List of regular temperaments: Difference between revisions

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|+ Rank-2 Temperaments
|+ Rank-2 Temperaments
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! Family !! Name !! Subgroup !! Commas !! Ploidacot !! Usual Scale Type !! Badness (Cangwu) !! Generator size (CWE)
! Family !! Name !! Subgroup !! Ploidacot
!ETs      !! Usual Scale Type  
!Description!! Commas !! Badness (Cangwu) !! Generator size (CWE)
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|rowspan="2"| Syntonic || Meantone || 2.3.5 || 81/80 || monocot || softer diatonic, m-chromatic || .778 || 497c
| rowspan="3" | Syntonic || Meantone || 2.3.5 || monocot
|7, 12|| softer diatonic, m-chromatic  
|Common historical temperament for 5-limit diatonic harmony.|| 81/80 || .778 || 497c
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| Septimal Meantone || 2.3.5.7 || 81/80, 225/224 || monocot || softer diatonic, m-chromatic || .834 || 497c
| Septimal Meantone || 2.3.5.7 || monocot
|19, 31|| softer diatonic, m-chromatic  
|Natural extension of the above to 2...7.||  81/80, 225/224 || .834 || 497c
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|rowspan="2"| Archy || Archy || 2.3.7 || 64/63 || monocot || harder diatonic, p-chromatic || .803 || 491c
|Flattone
|2.3.5.7
|monocot
|19, 26
|softer diatonic, m-chromatic
|Less accurate extension, more melodic intuition, easily extends to higher limits. 7-form version of meantone.
|525/512, 81/80
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| Superpyth || 2.3.5.7 || 64/63, 245/243 || monocot || harder diatonic, p-chromatic || 1.298 || 490c
| rowspan="2" | Archy || Archy || 2.3.7 || monocot
|5, 22|| soft pentic, harder diatonic, p-chromatic  
|2.3.7 counterpart of meantone, which sharpens the fifth.|| 64/63 || .803 || 491c
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|rowspan="4"| Mabilic || Mabilic || 2.5.7 || 1071875/1048576 || alpha-triseph || antidiatonic, armotonic, 9L 7s
| Superpyth || 2.3.5.7 || monocot
|22, 27|| soft pentic, harder diatonic, p-chromatic
|Extension of the above to 2...7, favoring flatter tunings.|| 64/63, 245/243 || 1.298 || 490c
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| Trismegistus || 2.3.5.7 || 1029/1024, 3125/3072 || alpha-triseph || antidiatonic, armotonic, 9L 7s  
| rowspan="4" | Mabilic || Mabilic || 2.5.7 || alpha-triseph  
|7, 9|| antidiatonic, armotonic, 9L 7s  
|Basic antidiatonic temperament with no 3.|| mabilisma
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| Semabila || 2.3.5.7 || 49/48, 28672/28125 || alpha-triseph || antidiatonic, armotonic, 9L 7s  
| Trismegistus || 2.3.5.7 || alpha-triseph  
|16, 25|| antidiatonic, armotonic, 9L 7s  
|High-accuracy but high complexity extension of prime 3.|| gamelisma, magisma
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| Mavila || 2.3.5.7 || 36/35, 135/128 || monocot || antidiatonic, armotonic, 7L 9s
| Semabila || 2.3.5.7 || alpha-triseph
|9, 25|| antidiatonic, armotonic, 9L 7s
|Combination of mabilic and semaphore.|| 49/48, 28672/28125
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|rowspan="2"| Porcupine || Porcupine || 2.3.5.11 || 250/243, 100/99 || omega-tricot || onyx, pine
| Mavila || 2.3.5.7 || monocot
|7, 9|| antidiatonic, armotonic, 7L 9s
|Exotemperament serving as an antidiatonic analog of meantone.|| 36/35, 135/128
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| Septimal Porcupine || 2.3.5.7.11 || 250/243, 100/99, 64/63 || omega-tricot || onyx, pine
| rowspan="2" | Porcupine || Porcupine || 2.3.5.11 || omega-tricot
|15, 22|| onyx, pine
|Moderate-accuracy 2.3.5.11 temperament with a ~160c generator and a heptatonic MOS.|| 250/243, 100/99  
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|rowspan="4"| Gamelic || Slendric, Wonder || 2.3.7 || 1029/1024 || tricot || 1L 4s, machinoid, 5L 6s
| Septimal Porcupine || 2.3.5.7.11 || omega-tricot
|15, 22|| onyx, pine
|Extension of the above to the full 11-limit.|| 250/243, 100/99, 64/63
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| Mothra || 2.3.5.7 || 81/80, 1029/1024 || tricot || 1L 4s, machinoid, 5L 6s
| rowspan="4" | Gamelic || Slendric, Wonder || 2.3.7 || tricot
|5, 31|| 1L 4s, machinoid, 5L 6s
|Splits the fifth in 3 parts, each of which is 8/7. Little relation to actual [[Slendro tuning]]. Contains a pentatonic similar to porcupine's heptatonic.|| gamelisma
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| Rodan || 2.3.5.7 || 245/243, 1029/1024 || tricot || 1L 4s, machinoid, 5L 6s
| Mothra || 2.3.5.7 || tricot
|26, 31|| 1L 4s, machinoid, 5L 6s
|Meantone extension of the above.|| 81/80, gamelisma
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| Valentine || 2.3.5.7 || 126/125, 1029/1024 || enneacot || 15L 1s, [[Carlos Alpha]]
| Rodan || 2.3.5.7 || tricot
|41, 46|| 1L 4s, machinoid, 5L 6s
|More accurate extension of the above.|| 245/243, gamelisma
|-
| Valentine || 2.3.5.7 || enneacot  
|15, 16|| 15L 1s, [[Carlos Alpha]]
|Scale with small steps strongly associated with Carlos Alpha.|| 126/125, gamelisma
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| rowspan="3" |Diaschismic
|Diaschismic
|2.3.5.7.17
|diploid monocot
|12, 34
|2L 8s, 10L 2s
|Temperament characterized by a perfect semioctave and a sharpened fifth or semitone generator. Two generators down reaches 5/4.
|diaschisma, 126/125
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|Srutal
|2.3.5.7.17
|diploid monocot
|46, 80
|2L 8s, 10L 2s
|Very complex but accurate 7-limit diaschismic.
|diaschisma, ragisma
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|Pajara
|2.3.5.7.17
|diploid monocot
|12, 22
|2L 8s, 10L 2s
|Jubilic archytas diaschismic temperament. Contains jubilic chord structure and is strongly associated with 22edo.
|diaschisma, 50/49
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Revision as of 21:25, 11 December 2025

