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]] 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]].
The '''letter comma notation''' (LCN) is a notation scheme developed by [[User:CompactStar|CompactStar]] for [[just intonation]] up to the [[101-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 ==
== Commas ==
{|class="wikitable"
{|class="wikitable"
|-
|-
!Prime limit
!Prime limit
!Letter
!Letter
!Ratio
!Comma
!Letter
|-
!Ratio
|3
|b
|[[531441/524288]]
|-
|-
|5
|5
|H
|c
|[[81/80]]
|[[81/80]]
|I
|80/81
|-
|-
|7
|7
|J
|d
|[[64/63]]
[[64/63]]
|K
|63/64
|-
|-
|11
|11
|L
|e
|[[33/32]]
|[[33/32]]
|M
|32/33
|-
|-
|13
|13
|N
|f
|[[1053/1024]]
|[[1053/1024]]
|O
|1024/1053
|-
|-
|17
|17
|P
|g
|[[4131/4096]]
|[[2187/2176]]
|Q
|4096/4131
|-
|-
|19
|19
|R
|h
|[[513/512]]
|[[513/512]]
|S
|512/513
|-
|-
|23
|23
|T
|i
|[[736/729]]
|[[736/729]]
|U
|729/736
|-
|-
|29
|29
|V
|j
|[[261/256]]
|[[261/256]]
|W
|256/261
|-
|-
|31
|31
|X
|k
|[[32/31]]
|[[248/243]]
|Y
|-
|31/32
|37
|l
|[[37/36]]
|-
|41
|m
|[[82/81]]
|-
|43
|n
|[[129/128]]
|-
|47
|o
|[[48/47]]
|-
|53
|p
|[[54/53]]
|-
|59
|q
|[[243/236]]
|-
|61
|r
|[[244/243]]
|-
|67
|s
|[[16384/16281]]
|-
|71
|t
|[[72/71]]
|-
|73
|u
|[[73/72]]
|-
|79
|v
|[[81/79]]
|-
|83
|w
|[[256/249]]
|-
|89
|x
|[[729/712]]
|-
|97
|y
|[[97/96]]
|-
|101
|z
|[[8192/8181]]
|}
|}
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. When letters are stacked, they are put in alphabetical order, so [[7/5]] is IJd5.
== For tempered systems ==
This system can also be used to notate [[regular temperament]]s, including both [[equal temperament]]s and multirank temperaments. It should be noted that [[EDO]] systems will have many different temperament interpretations, and thus typically will have many different possible notations. Ffor example, 24edo can be notated as a [[2.3.7 subgroup]] system with the quarter-tone represented by 64/63 (J and K), as a [[2.3.11 subgroup]] system with the quarter-tone as 33/32 (L and M), and so on.

Revision as of 02:16, 18 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 101-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.

Commas

Prime limit Letter Comma
3 b 531441/524288
5 c 81/80
7 d

64/63

11 e 33/32
13 f 1053/1024
17 g 2187/2176
19 h 513/512
23 i 736/729
29 j 261/256
31 k 248/243
37 l 37/36
41 m 82/81
43 n 129/128
47 o 48/47
53 p 54/53
59 q 243/236
61 r 244/243
67 s 16384/16281
71 t 72/71
73 u 73/72
79 v 81/79
83 w 256/249
89 x 729/712
97 y 97/96
101 z 8192/8181
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