User:Zhenlige/Chromatic notation: Difference between revisions

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{| class="wikitable"
{| class="wikitable"
|-
|-
! colspan="2" | Interval
! colspan="3" | Interval
! rowspan="2" | Abbrev.
! rowspan="2" | Abbrev.
! colspan="2" | Steps
! colspan="2" | Steps
Line 12: Line 12:
! colspan="2" | Approximate ratios
! colspan="2" | Approximate ratios
|-
|-
! Degree !! Quality
! Degree !! Degree name<br>from [[12edo]] !! Quality
! L !! s
! L !! s
! [[schismatic]] !! additional<br>in [[garibaldi]]
! [[schismatic]] !! additional<br>in [[garibaldi]]
|-
|-
| Unison<br>Zero-tone<br>Zero-sem  
| Unison<br>Zero-tone<br>Zero-sem
| Unison
|Perfect|| PU / P0s || 0 || 0 || 0 || [[1/1|P1]] || [[1/1]] ||
|Perfect|| PU / P0s || 0 || 0 || 0 || [[1/1|P1]] || [[1/1]] ||
|-
|-
| rowspan="2" | Semitone<br>Sem / Monosem / 1-sem
| rowspan="2" | Semitone<br>Sem / Monosem / 1-sem
| rowspan="2" | Minor 2nd
|Minor|| ms / m1s || 0 || 1 || 2 || m2 || [[135/128]], [[256/243]] || [[21/20]]
|Minor|| ms / m1s || 0 || 1 || 2 || m2 || [[135/128]], [[256/243]] || [[21/20]]
|-
|-
|Major|| Ms / M1s || 1 || 0 || 3 || A1 || [[16/15]] || [[15/14]]
|Major|| Ms / M1s || 1 || 0 || 3 || A1 || [[16/15]] || [[15/14]]
|-
|-
| rowspan="2" | Tone<br>Monotone / 1-tone<br>Disem / 2-sem  
| rowspan="2" | Tone<br>Monotone / 1-tone<br>Disem / 2-sem
| rowspan="2" | Major 2nd
|Minor|| mt / m1t / m2s || 0 || 2 || 4 || d3 || [[10/9]] ||
|Minor|| mt / m1t / m2s || 0 || 2 || 4 || d3 || [[10/9]] ||
|-
|-
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|-
|-
| rowspan="2" | Sesquitone<br>Trisem / 3-sem
| rowspan="2" | Sesquitone<br>Trisem / 3-sem
| rowspan="2" | Minor 3rd
|Minor|| mS / m3s || 1 || 2 || 7 || m3 || [[32/27]] ||
|Minor|| mS / m3s || 1 || 2 || 7 || m3 || [[32/27]] ||
|-
|-
Line 35: Line 39:
|-
|-
| rowspan="2" | Ditone / 2-tone<br>Tetrasem / 4-sem
| rowspan="2" | Ditone / 2-tone<br>Tetrasem / 4-sem
| rowspan="2" | Major 3rd
|Minor|| m2t / m4s || 1 || 3 || 9 || d4 || [[5/4]] || [[56/45]]
|Minor|| m2t / m4s || 1 || 3 || 9 || d4 || [[5/4]] || [[56/45]]
|-
|-
|Major|| M2t / M4s || 2 || 2 || 10 || M3 || [[81/64]] || [[80/63]], [[63/50]]
|Major|| M2t / M4s || 2 || 2 || 10 || M3 || [[81/64]] || [[80/63]], [[63/50]]
|-
|-
| rowspan="2" | Fourth<br>Pentasem / 5-sem
| rowspan="2" | Pentasem / 5-sem
| rowspan="2" | Fourth
|Perfect|| Pf / P5s || 2 || 3 || 12 || P4 || [[4/3]] ||
|Perfect|| Pf / P5s || 2 || 3 || 12 || P4 || [[4/3]] ||
|-
|-
Line 45: Line 51:
|-
|-
| rowspan="2" | [[Tritone]] / 3-tone<br>Hexasem / 6-sem
| rowspan="2" | [[Tritone]] / 3-tone<br>Hexasem / 6-sem
| rowspan="2" | Tritone
|Minor|| m3t / m6s || 2 || 4 || 14 || d5 || [[45/32]] || [[7/5]]
|Minor|| m3t / m6s || 2 || 4 || 14 || d5 || [[45/32]] || [[7/5]]
|-
|-
|Major|| M3t / M6s || 3 || 3 || 15 || A4 || [[64/45]] || [[10/7]]
|Major|| M3t / M6s || 3 || 3 || 15 || A4 || [[64/45]] || [[10/7]]
|-
|-
| rowspan="2" | Fifth<br>Heptasem / 7-sem
| rowspan="2" | Heptasem / 7-sem
| rowspan="2" | Fifth
|Diminished|| dF / d7s || 2 || 5 || 16 || d6 || [[40/27]] ||
|Diminished|| dF / d7s || 2 || 5 || 16 || d6 || [[40/27]] ||
|-
|-
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|-
|-
| rowspan="2" | Tetratone / 4-tone<br>Octasem / 8-sem
| rowspan="2" | Tetratone / 4-tone<br>Octasem / 8-sem
| rowspan="2" | Minor 6th
|Minor|| m4t / m8s || 3 || 5 || 19 || m6 || [[128/81]] || [[63/40]], [[100/63]]
|Minor|| m4t / m8s || 3 || 5 || 19 || m6 || [[128/81]] || [[63/40]], [[100/63]]
|-
|-
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|-
|-
| rowspan="2" | Nonasem / 9-sem
| rowspan="2" | Nonasem / 9-sem
| rowspan="2" | Major 6th
|Minor|| m9s || 3 || 6 || 21 || d7 || [[5/3]] ||
|Minor|| m9s || 3 || 6 || 21 || d7 || [[5/3]] ||
|-
|-
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|-
|-
| rowspan="2" | Pentatone / 5-tone<br>Decasem / 10-sem
| rowspan="2" | Pentatone / 5-tone<br>Decasem / 10-sem
| rowspan="2" | Minor 7th
|Minor|| m5t / m10s || 4 || 6 || 24 || m7 || [[16/9]] ||
|Minor|| m5t / m10s || 4 || 6 || 24 || m7 || [[16/9]] ||
|-
|-
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|-
|-
| rowspan="2" | Undecasem / 11-sem
| rowspan="2" | Undecasem / 11-sem
| rowspan="2" | Major 7th
|Minor|| m11s || 4 || 7 || 26 || d8 || [[15/8]] || [[28/15]]
|Minor|| m11s || 4 || 7 || 26 || d8 || [[15/8]] || [[28/15]]
|-
|-
|Major|| M11s || 5 || 6 || 27 || M7 || [[243/128]], [[256/135]] || [[40/21]]
|Major|| M11s || 5 || 6 || 27 || M7 || [[243/128]], [[256/135]] || [[40/21]]
|-
|-
| Octave / Ditave / Period<br>Hexatone / 6-tone<br>Dodecasem / 12-sem  
| Octave / Ditave / Period<br>Hexatone / 6-tone<br>Dodecasem / 12-sem
| Octave
|Perfect|| PO / P6t / P12s || 5 || 7 || 29 || [[2/1|P8]] || [[2/1]] ||
|Perfect|| PO / P6t / P12s || 5 || 7 || 29 || [[2/1|P8]] || [[2/1]] ||
|}
|}

