List of regular temperaments: Difference between revisions

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|+ Rank-2 Temperaments
|+ Rank-2 Temperaments
|-
|-
! Form !! Family !! Name !! Subgroup
! Form !! Family !! Name  
![[Ploidacot]]!! ETs
!Generator
!Usual Scale Type!! Description !! Commas  
![[Ploidacot]]
!Usual Scale Type!! ETs !! Description !! Subgroup !! Commas  
!Accuracy (Vector)
!Accuracy (Vector)
!Generator size
|-
|-
| rowspan="3" | 7 || rowspan="4" | Syntonic || Meantone || 2.3.5
| rowspan="3" | 7 || rowspan="4" | Syntonic || Meantone  
|monocot|| 7, 12
|softer diatonic, m-chromatic|| Common historical temperament for 5-limit diatonic harmony. || 81/80
|Medium
|692-697c
|692-697c
|monocot
|softer diatonic, m-chromatic|| 7, 12 || Common historical temperament for 5-limit diatonic harmony. || 2.3.5 || 81/80
|4 Medium
|-
|-
| Septimal Meantone || 2.3.5.7
| Septimal Meantone  
|monocot|| 19, 31
|softer diatonic, m-chromatic||  Canonical extension of the above to 2...7. || 81/80, 225/224
|Medium
|695-697c
|695-697c
|monocot
|softer diatonic, m-chromatic|| 19, 31 ||  Canonical extension of the above to 2...7. || 2.3.5.7 || 81/80, 225/224
|4 Medium
|-
|-
|Flattone
|Flattone
|2.3.5.7
|692-694c
|monocot
|monocot
|softer diatonic, m-chromatic
|19, 26
|19, 26
|softer diatonic, m-chromatic
|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.
|2.3.5.7
|525/512, 81/80
|525/512, 81/80
|Low
|6 Low
|692-694c
|-
|-
|12
|12
|Injera
|Injera
|2.3.5.7
|92-96c
|diploid monocot
|diploid monocot
|thalassic
|12, 26
|12, 26
|thalassic
|Adds a 600c tritone representing 7/5 to meantone.
|Adds a 600c tritone representing 7/5 to meantone.
|2.3.5.7
|81/80, 50/49
|81/80, 50/49
|Medium-low
|5 Medium-low
|92-96c
|-
|-
| rowspan="4" |7
| rowspan="4" |7
| rowspan="2" | Porcupine || Porcupine || 2.3.5.11
| rowspan="2" | Porcupine || Porcupine  
|omega-tricot|| 15, 22  
|161-166c
|onyx, pine|| Moderate-accuracy 2.3.5.11 temperament with a ~160c generator and a heptatonic MOS.  
|omega-tricot
|onyx, pine|| 15, 22 || Moderate-accuracy 2.3.5.11 temperament with a ~160c generator and a heptatonic MOS. || 2.3.5.11
|250/243, 100/99
|250/243, 100/99
|Medium-low
|5 Medium-low
|161-166c
|-
|-
| Septimal Porcupine || 2.3.5.7.11
| Septimal Porcupine  
|omega-tricot|| 15, 22  
|161-163c
|onyx, pine|| Extension of the above to the full 11-limit.  
|omega-tricot
|onyx, pine|| 15, 22 || Extension of the above to the full 11-limit. || 2.3.5.7.11
|250/243, 100/99, 64/63
|250/243, 100/99, 64/63
|Medium-low
|5 Medium-low
|161-163c
|-
|-
| Interclassical || Interclassical, Dicot || 2.3.5
| Interclassical || Interclassical, Dicot  
|dicot|| 7, 10
|670-680c, 720-730c
|mosh, dicoid|| 5-limit exotemperament equating 5/4 and 6/5 to the same interval.  
|dicot
|mosh, dicoid|| 7, 10|| 5-limit exotemperament equating 5/4 and 6/5 to the same interval. || 2.3.5
|25/24
|25/24
|Very low
|7 Very low
|670-680c, 720-730c
|-
|-
| Tetracot [rename] || Tetracot [rename] || 2.3.5.11
| Tetracot || Tetracot  
|tetracot|| 34, 41
|175-180c
|archeotonic, 7L6s|| Interprets (3/2)^(1/4) as 10/9.  
|tetracot
|archeotonic, 7L6s|| 34, 41|| Interprets (3/2)^(1/4) as 10/9. || 2.3.5.11
|100/99, 243/242
|100/99, 243/242
|High (2.3.5), Medium (extensions)
|2 High (2.3.5), Medium (extensions)
|175-180c
|-
|-
| rowspan="8" |12
| rowspan="8" |12
| rowspan="2" |Diminished
| rowspan="2" |Diminished
|Diminished
|Diminished
|2.3.5
|685-700c
|tetraploid monocot
|tetraploid monocot
|tetrawood, 4L 8s
|12, 16
|12, 16
|tetrawood, 4L 8s
|Sets 6/5 to 300 cents; a step up from 600 cents is 3/2.
|Sets 6/5 to 300 cents; a step up from 600 cents is 3/2.
|2.3.5
|648/625
|648/625
|Medium-low
|5 Medium-low
|685-700c
|-
|-
|Dimisept
|Dimisept
|2.3.5.7
|685-700c
|tetraploid monocot
|tetraploid monocot
|tetrawood, 4L 8s
|12, 16
|12, 16
|tetrawood, 4L 8s
|Exotempered extension of the above that sets 7/6 to 300 cents.
|Exotempered extension of the above that sets 7/6 to 300 cents.
|2.3.5.7
|36/35, 50/49
|36/35, 50/49
|Very low
|7 Very low
|685-700c
|-
|-
|Augmented
|Augmented
|Augmented
|Augmented
|2.3.5.7
|705-715c
|triploid monocot
|triploid monocot
|triwood, tcherepnin
|12, 15
|12, 15
|triwood, tcherepnin
|Sets 5/4 to 400 cents, a step down from 800c is 3/2 and 2 steps up is 7/4.
|Sets 5/4 to 400 cents, a step down from 800c is 3/2 and 2 steps up is 7/4.
|2.3.5.7
|128/125
|128/125
|Low
|6 Low
|705-715c
|-
|-
| rowspan="2" |Schismic
| rowspan="2" |Schismic
|Schismic
|Schismic
|2.3.5
|701-702c
|monocot
|monocot
|harder diatonic, p-chromatic
|41, 53
|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.
