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.

Interval			Abbrev.	Steps		29edo tuning (steps)	Equivalent diatonic degree	Approximate ratios
Degree	Degree name from 12edo	Quality	Abbrev.	L	s	29edo tuning (steps)	Equivalent diatonic degree	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
Semitone Sem / 1-sem	Minor 2nd	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
Tone / 1-tone 2-sem	Major 2nd	Wide	W2s / WM2	1	1	5	M2	9/8
3-sem	Minor 3rd	Narrow	n3s / nm3	1	2	7	m3	32/27
3-sem	Minor 3rd	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
Ditone / 2-tone 4-sem	Major 3rd	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
5-sem	Fourth	Augmented	A5s / A4	3	2	13	A3	27/20
Tritone / 3-tone 6-sem	Tritone	Narrow	n6s / nT	2	4	14	d5	45/32	7/5
Tritone / 3-tone 6-sem	Tritone	Wide	W6s / WT	3	3	15	A4	64/45	10/7
7-sem	Fifth	Diminished	d7s / d5	2	5	16	d6	40/27
7-sem	Fifth	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
Tetratone / 4-tone 8-sem	Minor 6th	Wide	W8s / Wm6	4	4	20	A5	8/5	45/28
9-sem	Major 6th	Narrow	n9s / nM6	3	6	21	d7	5/3
9-sem	Major 6th	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
Pentatone / 5-tone 10-sem	Minor 7th	Wide	W10s / Wm7	5	5	25	A6	9/5
11-sem	Major 7th	Narrow	n11s / nM7	4	7	26	d8	15/8	28/15
11-sem	Major 7th	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 requires many fifths to get some primes. 12edo diatonic names are used in the table below.


Interval	Pontiac	Garibaldi
5/4	nM3	nM3
7/4	sm7	3SM6*

* triple-super major 6th