sval name: 3&7
 
[[Tp_tuning|POT2 generator]]: ~16/13 = 357.677
 
[[TOP_tuning|POTT generator]]: ~16/13 = 1200 - 300 log₂(7) (357.794)
 
Gencom: [2, 16/13; 28672/28561]
 
Gencom mapping: [<1 0 0 4 0 4|, <0 0 0 -4 0 -1|]
 
Mapping: [<1 4 4|, <0 -4 -1|]
 
EDOS: 3, 7, 10, 27, 37, 47, 57, 104
 
RMS error: 0.1423


== Tridec ==
== Tridec ==
Subgroup: 2.7/5.11/5.13/5
{{See also| Subgroup temperaments #Tridec }}
 
Commas: 847/845, 1001/1000
 
Sval name: 5&8
 
[[Tp_tuning|POT2 generator]]: ~13/10 = 454.556
 
[[Gencom|Gencom]]: [2 13/10; 847/845 1001/1000]
 
Gencom mapping: [<1 0 -3/4 5/4 -3/4 1/4|, <0 0 0 -4 3 1|]
 
Mapping: [<1 2 0 1|, <0 -4 3 1|]
 
EDOs: 5, 8, 21, 29, 37, 66, 169, 235, 404c, 639c, 953bc
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.1613 cents
 
[[File:tridec_235edo.png|alt=tridec_235edo.png|tridec_235edo.png]]


[[Tridec8|Eight note albitonic scale]]
[[File:tridec_235edo.png|right|alt=tridec_235edo.png|Tridec in 235edo]]


[[Tridec13|Thirteen note chromatic scale]]
Scales:
* [[Tridec8]] – 8-tone albitonic scale
* [[Tridec13]] – 13-tone chromatic scale


== Nestoria ==
== Nestoria ==
Subgroup: 2.3.5.19
{{See also| Schismatic family #Nestoria (2.3.5.19)}}


Commas: 361/360, 513/512
[[File:nestoria_171edo.png|right|alt=nestoria_171edo.png|Nestoria in 171edo]]


Sval name: 12&29
Scales:  
 
* [[Nestoria7]] – 7-tone albitonic scale
Related temperament: [[Schismatic_family|schismatic]]
* [[Nestoria12]] – 12-tone chromatic scale
 
* [[Nestoria17]] – 17-tone mega chromatic scale
[[Tp_tuning|POT2 generator]]: ~3/2 = 701.746
 
[[Gencom|Gencom]]: [2 3/2; 361/360 513/512]
 
Gencom mapping: [<1 1 7 0 0 0 0 6|, <0 1 -8 0 0 0 0 -3|]
 
Mapping: [<1 0 15 9|, <0 1 -8 -3|]
 
EDOs: 7, 12, 17, 29, 41, 53, 118, 171, 460d, 631d
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.1763 cents
 
[[File:nestoria_171edo.png|alt=nestoria_171edo.png|nestoria_171edo.png]]
 
[[nestoria7|Seven note albitonic scale]]
 
[[nestoria12|Twelve note chromatic scale]]
 
[[nestoria17|Seventeen note mega chromatic scale]]


== Orgone ==
== Orgone ==
Subgroup: 2.7.11
{{Main| Orgone }}
 
{{See also| Orgonia #Orgone }}
Commas: 65536/65219
 
Svals: 4&7
 
Related temperament: [[Gamelismic_clan#superkleismic|superkleismic]]
 
[[Tp_tuning|POT2 generator]]: ~77/64 = 323.372
 
[[Gencom|Gencom]]: [2 77/64; 65536/65219]
 
Gencom mapping: [<1 0 0 2 4|, <0 0 0 3 -2|]
 
Mapping: [<1 2 4|, <0 3 -2|]
 
EDOs: 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|orgone_308edo.jpg]]
[[File:orgone_308edo.jpg|right|alt=orgone_308edo.jpg|Orgone in 308edo]]


[[orgone7|Seven note albitonic scale]]
Scales:
 
* [[Orgone7]] – 7-tone albitonic scale
[[orgone11|Eleven note chromatic scale]]
* [[Orgone11]] – 11-tone chromatic scale
 
* [[Orgone15]] – 15-tone mega-chromatic scale
[[orgone15|Fifteen note mega chromatic scale]]


== Marveltwintri ==
== Marveltwintri ==
Subgroup: 2.5/3.13/9
{{See also| Subgroup temperaments #Marveltwintri }}


Comma: 325/324
[[File:marveltwintri_321edo.png|right|alt=marveltwintri_321edo.png|Marveltwintri in 321edo]]


Svalname: 3&4
Scales:  
 
* [[Marveltwintri7]] – 7-tone albitonic scale
[[Tp_tuning|POT2 generator]]: ~6/5 = 317.139
* [[Marveltwintri11]] – 11-tone chromatic scale
 
* [[Marveltwintri15]] – 15-tone mega-chromatic scale
[[Gencom|Gencom]]: [2 6/5; 325/324]
 
Gencom mapping: [<1 -1/6 5/6 0 0 -1/3|, <0 -1/2 -3/2 0 0 1|]
 
Mapping: [<1 0 2|, <0 1 -2|]
 
EDOs: 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|marveltwintri_321edo.png]]
 
[[marveltwintri7|Seven note albitonic scale]]
 
[[marveltwintri11|Eleven note chromatic scale]]
 
[[marveltwintri15|Fifteen note mega chromatic scale]]


== Cata ==
== Cata ==
Subgroup: 2.3.5.13
{{Main| Kleismic }}
 
{{See also| Kleismic family #Cata }}
Commas: 325/324, 625/624
 
Sval name: 15&19
 
Related temperament: [[Kleismic_family|catakleismic]]
 
[[Tp_tuning|POT2 generator]]: ~6/5 = 317.076
 
[[Gencom|Gencom]]: [2 6/5; 325/324 625/624]
 
Gencom mapping: [<1 0 1 0 0 0|, <0 6 5 0 0 14|]
 
Mapping: [<1 0 1 0|, <0 6 5 14|]
 
EDOs: 7, 11, 15, 19, 34, 53, 140, 193, 246, 1177cd
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.2450 cents
 
[[File:cata_246edo.jpg|alt=cata_246edo.jpg|cata_246edo.jpg]]
 
[[cata7|Seven note albitonic scale]]
 
[[cata11|Eleven note mega albitonic scale]]


[[cata15|Fifteen note chromatic scale]]
[[File:cata_246edo.jpg|right|alt=cata_246edo.jpg|Cata in 246edo]]


[[cata19|Nineteen note mega chromatic scale]]
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 ==
Subgroup: 2.3.11/5.13/5
{{See also| Subgroup temperaments #Bridgetown }}


Commas: 352/351, 676/675
[[File:bridgetown_29edo.png|right|alt=bridgetown_29edo.png|Bridgetown in 29edo]]


Sval name: 5&24
Scales:  
* [[Bridgetown9]] – 9-tone albitonic scale
* [[Bridgetown14]] – 14-tone chromatic scale


Related temperaments: [[Chromatic_pairs#Haumea|haumea]], [[The_Archipelago|barbados]]
; 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]]
[[Tp_tuning|POT2 generator]]: ~15/13 = 248.399
* ''Route 14 in Bridgetown'' (2011) by [[Chris Vaisvil]] – [https://www.chrisvaisvil.com/tuning-survey-october-26th-2011/ blog] | [https://web.archive.org/web/20201127012744/http://micro.soonlabel.com/tuning-survey/daily20111026-bridgetown-14.mp3 play] – in Bridgetown[14] for flute, bassoons, and contra-bassoon
 
[[Gencom|Gencom]]: [2 15/13; 352/351 676/675]
 
Gencom mapping: [<1 2 -5/3 0 4/3 1/3|, <0 -2 4 0 -5 1|]
 
Mapping: [<1 0 -6 -1|, <0 2 9 3|]
 
EDOs: 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|alt=bridgetown_29edo.png|bridgetown_29edo.png]]
 
[[bridgetown9|Nine note albitonic scale]]
 
[[bridgetown14|Fourteen note chromatic scale]]
 
=== Music ===
<span style=""><span style="">[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/Paint%20in%20the%20Water%2029.mp3 Paint in the Water 29]</span></span> by [[Igliashon_Jones|Igliashon Jones]]
 
<span style=""><span style="">[http://micro.soonlabel.com/tuning-survey/daily20111026-bridgetown-14.mp3 Route 14 in Bridgetown]</span></span> by [[Chris_Vaisvil|Chris Vaisvil]]


== Haumea ==
== Haumea ==
Subgroup: 2.3.7/5.11/5.13/5
{{See also| Subgroup temperaments #Haumea }}
 
Commas: 352/351, 676/675, 847/845
 
Related temperaments: [[Chromatic_pairs#Bridgetown|bridgetown]], [[Hemifamity_family#Namaka|namaka]], hemigari, barbados, parizekmic


[[Tp_tuning|POT2 generator]]: ~15/13 = 248.491
Scales:  
 
* [[Haumea5]] – 5-tone haplotonic scale
[[Gencom|Gencom]]: [2 15/13; 352/351 676/675 847/845]
* [[Haumea9]] – 9-tone albitonic scale
 
* [[Haumea14]] – 14-tone chromatic scale
Gencom mapping: [&lt;1 2 -3/4 -11/4 9/4 5/4|, &lt;0 -2 0 12 -9 -3|]
* [[Haumea19]] – 19-tone mega-chromatic scale
 
Mapping: [&lt;1 0 10 -6 -1|, &lt;0 2 -12 9 3|]
 
EDOs: 24, 29, 111, 140, 169, 198, 565d, 763bd, 961bd
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.2668 cents
 
[[haumea5|Five note haplotonic scale]]
 
[[haumea9|Nine note albitonic scale]]
 
[[haumea14|Fourteen note chromatic scale]]
 
[[haumea19|Nineteen note mega chromatic scale]]


== Neutral ==
== Neutral ==
Subgroup: 2.3.11
{{See also| Rastmic clan #Neutral }}
 
Commas: 243/242
 
Svalname: 7&amp;17
 
[[Tp_tuning|POT2 generator]]: ~11/9 = 350.525


[[Gencom|Gencom]]: [2 11/9; 243/242]
[[File:neutral_380edo.png|right|alt=neutral_380edo.png|Neutral in 380edo]]


Gencom mapping: [&lt;1 1 0 0 2|, &lt;0 2 0 0 5|]
Scales:  
* [[Neutral7]] – 7-tone albitonic scale
* [[Neutral10]] – 10-tone chromatic scale
* [[Neutral17]] – 17-tone mega-chromatic scale


Mapping: [&lt;1 1 2|, &lt;0 2 5|]
; Music
 
* [https://soundcloud.com/jdfreivald/mo-happy-happy ''Mo - Happy - Happy''] [http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/mo-happy-happy.mp3 play] by [[Jake Freivald]] in Neutral[7], 24edo tuning
EDOs: 7, 17, 24, 65, 89, 202, 291, 380
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.3021 cents
 
[[File:neutral_380edo.png|alt=neutral_380edo.png|neutral_380edo.png]]
 
[[neutral7|Seven note albitonic scale]]
 
[[neutral10|Ten note chromatic scale]]
 
[[neutral17|Seventeen note mega chromatic scale]]
 
=== Music ===
[https://soundcloud.com/jdfreivald/mo-happy-happy Mo - Happy - Happy] [http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/mo-happy-happy.mp3 play] by Jake Freivald in Neutral[7], 24et tuning


== Slendric ==
== Slendric ==
Line 345: Line 127:
:''See also: [[Gamelismic clan #Slendric]] and [[No-fives subgroup temperaments #Slendric]]''
:''See also: [[Gamelismic clan #Slendric]] and [[No-fives subgroup temperaments #Slendric]]''


Subgroup: 2.3.7
[[File:slendric_190edo.jpg|right|alt=slendric_190edo.jpg|Slendric in 190edo]]
 
Comma list: 1029/1024
 
Sval name: 5&amp;21
 
[[Tp tuning|POT2 generator]]: ~8/7 = 233.688
 
[[Gencom]]: [2 8/7; 1029/1024]
 
Gencom mapping: [{{val| 1 1 0 3 }}, {{val| 0 3 0 -1 }}]
 
Mapping: [{{val| 1 1 3 }}, {{val| 0 3 -1 }}]
 
