List of regular temperaments: Difference between revisions

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{| class="wikitable sortable"
:''Main article: [[Regular temperament]]''
 
== Rank-2 ==
 
=== 2.3.5.x families ===
{| class="wikitable sortable" style="font-size:0.8em"
|+ Rank-2 Temperaments
|+ Rank-2 Temperaments
|-
|-
! Family !! Name !! Subgroup !! Commas !! Ploidacot !! Usual Scale Type !! Badness (Cangwu) !! Generator size (CWE)
! Form !! Family !! Name !! Subgroup  
![[Ploidacot]]!! ETs
!Usual Scale Type!! Description !! Commas
!Accuracy (Vector)
!Generator size
|-
|-
|rowspan="2"| Syntonic || Meantone || 2.3.5 || 81/80 || monocot || softer diatonic, m-chromatic || .778 || 497c
| rowspan="3" | 7 || rowspan="4" | Syntonic || Meantone || 2.3.5  
|monocot|| 7, 12
|softer diatonic, m-chromatic|| Common historical temperament for 5-limit diatonic harmony. || 81/80
|Medium
|692-697c
|-
|-
| 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|| Canonical extension of the above to 2...7. || 81/80, 225/224
|Medium
|695-697c
|-
|-
|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
|Low
|692-694c
|-
|-
| Superpyth || 2.3.5.7 || 64/63, 245/243 || monocot || harder diatonic, p-chromatic || 1.298 || 490c
|12
|Injera
|2.3.5.7
|diploid monocot
|12, 26
|thalassic
|Adds a 600c tritone representing 7/5 to meantone.
|81/80, 50/49
|Medium-low
|92-96c
|-
|-
|rowspan="4"| Mabilic || Mabilic || 2.5.7 || || alpha-triseph || antidiatonic, armotonic, 9L 7s
| rowspan="4" |7
| 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
|Medium-low
|161-166c
|-
|-
| Trismegistus || 2.3.5.7 || || alpha-triseph || antidiatonic, armotonic, 9L 7s
| 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
|Medium-low
|161-163c
|-
|-
| Semabila || 2.3.5.7 || || alpha-triseph || antidiatonic, armotonic, 9L 7s
| 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
|Very low
|670-680c, 720-730c
|-
|-
| Mavila || 2.3.5.7 || || monocot || antidiatonic, armotonic, 7L 9s
| 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
|High (2.3.5), Medium (extensions)
|175-180c
|-
|-
|rowspan="2"| Porcupine || Porcupine || 2.3.5.11 || || omega-tricot || onyx, pine
| rowspan="8" |12
| rowspan="2" |Diminished
|Diminished
|2.3.5
|tetraploid monocot
|12, 16
|tetrawood, 4L 8s
|Sets 6/5 to 300 cents; a step up from 600 cents is 3/2.
|648/625
|Medium-low
|685-700c
|-
|-
| Septimal porcupine || 2.3.5.7.11 || || omega-tricot || onyx, pine
|Dimisept
|2.3.5.7
|tetraploid monocot
|12, 16
|tetrawood, 4L 8s
|Exotempered extension of the above that sets 7/6 to 300 cents.
|36/35, 50/49
|Very low
|685-700c
|-
|-
|rowspan="4"| Gamelic || Slendric, Wonder || 2.3.7 || || tricot || 1L 4s, machinoid, 5L 6s
|Augmented
|Augmented
|2.3.5.7
|triploid monocot
|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.
|128/125
|Low
|705-715c
|-
|-
| Mothra || 2.3.5.7.11 || || tricot || 1L 4s, machinoid, 5L 6s
| 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
|Very high
|701-702c
|-
|-
| Rodan || 2.3.5.7.11 || || tricot || 1L 4s, machinoid, 5L 6s
|Garibaldi
|2.3.5.7
|monocot
|41, 53
|harder diatonic, p-chromatic
|7-limit interpretation of Pythagorean tuning. It is most accurate when the fifth is tuned slightly sharp.
|schisma, 225/224
|Medium-high
|702-703c
|-
|-
| Valentine || 2.3.5.7 || || enneacot || 15L 1s, [[Carlos Alpha]]
|Misty
|Misty
|2.3.5
|triploid monocot
|12, 51
|
|5/4 is 4 times the difference between 3/2 and 800c.
|misty comma
|Medium-high
|701-708c
|-
| rowspan="3" |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, 136/135
|Medium
|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, 136/135
|Medium
|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, 136/135
|Medium-low
|109-111c
|-
| rowspan="2" |3
|Magic
|Magic
|2.3.5
|alpha-pentacot
|19, 22
|mosh, sephiroid
|Stacks five flattened major thirds to form a perfect twelfth. 5/4-generated analog of Meantone.
|magisma
|Medium
|378-382c
|-
|Wurschmidt
|Wurschmidt
|2.3.5.11.23
|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.
|576/575, 12167/12150
|Medium-high
|386-389c
|-
|8
|Father
|Father
|2.3.5
|monocot
|3, 5
|antipentic
|Extremely inaccurate exotemperament which equates 5/4 with 4/3.
|16/15
|Extremely low
|720-800c
|-
|4
|Kleismic
|Kleismic, Cata
|2.3.5.13
|alpha-hexacot
|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.
|kleisma, 325/324
|High
|317c
|-
| rowspan="3" |10
| rowspan="3" |Negri
|Negri
|2.3.5
|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.
|16875/16384
|Medium-low
|124-128c
|-
|Semibuzzard
|2.3.5.7.11
|
|10, 28
|taric
|Weak Jubilismic or Buzzard extension of Negri allowing intervals of 7 to be reached with a 600-cent offset.
|16875/16384, 50/49, 243/242
|Low
|124-128c
|-
|Negrisept
|2.3.5.7
|
|10, 19
|
|Semaphore extension of negri.
|16875/16384, 49/48
|Very low
|124-128c
|}
 