|5-limit interpretation of Pythagorean tuning, best tuned when the fifth is flattened by a fraction of a cent.
|2.3.5
|schisma
|schisma
|Very high
|1 Very high
|701-702c
|-
|-
|Garibaldi
|Garibaldi
|2.3.5.7
|702-703c
|monocot
|monocot
|harder diatonic, p-chromatic
|41, 53
|41, 53
|harder diatonic, p-chromatic
|7-limit interpretation of Pythagorean tuning. It is most accurate when the fifth is tuned slightly sharp.
|7-limit interpretation of Pythagorean tuning. It is most accurate when the fifth is tuned slightly sharp.
|2.3.5.7
|schisma, 225/224
|schisma, 225/224
|Medium-high
|3 Medium-high
|702-703c
|-
|-
|Misty
|Misty
|Misty
|Misty
|2.3.5
|701-708c
|triploid monocot
|triploid monocot
|
|12, 51
|12, 51
|
|5/4 is 4 times the difference between 3/2 and 800c.
|5/4 is 4 times the difference between 3/2 and 800c.
|2.3.5
|misty comma
|misty comma
|Medium-high
|3 Medium-high
|701-708c
|-
|-
| rowspan="3" |Diaschismic
| rowspan="3" |Diaschismic
|Diaschismic
|Diaschismic
|2.3.5.17
|100-111c
|diploid monocot
|diploid monocot
|jaric, 10L 2s
|12, 34
|12, 34
|jaric, 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.
|2.3.5.17
|diaschisma, 136/135
|diaschisma, 136/135
|Medium
|4 Medium
|100-111c
|-
|-
|Septimal Diaschismic
|Septimal Diaschismic
|2.3.5.7.17
|103-104c
|diploid monocot
|diploid monocot
|jaric, 10L 2s
|12, 34
|12, 34
|jaric, 10L 2s
|Rather complex 7-limit extension of the above.
|Rather complex 7-limit extension of the above.
|2.3.5.7.17
|diaschisma, 126/125, 136/135
|diaschisma, 126/125, 136/135
|Medium
|4 Medium
|103-104c
|-
|-
|10
|10
|Pajara
|Pajara
|2.3.5.7.17
|109-111c
|diploid monocot
|diploid monocot
|jaric, 10L 2s
|12, 22
|12, 22
|jaric, 10L 2s
|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.
|2.3.5.7.17
|diaschisma, 50/49, 136/135
|diaschisma, 50/49, 136/135
|Medium-low
|5 Medium-low
|109-111c
|-
|-
| rowspan="2" |3
| rowspan="2" |3
|Magic
|Magic
|Magic
|Magic
|2.3.5
|378-382c
|alpha-pentacot
|alpha-pentacot
|mosh, sephiroid
|19, 22
|19, 22
|mosh, sephiroid
|Stacks five flattened major thirds to form a perfect twelfth. 5/4-generated analog of Meantone.
|Stacks five flattened major thirds to form a perfect twelfth. 5/4-generated analog of Meantone.
|2.3.5
|magisma
|magisma
|Medium
|4 Medium
|378-382c
|-
|-
|Wurschmidt
|Wurschmidt
|Wurschmidt
|Wurschmidt
|2.3.5.11.23
|386-389c
|beta-octacot
|beta-octacot
| -
|31, 34
|31, 34
| -
|Eight 5/4s stack to 3/2 and three 25/24s stack to two 16/15s. 5/4-generated analog of Schismic. Bad for MOSes.
|Eight 5/4s stack to 3/2 and three 25/24s stack to two 16/15s. 5/4-generated analog of Schismic. Bad for MOSes.
|2.3.5.11.23
|576/575, 12167/12150
|576/575, 12167/12150
|Medium-high
|3 Medium-high
|386-389c
|-
|-
|8
|8
|Father
|Father
|Father
|Father
|2.3.5
|720-800c
|monocot
|monocot
|antipentic
|3, 5
|3, 5
|antipentic
|Extremely inaccurate exotemperament which equates 5/4 with 4/3.
|Extremely inaccurate exotemperament which equates 5/4 with 4/3.
|2.3.5
|16/15
|16/15
|Extremely low
|8 Extremely low
|720-800c
|-
|-
|4
|4
|Kleismic
|Kleismic
|Kleismic, Cata
|Kleismic, Cata
|2.3.5.13
|317c
|alpha-hexacot
|alpha-hexacot
|smitonic, 4L7s, 4L11s
|19, 34
|19, 34
|smitonic, 4L7s, 4L11s
|A highly accurate temperament equating a stack of six slightly sharp 6/5's to one 3/1 and three 6/5's to one 26/15.
|A highly accurate temperament equating a stack of six slightly sharp 6/5's to one 3/1 and three 6/5's to one 26/15.
|2.3.5.13
|kleisma, 325/324
|kleisma, 325/324
|High
|2 High
|317c
|-
|-
| rowspan="3" |10
| rowspan="3" |10
| rowspan="3" |Negri
| rowspan="3" |Negri
|Negri
|Negri
|2.3.5
|124-128c
|omega-tetracot
|omega-tetracot
|
|10, 19
|10, 19
|
|Generator is a sharp minor second of 16/15 which stacks 3 times to 5/4, and can be seen as a counterpart of Porcupine.
|Generator is a sharp minor second of 16/15 which stacks 3 times to 5/4, and can be seen as a counterpart of Porcupine.
|2.3.5
|16875/16384
|16875/16384
|Medium-low
|5 Medium-low
|124-128c
|-
|-
|Semibuzzard
|Semibuzzard
|2.3.5.7.11
|124-128c
|
|
|taric
|10, 28
|10, 28
|taric
|Weak Jubilismic or Buzzard extension of Negri allowing intervals of 7 to be reached with a 600-cent offset.
|Weak Jubilismic or Buzzard extension of Negri allowing intervals of 7 to be reached with a 600-cent offset.
|2.3.5.7.11
|16875/16384, 50/49, 243/242
|16875/16384, 50/49, 243/242
|Low
|6 Low
|124-128c
|-
|-
|Negrisept
|Negrisept
|2.3.5.7
|124-128c
|
|
|
|10, 19
|10, 19
|
|Semaphore extension of negri.
|Semaphore extension of negri.
|2.3.5.7
|16875/16384, 49/48
|16875/16384, 49/48
|Very low
|7 Very low
|124-128c
|}
|}


