List of regular temperaments: Difference between revisions

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m Delete badness column (badness measures are just opaque heuristics)
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! Family !! Name !! Subgroup !! Ploidacot  
! Family !! Name !! Subgroup !! Ploidacot  
!ETs      !! Usual Scale Type  
!ETs      !! Usual Scale Type  
!Description!! Commas !! Badness (Cangwu) !! Generator size (CWE)
!Description!! Commas !! Generator size (CWE)
|-
|-
| rowspan="3" | Syntonic || Meantone || 2.3.5 || monocot  
| rowspan="3" | Syntonic || Meantone || 2.3.5 || monocot  
|7, 12|| softer diatonic, m-chromatic  
|7, 12|| softer diatonic, m-chromatic  
|Common historical temperament for 5-limit diatonic harmony.|| 81/80 || .778 || 503c
|Common historical temperament for 5-limit diatonic harmony.|| 81/80 || 503c
|-
|-
| Septimal Meantone || 2.3.5.7 || monocot  
| Septimal Meantone || 2.3.5.7 || monocot  
|19, 31|| softer diatonic, m-chromatic  
|19, 31|| softer diatonic, m-chromatic  
|Natural extension of the above to 2...7.||  81/80, 225/224 || .834 || 503c
|Natural extension of the above to 2...7.||  81/80, 225/224 || 503c
|-
|-
|Flattone
|Flattone
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|Less accurate extension, more melodic intuition, easily extends to higher limits. 7-form version of meantone.
|Less accurate extension, more melodic intuition, easily extends to higher limits. 7-form version of meantone.
|525/512, 81/80
|525/512, 81/80
|
|
|
|-
|-
| rowspan="2" | Archy || Archy || 2.3.7 || monocot  
| rowspan="2" | Archy || Archy || 2.3.7 || monocot  
|5, 22|| soft pentic, harder diatonic, p-chromatic  
|5, 22|| soft pentic, harder diatonic, p-chromatic  
|2.3.7 counterpart of meantone, which sharpens the fifth.|| 64/63 || .803 || 491c
|2.3.7 counterpart of meantone, which sharpens the fifth.|| 64/63 || 491c
|-
|-
| Superpyth || 2.3.5.7 || monocot  
| Superpyth || 2.3.5.7 || monocot  
|22, 27|| soft pentic, harder diatonic, p-chromatic  
|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  
|Extension of the above to 2...7, favoring flatter tunings.|| 64/63, 245/243 || 490c  
|-
|-
| rowspan="4" | Mabilic || Mabilic || 2.5.7 || alpha-triseph  
| rowspan="4" | Mabilic || Mabilic || 2.5.7 || alpha-triseph  
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|9, 25|| antidiatonic, armotonic, 9L 7s  
|9, 25|| antidiatonic, armotonic, 9L 7s  
|Combination of mabilic and semaphore.|| 49/48, 28672/28125  
|Combination of mabilic and semaphore.|| 49/48, 28672/28125  
|
|-
|-
| Mavila || 2.3.5.7 || monocot  
| Mavila || 2.3.5.7 || monocot  

Revision as of 20:18, 19 December 2025

Main article: Regular temperament
Rank-2 Temperaments
Family Name Subgroup Ploidacot ETs Usual Scale Type Description Commas 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 503c
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 503c
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 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 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