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 degrees are named as 0-indexed numbers of “sem”, which stands for “semitone”, referring to the chromatic step. 12edo diatonic interval names can also be used for representing degrees, with A4 and d5 merged into “tritone”. The 5L 7s major, minor, augmented and diminished are renamed to wide (W), narrow (n), super (S) and sub (s) respectively, to avoid ambiguity. 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. Mid or neutral degrees should be abbreviated as “m” or “~” to avoid confusion with “n” which stands for narrow.

Chromatic interval degrees

Interval			Abbrev.	Steps		29edo tuning (steps)	Equivalent diatonic degree	Approximate ratios
Degree	Degree name from 12edo diatonic	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 second	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 second	Narrow	n2s / nM2	0	2	4	d3	10/9
		Wide	W2s / WM2	1	1	5	M2	9/8
3-sem	Minor third	Narrow	n3s / nm3	1	2	7	m3	32/27
		Wide	W3s / Wm3	2	1	8	A2	6/5
Ditone / 2-tone 4-sem	Major third	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 sixth	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 sixth	Narrow	n9s / nM6	3	6	21	d7	5/3
		Wide	W9s / WM6	4	5	22	M6	27/16
Pentatone / 5-tone 10-sem	Minor seventh	Narrow	n10s / nm7	4	6	24	m7	16/9
		Wide	W10s / Wm7	5	5	25	A6	9/5
11-sem	Major seventh	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

The 12edo diatonic based interval names along the chain of fifths is P1-P5-WM2-WM6-WM3-WM7-WT-Wm2-Wm6-Wm3-Wm7-S4-S1-S5-SM2-… with the quality goes as perfect - wide major - wide minor - super - super major - super minor - double super … .

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 that require many fifths to get some primes, making diatonic notation very unintuitive, or that have interdiatonic degrees such as the half octave.

Interval mappings in some temperaments
(12edo diatonic based names)

Interval	Ponta	Cassandra	Leapday	Diaschismic
5/4	nM3	nM3	Sm3	~M3
7/4	3SM6	sm7	SM6	1/2-sm7
11/8	7s5	2S4	S4	1/2-sT
13/8		Sm6	Wm6	1/2-sM6
17/16			2S1	~m2

Interval mappings in some temperaments
(n-sem names)

Interval	Ponta	Cassandra	Leapday	Diaschismic
5/4	n4s	n4s	S3s	~4s
7/4	3S9s	s10s	S9s	1/2-s10s
11/8	7s7s	2S5s	S5s	1/2-s6s
13/8		S8s	W8s	1/2-s9s
17/16			2S0s	~1s