List of commas

From Xenharmonic Reference
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This is a list of small intervals separating just intonation intervals in the 63-odd-limit.

5-limit

31-odd-limit (commas < 50c)

Name S-expression Simplest interval pair Ratio Cents Associated temperaments and other notes
syntonic comma S9 9/8 ~ 10/9 81/80 21.5c Meantone. Formal comma for 5-limit.
augmented diesis 25/24 ~ 16/15 128/125 41.1c Augmented (temperament)
porcupine comma 27/25 ~ 10/9 250/243 49.2c The 5-limit restriction of Porcupine

63-odd-limit (commas < 25c)

Name S-expression Simplest interval pair Ratio Cents Associated temperaments and other notes
diaschisma 45/32 ~ 64/45 2048/2025 19.6c Diaschismic

2.3.7

31-odd-limit (commas < 50c)

Name S-expression Simplest interval pair Ratio Cents Associated temperaments and other notes
archytas comma S8 9/8 ~ 8/7 64/63 27.3c Archy (Superpyth). Formal comma for 7-limit.
interseptimal comma S7 8/7 ~ 7/6 49/48 35.7c Semaphore

63-odd-limit (commas < 25c)

Name S-expression Simplest interval pair Ratio Cents Associated temperaments and other notes
gamelisma S7/S8 64/49 ~ 21/16 1029/1024 8.4c Slendric

7-limit

31-odd-limit (commas < 50c)

Name S-expression Simplest interval pair Ratio Cents Associated temperaments and other notes
marvel comma S15 16/15 ~ 15/14 225/224 7.7c Marvel, such as septimal meantone
avicennma 21/16 ~ 32/25 525/512 43.4c
starling comma 25/21 ~ 6/5 126/125 13.8c
jubilisma S5/S7 10/7 ~ 7/5 50/49 35c Shows up in temperaments like pajara and 26edo
mint comma S6 7/6 ~ 6/5 36/35 48.8c Shows up in dominant and dimisept. Idiosyncratic 7-limit formal comma used by

Ben Johnston notation.

63-odd-limit (commas < 25c)

Name S-expression Simplest interval pair Ratio Cents Associated temperaments and other notes
breedsma S49 50/49 ~ 49/48 2401/2400 0.7c
SS
stupid-sounding comma name tbh
orwellisma S6/S7 49/48 ~ 36/35 1728/1715 13.1c Shows up in orwell
sensamagic comma S7/S9 9/7 ~ 35/27 245/243 14.2c Important to tritave-based harmony.
keema 36/35 ~ 25/24 875/864 21.9c Evenly spaces the basic 7-limit thirds. Found in magic and porcupine.
nuwell comma 54/49 ~ 49/45 2430/2401 20.8c Found in orwell and nusecond.
octagar comma S19 * S20^2 63/50 ~ 80/63 4000/3969 13.5c

2.3.5.11

31-odd-limit (commas < 50c)

Name S-expression Simplest interval pair Ratio Cents Associated temperaments and other notes
cake comma S9*S10 11/9 ~ 5/4 45/44 38.9c Related to the main 11-limit formal comma (not included here) by the syntonic comma.
ptolemisma S10 11/10 ~ 10/9 100/99 17.4c Shows up in porcupine and flattone.
telepathma S10*S11 12/11 ~ 10/9 55/54 31.8c Shows up in pajara (with the 11-limit extension for the sharp tuning) and in porcupine.
SS
A432 music is detuned by this amount (but is not in and of itself xenharmonic). (Surprisingly, this is not related to the origin of the comma name.)
biyatisma S11 12/11 ~ 11/10 121/120 14.4c
rastma S9/S11 11/9 ~ 27/22 243/242 7.1c Shows up in 11-limit neutral temperaments.

11-limit

31-odd-limit (commas < 40c)

Name S-expression Simplest interval pair Ratio Cents Associated temperaments and other notes
werckisma S21 22/21 ~ 21/20 441/440 3.9c
mothwellsma 9/7 ~ 14/11 99/98 17.6c Involved in the flat pajara extension.
konbini comma S12 * S13 * S14 7/5 ~ 11/8 56/55 31.2c
valinorsma S8/S10 25/22 ~ 8/7 176/175 9.9c
pakkanen comma 28/25 ~ 25/22 625/616 25.1c

63-odd-limit (commas < 15c)

Name S-expression Simplest interval pair Ratio Cents Associated temperaments and other notes
keenanisma S33*S34*S35 12/11 ~ 35/32 385/384 4.5c
fwiwisma 45/44 ~ 64/63 2835/2816 11.6c
lehmerisma S22/S24, S55 56/55 ~ 55/54 3025/3024 0.6c
moctdelisma 55/49 ~ 28/25 1375/1372 3.8c
swetisma S12/S14 49/40 ~ 27/22 540/539 3.2c Equates the 7-limit and 11-limit neutral thirds
pentacircle comma 33/28 ~ 32/27 896/891 9.7c
unnamed 49/44 ~ 55/49 (2420/2401) 13.6c

2.3.7.13

31-odd-limit (commas < 50c)

Name S-expression Simplest interval pair Ratio Cents Associated temperaments and other notes
squbema S27 28/27 ~ 27/26 729/728 2.4c
buzurgisma S13 14/13 ~ 13/12 169/168 10.3c

63-odd-limit (commas < 25c)

Name S-expression Simplest interval pair Ratio Cents Associated temperaments and other notes
harmoneutral comma 16/13 ~ 39/32 512/507 17c Shows up in 13-limit neutral temperaments

13-limit

31-odd-limit (commas < 30c)

Name S-expression Simplest interval pair Ratio Cents Associated temperaments and other notes
animist comma S14*S15 8/7 ~ 15/13 105/104 16.6c
gassorma 13/11 ~ 25/21 275/273 12.6c
grossma S12 13/12 ~ 12/11 144/143 12.1c
mynucuma 15/14 ~ 14/13 196/195 8.9c
winmeanma S11*S12 13/12 ~ 12/10 66/65 26.4c
wilsorma S13*S14*S15 5/4 ~ 16/13 65/64 26.8c
biome comma S13*S14 9/7 ~ 13/10 91/90 19.1c Shows up in archy temperament.
unnamed 27/26 ~ 22/21 572/567 15.2c
negustma S12*S13 13/11 ~ 7/6 78/77 22.3c
major minthma 27/22 ~ 16/13 352/351 4.9c
ratwolfsma S26 * S27 14/13 ~ 27/25 351/350 4.9c
island comma S26 27/26 ~ 26/25 676/675 2.6c Equally divides 4/3 into two 15/13s.
marveltwin comma S25 * S26 13/12 ~ 27/25 325/324 5.3c
tunbarsma S25 26/25 ~ 25/24 625/624 2.7c
lummisma 49/44 ~ 39/35 1716/1715 1c

63-odd-limit (commas < 10c)

Name S-expression Simplest interval pair Ratio Cents Associated temperaments and other notes
huntma S15*S64 49/48 ~ 40/39 640/637 8.1c
minor minthma 13/11 ~ 33/28 364/363 4.8c Involved in some neogothic-related temperaments
unnamed 55/52 ~ 52/49 2704/2695 5.8c
pentacircle comma 33/28 ~ 32/27 896/891 9.7c
sinaisma S64*S65 63/52 ~ 40/33 2080/2079 0.8c
catadictma 40/33 ~ 39/32 1287/1280 9.4c
diagassormisma 78/55 ~ 55/39 3042/3025 9.7c
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