=== 2.3.7.x families ===
{| class="wikitable sortable" style="font-size:0.8em"
|-
! Form !! Family !! Name !! Subgroup
![[Ploidacot]]!! ETs
!Usual Scale Type!! Description !! Commas
!Accuracy
!Generator size
|-
| 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
|Medium-low
|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
|Medium-low
|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 [[Equipentatonic#Slendro|Slendro tuning]].
|gamelisma
|Medium-high
|231-234c
|-
|Mothra
|2.3.5.7
|tricot
|26, 31
|1L 4s, machinoid, 5L 6s
|Meantone extension of the above.
|81/80, gamelisma
|Medium
|231c
|-
|Rodan
|2.3.5.7
|tricot
|41, 46
|1L 4s, machinoid, 5L 6s
|More accurate extension of the above.
|245/243, gamelisma
|Medium
|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
|Medium-high
|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
|Medium-high
|78c
|-
|Buzzard
|Buzzard
|2.3.5.7.13
|alpha-tetracot
|53, 58
|
|Sharpens the 21/16 so that four of them stacks to the 3/1.
|buzzardsma
|Medium
|474-478c
|-
|Interseptimal
|Interseptimal, Semaphore
|2.3.7
|alpha-dicot
|5, 19
|4L 1s, semiquartal
|Equipentatonic, inaccurate 7-limit temperament.
|49/48
|Low
|240-250c
|-
|13
|Squares
|Squares
|2.3.7.11
|beta-tetracot
|14, 17
|3L 5s, 3L 8s, 3L 11s
|No-fives temperament generated by a flattened 9/7 equated with 14/11.
|99/98, 243/242
|Medium
|424-426c
|}
 
=== 2.3.x families ===
{| class="wikitable sortable" style="font-size:0.8em"
|-
! Form !! Family !! Name !! Subgroup
![[Ploidacot]]!! ETs
!Usual Scale Type!! Description !! Commas
!Accuracy
!Generator size
|-
| rowspan="4" |7
| 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
|Medium-high
|345-355c
|-
| Mohajira || 2.3.5.11
|dicot|| 24, 31
|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.
|243/242, 81/80
|Medium-low
|347-350c
|-
| rowspan="2" |Intratridecimal
|Intratridecimal
|2.3.13
|dicot
|27, 10
|mosh, dicoid
|Maps 16/13 and its fifth complement to a perfect neutral third.
|512/507
|Medium
|350-360c
|-
|(To be named)
|2.3.7.13
|dicot
|27, 10
|mosh, dicoid
|Archy extension of the above.
|512/507, 64/63
|Medium-low
|355-360c
|}
 
=== 2.3.5.7.x families ===
{| class="wikitable sortable" style="font-size:0.8em"
|-
! Form !! Family !! Name !! Subgroup
![[Ploidacot]]!! ETs
!Usual Scale Type!! Description !! Commas
!Accuracy
!Generator size
|-
|7
|Amity
|Amity
|2.3.5.7
|gamma-pentacot
|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.
|4375/4374, 5120/5103
|High
|338-340c
|-
|12
|Compton
|Compton
|2.3.5.7
|dodecaploid acot
|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.
|pythagorean comma
|Medium-high
|385c
|-
| rowspan="2" |4
|Doublewide
|Doublewide
|2.3.5.7
|
|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
|Medium-low
|325c
|-
|Myna
|Myna
|2.3.5.7
|beta-decacot
|27, 31
| -
|Sets 25/24 equal to twice 36/35.
|126/125, 1728/1715
|Medium-high
|309-311c
|-
| rowspan="2" |9
|Orwell
|Orwell
|2.3.5.7.11
|alpha-heptacot
|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.
|99/98, 121/120, 176/175
|Medium-high
|270-273c
|-
|Ennealimmal
|Ennealimmal
|2.3.5.7
|enneaploid dicot
|27, 45
|enneawood
|Divides the octave into nine equal parts representing 27/25 and half of 7/6.
|2401/2400, 4375/4374
|Very high
|44-53c
|-
|8
|Nusecond
|Nusecond
|2.3.5.7.11
|
|31, 70
|onyx, pine
|Generator is a neutral second, but places primes at high complexity, preferring ratios between them.
|126/125, 2430/2401
|Medium
|154-155c
|}
 