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{| class="wikitable sortable" style="font-size:0.8em"
{| class="wikitable sortable" style="font-size:0.8em"
|-
|-
! Form !! Family !! Name !! Subgroup
! Form !! Family !! Name  
![[Ploidacot]]!! ETs
!Generator
!Usual Scale Type!! Description !! Commas  
![[Ploidacot]]
!Usual Scale Type!! ETs !! Description !! Subgroup !! Commas  
!Accuracy
!Accuracy
!Generator size
|-
|-
| rowspan="9" |5
| rowspan="9" |5
| rowspan="2" | Archy || Archy || 2.3.7
| rowspan="2" | Archy || Archy  
|monocot|| 5, 22
|709-720c
|soft pentic, harder diatonic, p-chromatic|| 2.3.7 counterpart of Meantone, which sharpens the fifth.  
|monocot
|soft pentic, harder diatonic, p-chromatic|| 5, 22|| 2.3.7 counterpart of Meantone, which sharpens the fifth. || 2.3.7
|64/63
|64/63
|Medium-low
|5 Medium-low
|709-720c
|-
|-
| Superpyth || 2.3.5.7
| Superpyth  
|monocot|| 22, 27
|709-711c
|soft pentic, harder diatonic, p-chromatic|| Extension of the above to 2...7, favoring flatter tunings.  
|monocot
|soft pentic, harder diatonic, p-chromatic|| 22, 27|| Extension of the above to 2...7, favoring flatter tunings. || 2.3.5.7
|64/63, 245/243
|64/63, 245/243
|Medium-low
|5 Medium-low
|709-711c
|-
|-
| rowspan="5" |Gamelic
| rowspan="5" |Gamelic
|Slendric, Wonder
|Slendric, Wonder
|2.3.7
|231-234c
|tricot
|tricot
|1L 4s, machinoid, 5L 6s
|5, 31
|5, 31
|1L 4s, machinoid, 5L 6s
|Splits the fifth in 3 parts, each of which is 8/7. Little relation to actual [[Equipentatonic#Slendro|Slendro tuning]].  
|Splits the fifth in 3 parts, each of which is 8/7. Little relation to actual [[Equipentatonic#Slendro|Slendro tuning]].  
|2.3.7
|gamelisma
|gamelisma
|Medium-high
|3 Medium-high
|231-234c
|-
|-
|Mothra
|Mothra
|2.3.5.7
|231c
|tricot
|tricot
|1L 4s, machinoid, 5L 6s
|26, 31
|26, 31
|1L 4s, machinoid, 5L 6s
|Meantone extension of the above.
|Meantone extension of the above.
|2.3.5.7
|81/80, gamelisma
|81/80, gamelisma
|Medium
|4 Medium
|231c
|-
|-
|Rodan
|Rodan
|2.3.5.7
|234c
|tricot
|tricot
|1L 4s, machinoid, 5L 6s
|41, 46
|41, 46
|1L 4s, machinoid, 5L 6s
|More accurate extension of the above.
|More accurate extension of the above.
|2.3.5.7
|245/243, gamelisma
|245/243, gamelisma
|Medium
|4 Medium
|234c
|-
|-
|Miracle
|Miracle
|2.3.5.7.11
|117c
|hexacot
|hexacot
|antisinatonic, 10L 1s
|31, 41
|31, 41
|antisinatonic, 10L 1s
|Generated by a 15/14~16/15 semitone, two of which reach a slendric 8/7.
|Generated by a 15/14~16/15 semitone, two of which reach a slendric 8/7.
|2.3.5.7.11
|225/224, 243/242, gamelisma
|225/224, 243/242, gamelisma
|Medium-high
|3 Medium-high
|117c
|-
|-
|Valentine
|Valentine
|2.3.5.7
|78c
|enneacot
|enneacot
|15L 1s,  [[Carlos Alpha]]
|15, 16
|15, 16
|15L 1s,  [[Carlos Alpha]]
|Scale with small steps strongly associated with Carlos Alpha.
|Scale with small steps strongly associated with Carlos Alpha.
|2.3.5.7
|126/125, gamelisma
|126/125, gamelisma
|Medium-high
|3 Medium-high
|78c
|-
|-
|Buzzard
|Buzzard
|Buzzard
|Buzzard
|2.3.5.7.13
|474-478c
|alpha-tetracot
|alpha-tetracot
|
|53, 58
|53, 58
|
|Sharpens the 21/16 so that four of them stacks to the 3/1.
|Sharpens the 21/16 so that four of them stacks to the 3/1.
|2.3.5.7.13
|buzzardsma
|buzzardsma
|Medium
|4 Medium
|474-478c
|-
|-
|Interseptimal
|Interseptimal
|Interseptimal, Semaphore
|Interseptimal, Semaphore
|2.3.7
|240-250c
|alpha-dicot
|alpha-dicot
|4L 1s, semiquartal
|5, 19
|5, 19
|4L 1s, semiquartal
|Equipentatonic, inaccurate 7-limit temperament.
|Equipentatonic, inaccurate 7-limit temperament.
|2.3.7
|49/48
|49/48
|Low
|6 Low
|240-250c
|-
|-
|13
|13
|Squares
|Squares
|Squares
|Squares
|2.3.7.11
|424-426c
|beta-tetracot
|beta-tetracot
|3L 5s, 3L 8s, 3L 11s
|14, 17
|14, 17
|3L 5s, 3L 8s, 3L 11s
|No-fives temperament generated by a flattened 9/7 equated with 14/11.
|No-fives temperament generated by a flattened 9/7 equated with 14/11.
|2.3.7.11
|99/98, 243/242
|99/98, 243/242
|Medium
|4 Medium
|424-426c
|}
|}


