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== Intervals ==
== Intervals ==
The names according to [[quasi-diatonic MOS notation]] are not intuitional, so different names are given here. “Sem” stands for “'''sem'''itone”. [[12edo]] diatonic interval names can also be used for representing degrees, with A4 and d5 merged into “tritone”.
The degrees are named as 0-indexed numbers of “sem”, which stands for “'''sem'''itone”, 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.
{| class="wikitable"
{| class="wikitable"
|-
|+ Chromatic interval degrees
! colspan="3" | Interval
! colspan="3" | Interval
! rowspan="2" | Abbrev.
! rowspan="2" | Abbrev.
! colspan="2" | Steps
! colspan="2" | Steps
! rowspan="2" | 29edo<br>tuning<br>(steps)
! rowspan="2" | 29edo<br>tuning<br>(steps)
! rowspan="2" | Equivalent<br>diatonic<br>interval
! rowspan="2" | Equivalent<br>diatonic<br>degree
! colspan="2" | Approximate ratios
! colspan="2" | Approximate ratios
|-
|-
! Degree !! Degree name<br>from [[12edo]] !! Quality
! Degree !! Degree name<br>from [[12edo]] diatonic !! Quality
! L !! s
! L !! s
! [[schismatic]] !! additional<br>in [[garibaldi]]
! [[schismatic]] !! additional<br>in [[garibaldi]]
|-
|-
| Unison<br>Zero-tone<br>Zero-sem
| Unison<br>0-tone<br>0-sem
| Unison
| Unison
|Perfect|| PU / P0s || 0 || 0 || 0 || [[1/1|P1]] || [[1/1]] ||
|Perfect|| P0s / P1 || 0 || 0 || 0 || '''[[1/1|P1]]''' || [[1/1]] ||
|-
|-
| rowspan="2" | Semitone<br>Sem / Monosem / 1-sem
| rowspan="2" | Semitone<br>Sem / 1-sem
| rowspan="2" | Minor 2nd
| rowspan="2" | Minor second
|Minor|| ms / m1s || 0 || 1 || 2 || m2 || [[135/128]], [[256/243]] || [[21/20]]
|Narrow|| n1s / nm2 || 0 || 1 || 2 || '''m2''' || [[135/128]], [[256/243]] || [[21/20]]
|-
|-
|Major|| Ms / M1s || 1 || 0 || 3 || A1 || [[16/15]] || [[15/14]]
|Wide|| W1s / Wm2 || 1 || 0 || 3 || A1 || [[16/15]] || [[15/14]]
|-
|-
| rowspan="2" | Tone<br>Monotone / 1-tone<br>Disem / 2-sem
| rowspan="2" | Tone / 1-tone<br>2-sem
| rowspan="2" | Major 2nd
| rowspan="2" | Major second
|Minor|| mt / m1t / m2s || 0 || 2 || 4 || d3 || [[10/9]] ||
|Narrow|| n2s / nM2 || 0 || 2 || 4 || d3 || [[10/9]] ||
|-
|-
|Major|| Mt / M1t / M2s || 1 || 1 || 5 || M2 || [[9/8]] ||
|Wide|| W2s / WM2 || 1 || 1 || 5 || '''M2''' || [[9/8]] ||
|-
|-
| rowspan="2" | Sesquitone<br>Trisem / 3-sem
| rowspan="2" | 3-sem
| rowspan="2" | Minor 3rd
| rowspan="2" | Minor third
|Minor|| mS / m3s || 1 || 2 || 7 || m3 || [[32/27]] ||
|Narrow|| n3s / nm3 || 1 || 2 || 7 || '''m3''' || [[32/27]] ||
|-
|-
|Major|| MS / M3s || 2 || 1 || 8 || A2 || [[6/5]] ||
|Wide|| W3s / Wm3 || 2 || 1 || 8 || A2 || [[6/5]] ||
|-
|-
| rowspan="2" | Ditone / 2-tone<br>Tetrasem / 4-sem
| rowspan="2" | Ditone / 2-tone<br>4-sem
| rowspan="2" | Major 3rd
| rowspan="2" | Major third
|Minor|| m2t / m4s || 1 || 3 || 9 || d4 || [[5/4]] || [[56/45]]
|Narrow|| n4s / nM3 || 1 || 3 || 9 || d4 || [[5/4]] || [[56/45]]
|-
|-
|Major|| M2t / M4s || 2 || 2 || 10 || M3 || [[81/64]] || [[80/63]], [[63/50]]
|Wide|| W4s / WM3 || 2 || 2 || 10 || '''M3''' || [[81/64]] || [[80/63]], [[63/50]]
|-
|-
| rowspan="2" | Pentasem / 5-sem
| rowspan="2" | 5-sem
| rowspan="2" | Fourth
| rowspan="2" | Fourth
|Perfect|| Pf / P5s || 2 || 3 || 12 || P4 || [[4/3]] ||
|Perfect|| P5s / P4 || 2 || 3 || 12 || '''P4''' || [[4/3]] ||
|-
|-
|Augmented|| Af / A5s || 3 || 2 || 13 || A3 || [[27/20]] ||
|Super|| S5s / S4 || 3 || 2 || 13 || A3 || [[27/20]] ||
|-
|-
| rowspan="2" | [[Tritone]] / 3-tone<br>Hexasem / 6-sem
| rowspan="2" | [[Tritone]] / 3-tone<br>6-sem
| rowspan="2" | Tritone
| rowspan="2" | Tritone
|Minor|| m3t / m6s || 2 || 4 || 14 || d5 || [[45/32]] || [[7/5]]
|Narrow|| n6s / nT || 2 || 4 || 14 || '''d5''' || [[45/32]] || [[7/5]]
|-
|-