=== No-threes families ===
{| class="wikitable sortable" style="font-size:0.8em"
|-
! Form !! Family !! Name !! Subgroup
![[Ploidacot]]!! ETs
!Usual Scale Type!! Description !! Commas
!
!Generator size
|-
| rowspan="4" |7
| 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
|Medium
|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
|Medium
|672-675c
|-
| Semabila || 2.3.5.7
|alpha-triseph|| 9, 25
|antidiatonic, armotonic, 9L 7s|| Combination of Mabilic and Semaphore.
|49/48, 28672/28125
|Low
|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
|Very low
|675-680c
|-
|11
|Orgonismic
|Orgone, Orgonic
|2.7.11
|trimech<sup>[b]</sup>
|15, 26
|4L7s
|A high-accuracy rank-2 temperament generated by a tempered 77/64.
|65536/65219
|Medium-high
|320-325c
|-
|6
|Hemimean
|Didacus
|2.5.7
|diseph
|6, 25
|1L 5s, 6L 1s
|Every other step of septimal meantone.
|3136/3125
|High
|192-196c
|}
 
=== Non-octave families ===
{| class="wikitable sortable" style="font-size:0.8em"
|+ Rank-2 Temperaments
|-
! Form !! Family !! Name !! Subgroup
![[Ploidacot]]!! ETs
!Usual Scale Type!! Description !! Commas
!Accuracy
!Generator size
|-
|b13
| rowspan="2" |Sensamagic
|Sensamagic
|3.5.7
|monogem<sup>[c]</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.
|245/243
|Medium-high
|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
|Medium
|440-445c
|}
[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 ==
{| class="wikitable sortable" style="font-size:0.8em"
|-
! 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. || ~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 ==
* [https://en.xen.wiki/w/Survey_of_efficient_temperaments_by_subgroup Survey of efficient temperaments by subgroup (Xen Wiki)]

Latest revision as of 06:53, 7 February 2026

Main article: Regular temperament

Rank-2

2.3.5.x families

Rank-2 Temperaments
Form Family Name Subgroup Ploidacot ETs Usual Scale Type Description Commas Accuracy (Vector) 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 Medium 692-697c
Septimal Meantone 2.3.5.7 monocot 19, 31 softer diatonic, m-chromatic Canonical extension of the above to 2...7. 81/80, 225/224 Medium 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 Low 692-694c
12 Injera 2.3.5.7 diploid monocot 12, 26 thalassic Adds a 600c tritone representing 7/5 to meantone. 81/80, 50/49 Medium-low 92-96c
7 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 Medium-low 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 Medium-low 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 Very low 670-680c, 720-730c
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 High (2.3.5), Medium (extensions) 175-180c
12 Diminished Diminished 2.3.5 tetraploid monocot 12, 16 tetrawood, 4L 8s Sets 6/5 to 300 cents; a step up from 600 cents is 3/2. 648/625 Medium-low 685-700c
Dimisept 2.3.5.7 tetraploid monocot 12, 16 tetrawood, 4L 8s Exotempered extension of the above that sets 7/6 to 300 cents. 36/35, 50/49 Very low 685-700c
Augmented Augmented 2.3.5.7 triploid monocot 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. 128/125 Low 705-715c
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 Very high 701-702c
Garibaldi 2.3.5.7 monocot 41, 53 harder diatonic, p-chromatic 7-limit interpretation of Pythagorean tuning. It is most accurate when the fifth is tuned slightly sharp. schisma, 225/224 Medium-high 702-703c
Misty Misty 2.3.5 triploid monocot 12, 51 5/4 is 4 times the difference between 3/2 and 800c. misty comma Medium-high 701-708c
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, 136/135 Medium 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, 136/135 Medium 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, 136/135 Medium-low 109-111c
3 Magic Magic 2.3.5 alpha-pentacot 19, 22 mosh, sephiroid Stacks five flattened major thirds to form a perfect twelfth. 5/4-generated analog of Meantone. magisma Medium 378-382c
Wurschmidt Wurschmidt 2.3.5.11.23 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. 576/575, 12167/12150 Medium-high 386-389c
8 Father Father 2.3.5 monocot 3, 5 antipentic Extremely inaccurate exotemperament which equates 5/4 with 4/3. 16/15 Extremely low 720-800c
4 Kleismic Kleismic, Cata 2.3.5.13 alpha-hexacot 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. kleisma, 325/324 High 317c
10 Negri Negri 2.3.5 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. 16875/16384 Medium-low 124-128c
Semibuzzard 2.3.5.7.11 10, 28 taric Weak Jubilismic or Buzzard extension of Negri allowing intervals of 7 to be reached with a 600-cent offset. 16875/16384, 50/49, 243/242 Low 124-128c
Negrisept 2.3.5.7 10, 19 Semaphore extension of negri. 16875/16384, 49/48 Very low 124-128c