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{| class="wikitable sortable" style="font-size:0.8em"
{| class="wikitable sortable" style="font-size:0.8em"
|-
|-
! Form !! Family !! Name !! Subgroup
! Form !! Family !! Name  
![[Ploidacot]]!! ETs
!Generator
!Usual Scale Type!! Description !! Commas  
![[Ploidacot]]
!Usual Scale Type!! ETs !! Description !! Subgroup !! Commas  
!Accuracy
!Accuracy
!Generator size
|-
|-
| rowspan="4" |7
| rowspan="4" |7
| rowspan="2" | Rastmic || Rastmic || 2.3.11
| rowspan="2" | Rastmatic || Rastmatic
|dicot|| 7, 10
|345-355c
|mosh, dicoid|| Maps 11/9 and its fifth complement to a perfect neutral third.  
|dicot
|mosh, dicoid|| 7, 10|| Maps 11/9 and its fifth complement to a perfect neutral third. || 2.3.11
|243/242
|243/242
|Medium-high
|3 Medium-high
|345-355c
|-
|-
| Mohajira || 2.3.5.11
| Mohajira  
|dicot|| 24, 31
|347-350c
|mosh, dicoid|| Meantone extension of the above. Can optionally be extended to set 7/4 equal to the semiflat minor seventh, or via a strong meantone extension.  
|dicot
|mosh, dicoid|| 24, 31|| Meantone extension of the above. Can optionally be extended to set 7/4 equal to the semiflat minor seventh, or via a strong meantone extension. || 2.3.5.11
|243/242, 81/80
|243/242, 81/80
|Medium-low
|5 Medium-low
|347-350c
|-
|-
| rowspan="2" |Intratridecimal
| rowspan="2" |Intratridecimal
|Intratridecimal
|Intratridecimal
|2.3.13
|350-360c
|dicot
|dicot
|mosh, dicoid
|27, 10
|27, 10
|mosh, dicoid
|Maps 16/13 and its fifth complement to a perfect neutral third.
|Maps 16/13 and its fifth complement to a perfect neutral third.
|2.3.13
|512/507
|512/507
|Medium
|4 Medium
|350-360c
|-
|-
|(To be named)
|(To be named)
|2.3.7.13
|355-360c
|dicot
|dicot
|mosh, dicoid
|27, 10
|27, 10
|mosh, dicoid
|Archy extension of the above.
|Archy extension of the above.
|2.3.7.13
|512/507, 64/63
|512/507, 64/63
|Medium-low
|5 Medium-low
|355-360c
|}
|}


