List of regular temperaments: Difference between revisions

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|+ Rank-2 Temperaments
|+ Rank-2 Temperaments
|-
|-
! Family !! Name !! Subgroup !! Ploidacot
! Form !! Family !! Name !! Subgroup  
!ETs       !! Usual Scale Type  
!Ploidacot      !! ETs  
!Description!! Commas !! Generator size  
!Usual Scale Type!! Description !! Commas  
!Generator size
|-
|-
| rowspan="3" | Syntonic || Meantone || 2.3.5 || monocot
| rowspan="13" | 7 || rowspan="3" | Syntonic || Meantone || 2.3.5  
|7, 12|| softer diatonic, m-chromatic  
|monocot|| 7, 12  
|Common historical temperament for 5-limit diatonic harmony.|| 81/80 || 692-697c
|softer diatonic, m-chromatic|| 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  
|19, 31|| softer diatonic, m-chromatic  
|monocot|| 19, 31  
|Natural extension of the above to 2...7.|| 81/80, 225/224 || 695-697c
|softer diatonic, m-chromatic||  Natural extension of the above to 2...7. || 81/80, 225/224
|695-697c
|-
|-
|Flattone
|Flattone
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|692-694c
|692-694c
|-
|-
| rowspan="2" | Archy || Archy || 2.3.7 || monocot
| rowspan="4" | Mabilic || Mabilic || 2.5.7  
|5, 22|| soft pentic, harder diatonic, p-chromatic
|alpha-triseph<sup>[a]</sup>|| 7, 9  
|2.3.7 counterpart of Meantone, which sharpens the fifth.|| 64/63 || 709-720c
|antidiatonic, armotonic, 9L 7s|| Basic antidiatonic temperament with no 3. || mabilisma
|-
| 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
|-
| rowspan="4" | Mabilic || Mabilic || 2.5.7 || alpha-triseph<sup>[a]</sup>
|7, 9|| antidiatonic, armotonic, 9L 7s  
|Basic antidiatonic temperament with no 3.|| mabilisma  
|668-680c
|668-680c
|-
|-
| Trismegistus || 2.3.5.7 || alpha-triseph  
| Trismegistus || 2.3.5.7  
|16, 25|| antidiatonic, armotonic, 9L 7s  
|alpha-triseph|| 16, 25  
|High-accuracy but high complexity extension of prime 3.|| gamelisma, magisma  
|antidiatonic, armotonic, 9L 7s|| High-accuracy but high complexity extension of prime 3. || gamelisma, magisma  
|672-675c
|672-675c
|-
|-
| Semabila || 2.3.5.7 || alpha-triseph  
| Semabila || 2.3.5.7
|9, 25|| antidiatonic, armotonic, 9L 7s  
|alpha-triseph|| 9, 25  
|Combination of Mabilic and Semaphore.|| 49/48, 28672/28125  
|antidiatonic, armotonic, 9L 7s|| Combination of Mabilic and Semaphore.  
|49/48, 28672/28125
|668-672c
|668-672c
|-
|-
| Mavila || 2.3.5.7 || monocot
| Mavila || 2.3.5.7  
|7, 9|| antidiatonic, armotonic, 7L 9s  
|monocot|| 7, 9  
|Exotemperament serving as an antidiatonic analog of meantone.|| 36/35, 135/128  
|antidiatonic, armotonic, 7L 9s|| Exotemperament serving as an antidiatonic analog of meantone.  
|36/35, 135/128
|675-680c
|675-680c
|-
|-
| rowspan="2" | Porcupine || Porcupine || 2.3.5.11 || omega-tricot  
| rowspan="2" | Porcupine || Porcupine || 2.3.5.11  
|15, 22|| onyx, pine
|omega-tricot|| 15, 22  
|Moderate-accuracy 2.3.5.11 temperament with a ~160c generator and a heptatonic MOS.|| 250/243, 100/99  
|onyx, pine|| Moderate-accuracy 2.3.5.11 temperament with a ~160c generator and a heptatonic MOS.  
|250/243, 100/99
