User:CompactStar/JI notation: Difference between revisions
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(This may be moved to mainspace when it is more fleshed out) | (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 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]). | 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 == | == Commas == | ||
{|class="wikitable" | {|class="wikitable" | ||
| Line 18: | Line 18: | ||
|- | |- | ||
|13 | |13 | ||
| | |144/143 | ||
|13/8 = | |13/8 = Ad[-13] | ||
|- | |- | ||
|17 | |17 | ||
| Line 34: | Line 34: | ||
|- | |- | ||
|29 | |29 | ||
| | |261/256 | ||
|29/16 = | |29/16 = Bb[=29] | ||
|- | |- | ||
|31 | |31 | ||
| Line 42: | Line 42: | ||
|- | |- | ||
|37 | |37 | ||
| | |297/296 | ||
|37/32 = | |37/32 = Dt[-37] | ||
|- | |||
|41 | |||
|82/81 | |||
|41/32 = E[+41] | |||
|- | |||
|43 | |||
|129/128 | |||
|43/32 = F[+43] | |||
|- | |||
|47 | |||
|517/512 | |||
|47/32 = Gd[+43] | |||
|- | |||
|53 | |||
|583/576 | |||
|53/32 = Ad[+43] | |||
|} | |} | ||
Revision as of 08:47, 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[+43] |
| 53 | 583/576 | 53/32 = Ad[+43] |