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{| class="wikitable sortable" style="font-size:0.8em"
{| class="wikitable sortable" style="font-size:0.8em"
|-
|-
! Form !! Family !! Name !! Subgroup
! Form !! Family !! Name  
![[Ploidacot]]!! ETs
!Generator
!Usual Scale Type!! Description !! Commas  
![[Ploidacot]]
!Usual Scale Type!! ETs !! Description !! Commas !! Subgroup
!Accuracy
!Accuracy
!Generator size
|-
|-
|7
|7
|Amity
|Amity
|Amity
|Amity
|2.3.5.7
|338-340c
|gamma-pentacot
|gamma-pentacot
|7L 18s, 7L 25s
|46, 53
|46, 53
|7L 18s, 7L 25s
|Sets the spacing of the thirds to 7/6-#-6/5-#-#-5/4-#-9/7; mostly appears as a structural element of EDOs rather than an independent structure.
|Sets the spacing of the thirds to 7/6-#-6/5-#-#-5/4-#-9/7; mostly appears as a structural element of EDOs rather than an independent structure.
|4375/4374, 5120/5103
|4375/4374, 5120/5103
|High
|2.3.5.7
|338-340c
|2 High
|-
|-
|12
|12
|Compton
|Compton
|Compton
|Compton
|2.3.5.7
|385c
|dodecaploid acot
|dodecaploid acot
|dodecawood
|12, 60
|12, 60
|dodecawood
|Acts as a closed circle of 12 fifths (see [[12edo]]), but with 5/4 flattened by a diesis from 400c, and 7/4 flattened by twice that amount from 1000c.
|Acts as a closed circle of 12 fifths (see [[12edo]]), but with 5/4 flattened by a diesis from 400c, and 7/4 flattened by twice that amount from 1000c.
|pythagorean comma
|pythagorean comma
|Medium-high
|2.3.5.7
|385c
|3 Medium-high
|-
|-
| rowspan="2" |4
| rowspan="2" |4
|Doublewide
|Doublewide
|Doublewide
|Doublewide
|2.3.5.7
|325c
|
|
|
|22, 48
|22, 48
|
|Sets 6/5 and 7/6 the same distance from the 300c period, so that four ~25c generators stack to the semitone separating 3/2 from 600c.
|Sets 6/5 and 7/6 the same distance from the 300c period, so that four ~25c generators stack to the semitone separating 3/2 from 600c.
|50/49, 875/864
|50/49, 875/864
|Medium-low
|2.3.5.7
|325c
|5 Medium-low
|-
|-
|Myna
|Myna
|Myna
|Myna
|2.3.5.7
|309-311c
|beta-decacot
|beta-decacot
| -
|27, 31
|27, 31
| -
|Sets 25/24 equal to twice 36/35.
|Sets 25/24 equal to twice 36/35.
|126/125, 1728/1715
|126/125, 1728/1715
|Medium-high
|2.3.5.7
|309-311c
|3 Medium-high
|-
|-
| rowspan="2" |9
| rowspan="2" |9
|Orwell
|Orwell
|Orwell
|Orwell
|2.3.5.7.11
|270-273c
|alpha-heptacot
|alpha-heptacot
|gramitonic
|22, 31
|22, 31
|gramitonic
|Generator is a sharpened 7/6. Interval chain finds 7/6, 11/8, 8/5, 15/8, 11/10, 9/7, 3/2.  
|Generator is a sharpened 7/6. Interval chain finds 7/6, 11/8, 8/5, 15/8, 11/10, 9/7, 3/2.  
|99/98, 121/120, 176/175
|99/98, 121/120, 176/175
|Medium-high
|2.3.5.7.11
|270-273c
|3 Medium-high
|-
|-
|Ennealimmal
|Ennealimmal
|Ennealimmal
|Ennealimmal
|2.3.5.7
|44-53c
|enneaploid dicot
|enneaploid dicot
|enneawood
|27, 45
|27, 45
|enneawood
|Divides the octave into nine equal parts representing 27/25 and half of 7/6.
|Divides the octave into nine equal parts representing 27/25 and half of 7/6.
|2401/2400, 4375/4374
|2401/2400, 4375/4374
|Very high
|2.3.5.7
|44-53c
|1 Very high
|-
|-
|8
|8
|Nusecond
|Nusecond
|Nusecond
|Nusecond
|2.3.5.7.11
|154-155c
|
|
|onyx, pine
|31, 70
|31, 70
|onyx, pine
|Generator is a neutral second, but places primes at high complexity, preferring ratios between them.
|Generator is a neutral second, but places primes at high complexity, preferring ratios between them.
|126/125, 2430/2401
|126/125, 2430/2401
|Medium
|2.3.5.7.11
|154-155c
|4 Medium
|}
|}


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{| class="wikitable sortable" style="font-size:0.8em"
{| class="wikitable sortable" style="font-size:0.8em"
|-
|-
! Form !! Family !! Name !! Subgroup
! Form !! Family !! Name  
![[Ploidacot]]!! ETs
!Generator
!Usual Scale Type!! Description !! Commas  
![[Ploidacot]]
!
!Usual Scale Type!! ETs !! Description !! Commas !! Subgroup
!Generator size
!Error
|-
|-
| rowspan="4" |7
| rowspan="4" |7
| rowspan="4" | Mabilic || Mabilic || 2.5.7
| rowspan="4" | Mabilic || Mabilic  
|alpha-triseph<sup>[a]</sup>|| 7, 9
|antidiatonic, armotonic, 9L 7s|| Basic antidiatonic temperament with no 3. || mabilisma
|Medium
|668-680c
|668-680c
|alpha-triseph<sup>[a]</sup>
|antidiatonic, armotonic, 9L 7s|| 7, 9 || Basic antidiatonic temperament with no 3. || mabilisma|| 2.5.7
|4 Medium
|-
|-
| Trismegistus || 2.3.5.7
| Trismegistus  
|alpha-triseph|| 16, 25
|antidiatonic, armotonic, 9L 7s|| High-accuracy but high complexity extension of prime 3. || gamelisma, magisma
|Medium
|672-675c
|672-675c
|alpha-triseph
|antidiatonic, armotonic, 9L 7s|| 16, 25 || High-accuracy but high complexity extension of prime 3. || gamelisma, magisma || 2.3.5.7
|4 Medium
|-
|-
| Semabila || 2.3.5.7
| Semabila  
|alpha-triseph|| 9, 25
|antidiatonic, armotonic, 9L 7s|| Combination of Mabilic and Semaphore.
|49/48, 28672/28125
|Low
|668-672c
|668-672c
|alpha-triseph
|antidiatonic, armotonic, 9L 7s|| 9, 25 || Combination of Mabilic and Semaphore.
|49/48, 28672/28125|| 2.3.5.7
|6 Low
|-
|-
| Mavila || 2.3.5.7
| Mavila  
|monocot|| 7, 9
|antidiatonic, armotonic, 7L 9s|| Exotemperament serving as an antidiatonic analog of meantone.
|36/35, 135/128
|Very low
|675-680c
|675-680c
|monocot
|antidiatonic, armotonic, 7L 9s|| 7, 9 || Exotemperament serving as an antidiatonic analog of meantone.
|36/35, 135/128|| 2.3.5.7
|7 Very low
|-
|-
|11
| rowspan="2" |11
|Orgonismic
| rowspan="2" |Orgonismic
|Orgone, Orgonic
|Orgone, Orgonic
|2.7.11
|320-325c
|trimech<sup>[b]</sup>
|trimech<sup>[b]</sup>
|4L7s
|15, 26
|15, 26
|4L7s
|A high-accuracy rank-2 temperament generated by a tempered 77/64.
|A high-accuracy rank-2 temperament generated by a tempered 77/64.
|65536/65219
|65536/65219
|Medium-high
|2.7.11
|3 Medium-high
|-
|Superkleismic
|320-325c
|320-325c
|trimech
|4L7s
|15, 26
|The main (albeit less accurate) extension of orgone to the full 11-limit.
|100/99, 245/242, 385/384
|2...11
|4 Medium
|-
|-
|6
|6
|Hemimean
|Hemimean
|Didacus
|Didacus
|2.5.7
|192-196c
|diseph
|diseph
|1L 5s, 6L 1s
|6, 25
|6, 25
|1L 5s, 6L 1s
|Every other step of septimal meantone.
|Every other step of septimal meantone.
|3136/3125
|3136/3125
|High
|2.5.7
|192-196c
|2 High
|}
|}


