Vector at 00:35, 8 October 2026

2026-10-08T00:35:13Z

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 |625/624
 |2.7c
+|
 |}
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 |3042/3025
 |9.7c
+|
 |}

Vector at 06:40, 6 October 2026

2026-10-06T06:40:19Z

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Vector: Created page with "This is a list of small intervals separating just intonation intervals in the 63-odd-limit. == 5-limit == === 31-odd-limit (commas < 50c) === {| class="wikitable" !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/..."

2026-10-01T03:24:40Z

Created page with "This is a list of small intervals separating just intonation intervals in the 63-odd-limit. == 5-limit == === 31-odd-limit (commas < 50c) === {| class="wikitable" !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/..."

New page

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

== 5-limit ==

=== 31-odd-limit (commas < 50c) ===
{| class="wikitable"
!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) ===
{| class="wikitable"
!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) ===
{| class="wikitable"
!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) ===
{| class="wikitable"
!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) ===
{| class="wikitable"
!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) ===
{| class="wikitable"
!Name
!S-expression
!Simplest interval pair
!Ratio
!Cents
!Associated temperaments and other notes
|-
|breedsma
|S49
|50/49 ~ 49/48
|2401/2400
|0.7c
|{{UserTag|SS|Vector|cebaff|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) ===
{| class="wikitable"
!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.{{UserTag|SS|Vector|cebaff|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) ===
{| class="wikitable"
!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) ===
{| class="wikitable"
!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) ===
{| class="wikitable"
!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
|17.6c
|
|}

=== 63-odd-limit (commas < 25c) ===
{| class="wikitable"
!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
|}

List of commas - Revision history

Vector at 00:35, 8 October 2026

Vector at 06:40, 6 October 2026