Vector: Created page with "A '''formal comma''' is a comma used as an accidental in a just intonation notation system. Usually, there is a single formal comma for each prime, which is in the 2.3.p subgroup for prime p and contains one factor of p, and thus a formal comma serves as an assignment of a prime harmonic to a particular Pythagorean interval. The functional structure of a just intonation notation system essentially comes down to defining a set of formal commas. The 2.3 subgroup here may b..."

2026-03-08T01:19:29Z

Created page with "A '''formal comma''' is a comma used as an accidental in a just intonation notation system. Usually, there is a single formal comma for each prime, which is in the 2.3.p subgroup for prime p and contains one factor of p, and thus a formal comma serves as an assignment of a prime harmonic to a particular Pythagorean interval. The functional structure of a just intonation notation system essentially comes down to defining a set of formal commas. The 2.3 subgroup here may b..."

New page

A '''formal comma''' is a comma used as an accidental in a just intonation notation system. Usually, there is a single formal comma for each prime, which is in the 2.3.p subgroup for prime p and contains one factor of p, and thus a formal comma serves as an assignment of a prime harmonic to a particular Pythagorean interval. The functional structure of a just intonation notation system essentially comes down to defining a set of formal commas. The 2.3 subgroup here may be replaced with 2.sqrt(3) as in [[Notation#Just notation systems|Neutral FJS]].

A formal comma may be denoted either by its ratio, as with any just interval (e.g. 81/80) or in the 2.3.p or 2.sqrt(3).p case by assigning a reduced prime harmonic to a Pythagorean interval (e.g. 5/4 = M3).
{| class="wikitable"
|+
! rowspan="2" |Prime
! colspan="2" |Functional Just System
! rowspan="2" |HEJI notation
! rowspan="2" |Color notation**
! colspan="2" |Sagittal notation
! rowspan="2" |Ben Johnston notation*
|-
!Neutral
!Pythagorean
!Prime factor
!Full** (prime intervals***)
|-
|5
| colspan="5" |81/80
|81/80, 32805/32768
|''81/80*''
|-
|7
| colspan="6" |64/63
|36/35
|-
|11
|sqrt(243/242)
| colspan="2" |33/32
|33/32, 729/704
|33/32
|33/32, 729/704
|33/32
|-
|13
|sqrt(512/507)
|1053/1024
|27/26
|27/26, 1053/1024
|27/26
|27/26, 1053/1024
|65/64
|-
|17
| colspan="2" |4131/4096
|2187/2176
| colspan="2" |4131/4096
|2187/2176, 4131/4096
|51/50
|-
|19
| colspan="6" |513/512
|96/95
|-
|23
| colspan="3" |736/729
|16767/16384
| colspan="2" |736/729
|46/45
|}
<nowiki>*</nowiki>Ben Johnston notation uses the 5-limit Zarlino scale for nominals, which means that 81/80 has a different role in the system than other formal commas. As a result, Ben Johnston formal commas are generally 2.3.5.p instead of 2.3.p.

<nowiki>**</nowiki> Color notation and sagittal notation have multiple formal commas for some primes.

<nowiki>***</nowiki> Sagittal notation has formal commas for some composite intervals, allowing intervals such as 14/11 to be notated as the diatonic intervals they are near melodically. More info available on the [[Sagittal notation]] page.

Formal comma - Revision history