Line 565: Line 575:
|+ Rank-2 Temperaments
|+ Rank-2 Temperaments
|-
|-
! Form !! Family !! Name !! Subgroup
! Form !! Family !! Name  
![[Ploidacot]]!! ETs
!Generator
!Usual Scale Type!! Description !! Commas  
![[Ploidacot]]
!Usual Scale Type!! ETs !! Description !! Commas !! Subgroup
!Accuracy
!Accuracy
!Generator size
|-
|-
|b13
|b13
| rowspan="2" |Sensamagic
| rowspan="2" |Sensamagic
|Sensamagic
|Sensamagic
|3.5.7
|435-440c
|monogem<sup>[c]</sup>
|monogem<sup>[c]</sup>
|lambda
|b4, b9<sup>[d]</sup>
|b4, b9<sup>[d]</sup>
|lambda
|Basic tritave temperament that stacks 9/7 twice to reach 5/3. Generates the lambda (4L5s{{angbr|3/1}}) MOS scale, or can be used with octaves as Sensamagic.2.
|Basic tritave temperament that stacks 9/7 twice to reach 5/3. Generates the lambda (4L5s{{angbr|3/1}}) MOS scale, or can be used with octaves as Sensamagic.2.
|245/243
|245/243
|Medium-high
|3.5.7
|435-440c
|3 Medium-high
|-
|-
|8
|8
|Sensi
|Sensi
|2.3.5.7.13
|440-445c
|beta-heptacot
|beta-heptacot
|3L 2s, checkertonic
|19, 27
|19, 27
|3L 2s, checkertonic
|Very sharp extension of Sensamagic, which finds the octave at 125/63.
|Very sharp extension of Sensamagic, which finds the octave at 125/63.
|91/90, 126/125, 169/168
|91/90, 126/125, 169/168
|Medium
|2.3.5.7.13
|440-445c
|4 Medium
|}
|}
[a] seph = divisions of 5/4
[a] seph = divisions of 5/4