EDOs: 5, 6, 11, 16, 21, 26, 31, 36, 41, 77, 113, 190
 
[[Tp tuning #T2 tuning|RMS error]]: 0.3202 cents
 
[[File:slendric_190edo.jpg|alt=slendric_190edo.jpg|slendric_190edo.jpg]]
 
[[slendric5|Five note haplotonic scale]]
 
[[slendric6|Six note haplotonic scale]]


[[slendric11|Eleven note albitonic scale]]
Scales:
 
* [[Slendric5]] – 5-tone haplotonic scale
[[slendric16|Sixteen note chromatic scale]]
* [[Slendric6]] – 6-tone haplotonic scale
* [[Slendric11]] – 11-tone albitonic scale
* [[Slendric16]] – 16-tone chromatic scale


== Huntington ==
== Huntington ==
Subgroup: 2.5.7.13
{{See also| No-threes subgroup temperaments #Huntington }}
 
Commas: 640/637, 10985/10976
 
Sval name: 10&amp;27
 
[[Tp_tuning|POT2 generator]]: ~16/13 = 357.002
 
[[Gencom|Gencom]]: [2 16/13; 640/637 10985/10976]
 
Gencom mapping: [&lt;1 0 5 4 0 4|, &lt;0 0 -9 -4 0 -1|]


Mapping: [&lt;1 5 4 4|, &lt;0 -9 -4 -1|]
[[File:huntington_400edo.jpg|right|alt=huntington_400edo.jpg|Huntington in 400edo]]


EDOs: 7, 10, 17, 27, 37, 84, 121, 279cd, 400cd
Scales:  
 
* [[Huntington7]] – 7-tone haplotonic scale
[[Tp_tuning#T2 tuning|RMS error]]: 0.3452 cents
* [[Huntington10]] – 10-tone albitonic scale
 
* [[Huntington17]] – 17-tone chromatic scale
[[File:huntington_400edo.jpg|alt=huntington_400edo.jpg|huntington_400edo.jpg]]
 
[[huntington7|Seven note haplotonic scale]]
 
[[huntington10|Ten note albitonic scale]]
 
[[huntington17|Seventeen note chromatic scale]]


== Tobago ==
== Tobago ==
Subgroup: 2.3.11.13/5
{{See also| Subgroup temperaments #Tobago }}
 
Commas: 243/242, 676/675
 
Sval name: 10&amp;14
 
Related temperaments: [[Chromatic_pairs#Neutral|neutral]], [[The_Archipelago|barbados]]
 
[[Tp_tuning|POT2 generator]]: ~15/13 = 249.312
 
[[Gencom|Gencom]]: [55/39 15/13; 243/242 676/675]
 
Gencom mapping: [&lt;2 4 -2 0 9 2|, &lt;0 -2 3/2 0 -5 -3/2|]
 
Mapping: [&lt;2 0 -1 -2], &lt;0 2 5 3]]
 
EDOs: 10, 14, 24, 58, 82, 130
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.3533 cents
 
[[tobago6|Six note haplotonic scale]]
 
[[tobago10|Ten note albitonic scale]]
 
[[tobago14|Fourteen note chromatic scale]]


[[tobago24|Twentyfour note quatertone scale]]
Scales:
* [[Tobago6]] – 6-tone haplotonic scale
* [[Tobago10]] – 10-tone albitonic scale
* [[Tobago14]] – 14-tone chromatic scale
* [[Tobago24]] – 24-tone quatertone scale


== Pepperoni ==
== Pepperoni ==
Subgroup: 2.3.11/7.13/7
{{See also| Parapyth }}
 
{{See also| Subgroup temperaments #Pepperoni }}
Commas: 352/351, 364/363
 
Sval name: 5&amp;12
 
Related temperament: The [[Peppermint-24|Pepper fifth]], which is (40200 + 600 sqrt(5))/59 = 704.096 cents, is a good pepperoni generator, hence the name.
 
[[Tp_tuning|POT2 generator]]: ~3/2 = 703.856
 
[[Gencom|Gencom]]: [2 3/2; 352/351 364/363]
 
Gencom mapping: [&lt;1 1 0 -8/3 1/3 7/3|, &lt;0 1 0 11/3 -1/3 -10/3|]
 
Mapping: [&lt;1 0 7 12|, &lt;0 1 -4 -7|]
 
EDOs: 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|alt=pepperoni_271edo.png|pepperoni_271edo.png]]


[[pepperoni7|Seven note albitonic scale]]
[[File:pepperoni_271edo.png|right|alt=pepperoni_271edo.png|Pepperoni in 271edo]]


[[pepperoni12|Twelve note chromatic scale]]
Scales:
* [[Pepperoni7]] – 7-tone albitonic scale
* [[Pepperoni12]] – 12-tone chromatic scale


== Wizz ==
== Wizz ==
Subgroup: 2.5.11
{{See also| No-threes subgroup temperaments #Wizz }}
 
Commas: 15625/15488
 
Sval name: 6&amp;16
 
Related temperaments: [[Marvel_temperaments#Wizard-11-limit|wizard]]
 
Generator: ~5/4 = 383.768
 
[[Gencom|Gencom]]: [125/88 5/4; 15625/15488]
 
Gencom mapping: [&lt;2 0 4 0 5| &lt;0 0 1 0 3|]
 
Mapping: [&lt;2 0 -7|, &lt;0 1 3|]
 
EDOs: 6, 16, 22, 28, 50, 122, 172, 222
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.3997
 
[[wizz6|Six note haplotonic scale]]
 
[[wizz10|Ten note albitonic scale]]


[[wizz16|Sixteen note chromatic scale]]
Scales:
* [[Wizz6]] – 6-tone haplotonic scale
* [[Wizz10]] – 10-tone albitonic scale
* [[Wizz16]] – 16-tone chromatic scale


== Bossier ==
== Bossier ==
Subgroup: 2.7.11.13
{{See also| No-threes subgroup temperaments #Bossier }}
 
Commas: 1573/1568, 15488/15379
 
Sval name: 3&amp;17
 
[[Tp_tuning|POT2 generator]]: ~14/11 = 421.309
 
[[Gencom|Gencom]]: [2 14/11; 1573/1568 15488/15379]
 
Gencom mapping: [&lt;1 0 0 0 1 3|, &lt;0 0 0 8 7 2|]
 
Mapping: [&lt;1 0 1 3|, &lt;0 8 7 2|]
 
EDOs: 17, 20, 37, 57, 94, 225, 319cd, 413bcd
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.4043 cents
 
[[File:bossier_225edo.jpg|alt=bossier_225edo.jpg|bossier_225edo.jpg]]
 
[[bossier8|Eight note albitonic scale]]


[[bossier11|Eleven note chromatic scale]]
[[File:bossier_225edo.jpg|right|alt=bossier_225edo.jpg|Bossier in 225edo]]


[[bossier14|Fourteen note mega chromatic scale]]
Scales:
* [[Bossier8]] – 8-tone albitonic scale
* [[Bossier11]] – 11-tone chromatic scale
* [[Bossier14]] – 14-tone mega-chromatic scale


== Penta (aka Mechanism) ==
== Penta a.k.a. mechanism ==
Subgroup: 2.9.7.11
{{See also| Subgroup temperaments #Penta a.k.a. mechanism }}


Commas: 896/891, 26411/26244
Scales:  
 
* [[Penta5]] – 5-tone haplotonic scale
Svalname: 8&amp;11
* [[Penta8]] – 8-tone albitonic scale
 
* [[Penta11]] – 11-tone chromatic scale
[[Tp_tuning|POT2 generator]]: ~9/7 = 438.465
* [[Penta19]] – 19-tone mega-chromatic scale
 
[[Gencom|Gencom]]: [2 9/7; 896/891 26411/26244]
 
Gencom mapping: [&lt;1 5/2 0 5 2|, &lt;0 -5/2 0 -6 4|]
 
Mapping: [&lt;1 0 -1 6|, &lt;0 5 6 -4|]
 
EDOs: 8, 11, 30, 41, 52
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.4262 cents
 
[[penta5|Five note haplotonic scale]]
 
[[penta8|Eight note albitonic scale]]
 
[[penta11|Eleven note chromatic scale]]
 
[[penta19|Nineteen note mega chromatic scale]]


== Bluebirds ==
== Bluebirds ==
Subgroup: 2.11.13
{{See also| No-threes subgroup temperaments #Bluebirds }}
 
Comma: 265837/262144
 
[[Tp_tuning|POT2 generator]]: ~143/128 = 182.368


Gencom: [2 143/128; 265837/262144]
Scales:  
 
* [[Bluebirds6]] – 6-tone haplotonic scale
Gencom mapping: [&lt;1 0 0 0 3 4|, &lt;0 0 0 0 3 -2|]
* [[Bluebirds7]] – 7-tone albitonic scale
 
* [[Bluebirds13]] – 13-tone chromatic scale
Mapping: [&lt;1 0 6|, &lt;0 3 -2|]
 
EDOs: 6, 7, 13, 33, 46, 79, 125c, 204bc, 329bc
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.4444 cents
 
[[bluebirds6|Six note haplotonic scale]]
 
[[bluebirds7|Seven note albitonic scale]]
 
[[bluebirds13|Thirteen note chromatic scale]]


== Marveltri ==
== Marveltri ==
Subgroup: 2.5.9/7
{{See also| Subgroup temperaments #Marveltri }}
 
Comma: 225/224
 
Sval name: 3&amp;13
 
Related temperaments: marvel, 22&amp;47, magic
 
[[Tp_tuning|POT2 generator]]: ~5/4 = 383.638
 
[[Gencom|Gencom]]: [2 5/4; 225/224]


Gencom mapping: [&lt;1 2/5 2 -1/5|, &lt;0 -4/5 1 2/5|]
Scales:  
 
* [[Marveltri7]] – 7-tone albitonic scale
Mapping: [&lt;1 0 5|, &lt;0 1 -2|]
* [[Marveltri10]] – 10-tone chromatic scale
 
* [[Marveltri13]] – 13-tone mega-chromatic scale
EDOs: 12, 13, 16, 19, 22, 25, 47, 69, 72, 97, 122, 269bc, 660bc
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.4801 cents
 
[[marveltri7|Seven note albitonic scale]]
 
[[marveltri10|Ten note chromatic scale]]
 
[[marveltri13|Thirteen note mega chromatic scale]]


== Edson ==
== Edson ==
Subgroup: 2.3.7/5.11/5.13/5
{{See also| Subgroup temperaments #Edson }}
 
Commas: 196/195, 352/351, 364/363
 
Related temperaments: [[Hemifamity_family#Pele|pele]], cassandra
 
[[Tp_tuning|POT2 generator]]: ~3/2 = 703.414
 
[[Gencom|Gencom]]: [2 3/2; 196/195, 352/351, 364/363]
 
Gencom mapping: [&lt;1 1 -5 -1 2 4|, &lt;0 1 29/4 5/4 -11/4 -23/4|]
 
Mapping: [&lt;1 0 10 17 22|, &lt;0 1 -6 -10 -13|]
 
EDOs: 12, 17, 29, 621bcde
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.5102 cents
 
[[edson5|Five note haplotonic scale]]
 
[[edson7|Seven note albitonic scale]]
 
[[edson12|Twelve note chromatic scale]]


[[edson17|Seventeen note mega chromatic scale]]
Scales:
* [[Edson5]] – 5-tone haplotonic scale
* [[Edson7]] – 7-tone albitonic scale
* [[Edson12]] – 12-tone chromatic scale
* [[Edson17]] – 17-tone mega-chromatic scale


== Photia ==
== Photia ==
Subgroup: 2.3.5.17.19
{{See also| Schismatic family #Photia (2.3.5.17) }}
 
Commas: 171/170, 256/255, 324/323
 
Sval name: 12&amp;41
 
Related temperament: [[Schismatic_family|schismatic]]
 
[[Tp_tuning|POT2 generator]]: ~3/2 = 701.470
 
[[Gencom|Gencom]]: [2 3/2; 171/170 256/255 324/323]
 
Gencom mapping: [&lt;1 1 7 0 0 0 0 6|, &lt;0 1 -8 0 0 0 7 -3|]
 
Mapping: [&lt;1 0 15 -7 9|, &lt;0 1 -8 7 -3|]