|161-166c
|161-166c
|-
|-
| Septimal Porcupine || 2.3.5.7.11 || omega-tricot  
| Septimal Porcupine || 2.3.5.7.11  
|15, 22|| onyx, pine
|omega-tricot|| 15, 22  
|Extension of the above to the full 11-limit.|| 250/243, 100/99, 64/63  
|onyx, pine|| Extension of the above to the full 11-limit.  
|250/243, 100/99, 64/63
|161-163c
|161-163c
|-
|-
| rowspan="5" | Gamelic || Slendric, Wonder || 2.3.7 || tricot  
| Interclassical || Interclassical, Dicot || 2.3.5
|5, 31|| 1L 4s, machinoid, 5L 6s
|dicot|| 7, 10
|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  
|mosh, dicoid|| 5-limit exotemperament equating 5/4 and 6/5 to the same interval.
|25/24
|670-680c, 720-730c
|-
| rowspan="2" | Rastmic || Rastmic || 2.3.11
|dicot|| 7, 10
|mosh, dicoid|| Maps 11/9 and its fifth complement to a perfect neutral third.
|243/242
|345-355c
|-
| Mohajira || 2.3.5.11
|dicot|| 24, 31
|mosh, dicoid|| Meantone extension of the above.
|243/242, 81/80
|347-350c
|-
| Tetracot [rename] || Tetracot [rename] || 2.3.5.11
|tetracot|| 34, 41
|archeotonic, 7L6s|| Interprets (3/2)^(1/4) as 10/9.
|100/99, 243/242
|175-180c
|-
| rowspan="9" |5
| 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
|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
|-
| rowspan="5" |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 [https://wiki.spoogly.website/Equipentatonic#Slendro Slendro tuning]. Contains a pentatonic similar to porcupine's heptatonic.
|gamelisma
|231-234c
|231-234c
|-
|-
| Mothra || 2.3.5.7 || tricot  
|Mothra
|26, 31|| 1L 4s, machinoid, 5L 6s
|2.3.5.7
|Meantone extension of the above.|| 81/80, gamelisma  
|tricot
|26, 31
|1L 4s, machinoid, 5L 6s
|Meantone extension of the above.
|81/80, gamelisma
|231c
|231c
|-
|-
| Rodan || 2.3.5.7 || tricot  
|Rodan
|41, 46|| 1L 4s, machinoid, 5L 6s
|2.3.5.7
|More accurate extension of the above.|| 245/243, gamelisma  
|tricot
|41, 46
|1L 4s, machinoid, 5L 6s
|More accurate extension of the above.
|245/243, gamelisma
|234c
|234c
|-
|-
| Miracle || 2.3.5.7.11 || hexacot  
|Miracle
|31, 41|| antisinatonic, 10L 1s
|2.3.5.7.11
|Generated by a 15/14~16/15 semitone, two of which reach a slendric 8/7.|| 225/224, 243/242, gamelisma  
|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
|117c
|-
|-
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|enneacot
|enneacot
|15, 16
|15, 16
|15L 1s, [[Carlos Alpha]]
|15L 1s, [https://wiki.spoogly.website/Carlos_Alpha Carlos Alpha]
|Scale with small steps strongly associated with Carlos Alpha.
|Scale with small steps strongly associated with Carlos Alpha.
|126/125, gamelisma
|126/125, gamelisma
|78c
|78c
|-
|Buzzard
|Buzzard
|2.3.5.7.13
|alpha-tetracot
|53, 58
|
|
|
|
|-
|Interseptimal
|Interseptimal, Semaphore
|2.3.7
|alpha-dicot
|5, 19
|4L 1s, semiquartal
|Equipentatonic, inaccurate 7-limit temperament.
|49/48
|240-250c
|-
| rowspan="4" |12
| rowspan="2" |Schismic
|Schismic
|2.3.5
|monocot
|41, 53
|harder diatonic, p-chromatic
|5-limit interpretation of Pythagorean tuning, best tuned when the fifth is flattened by a fraction of a cent.
|schisma
|701-702c
|-
|Garibaldi
|2.3.5.7
|monocot
|41, 53