Latest revision as of 00:38, 2 April 2026

Main article: Regular temperament

Rank-2

2.3.5.x families

Rank-2 Temperaments
Form Family Name Generator Ploidacot Usual Scale Type ETs Description Subgroup Commas Accuracy (Vector)
7 Syntonic Meantone 692-697c monocot softer diatonic, m-chromatic 7, 12 Common historical temperament for 5-limit diatonic harmony. 2.3.5 81/80 4 Medium
Septimal Meantone 695-697c monocot softer diatonic, m-chromatic 19, 31 Canonical extension of the above to 2...7. 2.3.5.7 81/80, 225/224 4 Medium
Flattone 692-694c monocot softer diatonic, m-chromatic 19, 26 Less accurate extension, more melodic intuition, easily extends to higher limits. 7-form version of Meantone. 2.3.5.7 525/512, 81/80 6 Low
12 Injera 92-96c diploid monocot thalassic 12, 26 Adds a 600c tritone representing 7/5 to meantone. 2.3.5.7 81/80, 50/49 5 Medium-low
7 Porcupine Porcupine 161-166c omega-tricot onyx, pine 15, 22 Moderate-accuracy 2.3.5.11 temperament with a ~160c generator and a heptatonic MOS. 2.3.5.11 250/243, 100/99 5 Medium-low
Septimal Porcupine 161-163c omega-tricot onyx, pine 15, 22 Extension of the above to the full 11-limit. 2.3.5.7.11 250/243, 100/99, 64/63 5 Medium-low
Interclassical Interclassical, Dicot 670-680c, 720-730c dicot mosh, dicoid 7, 10 5-limit exotemperament equating 5/4 and 6/5 to the same interval. 2.3.5 25/24 7 Very low
Tetracot Tetracot 175-180c tetracot archeotonic, 7L6s 34, 41 Interprets (3/2)^(1/4) as 10/9. 2.3.5.11 100/99, 243/242 2 High (2.3.5), Medium (extensions)
12 Diminished Diminished 685-700c tetraploid monocot tetrawood, 4L 8s 12, 16 Sets 6/5 to 300 cents; a step up from 600 cents is 3/2. 2.3.5 648/625 5 Medium-low
Dimisept 685-700c tetraploid monocot tetrawood, 4L 8s 12, 16 Exotempered extension of the above that sets 7/6 to 300 cents. 2.3.5.7 36/35, 50/49 7 Very low
Augmented Augmented 705-715c triploid monocot triwood, tcherepnin 12, 15 Sets 5/4 to 400 cents, a step down from 800c is 3/2 and 2 steps up is 7/4. 2.3.5.7 128/125 6 Low
Schismic Schismic 701-702c monocot harder diatonic, p-chromatic 41, 53 5-limit interpretation of Pythagorean tuning, best tuned when the fifth is flattened by a fraction of a cent. 2.3.5 schisma 1 Very high
Garibaldi 702-703c monocot harder diatonic, p-chromatic 41, 53 7-limit interpretation of Pythagorean tuning. It is most accurate when the fifth is tuned slightly sharp. 2.3.5.7 schisma, 225/224 3 Medium-high
Misty Misty 701-708c triploid monocot 12, 51 5/4 is 4 times the difference between 3/2 and 800c. 2.3.5 misty comma 3 Medium-high
Diaschismic Diaschismic 100-111c diploid monocot jaric, 10L 2s 12, 34 Temperament characterized by a perfect semioctave and a sharpened fifth or semitone generator. Two generators down reaches 5/4. 2.3.5.17 diaschisma, 136/135 4 Medium
Septimal Diaschismic 103-104c diploid monocot jaric, 10L 2s 12, 34 Rather complex 7-limit extension of the above. 2.3.5.7.17 diaschisma, 126/125, 136/135 4 Medium
10 Pajara 109-111c diploid monocot jaric, 10L 2s 12, 22 Jubilic archytas diaschismic temperament. Contains jubilic chord structure and is strongly associated with 22edo. 2.3.5.7.17 diaschisma, 50/49, 136/135 5 Medium-low
3 Magic Magic 378-382c alpha-pentacot mosh, sephiroid 19, 22 Stacks five flattened major thirds to form a perfect twelfth. 5/4-generated analog of Meantone. 2.3.5 magisma 4 Medium
Wurschmidt Wurschmidt 386-389c beta-octacot - 31, 34 Eight 5/4s stack to 3/2 and three 25/24s stack to two 16/15s. 5/4-generated analog of Schismic. Bad for MOSes. 2.3.5.11.23 576/575, 12167/12150 3 Medium-high
8 Father Father 720-800c monocot antipentic 3, 5 Extremely inaccurate exotemperament which equates 5/4 with 4/3. 2.3.5 16/15 8 Extremely low
4 Kleismic Kleismic, Cata 317c alpha-hexacot smitonic, 4L7s, 4L11s 19, 34 A highly accurate temperament equating a stack of six slightly sharp 6/5's to one 3/1 and three 6/5's to one 26/15. 2.3.5.13 kleisma, 325/324 2 High
10 Negri Negri 124-128c omega-tetracot 10, 19 Generator is a sharp minor second of 16/15 which stacks 3 times to 5/4, and can be seen as a counterpart of Porcupine. 2.3.5 16875/16384 5 Medium-low
Semibuzzard 124-128c taric 10, 28 Weak Jubilismic or Buzzard extension of Negri allowing intervals of 7 to be reached with a 600-cent offset. 2.3.5.7.11 16875/16384, 50/49, 243/242 6 Low
Negrisept 124-128c 10, 19 Semaphore extension of negri. 2.3.5.7 16875/16384, 49/48 7 Very low

2.3.7.x families

Form Family Name Generator Ploidacot Usual Scale Type ETs Description Subgroup Commas Accuracy
5 Archy Archy 709-720c monocot soft pentic, harder diatonic, p-chromatic 5, 22 2.3.7 counterpart of Meantone, which sharpens the fifth. 2.3.7 64/63 5 Medium-low
Superpyth 709-711c monocot soft pentic, harder diatonic, p-chromatic 22, 27 Extension of the above to 2...7, favoring flatter tunings. 2.3.5.7 64/63, 245/243 5 Medium-low
Gamelic Slendric, Wonder 231-234c tricot 1L 4s, machinoid, 5L 6s 5, 31 Splits the fifth in 3 parts, each of which is 8/7. Little relation to actual Slendro tuning. 2.3.7 gamelisma 3 Medium-high
Mothra 231c tricot 1L 4s, machinoid, 5L 6s 26, 31 Meantone extension of the above. 2.3.5.7 81/80, gamelisma 4 Medium
Rodan 234c tricot 1L 4s, machinoid, 5L 6s 41, 46 More accurate extension of the above. 2.3.5.7 245/243, gamelisma 4 Medium
Miracle 117c hexacot antisinatonic, 10L 1s 31, 41 Generated by a 15/14~16/15 semitone, two of which reach a slendric 8/7. 2.3.5.7.11 225/224, 243/242, gamelisma 3 Medium-high
Valentine 78c enneacot 15L 1s, Carlos Alpha 15, 16 Scale with small steps strongly associated with Carlos Alpha. 2.3.5.7 126/125, gamelisma 3 Medium-high
Buzzard Buzzard 474-478c alpha-tetracot 53, 58 Sharpens the 21/16 so that four of them stacks to the 3/1. 2.3.5.7.13 buzzardsma 4 Medium
Interseptimal Interseptimal, Semaphore 240-250c alpha-dicot 4L 1s, semiquartal 5, 19 Equipentatonic, inaccurate 7-limit temperament. 2.3.7 49/48 6 Low
13 Squares Squares 424-426c beta-tetracot 3L 5s, 3L 8s, 3L 11s 14, 17 No-fives temperament generated by a flattened 9/7 equated with 14/11. 2.3.7.11 99/98, 243/242 4 Medium

