- 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
