List of regular temperaments: Difference between revisions

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| 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 || 503c
|Common historical temperament for 5-limit diatonic harmony.|| 81/80 || 692-697c
|-
|-
| 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 || 503c
|Natural extension of the above to 2...7.||  81/80, 225/224 || 695-697c
|-
|-
|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
|
|692-694c
|-
|-
| 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 || 491c
|2.3.7 counterpart of meantone, which sharpens the fifth.|| 64/63 || 709-720c
|-
|-
| 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 || 490c
|Extension of the above to 2...7, favoring flatter tunings.|| 64/63, 245/243 || 709-711c
|-
|-
| rowspan="4" | Mabilic || Mabilic || 2.5.7 || alpha-triseph  
| rowspan="4" | Mabilic || Mabilic || 2.5.7 || alpha-triseph  
|7, 9|| antidiatonic, armotonic, 9L 7s  
|7, 9|| antidiatonic, armotonic, 9L 7s  
|Basic antidiatonic temperament with no 3.|| mabilisma  
|Basic antidiatonic temperament with no 3.|| mabilisma  
|668-680c
|-
|-
| Trismegistus || 2.3.5.7 || alpha-triseph  
| Trismegistus || 2.3.5.7 || alpha-triseph  
|16, 25|| antidiatonic, armotonic, 9L 7s  
|16, 25|| antidiatonic, armotonic, 9L 7s  
|High-accuracy but high complexity extension of prime 3.|| gamelisma, magisma  
|High-accuracy but high complexity extension of prime 3.|| gamelisma, magisma  
|672-675c
|-
|-
| Semabila || 2.3.5.7 || alpha-triseph  
| Semabila || 2.3.5.7 || alpha-triseph  
|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  
|668-672c
|-
|-
| Mavila || 2.3.5.7 || monocot  
| Mavila || 2.3.5.7 || monocot  
|7, 9|| antidiatonic, armotonic, 7L 9s  
|7, 9|| antidiatonic, armotonic, 7L 9s  
|Exotemperament serving as an antidiatonic analog of meantone.|| 36/35, 135/128  
|Exotemperament serving as an antidiatonic analog of meantone.|| 36/35, 135/128  
|675-680c
|-
|-
| rowspan="2" | Porcupine || Porcupine || 2.3.5.11 || omega-tricot  
| rowspan="2" | Porcupine || Porcupine || 2.3.5.11 || omega-tricot  
|15, 22|| onyx, pine
|15, 22|| onyx, pine
|Moderate-accuracy 2.3.5.11 temperament with a ~160c generator and a heptatonic MOS.|| 250/243, 100/99  
|Moderate-accuracy 2.3.5.11 temperament with a ~160c generator and a heptatonic MOS.|| 250/243, 100/99  
|161-166c
|-
|-
| Septimal Porcupine || 2.3.5.7.11 || omega-tricot  
| Septimal Porcupine || 2.3.5.7.11 || omega-tricot  
|15, 22|| onyx, pine
|15, 22|| onyx, pine
|Extension of the above to the full 11-limit.|| 250/243, 100/99, 64/63  
|Extension of the above to the full 11-limit.|| 250/243, 100/99, 64/63  
|161-163c
|-
|-
| rowspan="4" | Gamelic || Slendric, Wonder || 2.3.7 || tricot  
| rowspan="5" | Gamelic || Slendric, Wonder || 2.3.7 || tricot  
|5, 31|| 1L 4s, machinoid, 5L 6s
|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  
|Splits the fifth in 3 parts, each of which is 8/7. Little relation to actual [[Equipentatonic#Slendro|Slendro tuning]]. Contains a pentatonic similar to porcupine's heptatonic.|| gamelisma  
|231-234c
|-
|-
| Mothra || 2.3.5.7 || tricot  
| Mothra || 2.3.5.7 || tricot  
|26, 31|| 1L 4s, machinoid, 5L 6s
|26, 31|| 1L 4s, machinoid, 5L 6s
|Meantone extension of the above.|| 81/80, gamelisma  
|Meantone extension of the above.|| 81/80, gamelisma  
|231c
|-
|-
| Rodan || 2.3.5.7 || tricot  
| Rodan || 2.3.5.7 || tricot  
|41, 46|| 1L 4s, machinoid, 5L 6s
|41, 46|| 1L 4s, machinoid, 5L 6s
|More accurate extension of the above.|| 245/243, gamelisma  
|More accurate extension of the above.|| 245/243, gamelisma  
|234c
|-
|-
| Valentine || 2.3.5.7 || enneacot
| Miracle || 2.3.5.7.11 || hexacot
|15, 16|| 15L 1s, [[Carlos Alpha]]
|31, 41|| antisinatonic, 10L 1s
|Scale with small steps strongly associated with Carlos Alpha.|| 126/125, gamelisma  
|Generated by a 15/14~16/15 semitone, two of which reach a slendric 8/7.|| 225/224, 243/242, gamelisma  
|117c
|-
|-
| rowspan="3" |Diaschismic
|Valentine
|2.3.5.7
|enneacot
|15, 16
|15L 1s, [[Carlos Alpha]]
|Scale with small steps strongly associated with Carlos Alpha.
|126/125, gamelisma
|78c
|-
| rowspan="4" |Diaschismic
|Diaschismic
|Diaschismic
|2.3.5.7.17
|2.3.5.17
|diploid monocot
|diploid monocot
|12, 34
|12, 34
|2L 8s, 10L 2s
|2L 8s, 10L 2s
|Temperament characterized by a perfect semioctave and a sharpened fifth or semitone generator. Two generators down reaches 5/4.
|Temperament characterized by a perfect semioctave and a sharpened fifth or semitone generator. Two generators down reaches 5/4.
|diaschisma, 126/125
|diaschisma
|100-111c
|-
|-
|Srutal
|Septimal Diaschismic
|2.3.5.7.17
|2.3.5.7.17
|diploid monocot
|diploid monocot
|46, 80
|12, 34
|2L 8s, 10L 2s
|2L 8s, 10L 2s
|Very complex but accurate 7-limit diaschismic.
|Rather complex 7-limit extension of the above.
|diaschisma, ragisma
|diaschisma, 126/125
|103-104c
|-
| Srutal || 2.3.5.7.17 ||  diploid monocot
|46, 80|| 2L 8s, 10L 2s
| Very complex but accurate 7-limit diaschismic. || diaschisma, ragisma || 104-105c
|-
|-
|Pajara
|Pajara
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|Jubilic archytas diaschismic temperament. Contains jubilic chord structure and is strongly associated with 22edo.
|Jubilic archytas diaschismic temperament. Contains jubilic chord structure and is strongly associated with 22edo.
|diaschisma, 50/49
|diaschisma, 50/49
|109-111c
|-
|-
|| Orgonismic || Orgone || 2.7.11 || 
|Orgonismic
|15, 26|| 4L7s  
|Orgone
| A high-accuracy rank-2 temperament generated by a tempered 77/64. || 65536/65219 || 323.3c
|2.7.11
|trimech
|15, 26
|4L7s
|A high-accuracy rank-2 temperament generated by a tempered 77/64.
|65536/65219
|320-325c
|-
|-
|
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|

