User:CompactStar/Letter comma notation: Difference between revisions
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VERY WIP (I'll move it to the main namespace if it's finished.) | VERY WIP (I'll move it to the main namespace if it's finished.) | ||
The '''letter comma notation''' (LCN) is a notation scheme developed by [[User:CompactStar|CompactStar]] for [[just intonation]] up to the [[31-limit]] as well as [[regular temperament]]s based on it. It is based on [[3-limit]] notation with the letters H-Y used as accidentals representing higher-limit [[comma]]s (starting from H to avoid conflict with note names). Each comma is associated to a prime limit uses 2 letters, one for the ascending accidental and one for the descending accidental. It bears some similarities to [[SKULO interval names]] and the [[Functional Just System]]. | The '''letter comma notation''' (LCN) is a notation scheme developed by [[User:CompactStar|CompactStar]] for [[just intonation]] up to the [[31-limit]] as well as [[regular temperament]]s based on it. It is based on [[3-limit]] notation with the letters H-Y used as accidentals representing higher-limit [[comma]]s (starting from H to avoid conflict with note names). Each comma is associated to a [[prime limit]] and uses 2 letters, one for the ascending accidental and one for the descending accidental. It bears some similarities to [[SKULO interval names]] and the [[Functional Just System]]. | ||
== Accidentals == | == Accidentals == | ||
Revision as of 04:52, 8 April 2024
VERY WIP (I'll move it to the main namespace if it's finished.)
The letter comma notation (LCN) is a notation scheme developed by CompactStar for just intonation up to the 31-limit as well as regular temperaments based on it. It is based on 3-limit notation with the letters H-Y used as accidentals representing higher-limit commas (starting from H to avoid conflict with note names). Each comma is associated to a prime limit and uses 2 letters, one for the ascending accidental and one for the descending accidental. It bears some similarities to SKULO interval names and the Functional Just System.
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 | M | 32/33 |
| 13 | N | 1053/1024 | O | 1024/1053 |
| 17 | P | 4131/4096 | Q | 4096/4131 |
| 19 | R | 513/512 | S | 512/513 |
| 23 | T | 736/729 | U | 729/736 |
| 29 | V | 261/256 | W | 256/261 |
| 31 | X | 32/31 | Y | 31/32 |
The letters are placed before interval and note names, so 5/4 is IM3 (I-major third) and 7/4 is Km7 (K-minor seventh), and above C these would be IE and KBb.
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:
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