EDOs: 7, 12, 17, 29, 41, 53, 65, 142d, 207d, 272d
[[File:photia_65edo.png|right|alt=photia_65edo.png|Photia in 65edo]]


[[Tp_tuning#T2 tuning|RMS error]]: 0.5374 cents
Scales:
* [[Photia7]] – 7-tone albitonic scale
* [[Photia12]] – 12-tone chromatic scale


[[File:photia_65edo.png|alt=photia_65edo.png|photia_65edo.png]]
== Shoe a.k.a. llywelyn ==
{{See also| Llywelynsmic clan #Llywelyn a.k.a. shoe }}


[[photia7|Seven note albitonic scale]]
[[File:shoe_37edo.jpg|right|alt=shoe_37edo.jpg|Shoe in 37edo]]


[[photia12|Twelve note chromatic scale]]
Scales:
 
* [[Shoe5]] – 5-tone mini-haplotonic scale
== Shoe ==
* [[Shoe6]] – 6-tone haplotonic scale
Subgroup: 2.5.7.11.13
* [[Shoe11]] – 11-tone albitonic scale
 
* [[Shoe16]] – 16-tone chromatic scale
Commas: 176/175, 640/637, 847/845
 
Sval name: 16&amp;21
 
[[Tp_tuning|POT2 generator]]: ~8/7 = 227.108
 
[[Gencom|Gencom]]: [2 8/7; 176/175 640/637 847/845]
 
Gencom mapping: [&lt;1 0 1 3 1 2|, &lt;0 0 7 -1 13 9|]
 
Mapping: [&lt;1 1 3 1 2|, &lt;0 7 -1 13 9|]
 
EDOs: 16, 21, 37, 206bce, 243bce, 280bce, 317bce, 354bce, 391bce
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.5433 cents
 
[[File:shoe_37edo.jpg|alt=shoe_37edo.jpg|shoe_37edo.jpg]]
 
[[shoe5|shoe5]] - five note mini [[haplotonic_scale|haplotonic scale]]
 
[[shoe6|shoe6]] - six note [[haplotonic_scale|haplotonic scale]]
 
[[shoe11|shoe11]] - eleven note note [[albitonic_scale|albitonic scale]]
 
[[shoe16|shoe16]] - sixteen note [[chromatic_scale|chromatic scale]]


== Roulette ==
== Roulette ==
Subgroup: 2.5.7.11.13
{{See also | Hemimean clan #Roulette }}
 
Commas: 176/175, 1375/1372, 640/637
 
Sval name: 6&amp;25
 
Related temperament: [[Würschmidt_family|Hemiwürschmidt]]
 
[[Tp_tuning|POT2 generator]]: ~28/25 = 194.594
 
[[Gencom|Gencom]]: [2 28/25; 176/175 1375/1372 640/637]
 
Gencom mapping: [&lt;1 0 2 2 2 5|, &lt;0 0 2 5 9 -8|]
 
Mapping: [&lt;1 0 -3 -7 13|, &lt;0 2 5 9 -8|]
 
EDOs: 6, 7, 13, 19, 25, 31, 37
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.5567 cents
 
[[File:roulette_37edo.jpg|alt=roulette_37edo.jpg|roulette_37edo.jpg]]
 
[[roulette6|roulette6]] - six note [[haplotonic_scale|haplotonic scale]]
 
[[roulette7|roulette7]] - seven note [[albitonic_scale|albitonic scale]]


[[roulette13|roulette13]] - thirteen note [[chromatic_scale|chromatic scale]]
[[File:roulette_37edo.jpg|right|alt=roulette_37edo.jpg|Roulette in 37edo]]


[[roulette19|roulette19]] - nineteen note [[mega_chromatic_scale|mega chromatic scale]]
Scales:
* [[Roulette6]] – 6-tone haplotonic scale
* [[Roulette7]] – 7-tone albitonic scale
* [[Roulette13]] – 13-tone chromatic scale
* [[Roulette19]] – 19-tone mega-chromatic scale


== Silver ==
== Silver ==
Subgroup: 2.5.7.13.17
{{See also | No-threes subgroup temperaments #Silver }}
 
Commas: 170/169, 640/637, 5525/5488
 
Sval name: 10&amp;27
 
[[Tp_tuning|POT2 generator]]: ~13/8 = 842.711
 
[[Gencom|Gencom]]: [2 13/8; 170/169 640/637 5525/5488]
 
Gencom mapping: [&lt;1 0 -4 0 0 3 9|, &lt;0 0 9 4 0 1 -7|]
 
Mapping: [&lt;1 5 4 4 2|, &lt;0 -9 -4 -1 7|]
 
EDOs: 7, 10, 17, 27, 37, [[47edo|47]], 84, 131, 178e, 309cde, [[487edo|487bcdee]]
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.5886 cents
 
[[File:silver_487edo.jpg|alt=silver_487edo.jpg|silver_487edo.jpg]]
 
[[silver7|silver7]] -seven note [[haplotonic_scale|haplotonic scale]]


[[silver10|silver10]] - ten note [[albitonic_scale|albitonic scale]]
[[File:silver_487edo.jpg|right|alt=silver_487edo.jpg|Silver in 487edo]]


[[silver17|silver17]] - seventeen note [[chromatic_scale|chromatic scale]]
Scales:
* [[Silver7]] – 7-tone haplotonic scale
* [[Silver10]] – 10-tone albitonic scale
* [[Silver17]] – 17-tone chromatic scale


== Baldy ==
== Baldy ==
Subgroup: 2.9.5.7.13
{{See also| Subgroup temperaments #Baldy }}
 
Commas: 225/224, 325/324, 640/637
 
Sval name: 6&amp;35
 
Related temperament: [[Schismatic_family|Garibaldi]]
 
[[Tp_tuning|POT2 generator]]: ~9/8 = 204.090
 
[[Gencom|Gencom]]: [2 9/8; 225/224 325/324 640/637]
 
Gencom mapping: [&lt;1 3/2 3 4 0 2|, &lt;0 1/2 -4 -7 0 10|]
 
Mapping: [&lt;1 0 15 25 -28|, &lt;0 1 -4 -7 10|]
 
EDOs: 6, 11, 17, 23, 29, 35, 41, [[47edo|47]], 100, [[147edo|147]], 488cd, 635cd
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.5999 cents


[[File:baldy_147edo.jpg|alt=baldy_147edo.jpg|baldy_147edo.jpg]]
[[File:baldy_147edo.jpg|right|alt=baldy_147edo.jpg|Baldy in 147edo]]


[[baldy6|baldy6]] - six note [[haplotonic_scale|haplotonic scale]]
Scales
* [[Baldy6]] – 6-tone haplotonic scale
* [[Baldy11]] – 11-tone albitonic scale
* [[Baldy17]] – 17-tone chromatic scale


[[baldy11|baldy11]] - eleven note [[albitonic_scale|albitonic scale]]
[[baldy17|baldy17]] - seventeen note [[chromatic_scale|chromatic scale]]


== Guanyintet ==
== Guanyintet ==
Subgroup: 2.5.7/3.11/3
{{See also | Subgroup temperaments #Guanyintet }}
 
Commas: 176/175, 540/539
 
Svalname: 4&amp;9
 
Related temperaments: guanyin, orwell
 
[[Tp_tuning|POT2 generator]]: ~7/6 = 270.093
 
[[Gencom|Gencom]]: [2 7/6; 176/175 540/539]
 
Gencom mapping: [&lt;1 -4/3 3 -1/3 5/3|, &lt;0 4/3 -3 7/3 -11/3|]
 
Mapping: [&lt;1 0 2 -2|, &lt;0 3 -1 5|]


EDOs: 9, 31, 40, 49, 89, 191bc, 227bc, 231bc, 271bc, 311bc, 316bcd
Scales:  
 
* [[Guanyintet5]] – 5-tone haplotonic scale
[[Tp_tuning#T2 tuning|RMS error]]: 0.6028 cents
* [[Guanyintet9]] – 9-tone albitonic scale
 
* [[Guanyintet13]] – 13-tone chromatic scale
[[guanyintet5|Five note haplotonic scale]]
 
[[guanyintet9|Nine note albitonic scale]]
 
[[guanyintet13|Thirteen note chromatic scale]]


== Radon ==
== Radon ==
Subgroup: 2.3.7.11
{{See also| Gamelismic clan #Radon }}


Commas: 896/891, 1029/1024
[[File:radon_128edo.jpg|right|alt=radon_128edo.jpg|Radon in 128edo]]


Sval name: 5&amp;36
* [[Radon5]] – 5-tone haplotonic scale
 
* [[Radon11]] – 11-tone albitonic scale
Related temperament: [[Gamelismic_clan|Rodan]]
* [[Radon16]] – 16-tone chromatic scale
 
[[Tp_tuning|POT2 generator]]: ~8/7 = 234.381
 
[[Gencom|Gencom]]: [2 8/7; 896/891 1029/1024]
 
Gencom mapping: [&lt;1 1 0 3 6|, &lt;0 3 0 -1 -13|]
 
Mapping: [&lt;1 1 3 6|, &lt;0 3 -1 -13|]
 
{{EDOs|legend=1| 5, 36, 41, 87, 128}}
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.6502 cents
 
[[File:radon_128edo.jpg|alt=radon_128edo.jpg|radon_128edo.jpg]]
 
[[radon5|Five note haplotonic scale]]
 
[[radon11|Eleven note albitonic scale]]
 
[[radon16|Sixteen note chromatic scale]]


== Gariberttet ==
== Gariberttet ==
Subgroup: 2.5/3.7/3.13/11
{{See also | Subgroup temperaments #Gariberttet }}
 
Commas: 275/273, 847/845
 
Svalname: 4&amp;29
 
[[Tp_tuning|POT2 generator]]: ~13/11 = 293.679
 
[[Gencom|Gencom]]: [2 13/11; 275/273 847/845]
 
Gencom mapping: [&lt;1 0 0 0 0 0|, &lt;0 -8/3 1/3 7/3 -1/2 1/2|]


Mapping: [&lt;1 0 0 0|, &lt;0 3 5 1|]
Scales:  
 
* [[Gariberttet5]] – 5-tone haplotonic scale
EDOs: 29, 33, 37, 41, 45, 49, 78, 94, 143d, 237bd, 380bd
* [[Gariberttet9]] – 9-tone albitonic scale
 
* [[Gariberttet13]] – 13-tone chromatic scale
[[Tp_tuning#T2 tuning|RMS error]]: 0.6914 cents
 
[[gariberttet5|Five note haplotonic scale]]
 
[[gariberttet9|Nine note albitonic scale]]
 
[[gariberttet13|Thirteen note chromatic scale]]


== Namo ==
== Namo ==
Subgroup: 2.3.11.13
{{See also| Rastmic clan #Namo }}
 
Commas: 144/143, 243/242
 
Related temperament: [[Valinorismic_temperaments#Mandos|mandos]], mohajira, hemif
 
[[Tp_tuning|POT2 generator]]: ~11/9 = 351.488
 
[[Gencom|Gencom]]: [2 11/9; 144/143 243/242]
 
Gencom mapping: [&lt;1 1 0 0 2 4|, &lt;0 2 0 0 5 -1|]
 
Mapping: [&lt;1 1 2 4|, &lt;0 2 5 -1|]
 
EDOs: 7, 10, 17, 41, 58, 99cd
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.7038 cents
 
[[namo7|Seven note haplotonic scale]]
 
[[namo10|Ten note albitonic scale]]


[[namo17|Seventeen note chromatic scale]]
Scales:
* [[Namo7]] – 7-tone haplotonic scale
* [[Namo10]] – 10-tone albitonic scale
* [[Namo17]] – 17-tone chromatic scale


== Sentry ==
== Sentry ==
Subgroup: 2.5/3.9/7
{{See also | Subgroup temperaments #Sentry }}
 
Commas: 245/243
 
Svalname: 3&amp;5
 
Related temperaments: sensi
 
[[Tp_tuning|POT2 generator]]: ~9/7 = 440.902
 
[[Gencom|Gencom]]: [2 9/7; 245/243]
 
Gencom mapping: [&lt;1 0 0 0|, &lt;0 0 2 -1|]
 
Mapping: [&lt;1 0 0|, &lt;0 2 1|]
 