|Major|| M3t / M6s || 3 || 3 || 15 || A4 || [[64/45]] || [[10/7]]
|Wide|| W6s / WT || 3 || 3 || 15 || '''A4''' || [[64/45]] || [[10/7]]
|-
|-
| rowspan="2" | Heptasem / 7-sem
| rowspan="2" | 7-sem
| rowspan="2" | Fifth
| rowspan="2" | Fifth
|Diminished|| dF / d7s || 2 || 5 || 16 || d6 || [[40/27]] ||
|Sub|| s7s / s5 || 2 || 5 || 16 || d6 || [[40/27]] ||
|-
|-
|Perfect|| PF / P7s || 3 || 4 || 17 || [[Perfect fifth (diatonic interval category)|P5]] || [[3/2]] ||
|Perfect|| P7s / P5 || 3 || 4 || 17 || '''[[Perfect fifth (diatonic interval category)|P5]]''' || [[3/2]] ||
|-
|-
| rowspan="2" | Tetratone / 4-tone<br>Octasem / 8-sem
| rowspan="2" | Tetratone / 4-tone<br>8-sem
| rowspan="2" | Minor 6th
| rowspan="2" | Minor sixth
|Minor|| m4t / m8s || 3 || 5 || 19 || m6 || [[128/81]] || [[63/40]], [[100/63]]
|Narrow|| n8s / nm6 || 3 || 5 || 19 || '''m6''' || [[128/81]] || [[63/40]], [[100/63]]
|-
|-
|Major|| M4t / M8s || 4 || 4 || 20 || A5 || [[8/5]] || [[45/28]]
|Wide|| W8s / Wm6 || 4 || 4 || 20 || A5 || [[8/5]] || [[45/28]]
|-
|-
| rowspan="2" | Nonasem / 9-sem
| rowspan="2" | 9-sem
| rowspan="2" | Major 6th
| rowspan="2" | Major sixth
|Minor|| m9s || 3 || 6 || 21 || d7 || [[5/3]] ||
|Narrow|| n9s / nM6 || 3 || 6 || 21 || d7 || [[5/3]] ||
|-
|-
|Major|| M9s || 4 || 5 || 22 || M6 || [[27/16]] ||
|Wide|| W9s / WM6 || 4 || 5 || 22 || '''M6''' || [[27/16]] ||
|-
|-
| rowspan="2" | Pentatone / 5-tone<br>Decasem / 10-sem
| rowspan="2" | Pentatone / 5-tone<br>10-sem
| rowspan="2" | Minor 7th
| rowspan="2" | Minor seventh
|Minor|| m5t / m10s || 4 || 6 || 24 || m7 || [[16/9]] ||
|Narrow|| n10s / nm7 || 4 || 6 || 24 || '''m7''' || [[16/9]] ||
|-
|-
|Major|| M5t / M10s || 5 || 5 || 25 || A6 || [[9/5]] ||
|Wide|| W10s / Wm7 || 5 || 5 || 25 || A6 || [[9/5]] ||
|-
|-
| rowspan="2" | Undecasem / 11-sem
| rowspan="2" | 11-sem
| rowspan="2" | Major 7th
| rowspan="2" | Major seventh
|Minor|| m11s || 4 || 7 || 26 || d8 || [[15/8]] || [[28/15]]
|Narrow|| n11s / nM7 || 4 || 7 || 26 || d8 || [[15/8]] || [[28/15]]
|-
|-
|Major|| M11s || 5 || 6 || 27 || M7 || [[243/128]], [[256/135]] || [[40/21]]
|Wide|| W11s / WM7 || 5 || 6 || 27 || '''M7''' || [[243/128]], [[256/135]] || [[40/21]]
|-
|-
| Octave / Ditave / Period<br>Hexatone / 6-tone<br>Dodecasem / 12-sem
| Hexatone / 6-tone<br>12-sem
| Octave
| Octave
|Perfect|| PO / P6t / P12s || 5 || 7 || 29 || [[2/1|P8]] || [[2/1]] ||
|Perfect|| P12s / P8 || 5 || 7 || 29 || '''[[2/1|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 ==
== Note names ==
Line 101: Line 103:
| '''ε''' || E♭
| '''ε''' || E♭
|-
|-
| ↑ε || D♯
| ^ε || D♯
|-
|-
| '''E''' || '''E'''
| '''E''' || '''E'''
Line 109: Line 111:
| '''γ''' || G♭
| '''γ''' || G♭
|-
|-
| ↑γ || F♯
| ^γ || F♯
|-
|-
| '''G''' || '''G'''
| '''G''' || '''G'''
Line 115: Line 117:
| '''α''' || A♭
| '''α''' || A♭
|-
|-
| ↑α || G♯
| ^α || G♯
|-
|-
| '''A''' || '''A'''
| '''A''' || '''A'''
Line 121: Line 123:
| '''β''' || B♭
| '''β''' || B♭
|-
|-
| ↑β || A♯
| ^β || A♯
|-
|-
| '''B''' || '''B'''
| '''B''' || '''B'''
Line 129: Line 131:
| '''δ''' || D♭
| '''δ''' || D♭
|-
|-
| ↑δ || C♯
| ^δ || C♯
|-
|-
| '''D''' || '''D'''
| '''D''' || '''D'''
Line 136: Line 138:
== Staves ==
== 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 '''E'''γ'''α'''β'''C'''D'''E'''γ'''α'''.
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 '''E'''γ'''α'''β'''C'''D'''E'''γ'''α'''.
== 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.
{| class="wikitable"
|+ Interval mappings in some temperaments<br>(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
|}
{| class="wikitable"
|+ Interval mappings in some temperaments<br>(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
|}
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