Revision as of 20:39, 19 December 2025

Main article: Regular temperament

Rank-2

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. 81/80 692-697c
Septimal Meantone 2.3.5.7 monocot 19, 31 softer diatonic, m-chromatic Natural extension of the above to 2...7. 81/80, 225/224 695-697c
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, 81/80 692-694c
Archy Archy 2.3.7 monocot 5, 22 soft pentic, harder diatonic, p-chromatic 2.3.7 counterpart of meantone, which sharpens the fifth. 64/63 709-720c
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, 245/243 709-711c
Mabilic Mabilic 2.5.7 alpha-triseph 7, 9 antidiatonic, armotonic, 9L 7s Basic antidiatonic temperament with no 3. mabilisma 668-680c
Trismegistus 2.3.5.7 alpha-triseph 16, 25 antidiatonic, armotonic, 9L 7s High-accuracy but high complexity extension of prime 3. gamelisma, magisma 672-675c
Semabila 2.3.5.7 alpha-triseph 9, 25 antidiatonic, armotonic, 9L 7s Combination of mabilic and semaphore. 49/48, 28672/28125 668-672c
Mavila 2.3.5.7 monocot 7, 9 antidiatonic, armotonic, 7L 9s Exotemperament serving as an antidiatonic analog of meantone. 36/35, 135/128 675-680c
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, 100/99 161-166c
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, 64/63 161-163c
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 231-234c
Mothra 2.3.5.7 tricot 26, 31 1L 4s, machinoid, 5L 6s Meantone extension of the above. 81/80, gamelisma 231c
Rodan 2.3.5.7 tricot 41, 46 1L 4s, machinoid, 5L 6s More accurate extension of the above. 245/243, gamelisma 234c
Miracle 2.3.5.7.11 hexacot 31, 41 antisinatonic, 10L 1s Generated by a 15/14~16/15 semitone, two of which reach a slendric 8/7. 225/224, 243/242, gamelisma 117c
Valentine 2.3.5.7 enneacot 15, 16 15L 1s, Carlos Alpha Scale with small steps strongly associated with Carlos Alpha. 126/125, gamelisma 78c
Diaschismic Diaschismic 2.3.5.17 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 100-111c
Septimal Diaschismic 2.3.5.7.17 diploid monocot 12, 34 2L 8s, 10L 2s Rather complex 7-limit extension of the above. diaschisma, 126/125 103-104c
Srutal 2.3.5.7.17 diploid monocot 46, 80 2L 8s, 10L 2s Very complex but accurate 7-limit diaschismic. diaschisma, ragisma 104-105c
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, 50/49 109-111c
Orgonismic Orgone 2.7.11 trimech 15, 26 4L7s A high-accuracy rank-2 temperament generated by a tempered 77/64. 65536/65219 320-325c
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