EDOs: 8, 11, 19, 30, 41, 49, 52, 145b, 166c, 197bc, 215c, 264bc
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.7105 cents


[[sentry5|Five note haplotonic scale]]
Scales:
 
* [[Sentry5]] – 5-tone haplotonic scale
[[sentry8|Eight note albitonic scale]]
* [[Sentry8]] – 8-tone albitonic scale
 
* [[Sentry11]] – 11-tone chromatic scale
[[sentry11|Eleven note note chromatic scale]]


== Hemif ==
== Hemif ==
Subgroup: 2.3.7.11.13
{{See also| No-fives subgroup temperaments #Hemif }}


Commas: 144/143, 243/242, 364/363
[[File:hemif_58edo.jpg|right|alt=hemif_58edo.jpg|Hemif in 58edo]]


Related temperament: [[Breedsmic_temperaments|Hemififths]], namo
Scales:  
 
* [[Hemif7]] – 7-tone haplotonic scale
[[Tp_tuning|POT2 generator]]: ~11/9 = 351.691
* [[Hemif10]] – 10-tone albitonic scale
 
* [[Hemif17]] – 17-tone chromatic scale
[[Gencom|Gencom]]: [2 11/9; 144/143 243/242 364/363]
 
Gencom mapping: [&lt;1 1 0 -1 2 4|, &lt;0 2 0 13 5 -1|]
 
Mapping: [&lt;1 1 -1 2 4|, &lt;0 2 13 5 -1|]
 
EDOs: 7, 10, 17, 24, 41, 58
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.7167 cents
 
[[File:hemif_58edo.jpg|alt=hemif_58edo.jpg|hemif_58edo.jpg]]
 
[[hemif7|Seven note haplotonic scale]]
 
[[hemif10|Ten note albitonic scale]]
 
[[hemif17|Seventeen note chromatic scale]]


== Garibaldi ==
== Garibaldi ==
Subgroup: 2.3.5.7
{{Main| Garibaldi temperament }}
 
{{See also| Schismatic family #Garibaldi }}
Commas: 225/224, 3125/3087
 
Val name: 12&amp;29
 
[[Tp_tuning|POT2 generator]]: ~3/2 = 702.085
 
[[Gencom|Gencom]]: [2 3/2; 225/224 3125/3087]
 
Gencom mapping: [&lt;1 1 7 11], &lt;0 1 -8 -14|]
 
Mapping: [&lt;1 0 15 25|, &lt;0 1 -8 -14|]
 
EDOs: 7, 12, 17, 29, 41, 53, 94, 241c
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.7257 cents
 
[[File:garibaldi_94edo.png|alt=garibaldi_94edo.png|garibaldi_94edo.png]]
 
[[garibaldi12|Twelve note albitonic scale]]
 
[[garibaldi17|Seventeen note chromatic scale]]
 
== Mabila ==
Subgroup: 2.5.7
 
Comma: 1071875/1048576
 
Sval name: 7&amp;9
 
[[Tp_tuning|POT2 generator]]: ~175/128 = 527.236
 
[[Gencom|Gencom]]: [2 175/128; 1071875/1048576]
 
Gencom mapping: [&lt;1 0 1 5}, &lt;0, 0, 3, -5|]
 
Mapping: [&lt;1 1 5|, &lt;0 3 -5|]


EDOs: 7, 9, 16, 25, 41, 66, 305bc
[[File:garibaldi_94edo.png|right|alt=garibaldi_94edo.png|Garibaldi in 94edo]]


[[Tp_tuning#T2 tuning|RMS error]]: 0.7729 cents
Scales:
* [[Garibaldi12]] – 12-tone albitonic scale
* [[Garibaldi17]] – 17-tone chromatic scale


[[File:mabila_66edo.jpg|alt=mabila_66edo.jpg|mabila_66edo.jpg]]
== Mabilic ==
{{See also| No-threes subgroup temperaments #Mabilic }}


[[mabila7|Seven note haplotonic scale]]
[[File:mabila_66edo.jpg|right|alt=mabila_66edo.jpg|Mabilic in 66edo]]


[[mabila9|Nine note albitonic scale]]
Scales:
 
* [[Mabilic7]] – 7-tone haplotonic scale
[[mabila16|Sixteen note chromatic scale]]
* [[Mabilic9]] – 9-tone albitonic scale
* [[Mabilic16]] – 16-tone chromatic scale


== Indium ==
== Indium ==
Subgroup: 2.5/3.7/3.11/3
{{See also | Subgroup temperaments #Indium }}
 
Commas: 3025/3024, 3125/3087
 
Sval name: 8&amp;33
 
[[Tp_tuning|POT2 generator]]: ~12/11 = 147.010
 
[[Gencom|Gencom]]: [2 12/11; 3025/3024 3125/3087]
 
Gencom mapping: [&lt;1 -1/2 -1/2 -1/2 3/2|, &lt;0 -15/4 9/4 25/4 -19/4|]
 
Mapping: [&lt;1 0 0 2|, &lt;0 6 10 -1|]
 
EDOs: 33, 41, 49, 57, 106, 204, 253
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.7788 cents


[[File:indium_253edo.png|alt=indium_253edo.png|indium_253edo.png]]
[[File:indium_253edo.png|right|alt=indium_253edo.png|Indium in 253edo]]


[[indium8|Eight note albitonic scale]]
Scales:
* [[Indium8]] – 8-tone albitonic scale
* [[Indium17]] – 17-tone chromatic scale


[[indium17|Seventeen note chromatic scale]]
; Music
 
* ''The Cry of Indium'' (2011) by [[Chris Vaisvil]] – [https://www.chrisvaisvil.com/the-cry-of-indium/ blog] | [https://web.archive.org/web/20201127012551/http://micro.soonlabel.com/chromatic_pairs/indium17/daily20111101-indium17.mp3 play] – in Indium[17]
=== Music ===
<span style=""><span style="">[http://micro.soonlabel.com/chromatic_pairs/indium17/daily20111101-indium17.mp3 The Cry of Indium]</span></span> (in Indium 17) by [http://www.chrisvaisvil.com/ Chris Vaisvil] =&gt; [http://chrisvaisvil.com/?p=1532 details]


== Starlingtet ==
== Starlingtet ==
Subgroup: 2.5/3.7/3
{{See also | Subgroup temperaments #Starlingtet }}
 
Comma: 126/125
 
Svalname: 4&amp;15
 
Related temperaments: starling; becomes myna
 
[[Tp_tuning|POT2 generator]]: ~6/5 = 311.154
 
[[Gencom|Gencom]]: [2 6/5; 126/125]
 
Gencom mapping: [&lt;1 -1 0 1|, &lt;0 4/3 1/3 -5/3|]
 
Mapping: [&lt;1 0 -1|, &lt;0 1 3|]
 
EDOs: 15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b


[[Tp_tuning#T2 tuning|RMS error]]: 0.8398 cents
Scales:
 
* [[Starlingtet4]] – 4-tone haplotonic scale
[[starlingtet4|Four note haplotonic scale]]
* [[Starlingtet7]] – 7-tone albitonic scale
 
* [[Starlingtet11]] – 11-tone chromatic scale
[[starlingtet7|Seven note albitonic scale]]
 
[[starlingtet11|Eleven note chromatic scale]]


== Lovecraft ==
== Lovecraft ==
Subgroup: 2.11.13
{{See also | No-threes subgroup temperaments #Lovecraft }}
 
Commas: 1352/1331
 
[[Tp_tuning|POT2 generator]]: ~13/11 = 279.318


[[Gencom|Gencom]]: [2 13/11; 1352/1331]
[[File:lovecraft_116edo.png|right|alt=lovecraft_116edo.png|Lovecraft in 116edo]]


Gencom mapping: [&lt;1 0 0 0 3 3|, &lt;0 0 0 0 2 3|]
Scales:  
 
* [[Lovecraft5]] – 5-tone haplotonic scale
Mapping: [&lt;1 1 0|, &lt;0 2 3|]
* [[Lovecraft9]] – 9-tone albitonic scale
 
* [[Lovecraft13]] – 13-tone chromatic scale
EDOS: 13, 30, 43, 73, 116b
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.8449 cents
 
[[File:lovecraft_116edo.png|alt=lovecraft_116edo.png|lovecraft_116edo.png]]
 
[[lovecraft5|Five note haplotonic scale]]
 
[[lovecraft9|Nine note albitonic scale]]
 
[[lovecraft13|Thirteen note chromatic scale]]


== Blackbirds ==
== Blackbirds ==
Subgroup: 2.11.13
{{See also | No-threes subgroup temperaments #Blackbirds }}
 
Comma: 29282/28561


[[Tp_tuning|POT2 generator]]: ~11/8 = 546.660
Scales:  
 
* [[Blackbirds8]] – 8-tone albitonic scale
Gencom: [13/11 11/8; 29282/28561]
* [[Blackbirds12]] – 12-tone chromatic scale
 
* [[Blackbirds16]] – 16-tone mega-chromatic scale
Gencom mapping: [&lt;4 0 0 0 12 13|, &lt;0 0 0 0 1 1|]
 
Mapping: [&lt;4 0 1|, &lt;0 1 1|]
 
EDOs: 4, 16, 20, 24, 44, 68, 112c, 180bc
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.8685 cents
 
[[blackbirds8|Eight note albitonic scale]]
 
[[blackbirds12|Twelve note chromatic scale]]
 
[[blackbirds16|Sixteen note mega chromatic scale]]


== Laz ==
== Laz ==
Subgroup: 2.5.7/3.11/3.13/3
{{See also | Subgroup temperaments #Laz }}
 
Commas: 144/143, 176/175, 196/195
 
Related temperaments: [[Orwellismic_family#Guanyin-Georgian|georgian]], winston
 
[[Tp_tuning|POT2 generator]]: ~7/6 = 269.300
 
[[Gencom|Gencom]]: [2 7/6; 144/143 176/175 196/195]


Gencom mapping: [&lt;1 -5/4 3 -1/4 7/4 -1/4|, &lt;0 -1/4 -3 3/4 -21/4 19/4|]
Scales:  
 
* [[Laz5]] – 5-tone haplotonic scale
Mapping: [&lt;1 0 2 -2 6|, &lt;0 3 -1 5 -5|]
* [[Laz9]] – 9-tone albitonic scale
 
* [[Laz13]] – 13-tone chromatic scale
EDOs: 9, 31, 40, 49, 58, 156bde, 205bde
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.8790 cents
 
[[laz5|Five note haplotonic scale]]
 
[[laz9|Nine note albitonic scale]]
 
[[laz13|Thirteen note chromatic scale]]


== Myna ==
== Myna ==
Subgroup: 2.3.5.7
{{Main| Myna }}
 
{{See also| Starling temperaments #Myna }}
Commas: 126/125, 1728/1715
 
Val name: 4&amp;27
 
[[Tp_tuning|POT2 generator]]: ~6/5 = 310.146
 
[[Gencom|Gencom]]: [2 6/5; 126/125 1728/1715]
 
Gencom mapping: [&lt;1 -1 0 1|,&lt;0 10 9 7|]
 
Mapping: [&lt;1 9 9 8|, &lt;0 -10 -9 -7|]
 
EDOs: 4, 27, 31, 58, 89, 236c, 325cd
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.9516 cents
 
[[File:myna_89edo.jpg|alt=myna_89edo.jpg|myna_89edo.jpg]]


[[myna7|Seven note haplotonic scale]]
[[File:myna_89edo.jpg|right|alt=myna_89edo.jpg|Myna in 89edo]]


[[myna11|Eleven note albitonic scale]]
Scales:
 
* [[Myna7]] – 7-tone haplotonic scale
[[myna15|Fifteen note chromatic scale]]
* [[Myna11]] – 11-tone albitonic scale
* [[Myna15]] – 15-tone chromatic scale


== Greeley ==
== Greeley ==
Subgroup: 2.5/3.7/3.11/3
{{See also| Subgroup temperaments #Greeley }}
 
Commas: 121/120, 126/125
 
Related temperament: [[Porcupine_family#Opossum|Opossum]], [[Starling_temperaments#Nusecond temperament|Nusecond]]
 
[[Tp_tuning|POT2 generator]]: ~11/10 = 155.776
 
[[Gencom|Gencom]]: [2 11/10; 121/120 126/125]
 
