User:CompactStar/JI notation: Difference between revisions

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Pythagorean intervals use unmodified names (major second, minor third, etc.). Higher-limit interval names are created by stacking prefixes that raise or lower by a comma. The prefix for the highest prime comes first.
The naturals CDEFGAB correspond to Pythagorean intervals. Sharp and flat accidentals raise/lower by 2187/2048, and half-sharp and half-flat accidentals raise/lower by 33/32. To represent non-2.3.11 subgroup intervals, a comma-seperated list of primes, each of which multiplies the basic note by a comma, is added (e.g. 5/4 = E[-5], 13/10 = Fd[+13, -5]).
 
== Commas ==  
== Prefixes ==
{|class="wikitable"
{|class="wikitable"
|-
|-
!Prime
!Prime
!Comma
!Comma
!Raising prefix
!Notation of harmonic
!Lowering prefix
|-
|-
|5
|5
|[[81/80]]
|81/80
|over
|5/4 = E[-5]
|under
|-
|-
|7
|7
|[[64/63]]
|896/891
|super
|7/4 = At[+7]
|sub
|-
|13
|144/143
|13/8 = Ad[-13]
|-
|17
|2187/2176
|17/16 = C#[-17]
|-
|19
|513/512
|19/16 = Eb[+19]
|-
|23
|736/729
|23/16 = F#[+23]
|-
|29
|261/256
|29/16 = Bb[+29]
|-
|31
|1024/1023
|31/16 = Cd[-31]
|-
|37
|297/296
|37/32 = Dt[-37]
|-
|41
|82/81
|41/32 = E[+41]
|-
|43
|129/128
|43/32 = F[+43]
|-
|47
|517/512
|47/32 = Gd[+47]
|-
|53
|583/576
|53/32 = Ad[+53]
|}
== 15-odd-limit ==
{|class="wikitable"
|-
!Interval
!Notation
|-
|16/15
|Db[+5]
|-
|15/14
|Dd[-5, -7]
|-
|14/13
|Ctt[+7, +13]
|-
|13/12
|Dd[-13]
|-
|12/11
|Dd
|-
|11/10
|Dbt[+5]
|-
|10/9
|D[-5]
|-
|9/8
|D
|-
|8/7
|Ebd[-7]
|-
|15/13
|Dt[-5, +13]
|-
|7/6
|Dt[+7]
|-
|13/11
|Edd[-13]
|-
|6/5
|Eb[+5]
|}
|}

Latest revision as of 09:02, 11 June 2023

(This may be moved to mainspace when it is more fleshed out)

The naturals CDEFGAB correspond to Pythagorean intervals. Sharp and flat accidentals raise/lower by 2187/2048, and half-sharp and half-flat accidentals raise/lower by 33/32. To represent non-2.3.11 subgroup intervals, a comma-seperated list of primes, each of which multiplies the basic note by a comma, is added (e.g. 5/4 = E[-5], 13/10 = Fd[+13, -5]).

Commas

Prime Comma Notation of harmonic
5 81/80 5/4 = E[-5]
7 896/891 7/4 = At[+7]
13 144/143 13/8 = Ad[-13]
17 2187/2176 17/16 = C#[-17]
19 513/512 19/16 = Eb[+19]
23 736/729 23/16 = F#[+23]
29 261/256 29/16 = Bb[+29]
31 1024/1023 31/16 = Cd[-31]
37 297/296 37/32 = Dt[-37]
41 82/81 41/32 = E[+41]
43 129/128 43/32 = F[+43]
47 517/512 47/32 = Gd[+47]
53 583/576 53/32 = Ad[+53]

15-odd-limit

Interval Notation
16/15 Db[+5]
15/14 Dd[-5, -7]
14/13 Ctt[+7, +13]
13/12 Dd[-13]
12/11 Dd
11/10 Dbt[+5]
10/9 D[-5]
9/8 D
8/7 Ebd[-7]
15/13 Dt[-5, +13]
7/6 Dt[+7]
13/11 Edd[-13]
6/5 Eb[+5]
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