Fractional sharp notation

Revision as of 10:05, 7 February 2024 by CompactStar (talk | contribs)

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 commas in higher prime limits (starting from H to avoid conflict with note names, and skipping M to avoid conflict with the abbreviation for "major"). The rationale for using letters as accidentals is that they are ASCII-compatible, and easy to memorize if in alphabetical order. Letters are placed for

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.

For temperaments

Letter notation can be adapted to regular temperaments simply by using the notation of the just intervals being tempered.