User:Zhenlige/Chromatic notation

This page introduces a proposed notation system centering the 5L 7s chromatic scale. This system is suitable for temperaments with consonant intervals far away in the chain of fifths, such as schismatic. Adding more naturals is usually unnecessary, since the 12-comma is much smaller than the limma in JI. For the meantone chromatic scale 7L 5s, there are two approches to use this system, in anology to using the standard notation system for the antidiatonic scale.

Intervals

The names according to quasi-diatonic MOS notation are not intuitional, so different names are given here. “Sem” stands for “semitone”. 12edo diatonic interval names can also be used for representing degrees, with A4 and d5 merged into “tritone”. Note that diatonic major is always wide and diatonic minor is always narrow, which also applies to fourths and fifths as if they were named the same as other intervals. The 5L 7s augmented and diminished intervals are named “super” and “sub”, with abbreviation S and s.

Interval			Abbrev.	Steps		29edo tuning (steps)	Equivalent diatonic degree	Approximate ratios
Degree	Degree name from 12edo	Quality		L	s			schismatic	additional in garibaldi
Unison 0-tone 0-sem	Unison	Perfect	P0s / P1	0	0	0	P1	1/1
Semitone Sem / 1-sem	Minor 2nd	Narrow	n1s / nm2	0	1	2	m2	135/128, 256/243	21/20
		Wide	W1s / Wm2	1	0	3	A1	16/15	15/14
Tone / 1-tone 2-sem	Major 2nd	Narrow	n2s / nM2	0	2	4	d3	10/9
		Wide	W2s / WM2	1	1	5	M2	9/8
3-sem	Minor 3rd	Narrow	n3s / nm3	1	2	7	m3	32/27
		Wide	W3s / Wm3	2	1	8	A2	6/5
Ditone / 2-tone 4-sem	Major 3rd	Narrow	n4s / nM3	1	3	9	d4	5/4	56/45
		Wide	W4s / WM3	2	2	10	M3	81/64	80/63, 63/50
5-sem	Fourth	Perfect	P5s / P4	2	3	12	P4	4/3
		Super	S5s / S4	3	2	13	A3	27/20
Tritone / 3-tone 6-sem	Tritone	Narrow	n6s / nT	2	4	14	d5	45/32	7/5
		Wide	W6s / WT	3	3	15	A4	64/45	10/7
7-sem	Fifth	Sub	s7s / s5	2	5	16	d6	40/27
		Perfect	P7s / P5	3	4	17	P5	3/2
Tetratone / 4-tone 8-sem	Minor 6th	Narrow	n8s / nm6	3	5	19	m6	128/81	63/40, 100/63
		Wide	W8s / Wm6	4	4	20	A5	8/5	45/28
9-sem	Major 6th	Narrow	n9s / nM6	3	6	21	d7	5/3
		Wide	W9s / WM6	4	5	22	M6	27/16
Pentatone / 5-tone 10-sem	Minor 7th	Narrow	n10s / nm7	4	6	24	m7	16/9
		Wide	W10s / Wm7	5	5	25	A6	9/5
11-sem	Major 7th	Narrow	n11s / nM7	4	7	26	d8	15/8	28/15
		Wide	W11s / WM7	5	6	27	M7	243/128, 256/135	40/21
Hexatone / 6-tone 12-sem	Octave	Perfect	P12s / P8	5	7	29	P8	2/1

Note names

Latin letters ABCDEFG and Greek letters αβγδε are used. Latin letters represent the same notes as diatonic. Each Greek letter represents the note a diatonic chroma below the note marked with the corresponding Latin letter. Ups and downs are used for altering 12-commas.

Chromatic	Diatonic
D	D
ε	E♭
↑ε	D♯
E	E
F	F
γ	G♭
↑γ	F♯
G	G
α	A♭
↑α	G♯
A	A
β	B♭
↑β	A♯
B	B
C	C
δ	D♭
↑δ	C♯
D	D

Staves

A 9-lined staff is used. To improve readability, the lines alter between thin and thick. The first and last lines are thick. Only C-clef is used. C is always on a thick line. For the standard clef, the notes on the lines are EγαβCDEγα.

Applications

The chromatic notation is useful for notating temperaments which require many fifths to get some primes, making diatonic notation very unintuitive. 12edo diatonic names are used in the table below.

Interval	Ponta	Cassandra	Leapday
5/4	nM3	nM3	Sm3
7/4	3SM6	sm7	SM6
11/8	7s5	2S4	S4
13/8		Sm6	Wm6