Revision as of 06:52, 31 January 2026

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”.

Interval Abbrev. Steps 29edo
tuning
(steps) 		Equivalent
diatonic
interval 		Approximate ratios
Degree Degree name
from 12edo		 Quality L s schismatic additional
in garibaldi
Unison
Zero-tone
Zero-sem 		Unison Perfect PU / P0s 0 0 0 P1 1/1
Semitone
Sem / Monosem / 1-sem 		Minor 2nd Minor ms / m1s 0 1 2 m2 135/128, 256/243 21/20
Major Ms / M1s 1 0 3 A1 16/15 15/14
Tone
Monotone / 1-tone
Disem / 2-sem 		Major 2nd Minor mt / m1t / m2s 0 2 4 d3 10/9
Major Mt / M1t / M2s 1 1 5 M2 9/8
Sesquitone
Trisem / 3-sem 		Minor 3rd Minor mS / m3s 1 2 7 m3 32/27
Major MS / M3s 2 1 8 A2 6/5
Ditone / 2-tone
Tetrasem / 4-sem 		Major 3rd Minor m2t / m4s 1 3 9 d4 5/4 56/45
Major M2t / M4s 2 2 10 M3 81/64 80/63, 63/50
Pentasem / 5-sem Fourth Perfect Pf / P5s 2 3 12 P4 4/3
Augmented Af / A5s 3 2 13 A3 27/20
Tritone / 3-tone
Hexasem / 6-sem 		Tritone Minor m3t / m6s 2 4 14 d5 45/32 7/5
Major M3t / M6s 3 3 15 A4 64/45 10/7
Heptasem / 7-sem Fifth Diminished dF / d7s 2 5 16 d6 40/27
Perfect PF / P7s 3 4 17 P5 3/2
Tetratone / 4-tone
Octasem / 8-sem 		Minor 6th Minor m4t / m8s 3 5 19 m6 128/81 63/40, 100/63
Major M4t / M8s 4 4 20 A5 8/5 45/28
Nonasem / 9-sem Major 6th Minor m9s 3 6 21 d7 5/3
Major M9s 4 5 22 M6 27/16
Pentatone / 5-tone
Decasem / 10-sem 		Minor 7th Minor m5t / m10s 4 6 24 m7 16/9
Major M5t / M10s 5 5 25 A6 9/5
Undecasem / 11-sem Major 7th Minor m11s 4 7 26 d8 15/8 28/15
Major M11s 5 6 27 M7 243/128, 256/135 40/21
Octave / Ditave / Period
Hexatone / 6-tone
Dodecasem / 12-sem 		Octave Perfect PO / P6t / P12s 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.

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