2.3.7.x families

Form Family Name Subgroup Ploidacot ETs Usual Scale Type Description Commas Accuracy Generator size
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 Medium-low 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 Medium-low 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. gamelisma Medium-high 231-234c
Mothra 2.3.5.7 tricot 26, 31 1L 4s, machinoid, 5L 6s Meantone extension of the above. 81/80, gamelisma Medium 231c
Rodan 2.3.5.7 tricot 41, 46 1L 4s, machinoid, 5L 6s More accurate extension of the above. 245/243, gamelisma Medium 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 Medium-high 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 Medium-high 78c
Buzzard Buzzard 2.3.5.7.13 alpha-tetracot 53, 58 Sharpens the 21/16 so that four of them stacks to the 3/1. buzzardsma Medium 474-478c
Interseptimal Interseptimal, Semaphore 2.3.7 alpha-dicot 5, 19 4L 1s, semiquartal Equipentatonic, inaccurate 7-limit temperament. 49/48 Low 240-250c
13 Squares Squares 2.3.7.11 beta-tetracot 14, 17 3L 5s, 3L 8s, 3L 11s No-fives temperament generated by a flattened 9/7 equated with 14/11. 99/98, 243/242 Medium 424-426c

2.3.x families

Form Family Name Subgroup Ploidacot ETs Usual Scale Type Description Commas Accuracy Generator size
7 Rastmic Rastmic 2.3.11 dicot 7, 10 mosh, dicoid Maps 11/9 and its fifth complement to a perfect neutral third. 243/242 Medium-high 345-355c
Mohajira 2.3.5.11 dicot 24, 31 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. 243/242, 81/80 Medium-low 347-350c
Intratridecimal Intratridecimal 2.3.13 dicot 27, 10 mosh, dicoid Maps 16/13 and its fifth complement to a perfect neutral third. 512/507 Medium 350-360c
(To be named) 2.3.7.13 dicot 27, 10 mosh, dicoid Archy extension of the above. 512/507, 64/63 Medium-low 355-360c

2.3.5.7.x families

Form Family Name Subgroup Ploidacot ETs Usual Scale Type Description Commas Accuracy Generator size
7 Amity Amity 2.3.5.7 gamma-pentacot 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. 4375/4374, 5120/5103 High 338-340c
12 Compton Compton 2.3.5.7 dodecaploid acot 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. pythagorean comma Medium-high 385c
4 Doublewide Doublewide 2.3.5.7 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 Medium-low 325c
Myna Myna 2.3.5.7 beta-decacot 27, 31 - Sets 25/24 equal to twice 36/35. 126/125, 1728/1715 Medium-high 309-311c
9 Orwell Orwell 2.3.5.7.11 alpha-heptacot 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. 99/98, 121/120, 176/175 Medium-high 270-273c
Ennealimmal Ennealimmal 2.3.5.7 enneaploid dicot 27, 45 enneawood Divides the octave into nine equal parts representing 27/25 and half of 7/6. 2401/2400, 4375/4374 Very high 44-53c
8 Nusecond Nusecond 2.3.5.7.11 31, 70 onyx, pine Generator is a neutral second, but places primes at high complexity, preferring ratios between them. 126/125, 2430/2401 Medium 154-155c

No-threes families

Form Family Name Subgroup Ploidacot ETs Usual Scale Type Description Commas Generator size
7 Mabilic Mabilic 2.5.7 alpha-triseph[a] 7, 9 antidiatonic, armotonic, 9L 7s Basic antidiatonic temperament with no 3. mabilisma Medium 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 Medium 672-675c
Semabila 2.3.5.7 alpha-triseph 9, 25 antidiatonic, armotonic, 9L 7s Combination of Mabilic and Semaphore. 49/48, 28672/28125 Low 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 Very low 675-680c
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 Medium-high 320-325c
6 Hemimean Didacus 2.5.7 diseph 6, 25 1L 5s, 6L 1s Every other step of septimal meantone. 3136/3125 High 192-196c

Non-octave families

Rank-2 Temperaments
Form Family Name Subgroup Ploidacot ETs Usual Scale Type Description Commas Accuracy Generator size
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 Medium-high 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 Medium 440-445c

[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. ~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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