|harder diatonic, p-chromatic
|7-limit interpretation of Pythagorean tuning. Despite being an extension of the above, it is most accurate when the fifth is tuned slightly sharp.
|schisma, 225/224
|702-703c
|-
|-
| rowspan="3" |Diaschismic
| rowspan="3" |Diaschismic
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|103-104c
|103-104c
|-
|-
|10
|Pajara
|Pajara
|2.3.5.7.17
|2.3.5.7.17
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|109-111c
|109-111c
|-
|-
|11
|Orgonismic
|Orgonismic
|Orgone, Orgonic
|Orgone, Orgonic
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|320-325c
|320-325c
|-
|-
| rowspan="2" |Schismic
| rowspan="2" |3
|Schismic
|2.3.5
|monocot
|41, 53
|harder diatonic, p-chromatic
|5-limit interpretation of Pythagorean tuning, best tuned when the fifth is flattened by a fraction of a cent.
|schisma
|701-702c
|-
|Garibaldi
|2.3.5.7
|monocot
|41, 53
|harder diatonic, p-chromatic
|7-limit interpretation of Pythagorean tuning. Despite being an extension of the above, it is most accurate when the fifth is tuned slightly sharp.
|schisma, 225/224
|702-703c
|-
|Magic
|Magic
|Magic
|Magic
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|378-382c
|378-382c
|-
|-
| rowspan="2" |Rastmic
|Wurschmidt
|Rastmic
|Wurschmidt
|2.3.11
|2.3.5.11.23
|dicot
|beta-octacot
|7, 10
|31, 34
|mosh, dicoid
| -
|Maps 11/9 and its fifth complement to a perfect neutral third.
|Eight 5/4s stack to 3/2. Due to the sharp tuning of 5/4, MOS scales become quite awkward, however three 25/24s stack to two 16/15s. 2.5.3 analogue of schismic.
|243/242
|576/575, 12167/12150
|345-355c
|386-389c
|-
|Mohajira
|2.3.5.11
|dicot
|24, 31
|mosh, dicoid
|Meantone extension of the above.
|243/242, 81/80
|347-350c
|-
|Interclassical
|Interclassical, Dicot
|2.3.5
|dicot
|7, 10
|mosh, dicoid
|5-limit exotemperament equating 5/4 and 6/5 to the same interval.
|25/24
|670-680c, 720-730c
|-
|Father
|Father
|2.3
|monocot
|3, 5
|antipentic
|Extremely inaccurate exotemperament which equates 5/4 with 4/3.
|16/15
|720-800c
|-
|Interseptimal
|Interseptimal, Semaphore
|2.3.7
|alpha-dicot
|5, 19
|4L 1s, semiquartal
|Equipentatonic, inaccurate 7-limit temperament.
|49/48
|240-250c
|-
|Tetracot [rename]
|Tetracot [rename]
|2.3.5.11
|tetracot
|34, 41
|archeotonic, 7L6s
|Interprets (3/2)^(1/4) as 10/9.
|100/99, 243/242
|175-180c
|-
|-
|6
|Hemithirds
|Hemithirds
|Didacus
|Didacus
Line 229: Line 258:
|192c
|192c
|-
|-
|b13
| rowspan="3" |Sensamagic
| rowspan="3" |Sensamagic
|Sensamagic
|Sensamagic
Line 239: Line 269:
|435-440c
|435-440c
|-
|-
| rowspan="3" |8
|Sensi
|Sensi
|2.3.5.7.13
|2.3.5.7.13
Line 257: Line 288:
|~435c
|~435c
|-
|-
|Father
|Father
|2.3
|monocot
|3, 5
|antipentic
|Extremely inaccurate exotemperament which equates 5/4 with 4/3.
|16/15
|720-800c
|-
|4
|Kleismic
|Kleismic
|Kleismic, Cata
|Kleismic, Cata
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|325/324, 625/624
|325/324, 625/624
|317c
|317c
|-
|9
|Orwell
|Orwell
|2.3.5.7.11
|alpha-heptacot
|22, 31
|
|
|
|
|-
|10
|Negri
|Negri
|2.3.5.13
|omega-tetracot
|10, 19
|
|
|
|
|}
|}
[a] seph = divisions of 5/4
[a] seph = divisions of 5/4