2.3.x families

Form Family Name Generator Ploidacot Usual Scale Type ETs Description Subgroup Commas Accuracy
7 Rastmatic Rastmatic 345-355c dicot mosh, dicoid 7, 10 Maps 11/9 and its fifth complement to a perfect neutral third. 2.3.11 243/242 3 Medium-high
Mohajira 347-350c dicot mosh, dicoid 24, 31 Meantone extension of the above. Can optionally be extended to set 7/4 equal to the semiflat minor seventh, or via a strong meantone extension. 2.3.5.11 243/242, 81/80 5 Medium-low
Intratridecimal Intratridecimal 350-360c dicot mosh, dicoid 27, 10 Maps 16/13 and its fifth complement to a perfect neutral third. 2.3.13 512/507 4 Medium
(To be named) 355-360c dicot mosh, dicoid 27, 10 Archy extension of the above. 2.3.7.13 512/507, 64/63 5 Medium-low

2.3.5.7.x families

Form Family Name Generator Ploidacot Usual Scale Type ETs Description Commas Subgroup Accuracy
7 Amity Amity 338-340c gamma-pentacot 7L 18s, 7L 25s 46, 53 Sets the spacing of the thirds to 7/6-#-6/5-#-#-5/4-#-9/7; mostly appears as a structural element of EDOs rather than an independent structure. 4375/4374, 5120/5103 2.3.5.7 2 High
12 Compton Compton 385c dodecaploid acot dodecawood 12, 60 Acts as a closed circle of 12 fifths (see 12edo), but with 5/4 flattened by a diesis from 400c, and 7/4 flattened by twice that amount from 1000c. pythagorean comma 2.3.5.7 3 Medium-high
4 Doublewide Doublewide 325c 22, 48 Sets 6/5 and 7/6 the same distance from the 300c period, so that four ~25c generators stack to the semitone separating 3/2 from 600c. 50/49, 875/864 2.3.5.7 5 Medium-low
Myna Myna 309-311c beta-decacot - 27, 31 Sets 25/24 equal to twice 36/35. 126/125, 1728/1715 2.3.5.7 3 Medium-high
9 Orwell Orwell 270-273c alpha-heptacot gramitonic 22, 31 Generator is a sharpened 7/6. Interval chain finds 7/6, 11/8, 8/5, 15/8, 11/10, 9/7, 3/2. 99/98, 121/120, 176/175 2.3.5.7.11 3 Medium-high
Ennealimmal Ennealimmal 44-53c enneaploid dicot enneawood 27, 45 Divides the octave into nine equal parts representing 27/25 and half of 7/6. 2401/2400, 4375/4374 2.3.5.7 1 Very high
8 Nusecond Nusecond 154-155c onyx, pine 31, 70 Generator is a neutral second, but places primes at high complexity, preferring ratios between them. 126/125, 2430/2401 2.3.5.7.11 4 Medium

No-threes families

Form Family Name Generator Ploidacot Usual Scale Type ETs Description Commas Subgroup Error
7 Mabilic Mabilic 668-680c alpha-triseph[a] antidiatonic, armotonic, 9L 7s 7, 9 Basic antidiatonic temperament with no 3. mabilisma 2.5.7 4 Medium
Trismegistus 672-675c alpha-triseph antidiatonic, armotonic, 9L 7s 16, 25 High-accuracy but high complexity extension of prime 3. gamelisma, magisma 2.3.5.7 4 Medium
Semabila 668-672c alpha-triseph antidiatonic, armotonic, 9L 7s 9, 25 Combination of Mabilic and Semaphore. 49/48, 28672/28125 2.3.5.7 6 Low
Mavila 675-680c monocot antidiatonic, armotonic, 7L 9s 7, 9 Exotemperament serving as an antidiatonic analog of meantone. 36/35, 135/128 2.3.5.7 7 Very low
11 Orgonismic Orgone, Orgonic 320-325c trimech[b] 4L7s 15, 26 A high-accuracy rank-2 temperament generated by a tempered 77/64. 65536/65219 2.7.11 3 Medium-high
Superkleismic 320-325c trimech 4L7s 15, 26 The main (albeit less accurate) extension of orgone to the full 11-limit. 100/99, 245/242, 385/384 2...11 4 Medium
6 Hemimean Didacus 192-196c diseph 1L 5s, 6L 1s 6, 25 Every other step of septimal meantone. 3136/3125 2.5.7 2 High

Non-octave families

Rank-2 Temperaments
Form Family Name Generator Ploidacot Usual Scale Type ETs Description Commas Subgroup Accuracy
b13 Sensamagic Sensamagic 435-440c monogem[c] lambda b4, b9[d] 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 3.5.7 3 Medium-high
8 Sensi 440-445c beta-heptacot 3L 2s, checkertonic 19, 27 Very sharp extension of Sensamagic, which finds the octave at 125/63. 91/90, 126/125, 169/168 2.3.5.7.13 4 Medium

[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.

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 / Aberschismic 5120/5103 2.3.5.7 41, 46, 53 81/80 and 64/63 are equated. Sometimes used in aberrismic theory to interpret ternary scales as 2.3.5.7, and associated with argent tuning. ~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

See also

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