Gencom mapping: &lt;1 -5/4 -1/4 3/4 3/4|, &lt;0 9/4 1/4 -15/4 5/4|]
 
Mapping: [&lt;1 1 2 2|, &lt;0 -2 -6 -1|]
 
EDOs: 8, 15, 23, 54, 77, 100, 131d, 208bd
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.034 cents


[[File:greeley_100edo.png|alt=greeley_100edo.png|greeley_100edo.png]]
[[File:greeley_100edo.png|right|alt=greeley_100edo.png|Greeley in 100edo]]


[[greeley8|Eight note albitonic scale]]
Scales:
* [[Greeley8]] – 8-tone albitonic scale
* [[Greeley15]] – 15-tone chromatic scale


[[greeley15|Fifteen note chromatic scale]]
; Music
* ''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]


=== Music ===
== Ammon ==
<span style=""><span style="">[http://micro.soonlabel.com/tuning-survey/daily20111027-a-greely-steals-halloween.mp3 A Greeley Steals Halloween]</span></span> by [http://chrisvaisvil.com/?p=1485 Chris Vaisvil] in Greeley 15
{{See also| Subgroup temperaments #Ammon }}


== Semidim ==
[[File:semidim_770edo.png|right|alt=semidim_770edo.png|Ammon in 770edo]]
Subgroup: 2.5/3.7/3.11/3.13/3


Commas: 121/120, 169/168, 275/273
Scales:  
 
* [[Ammon8]] – 8-tone albitonic scale
Sval name: 8&amp;29
* [[Ammon13]] – 13-tone chromatic scale
 
[[Tp_tuning|POT2 generator]]: ~13/10 = 453.242
 
[[Gencom|Gencom]]: [2 13/10; 121/120 169/168 275/273]
 
Gencom mapping: [&lt;1 -3 0 2 0 1|, &lt;0 24/5 -6/5 -26/5 9/5 -1/5|]
 
Mapping: [&lt;1 3 5 3 4|, &lt;0 -6 -10 -3 -5|]
 
EDOs: 5, 8, 13, 21, 29, 37, 44, 45, 188bde,
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.052 cents
 
[[File:semidim_770edo.png|alt=semidim_770edo.png|semidim_770edo.png]]
 
[[semidim8|Eight note albitonic scale]]
 
[[semidim13|Thirteen note chromatic scale]]


== Mothwelltri ==
== Mothwelltri ==
Subgroup: 2.7/3.11
{{See also| Subgroup temperaments #Mothwelltri }}
 
Comma: 99/98
 
Svalname: 1&amp;4
 
Related temperament: Orwell
 
[[Tp_tuning|POT2 generator]]: ~7/6 = 273.174
 
[[Gencom|Gencom]]: [2 7/6; 99/98]
 
Gencom mapping: [&lt;1 -1/2 0 1/2 3|, &lt;0 -1/2 0 1/2 2|]
 
Mapping: [&lt;1 0 1|, &lt;0 1 2|]
 
EDOs: 9, 22, 40, 49c, 58c, 67c, 76c, 79, 101b, 123bc
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.064 cents
 
[[mothwelltri5|Five note haplotonic scale]]
 
[[mothwelltri9|Nine note albitonic scale]]


[[mothwelltri13|Thirteen note chromatic scale]]
Scales:
* [[Mothwelltri5]] – 5-tone haplotonic scale
* [[Mothwelltri9]] – 9-tone albitonic scale
* [[Mothwelltri13]] – 13-tone chromatic scale


== Sulis ==
== Sulis ==
Subgroup: 2.5.9/7.11/9
{{See also| Subgroup temperaments #Sulis }}
 
Commas: 99/98, 176/175
 
Related temperament: [[Marvel_family#Minerva|minerva]], würschmidt
 
[[Tp_tuning|POT2 generator]]: ~5/4 = 386.558
 
[[Gencom|Gencom]]: [2 5/4; 99/98 176/175]
 
Gencom mapping: [&lt;1 4/9 2 -1/9 -1/9|, &lt;0 -4/3 1 -2/3 4/3|]
 
Mapping: [&lt;1 0 5 -9|, &lt;0 1 -2 4|]
 
EDOs: 22, 25, 28, 31, 59, 90c, 149c
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.074 cents
 
[[sulis7|Seven note haplotonic scale]]


[[sulis10|Ten note albitonic scale]]
Scales:
 
* [[Sulis7]] – 7-tone haplotonic scale
[[sulis13|Thirteen note chromatic scale]]
* [[Sulis10]] – 10-tone albitonic scale
* [[Sulis13]] – 13-tone chromatic scale


== Skwares ==
== Skwares ==
Subgroup: 2.3.7.11
{{Main| Squares }}
 
{{See also| No-fives subgroup temperaments #Skwares }}
Commas: 99/98, 243/242
 
Related temperament: [[Meantone_family|squares]]
 
[[Tp_tuning|POT2 generator]]: ~9/7 = 425.244
 
[[Gencom|Gencom]]: [2 9/7; 99/98 243/242]
 
Gencom mapping: [&lt;1 3 0 6 7|, &lt;0 -4 0 -9 -10|]
 
Mapping: [&lt;1 3 6 7|, &lt;0 -4 -9 -10|]
 
EDOs: 5, 8, 11, 14, 17, 31, 48, 79, 127, 206bcd
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.099 cents
 
[[File:skwares_206edo.png|alt=skwares_206edo.png|skwares_206edo.png]]
 
[[skwares8|Eight note albitonic scale]]


[[skwares11|Eleven note mega albitonic scale]]
[[File:skwares_206edo.png|right|alt=skwares_206edo.png|Skwares in 206edo]]


[[skwares14|Fourteen note chromatic scale]]
Scales:
* [[Skwares8]] – 8-tone albitonic scale
* [[Skwares11]] – 11-tone mega-albitonic scale
* [[Skwares14]] – 14-tone chromatic scale


== Orwell ==
== Orwell ==
Subgroup: 2.3.5.7.11
{{Main| Orwell }}
 
{{See also| Semicomma family #Orwell }}
Commas: 99/98, 121/120, 176/175
 
Val name: 9&amp;22
 
[[Tp_tuning|POT2 generator]]: ~7/6 = 271.426
 
[[Gencom|Gencom]]: [2 7/6; 99/98 121/120 176/175]
 
Gencom mapping: [&lt;1 0 3 1 3|, &lt;0 7 -3 8 2|]
 
Mapping: [&lt;1 0 3 1 3|, &lt;0 7 -3 8 2|]
 
EDOs: 9, 22, 31, 53, 84e
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.151 cents
 
[[File:orwell_84edo.png|alt=orwell_84edo.png|orwell_84edo.png]]
 
[[orwell5|Five note haplotonic scale]]


[[orwell9|Nine note albitonic scale]]
[[File:orwell_84edo.png|right|alt=orwell_84edo.png|Orwell in 84edo]]


[[orwell13|Thirteen note chromatic scale]]
Scales:
* [[Orwell5]] – 5-tone haplotonic scale
* [[Orwell9]] – 9-tone albitonic scale
* [[Orwell13]] – 13-tone chromatic scale


== Magicaltet ==
== Magicaltet ==
Subgroup: 2.5/3.7.11
{{See also| Subgroup temperaments #Magicaltet }}
 
Commas: 100/99, 385/384
 
Related temperaments: 4&amp;7&amp;15, superkleismic, magic


[[Tp_tuning|POT2 generator]]: ~6/5 = 322.659
Scales:  
 
* [[Magicaltet7]] – 7-tone albitonic scale
[[Gencom|Gencom]]: [2 6/5; 100/99 385/384]
* [[Magicaltet11]] – 11-tone chromatic scale
 
* [[Magicaltet15]] – 15-tone mega-chromatic scale
Gencom mapping: [&lt;1 -1/2 1/2 2 4|, &lt;0 1/2 -1/2 3 -2|]
 
Mapping: [&lt;1 0 5 2|, &lt;0 1 -3 2|]
 
EDOs: 11, 15, 26, 67, 79cd, 93b, 94cd, 109cd, 119b, 124cd, 139cd, 212bd
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.206 cents
 
[[magicaltet7|Seven note albitonic scale]]
 
[[magicaltet11|Eleven note chromatic scale]]
 
[[magicaltet15|Fifteen note mega scale]]


== Magic ==
== Magic ==
Subgroup: 2.3.5.7.11
{{Main| Magic }}
{{See also| Magic family #Magic }}


Commas: 100/99, 225/224, 245/243
[[File:magic_145edo.jpg|right|alt=magic_145edo.jpg|Magic in 145edo]]


Val name: 19&amp;22
Scales:  
 
* [[Magic7]] – 7-tone haplotonic scale
[[Tp_tuning|POT2 generator]]: ~5/4 = 380.696
* [[Magic10]] – 10-tone albitonic scale
 
* [[Magic13]] – 13-tone chromatic scale
[[Gencom|Gencom]]: [2 5/4; 100/99 225/224 245/243]
* [[Magic16]] – 16-tone mega-chromatic scale
 
Gencom mapping: [&lt;1 0 2 -1 6|, &lt;0 5 1 12 -8|]
 
Mapping: [&lt;1 0 2 -1 6|, &lt;0 5 1 12 -8|]
 
EDOs: 19, 22, 41, 104, 145
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.226 cents
 
[[File:magic_145edo.jpg|alt=magic_145edo.jpg|magic_145edo.jpg]]
 
[[magic7|Seven note haplotonic scale]]
 
[[magic10|Ten note albitonic scale]]
 
[[magic13|Thirteen note chromatic scale]]
 
[[magic16|Sixteen note mega chromatic scale]]
 
=== Music ===
<span style="">[http://micro.soonlabel.com/magic/daily20120113-piano-magic16-.mp3 Chromatic piece in magic 16]</span> [http://www.chrisvaisvil.com/ Chris Vaisvil]


== Kiribati ==
== Kiribati ==
Subgroup: 2.9/5.7/3.11/9
{{See also| Subgroup temperaments #Kiribati }}


Commas: 100/99, 245/242
Scales:  
 
* [[Kiribati13]] – 13-tone chromatic scale
Related temperament: [[Octagar_family|nakika]], octacot
* [[Kiribati14]] – 14-tone chromatic scale
 
[[Tp_tuning|POT2 generator]]: ~21/20 = 87.892
 
[[Gencom|Gencom]]: [2 21/20; 100/99 245/242]
 
Gencom mapping: [&lt;1 1/10 -4/5 11/10 1/5|, &lt;0 -3/2 -1 3/2 1|]
 
Mapping: [&lt;1 1 1 0|, &lt;0 -2 3 4|]
 
EDOs: 13, 14, 27, 41, 55, 191bd, 232bcd, 273bcd
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.245 cents
 
[[kiribati13|Thirteen note chromatic scale]]
 
[[kiribati14|Fourteen note chromatic scale]]


== Score ==
== Score ==
Subgroup: 2.7.11.13
{{See also|No-threes subgroup temperaments #Score }}
 
Commas: 343/338, 847/832
 
[[Tp_tuning|POT2 generator]]: ~11/8 = 540.099
 
[[Gencom|Gencom]]: [2 11/8; 343/338 847/832]
 
Gencom mapping: [&lt;1 0 0 1 3 1|, &lt;0 0 0 4 1 6|]
 
Mapping: [&lt;1 1 3 1|, &lt;0 4 1 6|]
 
EDOs: 5, 7, 9, 11, 20
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.282 cents
 
[[File:score_20edo.jpg|alt=score_20edo.jpg|score_20edo.jpg]]
 
[[score5|Five note haplotonic scale]]
 
[[score7|Seven note albitonic scale]]
 
[[score9|Nine note mega albitonic scale]]
 
[[score11|Eleven note chromatic scale]]
 
== Sensation ==
Subgroup: 2.3.5.7.13
 
Commas: 91/90, 126/125, 169/168
 
Related temperaments: Sensi, Sensis, Sensus


[[Tp_tuning|POT2 generator]]: ~9/7 = 443.322
[[File:score_20edo.jpg|right|alt=score_20edo.jpg|Score in 20edo]]


[[Gencom|Gencom]]: [2 9/7; 91/90 126/125 169/168]
Scales:
 
* [[Score5]] – 5-tone haplotonic scale
Gencom mapping: [&lt;1 -1 -1 -2 0 0|, &lt;0 7 9 13 0 10|]
* [[Score7]] – 7-tone albitonic scale
 