Revision as of 23:00, 30 December 2025

Main article: Regular temperament

Rank-2

Rank-2 Temperaments
Form Family Name Subgroup Ploidacot ETs Usual Scale Type Description Commas Generator size
7 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
Mabilic Mabilic 2.5.7 alpha-triseph[a] 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
Interclassical Interclassical, Dicot 2.3.5 dicot 7, 10 mosh, dicoid 5-limit exotemperament equating 5/4 and 6/5 to the same interval. 25/24 670-680c, 720-730c
Rastmic Rastmic 2.3.11 dicot 7, 10 mosh, dicoid Maps 11/9 and its fifth complement to a perfect neutral third. 243/242 345-355c
Mohajira 2.3.5.11 dicot 24, 31 mosh, dicoid Meantone extension of the above. 243/242, 81/80 347-350c
Tetracot [rename] Tetracot [rename] 2.3.5.11 tetracot 34, 41 archeotonic, 7L6s Interprets (3/2)^(1/4) as 10/9. 100/99, 243/242 175-180c
5 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
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
Buzzard Buzzard 2.3.5.7.13 alpha-tetracot 53, 58
Interseptimal Interseptimal, Semaphore 2.3.7 alpha-dicot 5, 19 4L 1s, semiquartal Equipentatonic, inaccurate 7-limit temperament. 49/48 240-250c
12 Schismic Schismic 2.3.5 monocot 41, 53 harder diatonic, p-chromatic 5-limit interpretation of Pythagorean tuning, best tuned when the fifth is flattened by a fraction of a cent. schisma 701-702c
Garibaldi 2.3.5.7 monocot 41, 53 harder diatonic, p-chromatic 7-limit interpretation of Pythagorean tuning. Despite being an extension of the above, it is most accurate when the fifth is tuned slightly sharp. schisma, 225/224 702-703c
Diaschismic Diaschismic 2.3.5.17 diploid monocot 12, 34 jaric, 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 jaric, 10L 2s Rather complex 7-limit extension of the above. diaschisma, 126/125 103-104c
10 Pajara 2.3.5.7.17 diploid monocot 12, 22 jaric, 10L 2s Jubilic archytas diaschismic temperament. Contains jubilic chord structure and is strongly associated with 22edo. diaschisma, 50/49 109-111c
11 Orgonismic Orgone, Orgonic 2.7.11 trimech[b] 15, 26 4L7s A high-accuracy rank-2 temperament generated by a tempered 77/64. 65536/65219 320-325c
3 Magic Magic 2.3.5 alpha-pentacot 19, 22 mosh, sephiroid Stacks five flattened major thirds to form a perfect twelfth. magisma 378-382c
Wurschmidt Wurschmidt 2.3.5.11.23 beta-octacot 31, 34 - Eight 5/4s stack to 3/2. Due to the sharp tuning of 5/4, MOS scales become quite awkward, however three 25/24s stack to two 16/15s. 2.5.3 analogue of schismic. 576/575, 12167/12150 386-389c
6 Hemithirds Didacus 2.5.7.11 diseph 25, 31 archeotonic, 6L7s Has a "meantone" generator (tempered 28/25); essentially a restriction of Septimal Meantone to 2.9.5.7. 3136/3125, 176/175 192c
b13 Sensamagic Sensamagic 3.5.7 monogem[c] b4, b9[d] lambda Basic tritave temperament that stacks 9/7 twice to reach 5/3. Generates the lambda (4L5s⟨3/1⟩) MOS scale, or can be used with octaves as Sensamagic.2. 245/243 435-440c
8 Sensi 2.3.5.7.13 beta-heptacot 19, 27 3L 2s, checkertonic Very sharp extension of Sensamagic, which finds the octave at 125/63. 91/90, 126/125, 169/168 440-445c
Hedgehog 2.3.5.7 diploid alpha-tricot 14c[e], 22 ekic Porcupine extension of Sensamagic, which finds the octave at 49/25 (and consequently maps 7/5 to the semioctave). 50/49, 245/243 ~435c
Father Father 2.3 monocot 3, 5 antipentic Extremely inaccurate exotemperament which equates 5/4 with 4/3. 16/15 720-800c
4 Kleismic Kleismic, Cata 2.3.5.13 alpha-hexacot 19, 34 smitonic, 4L7s, 4L11s A highly accurate 5-limit temperament equating a stack of six slightly sharp 6/5's to one 3/1. 325/324, 625/624 317c
9 Orwell Orwell 2.3.5.7.11 alpha-heptacot 22, 31
10 Negri Negri 2.3.5.13 omega-tetracot 10, 19

[a] seph = divisions of 5/4

[b] mech = divisions of 7/4

[c] gem = divisions of 7/3 in a perfect twelfth (tritave) equivalent context

[d] A "b" prefixed to an equal temperament indicates the equal division of 3/1.

[e] A "c" suffixed to an equal temperament indicates that the second-best mapping of prime 5 is used.

Rank-3

Name Commas Subgroup ETs Description Generators
Marvel 225/224, 385/384 2.3.5.7.11 19, 22, 31 16/15 and 15/14 are equated, or equivalently 32/25 and 9/7 are equated. ~3/2, ~81/80
Hemifamity / Argentismic 5120/5103 2.3.5.7 41, 46, 53 81/80 and 64/63 are equated. Sometimes used in aberrismic theory. ~3/2, ~81/80
Parapyth(ic) 352/351, 896/891 2.3.7.11.13 41, 46, 63 Based on Margo Schulter's regular tuning construct called "parapyth". ~3/2, ~28/27
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