Main article: Regular temperament

Rank-2 Temperaments
Family Name Subgroup Ploidacot ETs Usual Scale Type Description Commas Badness (Cangwu) Generator size (CWE)
Syntonic Meantone 2.3.5 monocot 7, 12 softer diatonic, m-chromatic Common historical temperament for 5-limit diatonic harmony. 81/80 .778 497c
Septimal Meantone 2.3.5.7 monocot 19, 31 softer diatonic, m-chromatic Natural extension of the above to 2...7. 81/80, 225/224 .834 497c
Flattone 2.3.5.7 monocot 19, 26 softer diatonic, m-chromatic Less accurate extension, more melodic intuition, easily extends to higher limits. 7-form version of meantone. 525/512, 81/80
Archy Archy 2.3.7 monocot 5, 22 soft pentic, harder diatonic, p-chromatic 2.3.7 counterpart of meantone, which sharpens the fifth. 64/63 .803 491c
Superpyth 2.3.5.7 monocot 22, 27 soft pentic, harder diatonic, p-chromatic Extension of the above to 2...7, favoring flatter tunings. 64/63, 245/243 1.298 490c
Mabilic Mabilic 2.5.7 alpha-triseph 7, 9 antidiatonic, armotonic, 9L 7s Basic antidiatonic temperament with no 3. mabilisma
Trismegistus 2.3.5.7 alpha-triseph 16, 25 antidiatonic, armotonic, 9L 7s High-accuracy but high complexity extension of prime 3. gamelisma, magisma
Semabila 2.3.5.7 alpha-triseph 9, 25 antidiatonic, armotonic, 9L 7s Combination of mabilic and semaphore. 49/48, 28672/28125
Mavila 2.3.5.7 monocot 7, 9 antidiatonic, armotonic, 7L 9s Exotemperament serving as an antidiatonic analog of meantone. 36/35, 135/128
Porcupine Porcupine 2.3.5.11 omega-tricot 15, 22 onyx, pine Moderate-accuracy 2.3.5.11 temperament with a ~160c generator and a heptatonic MOS. 250/243, 100/99
Septimal Porcupine 2.3.5.7.11 omega-tricot 15, 22 onyx, pine Extension of the above to the full 11-limit. 250/243, 100/99, 64/63
Gamelic Slendric, Wonder 2.3.7 tricot 5, 31 1L 4s, machinoid, 5L 6s Splits the fifth in 3 parts, each of which is 8/7. Little relation to actual Slendro tuning. Contains a pentatonic similar to porcupine's heptatonic. gamelisma
Mothra 2.3.5.7 tricot 26, 31 1L 4s, machinoid, 5L 6s Meantone extension of the above. 81/80, gamelisma
Rodan 2.3.5.7 tricot 41, 46 1L 4s, machinoid, 5L 6s More accurate extension of the above. 245/243, gamelisma
Valentine 2.3.5.7 enneacot 15, 16 15L 1s, Carlos Alpha Scale with small steps strongly associated with Carlos Alpha. 126/125, gamelisma
Diaschismic Diaschismic 2.3.5.7.17 diploid monocot 12, 34 2L 8s, 10L 2s Temperament characterized by a perfect semioctave and a sharpened fifth or semitone generator. Two generators down reaches 5/4. diaschisma, 126/125
Srutal 2.3.5.7.17 diploid monocot 46, 80 2L 8s, 10L 2s Very complex but accurate 7-limit diaschismic. diaschisma, ragisma
Pajara 2.3.5.7.17 diploid monocot 12, 22 2L 8s, 10L 2s Jubilic archytas diaschismic temperament. Contains jubilic chord structure and is strongly associated with 22edo. diaschisma, 50/49
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