* [[Score9]] – 9-tone mega-albitonic scale
Mapping: [&lt;1 6 8 11 10|, &lt;0 -7 -9 -13 -10|]
* [[Score11]] – 11-tone chromatic scale
 
EDOs: 19, 27, 46, 111de, 157de
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.321 cents
 
[[sensi5|Five note haplotonic scale]]
 
[[sensi8|Eight note albitonic scale]]
 
[[sensi11|Eleven note mega albitonic scale]]
 
[[sensi19|Nineteen note chromatic scale]]


== Sensi ==
== Sensi ==
Subgroup: 2.3.5.7
{{Main| Sensi }}
 
{{See also| Sensipent family #Sensi }}
Commas: 126/125, 245/243
 
Val name: 19&amp;27
 
[[Tp_tuning|POT2 generator]]: ~9/7 = 443.383
 
[[Gencom|Gencom]]: [2 9/7; 126/125 245/243]
 
Gencom mapping: [&lt;1 -1 -1 -2|, &lt;0 7 9 13|]
 
Mapping: [&lt;1 6 8 11|, &lt;0 -7 -9 -13|]
 
EDOs: 5, 8, 11, 19, 27, 46, 157d, 203cd, 249cd, 295cd
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.323 cents
 
[[File:sensi_46edo.jpg|alt=sensi_46edo.jpg|sensi_46edo.jpg]]


[[sensi5|Five note haplotonic scale]]
[[File:sensi_46edo.jpg|right|alt=sensi_46edo.jpg|Sensi in 46edo]]


[[sensi8|Eight note albitonic scale]]
Scales:
* [[Sensi5]] – 5-tone haplotonic scale
* [[Sensi8]] – 8-tone albitonic scale
* [[Sensi11]] – 11-tone mega-albitonic scale
* [[Sensi19]] – 19-tone chromatic scale


[[sensi11|Eleven note mega albitonic scale]]
=== Sensation ===
{{Main| Sensi }}
{{See also| Sensipent family #Sensi }}


[[sensi19|Nineteen note chromatic scale]]
Scales:
* [[Sensi5]] – 5-tone haplotonic scale
* [[Sensi8]] – 8-tone albitonic scale
* [[Sensi11]] – 11-tone mega-albitonic scale
* [[Sensi19]] – 19-tone chromatic scale


== Meantone ==
== Meantone ==
Subgroup: 2.3.5.7
{{Main| Meantone }}
 
{{See also| Meantone family #Meantone }}
Commas: 81/80, 126/125
 
Val name: 12&amp;19
 
[[Tp_tuning|POT2 generator]]: ~3/2 = 696.495
 
[[Gencom|Gencom]]: [2 3/2; 81/80 126/125]
 
Gencom mapping: [&lt;1 1 0 -3|, &lt;0 1 4 10|]
 
Mapping: [&lt;1 0 -4 -13|, &lt;0 1 4 10|]
 
EDOs: 5, 7, 12, 19, 31, 81, 112b, 143b
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.382 cents
 
[[File:meantone_31edo.jpg|alt=meantone_31edo.jpg|meantone_31edo.jpg]]
 
[[meantone5|Five note haplotonic scale]]


[[meantone7|Seven note albitonic scale]]
[[File:meantone_31edo.jpg|right|alt=meantone_31edo.jpg|Meantone in 31edo]]


[[meantone12|Twelve note chromatic scale]]
Scales:
* [[Meantone5]] – 5-tone haplotonic scale
* [[Meantone7]] – 7-tone albitonic scale
* [[Meantone12]] – 12-tone chromatic scale


== Mohaha ==
== Mohaha ==
Subgroup: 2.3.5.11
{{See also| Rastmic clan #Mohaha }}
 
Commas: 81/80, 121/120
 
Related temperament: [[Meantone_family|mohajira]]
 
[[Tp_tuning|POT2 generator]]: ~11/9 = 348.094
 
[[Gencom|Gencom]]: [2 11/9; 81/80 121/120]
 
Gencom mapping: [&lt;1 1 0 0 2|, &lt;[0 2 8 0 5|]
 
Mapping: [&lt;1 1 0 2|, &lt;0 2 8 5|]
 
EDOs: 24, 31, 55, 69d, 100d, 131bd
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.392 cents


[[File:mohaha_131edo.png|alt=mohaha_131edo.png|mohaha_131edo.png]]
[[File:mohaha_131edo.png|right|alt=mohaha_131edo.png|Mohaha in 131edo]]


[[mohaha7|Seven note albitonic scale]]
Scales:
* [[Mohaha7]] – 7-tone albitonic scale
* [[Mohaha10]] – 10-tone chromatic scale


[[mohaha10|Ten note chromatic scale]]
Music:
; [[Billy Stiltner]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/mohaha10ping2.mp3 ''Mohaha10ping2'']{{dead link}}


=== Music ===
=== Mohoho ===
[http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/mohaha10ping2.mp3 Mohaha10ping2] by [[Billy_Stiltner|Billy Stiltner]]
{{See also| Rastmic clan #Mohoho }}


== Joan ==
== Joan ==
Subgroup: 2.9.7.11
{{See also| Subgroup temperaments #Joan }}
 
Commas: 99/98, 9317/9216
 
Related temperaments: casablanca, orwell
 
[[Tp_tuning|POT2 generator]]: ~11/8 = 542.672 cents
 
Gencom: [2 11/8; 99/98 9317/9216]
 
Gencom mapping: [&lt;1 0 0 1 3|, &lt;0 7/2 0 4 1|]
 
Mapping: [&lt;1 0 1 3|, &lt;0 7 4 1|]
 
EDOs: 11, 20, 31, 42, 115bd, 157bd
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.424 cents
 
[[joan5|Five note haplotonic scale]]
 
[[joan7|Seven note albitonic scale]]


[[joan9|Nine note mega albitonic scale]]
Scales:
 
* [[Joan5]] – 5-tone haplotonic scale
[[joan11|Eleven note chromatic scale]]
* [[Joan7]] – 7-tone albitonic scale
* [[Joan9]] – 9-tone mega-albitonic scale
* [[Joan11]] – 11-tone chromatic scale


== Tutone ==
== Tutone ==
Subgroup: 2.9.5.7.11
{{See also| Hemimean clan #Tutone }}
 
Commas: 81/80, 99/98, 126/125
 
Related temperaments: [[Meantone_family|meantone]], [[Hemimean_family#Belobog|belobog]], hemithirds, hemiwürschmidt
 
[[Tp_tuning|POT2 generator]]: ~9/8 = 193.937
 
[[Gencom|Gencom]]: [2 9/8; 81/80 99/98 126/125]
 
Gencom mapping: [&lt;1 3/2 2 2 2|, &lt;0 1/2 2 5 9|]
 
Mapping: [&lt;1 0 -4 -13 -25|, &lt;0 1 2 5 9|]
 
EDOs: 25, 31, 68b, 99b


[[Tp_tuning#T2 tuning|RMS error]]: 1.439 cents
[[File:tutone_99edo.png|right|alt=tutone_99edo.png|Tutone in 99edo]]


[[tutone6|Six note haplotonic scale]]
Scales:
 
* [[Tutone6]] – 6-tone haplotonic scale
[[tutone7|Seven note albitonic scale]]
* [[Tutone7]] – 7-tone albitonic scale
 
* [[Tutone13]] – 13-tone chromatic scale
[[tutone13|Thirteen note chromatic scale]]
 
[[File:tutone_99edo.png|alt=tutone_99edo.png|tutone_99edo.png]]


== Stacks ==
== Stacks ==
Subgroup: 2.9.15.7.11.13
{{See also|Subgroup temperaments #Stacks (a.k.a. 2magic) }}


Commas: 100/99, 105/104, 144/143, 196/195
Scales:  
 
* [[Stacks5]] – 5-tone haplotonic scale
Related temperament: [[Magic_family#Magic-13-limit|magic]]
* [[Stacks8]] – 8-tone albitonic scale
 
* [[Stacks11]] – 11-tone chromatic scale
Svalname: 11&amp;30
* [[Stacks19]] – 19-tone mega-chromatic scale
 
[[Tp_tuning|POT2 generator]]: ~9/7 = 439.146
 
[[Gencom|Gencom]]: [2 9/7; 100/99 105/104 144/143 196/195]
 
Gencom mapping: [&lt;1 5/2 5/2 5 2 7|, &lt;0 -5/2 -1/2 -6 4 -9|]
 
Mapping: [&lt;1 0 2 -1 6 -2|, &lt;0 5 3 6 -4 9|]
 
EDOs: 11, 30, 41, 153cdef, 194cdef, 235cdef
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.540 cents
 
[[stacks5|Five note haplotonic scale]]
 
[[stacks8|Eight note albitonic scale]]
 
[[stacks11|Eleven note note chromatic scale]]
 
[[stacks19|Nineteen note note mega chromatic scale]]


== Bleu ==
== Bleu ==
Subgroup: 2.3.7.11.13
{{See also| No-fives subgroup temperaments #Bleu }}
 
Commas: 78/77, 99/98, 144/143
 
Sval name: 9&amp;17
 
[[Tp_tuning|POL2 generator]]: ~13/12 = 139.990
 
[[Gencom|Gencom]]: [2 13/12; 78/77 99/98 144/143]
 
Gencom mapping: [&lt;1 1 0 2 3 3|, &lt;0 5 0 7 4 6|]


Mapping: [&lt;1 1 2 3 3|, &lt;0 5 7 4 6|]
Scales:  
 
* [[Bleu8]] – 8-tone haplotonic scale
EDOs: [[17edo|17]], [[43edo|43]], [[60edo|60c]]
* [[Bleu9]] – 9-tone albitonic scale
 
* [[Bleu17]] – 17-tone chromatic scale
[[Tp_tuning#T2 tuning|RMS error]]: 1.752 cents
 
[[File:blue_60edo.png|alt=blue_60edo.png|blue_60edo.png]]
 
[[bleu8|bleu8]] - Eight note [[haplotonic_scale|haplotonic scale]]
 
[[bleu9|bleu9]] - Nine note [[albitonic_scale|albitonic scale]]
 
[[bleu17|bleu17]] - Seventeen note [[chromatic_scale|chromatic scale]]
 
[http://micro.soonlabel.com/temperaments/Bleu/20131103_2-11-13-subgroup-Bleu17_a-well-worn-riff.mp3 On a Well Worn Riff (Bleu 17)] by [http://chrisvaisvil.com/on-a-well-worn-riff-bleu-17/ Chris Vaisvil]


== Sephiroth ==
== Sephiroth ==
Subgroup: 2.5.11.13.17
{{See also| No-threes subgroup temperaments #Sephiroth }}
 
Commas: 65/64, 170/169, 221/220
 
Related temperament: [[Muggles]]
 
[[Tp_tuning|POT2 generator]]: ~5/4 = 372.236
 
[[Gencom|Gencom]]: [2 5/4; 65/64 170/169 221/220]
 
Gencom mapping: [&lt;1 0 2 0 5 4 5|, &lt;0 0 1 0 -5 -1 -3|]
 
Mapping: [&lt;1 0 15 6 11|, &lt;0 1 -5 -1 -3|]
 
EDOs: 10, 13, 16, 29
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.774 cents
 
[[sephiroth7|Seven note haplotonic scale]]
 
[[sephiroth10|Ten note albitonic scale]]
 
[[sephiroth13|Thirteen note chromatic scale]]


[[sephiroth16|Sixteen note mega chromatic scale]]
Scales:
* [[Sephiroth7]] – 7-tone haplotonic scale
* [[Sephiroth10]] – 10-tone albitonic scale
* [[Sephiroth13]] – 13-tone chromatic scale
* [[Sephiroth16]] – 16-tone mega-chromatic scale


== Archy ==
== Archy ==
Subgroup: 2.3.7
{{Main| Superpyth }}
 
{{See also| Archytas clan #Archy }}
Comma: 64/63
 
[[Tp_tuning|POT2 generator]]: ~3/2 = 709.321
 
Gencom: [2 3/2; 64/63]
 
Gencom mapping: [&lt;1 1 0 4|, &lt;0 1 0 -2|]
 
Mapping: [&lt;1 2 2|, &lt;0 -1 2|]


