Fractional sharp notation

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Revision as of 09:47, 7 February 2024 by CompactStar (talk | contribs)
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VERY WIP (I'll move it to the main namespace if it's finished.)

The letter notation is a notation scheme developed by CompactStar for just intonation up to the 31-limit and some regular temperaments. It is Pythagorean notation with the letters H-Z used as accidentals for higher prime limits (starting from H to avoid conflict with note names, and skipping M to avoid potential confusion with the abbreviation for "major").

Accidentals

Prime limit Letter Ratio Letter Ratio
5 H 81/80 I 80/81
7 J 64/63 K 63/64
11 L 33/32 N 32/33
13 O 1053/1024 P 1024/1053
17 Q 4131/4096 R 4096/4131
19 S 513/512 T 512/513
23 U 736/729 V 729/736
29 W 261/256 X 256/261
31 Y 32/31 Z 31/32

For example, 5/4 is IM3 (I-major third), 7/4 is Km7 (K-minor seventh) and 11/8 is LP4 (L-perfect fourth). Above C, these would be written IE, KBb and LF respectively.

This system can also be used to notate regular temperaments (including both equal temperaments and rank-2 or higher). For example, 24edo could be notated by using 12edo notation together with L/M to denote the tempered 33/32 quartertone of 50 cents:

Notation