EDOs: 5, 12, 17, 22, 27, 137bc
Scales:  
* [[Archy5]] – 5-tone haplotonic scale
* [[Archy7]] – 7-tone albitonic scale
* [[Archy12]] – 12-tone chromatic scale


[[Tp_tuning#T2 tuning|RMS error]]: 1.856 cents
=== Supra ===
{{Main| Superpyth }}
{{See also| Archytas clan #Supra }}


[[archy5|Five note haplotonic scale]]
[[File:supra_56edo.png|right|alt=supra_56edo.png|Supra in 56edo]]


[[archy7|Seven note albitonic scale]]
Scales:
* [[Supra7]] – 7-tone [[albitonic scale]]
* [[Supra12]] – 12-tone [[chromatic scale]]


[[archy12|Twelve note chromatic scale]]
=== Supraphon ===
{{Main| Superpyth }}
{{See also| Archytas clan #Supraphon }}


== Suhajira ==
== Suhajira ==
Subgroup: 2.3.7.11
{{See also| Archytas clan #Suhajira }}
 
Commas: 64/63, 243/242


[[Tp_tuning|POL2 generator]]: ~11/9 = 353.958
Scales:  
 
* [[Suhajira7]] – 7-tone haplotonic scale
[[Gencom|Gencom]]: [2 11/9; 64/63 243/242]
* [[Suhajira10]] – 10-tone albitonic scale
 
* [[Suhajira17]] – 17-tone chromatic scale
Gencom mapping: [&lt;1 1 0 4 2|, &lt;0 2 0 -4 5|]
 
Mapping: [&lt;1 1 4 2|, &lt;0 2 -4 5|]
 
EDOs: 7, 10, 17, 61de
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.968 cents
 
[[suhajira7|suhajira7]] - Seven note [[haplotonic_scale|haplotonic scale]]
 
[[suhajira10|suhajira10]] - Ten note [[albitonic_scale|albitonic scale]]
 
[[suhajira17|suhajira17]] - note [[chromatic_scale|chromatic scale]]
 
== Mohoho ==
Subgroup: 2.3.5.11.13
 
Commas: 66/65, 81/80, 121/120
 
[[Tp_tuning|POT2 generator]]: ~11/9 = 348.916
 
[[Gencom|Gencom]]: [2 11/9; 66/65 81/80 121/120]
 
Gencom mapping: [&lt;1 1 0 0 2 4|, &lt;0 2 8 0 5 -1|]
 
Mapping: [&lt;1 1 0 2 4|, &lt;0 2 8 5 -1|]
 
EDOs: 17c, 24, 31, 55, 86de, 141cde
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.971 cents
 
== Supra ==
Subgroup: 2.3.7.11
 
Commas: 64/63, 99/98
 
Related temperament: [[Suprapyth|suprapyth]]
 
[[Tp_tuning|POT2 generator]]: ~3/2 = 707.192
 
[[Gencom|Gencom]]: [2 3/2; 64/63 99/98]
 
Gencom mapping: [&lt;1 1 0 4 7|, &lt;0 1 0 -2 -6|]
 
Mapping: [&lt;1 0 6 13|, &lt;0 1 -2 -6|]
 
EDOs: 5, 7, 12, 17, 22, 34c, 39c, 56c
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.977 cents
 
[[File:supra_56edo.png|alt=supra_56edo.png|supra_56edo.png]]
 
[[supra7|Seven note albitonic scale]]
 
[[supra12|Twelve note chromatic scale]]


== Machine ==
== Machine ==
Subgroup: 2.9.7.11
{{See also| Subgroup temperaments #Machine}}
 
Commas: 64/63, 99/98
 
[[Tp_tuning|POT2 generator]]: ~9/8 = 214.384
 
[[Gencom|Gencom]]: [2 9/8; 64/63 99/98]
 
Gencom mapping: [&lt;1 3/2 0 3 4|, &lt;0 1/2 0 -1 -3|]
 
Mapping: [&lt;1 0 6 13|, &lt;0 1 -1 -3|]
 
EDOs: 5, 6, 11, 17, 28
 
[[Tp_tuning#T2 tuning|RMS error]]: 1.977 cents
 
[[File:machine_28edo.png|alt=machine_28edo.png|machine_28edo.png]]


[[machine5|Five note haplotonic scale]]
[[File:machine_28edo.png|right|alt=machine_28edo.png|Machine in 28edo]]


[[machine6|Six note albitonic scale]]
Scales:
 
* [[Machine5]] – 5-tone haplotonic scale
[[machine11|Eleven note chromatic scale]]
* [[Machine6]] – 6-tone albitonic scale
* [[Machine11]] – 11-tone chromatic scale


== Deutone ==
== Deutone ==
Subgroup: 2.9.5.7.13
{{See also| Hemimean clan #Deutone }}
 
Commas: 65/64, 81/80, 91/90
 
Related temperament: [[Meantone_family|meanpop]]
 
[[Tp_tuning|POT2 generator]]: ~9/8 = 191.059
 
[[Gencom|Gencom]]: [2 9/8; 65/64 81/80 91/90]
 
Gencom mapping: [&lt;1 3/2 2 2 0 4|, &lt;0 1/2 2 5 0 -2|]
 
Mapping: [&lt;1 0 -4 -13 10|, &lt;0 1 2 5 -2|]
 
EDOs: 6, 7, 13, 19, 25e, 44de
 
[[Tp_tuning#T2 tuning|RMS error]]: 2.003 cents
 
[[File:deutone_44edo.png|alt=deutone_44edo.png|deutone_44edo.png]]
 
[[deutone6|Six note haplotonic scale]]
 
[[deutone7|seven note albitonic scale]]
 
[[deutone13|Thirteen note chromatic scale]]
 
== Supraphon ==
Subgroup: 2.3.7.11.13
 
Commas: 64/63, 78/77, 99/98
 
[[Tp_tuning|POT2 generator]]: ~3/2 = 706.137
 
[[Gencom|Gencom]]: [2 3/2; 64/63 78/77 99/98]


Gencom mapping: [&lt;1 1 0 4 7 9|, &lt;0 1 0 -2 -6 -9|]
[[File:deutone_44edo.png|right|alt=deutone_44edo.png|Deutone in 44edo]]


Mapping: [&lt;1 0 6 13 18|, &lt;0 1 -2 -6 -9|]
Scales:  
 
* [[Deutone6]] – 6-tone haplotonic scale
EDOs: 5, 7, 12, 17
* [[Deutone7]] – 7-tone albitonic scale
 
* [[Deutone13]] – 13-tone chromatic scale
[[Tp_tuning#T2 tuning|RMS error]]: 2.095 cents


== Negra ==
== Negra ==
Subgroup: 2.3.5.7.13
{{Main| Negri }}
 
{{See also| Marvel temperaments #Negri }}
Commas: 49/48, 65/64, 91/90
 
Related temperament: [[Marvel_temperaments#Negri-13-limit|negri]]
 
[[Tp_tuning|POT2 generator]]: ~14/13~13/12 = 125.567 cents
 
[[Gencom|Gencom]]: [2 14/13;
 
Gencom mapping: [&lt;1 2 2 3 0 4|, &lt;0 -4 3 -2 0 -3|]
 
Mapping: [&lt;1 2 2 3 4|, &lt;0 -4 3 -2 -3|]
 
EDOs: 9, 10, 19, 29, 67cd*f, 86cd*f
 
[[Tp_tuning#T2 tuning|RMS error]]: 2.147 cents


== Porkypine ==
== Porkypine ==
Subgroup: 2.3.5.11
{{Main| Porcupine }}
{{See also| Porcupine family #Porcupine }}


Commas: 55/54, 100/99
Scales:  
 
* [[Porkypine7]] – 7-tone haplotonic scale
[[Tp_tuning|POT2 generator]]: ~10/9 = 164.078
* [[Porkypine8]] – 8-tone albitonic scale
 
* [[Porkypine15]] – 15-tone chromatic scale
[[Gencom|Gencom]]: [2 10/9; 55/54 100/99]
 
Gencom mapping: [&lt;1 2 3 0 4|], &lt;0 -3 -5 0 -4|]
 
Mapping: [&lt;1 2 3 4|, &lt;0 3 5 4|]
 
EDOs: 7, 15, 22, 73cd, 95cd, 117bcd, 256bcdd
 
[[Tp_tuning#T2 tuning|RMS error]]: 2.287 cents
 
[[porkypine7|Seven note haplotonic scale]]
 
[[porkypine8|Eight note albitonic scale]]
 
[[porkypine15|Fifteen note chromatic scale]]


== Skateboard ==
== Skateboard ==
Subgroup: 2.5/3.7/3.11.13/9
{{See also| Subgroup temperaments #Skateboard }}
 
Commas: 56/55, 91/90, 100/99


Related temperament: [[Starling_family#Thrasher-13-limit|thrasher]]
Scales:  
 
* [[Skateboard7]] – 7-tone haplotonic scale
[[Tp_tuning|POT2 generator]]: ~6/5 = 313.842
* [[Skateboard11]] – 11-tone albitonic scale
 
* [[Skateboard15]] – 15-tone chromatic scale
[[Gencom|Gencom]]: [2 6/5; 56/55 91/90 100/99]
 
Gencom mapping: [&lt;1 -3/7 4/7 11/7 4 -6/7|, &lt;0 0 -1 -3 -2 2|]
 
Mapping: [&lt;1 0 -1 2 2|, &lt;0 1 3 2 -2|]
 
EDOs: 11, 15, 19, 23, 42d, 65d
 
[[Tp_tuning#T2 tuning|RMS error]]: 2.396 cents
 
[[skateboard7|Seven note haplotonic scale]]
 
[[skateboard11|Eleven note albitonic scale]]
 
[[skateboard15|Fifteen note chromatic scale]]


== Augment ==
== Augment ==
Subgroup: 2.5.7.11
{{See also| No-threes subgroup temperaments #Augment }}
 
Commas: 56/55, 128/125
 
Related temperament: [[Augmented_family|augmented]]
 
[[Tp_tuning|POT2 generator]]: ~8/7 = 228.275
 
[[Gencom|Gencom]]: [5/4 8/7; 56/55 128/125]
 
Gencom mapping: [&lt;3 0 7 9 11|, &lt;0 0 0 -1 -1|]
 
Mapping: [&lt;3 7 0 2|, &lt;0 0 1 1|]
 
EDOs: 3, 6, 9, 15, 21
 
[[Tp_tuning#T2 tuning|RMS error]]: 2.422 cents
 
[[File:augment_21edo.png|alt=augment_21edo.png|augment_21edo.png]]


[[augment6|Six note haplotonic scale]]
[[File:augment_21edo.png|right|alt=augment_21edo.png|Augment in 21edo]]


[[augment9|Nine note albitonic scale]]
Scales:
 
* [[Augment6]] – 6-tone haplotonic scale
[[augment12|Twelve note chromatic scale]]
* [[Augment9]] – 9-tone albitonic scale
* [[Augment12]] – 12-tone chromatic scale


== Semaphore ==
== Semaphore ==
Subgroup: 2.3.7
{{Main| Semaphore and godzilla }}
 
{{See also| Semaphoresmic clan #Semaphore }}
Comma: 49/48
 
[[Tp_tuning|POT2 generator]]: ~7/6 = 250.385
 
[[Gencom|Gencom]]: [2 7/6; 49/48]
 
Gencom mapping: [&lt;1 2 0 3}, &lt;0 -2 0 -1|]
 
Mapping: [&lt;1 0 2|, &lt;0 2 1|]


EDOs: 5, 9, 14, 19, 24, 67c, 91c
[[File:semaphore_24edo.png|right|alt=semaphore_24edo.png|Semaphore in 24edo]]


[[Tp_tuning#T2 tuning|RMS error]]: 2.523 cents
Scales:  
 
* [[Semaphore5]] – 5-tone haplotonic scale
[[File:semaphore_24edo.png|alt=semaphore_24edo.png|semaphore_24edo.png]]
* [[Semaphore9]] – 9-tone albitonic scale
 
* [[Semaphore14]] – 14-tone chromatic scale
[[semiphore5|Five note haplotonic scale]]
 
[[semiphore9|Nine note albitonic scale]]
 
[[semiphore14|Fourteen note chromatic scale]]


== Kryptonite ==
== Kryptonite ==
Subgroup: 2.5.7/3.11/3.13/3
{{See also| Subgroup temperaments #Kryptonite }}
 
Commas: 56/55, 78/77, 91/90
 
Related temperaments: [[Sengic_family|krypton]]
 
[[Tp_tuning|POT2 generator]]: ~13/12 = 132.428
 
[[Gencom|Gencom]]: [2 13/12; 56/55 78/77 91/90]
 
Gencom mapping: [&lt;1 -5/4 2 -1/4 3/4 3/4|, &lt;0 -1/2 3 3/2 -3/2 1/2|]
 
Mapping: [&lt;1 2 1 2 2|, &lt;0 -3 -2 1 -1|]
 
EDOs: 9, 63, 82bd, 91bde
 
[[Tp_tuning#T2 tuning|RMS error]]: 2.545 cents
 
[[kryptonite9|Nine note albitonic scale]]
 
[[kryptonite10|Ten note albitonic scale]]


[[kryptonite19|Nineteen note mega chromatic scale]]
Scales:
* [[Kryptonite9]] – 9-tone albitonic scale
* [[Kryptonite10]] – 10-tone albitonic scale
* [[Kryptonite19]] – 19-tone mega-chromatic scale


== Oregon ==
== Oregon ==
Subgroup: 2.9.15.7.11
{{See also| Orgonia #Oregon }}
 
Commas: 55/54, 64/63, 100/99
 
[[Tp_tuning|POT2 generator]]: ~6/5 = 325.495
 
[[Gencom|Gencom]]: [2 6/5; 55/54 64/63 100/99]
 
Gencom mapping: [&lt;1 2 3 2 4|, &lt;0 -3/2 -5/2 3 -2|]
 
Mapping: [&lt;1 1 1 5 2|, &lt;0 3 4 -3 2|]
 
EDOs: 7, 11, 37b, 48b, 59b
 
[[Tp_tuning#T2 tuning|RMS error]]: 2.550 cents
 
[[oregon7|Seven note haplotonic scale]]
 
[[oregon11|Eleven note albitonic scale]]


[[oregon15|Fifteen note chromatic scale]]
Scales:
* [[Oregon7]] – 7-tone haplotonic scale
* [[Oregon11]] – 11-tone albitonic scale
* [[Oregon15]] – 15-tone chromatic scale


== Antikythera ==
== Antikythera ==
Subgroup: 2.9.5.7
{{See also| Jubilismic clan #Antikythera }}
 
Commas: 50/49, 64/63
 
Related temperament: [[pajara|pajara]]
 
[[Tp_tuning|POT2 generator]]: ~8/7 = 214.095
 
[[Gencom|Gencom]]: [7/5 8/7; 50/49 64/63]
 
Gencom mapping: [&lt;2 3 5 6|, &lt;0 1/2 -1 -1|]
 
Mapping: [&lt;2 0 11 12|, &lt;0 1 -1 -1|]
 
EDOS: 4, 6, 10, 16, 22, 28
 
[[Tp_tuning#T2 tuning|RMS error]]: 2.572 cents
 
[[File:antikythera_28edo.png|alt=antikythera_28edo.png|antikythera_28edo.png]]
 
[[antikythera6|Six note haplotonic scale]]


[[antikythera10|Ten note albitonic scale]]
[[File:antikythera_28edo.png|right|alt=antikythera_28edo.png|Antikythera in 28edo]]


[[antikythera16|Sixteen note chromatic scale]]
Scales:
* [[Antikythera6]] – 6-tone haplotonic scale
* [[Antikythera10]] – 10-tone albitonic scale
* [[Antikythera16]] – 16-tone chromatic scale


== Glacial ==
== Glacial ==
Subgroup: 2.9.5.11.13
{{See also| Subgroup temperaments #Glacial }}
 
Commas: 45/44, 65/64, 81/80
 
[[Tp_tuning|POT2 generator]]: ~9/8 = 186.151
 
[[Gencom|Gencom]]: [2 9/8; 45/44 65/64 81/80]
 
Gencom mapping: [&lt;1 3/2 2 0 3 4|, &lt;0 1/2 2 0 3 -2|]
 
Mapping: [&lt;1 0 -4 -6 10|, &lt;0 1 2 3 -2|]
 
EDOs: 6, 13, 45be, 58bce, 71bce, 84bce
 
[[Tp_tuning#T2 tuning|RMS error]]: 2.887 cents
 
[[glacial6|Six note haplotonic scale]]
 
[[glacial7|Seven note albitonic scale]]


[[glacial13|Thirteen note chromatic scale]]
Scales:
* [[Glacial6]] – 6-tone haplotonic scale
* [[Glacial7]] – 7-tone albitonic scale
* [[Glacial13]] – 13-tone chromatic scale


== Leantone ==
== Leantone ==
Subgroup: 2.9.5.7.11
{{See also| Hemimean clan #Leantone }}
 
Commas: 45/44, 56/55, 81/80
 
Related temperament: [[Meanenneadecal|meanenneadecal]]
 
[[Tp_tuning|POT2 generator]]: ~9/8 = 192.500
 
[[Gencom|Gencom]]: [2 9/8; 45/44 56/55 81/80]
 
Gencom mapping: [&lt;1 3/2 2 2 3|, &lt;0 1/2 2 5 3|]
 
Mapping: [&lt;1 0 -4 -13 -6|, &lt;0 1 2 5 3|]


EDOs: 6, 7, 13, 19, 25, 31, 56, 81
[[File:leantone_81edo.png|right|alt=leantone_81edo.png|Leantone in 81edo]]


[[Tp_tuning#T2 tuning|RMS error]]: 3.882 cents
Scales:
* [[Leantone6]] – 6-tone haplotonic scale
* [[Leantone7]] – 7-tone albitonic scale
* [[Leantone13]] – 13-tone chromatic scale


[[File:leantone_81edo.png|alt=leantone_81edo.png|leantone_81edo.png]]
== Notes ==


* [[leantone6|Six note haplotonic scale]]
[[Category:Lists of scales]]
* [[leantone7|Seven note albitonic scale]]
[[Category:Tempered scales| ]]
* [[leantone13|Thirteen note chromatic scale]]
 
[[Category:Lists of temperaments]]
[[Category:Chromatic pairs| ]] <!-- main article -->
[[Category:Listen]]
[[Category:Listen]]
[[Category:Rank 2]]
[[Category:Rank 2]]
[[Category:Subgroup temperaments]]
 
{{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

See also: Subgroup temperaments § Terrain
terrain_3558edo.png
Terrain in 3558edo

Scales:

Music

Petrtri

See also: Subgroup temperaments § Petrtri
petrtri_385edo.png
Petrtri in 385edo

Scales:

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
tridec_235edo.png
Tridec in 235edo

Scales:

Nestoria

See also: Schismatic family § Nestoria (2.3.5.19)
nestoria_171edo.png
Nestoria in 171edo

Scales:

Orgone

Main article: Orgone
See also: Orgonia § Orgone
orgone_308edo.jpg
Orgone in 308edo

Scales:

Marveltwintri

See also: Subgroup temperaments § Marveltwintri
marveltwintri_321edo.png
Marveltwintri in 321edo

Scales:

Cata

Main article: Kleismic
See also: Kleismic family § 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

See also: Subgroup temperaments § Bridgetown
bridgetown_29edo.png
Bridgetown in 29edo

Scales:

Music

Haumea

See also: Subgroup temperaments § Haumea

Scales:

Neutral

See also: Rastmic clan § Neutral
neutral_380edo.png
Neutral in 380edo

Scales:

Music

Slendric

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

Scales:

Huntington

See also: No-threes subgroup temperaments § Huntington
huntington_400edo.jpg
Huntington in 400edo

Scales:

Tobago

See also: Subgroup temperaments § Tobago

Scales:

Pepperoni

See also: Parapyth
See also: Subgroup temperaments § Pepperoni
pepperoni_271edo.png
Pepperoni in 271edo

Scales:

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
bossier_225edo.jpg
Bossier in 225edo

Scales:

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:

Marveltri

See also: Subgroup temperaments § Marveltri

Scales:

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)
photia_65edo.png
Photia in 65edo

Scales:

Shoe a.k.a. llywelyn

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

See also: Hemimean clan § Roulette
roulette_37edo.jpg
Roulette in 37edo

Scales:

Silver

See also: No-threes subgroup temperaments § Silver
silver_487edo.jpg
Silver in 487edo

Scales:

Baldy

See also: Subgroup temperaments § Baldy
baldy_147edo.jpg
Baldy in 147edo

Scales

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


Guanyintet

See also: Subgroup temperaments § Guanyintet

Scales:

Radon

See also: Gamelismic clan § Radon
radon_128edo.jpg
Radon in 128edo
  • Radon5 – 5-tone haplotonic scale
  • Radon11 – 11-tone albitonic scale
  • Radon16 – 16-tone chromatic scale

Gariberttet

See also: Subgroup temperaments § Gariberttet

Scales:

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:

Hemif

See also: No-fives subgroup temperaments § Hemif
hemif_58edo.jpg
Hemif in 58edo

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
garibaldi_94edo.png
Garibaldi in 94edo

Scales:

Mabilic

See also: No-threes subgroup temperaments § Mabilic
mabila_66edo.jpg
Mabilic in 66edo

Scales:

Indium

See also: Subgroup temperaments § Indium
indium_253edo.png
Indium in 253edo

Scales:

Music

Starlingtet

See also: Subgroup temperaments § Starlingtet

Scales:

Lovecraft

See also: No-threes subgroup temperaments § Lovecraft
lovecraft_116edo.png
Lovecraft in 116edo

Scales:

Blackbirds

See also: No-threes subgroup temperaments § Blackbirds

Scales:

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
myna_89edo.jpg
Myna in 89edo

Scales:

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

Greeley

See also: Subgroup temperaments § Greeley
greeley_100edo.png
Greeley in 100edo

Scales:

Music

Ammon

See also: Subgroup temperaments § Ammon
semidim_770edo.png
Ammon in 770edo

Scales:

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

Mothwelltri

See also: Subgroup temperaments § Mothwelltri

Scales:

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
skwares_206edo.png
Skwares in 206edo

Scales:

Orwell

Main article: Orwell
See also: Semicomma family § Orwell
orwell_84edo.png
Orwell in 84edo

Scales:

Magicaltet

See also: Subgroup temperaments § Magicaltet

Scales:

Magic

Main article: Magic
See also: Magic family § 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

See also: Subgroup temperaments § Kiribati

Scales:

Score

See also: No-threes subgroup temperaments § 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

Main article: Sensi
See also: Sensipent family § 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

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
meantone_31edo.jpg
Meantone in 31edo

Scales:

Mohaha

See also: Rastmic clan § Mohaha
mohaha_131edo.png
Mohaha in 131edo

Scales:

Music:

Billy Stiltner

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
tutone_99edo.png
Tutone in 99edo

Scales:

Stacks

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

Scales:

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:

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
supra_56edo.png
Supra in 56edo

Scales:

Supraphon

Main article: Superpyth
See also: Archytas clan § Supraphon

Suhajira

See also: Archytas clan § Suhajira

Scales:

Machine

See also: Subgroup temperaments § Machine
machine_28edo.png
Machine in 28edo

Scales:

Deutone

See also: Hemimean clan § Deutone
deutone_44edo.png
Deutone in 44edo

Scales:

Negra

Main article: Negri
See also: Marvel temperaments § Negri

Porkypine

Main article: Porcupine
See also: Porcupine family § Porcupine

Scales:

Skateboard

See also: Subgroup temperaments § Skateboard

Scales:

Augment

See also: No-threes subgroup temperaments § Augment
augment_21edo.png
Augment in 21edo

Scales:

Semaphore

Main article: Semaphore and godzilla
See also: Semaphoresmic clan § Semaphore
semaphore_24edo.png
Semaphore in 24edo

Scales:

Kryptonite

See also: Subgroup temperaments § Kryptonite

Scales:

Oregon

See also: Orgonia § Oregon

Scales:

Antikythera

See also: Jubilismic clan § Antikythera
antikythera_28edo.png
Antikythera in 28edo

Scales:

Glacial

See also: Subgroup temperaments § Glacial

Scales:

Leantone

See also: Hemimean clan § Leantone
leantone_81edo.png
Leantone in 81edo

Scales:

Notes

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