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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”. 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.
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.
Line 12: Line 12:
! 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]]
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|-
|-
| rowspan="2" | Semitone<br>Sem / 1-sem
| rowspan="2" | Semitone<br>Sem / 1-sem
| rowspan="2" | Minor 2nd
| rowspan="2" | Minor second
|Narrow|| n1s / nm2 || 0 || 1 || 2 || '''m2''' || [[135/128]], [[256/243]] || [[21/20]]
|Narrow|| n1s / nm2 || 0 || 1 || 2 || '''m2''' || [[135/128]], [[256/243]] || [[21/20]]
|-
|-
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|-
|-
| rowspan="2" | Tone / 1-tone<br>2-sem
| rowspan="2" | Tone / 1-tone<br>2-sem
| rowspan="2" | Major 2nd
| rowspan="2" | Major second
|Narrow|| n2s / nM2 || 0 || 2 || 4 || d3 || [[10/9]] ||
|Narrow|| n2s / nM2 || 0 || 2 || 4 || d3 || [[10/9]] ||
|-
|-
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|-
|-
| rowspan="2" | 3-sem
| rowspan="2" | 3-sem
| rowspan="2" | Minor 3rd
| rowspan="2" | Minor third
|Narrow|| n3s / nm3 || 1 || 2 || 7 || '''m3''' || [[32/27]] ||
|Narrow|| n3s / nm3 || 1 || 2 || 7 || '''m3''' || [[32/27]] ||
|-
|-
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|-
|-
| rowspan="2" | Ditone / 2-tone<br>4-sem
| rowspan="2" | Ditone / 2-tone<br>4-sem
| rowspan="2" | Major 3rd
| rowspan="2" | Major third
|Narrow|| n4s / nM3 || 1 || 3 || 9 || d4 || [[5/4]] || [[56/45]]
|Narrow|| n4s / nM3 || 1 || 3 || 9 || d4 || [[5/4]] || [[56/45]]
|-
|-
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|-
|-
| rowspan="2" | Tetratone / 4-tone<br>8-sem
| rowspan="2" | Tetratone / 4-tone<br>8-sem
| rowspan="2" | Minor 6th
| rowspan="2" | Minor sixth
|Narrow|| n8s / nm6 || 3 || 5 || 19 || '''m6''' || [[128/81]] || [[63/40]], [[100/63]]
|Narrow|| n8s / nm6 || 3 || 5 || 19 || '''m6''' || [[128/81]] || [[63/40]], [[100/63]]
|-
|-
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|-
|-
| rowspan="2" | 9-sem
| rowspan="2" | 9-sem
| rowspan="2" | Major 6th
| rowspan="2" | Major sixth
|Narrow|| n9s / nM6 || 3 || 6 || 21 || d7 || [[5/3]] ||
|Narrow|| n9s / nM6 || 3 || 6 || 21 || d7 || [[5/3]] ||
|-
|-
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|-
|-
| rowspan="2" | Pentatone / 5-tone<br>10-sem
| rowspan="2" | Pentatone / 5-tone<br>10-sem
| rowspan="2" | Minor 7th
| rowspan="2" | Minor seventh
|Narrow|| n10s / nm7 || 4 || 6 || 24 || '''m7''' || [[16/9]] ||
|Narrow|| n10s / nm7 || 4 || 6 || 24 || '''m7''' || [[16/9]] ||
|-
|-
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|-
|-
| rowspan="2" | 11-sem
| rowspan="2" | 11-sem
| rowspan="2" | Major 7th
| rowspan="2" | Major seventh
|Narrow|| n11s / nM7 || 4 || 7 || 26 || d8 || [[15/8]] || [[28/15]]
|Narrow|| n11s / nM7 || 4 || 7 || 26 || d8 || [[15/8]] || [[28/15]]
|-
|-
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|Perfect|| P12s / P8 || 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 ==
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| '''ε''' || E♭
| '''ε''' || E♭
|-
|-
| ↑ε || D♯
| ^ε || D♯
|-
|-
| '''E''' || '''E'''
| '''E''' || '''E'''
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| '''γ''' || G♭
| '''γ''' || G♭
|-
|-
| ↑γ || F♯
| ^γ || F♯
|-
|-
| '''G''' || '''G'''
| '''G''' || '''G'''
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| '''α''' || A♭
| '''α''' || A♭
|-
|-
| ↑α || G♯
| ^α || G♯
|-
|-
| '''A''' || '''A'''
| '''A''' || '''A'''
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| '''β''' || B♭
| '''β''' || B♭
|-
|-
| ↑β || A♯
| ^β || A♯
|-
|-
| '''B''' || '''B'''
| '''B''' || '''B'''
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| '''δ''' || D♭
| '''δ''' || D♭
|-
|-
| ↑δ || C♯
| ^δ || C♯
|-
|-
| '''D''' || '''D'''
| '''D''' || '''D'''
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== Applications ==
== 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.
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"
{| class="wikitable"
|+
|+ Interval mappings in some temperaments<br>(12edo diatonic based names)
! Interval !! [[Pontiac]] !! [[Garibaldi]]
! Interval !! [[Ponta]] !! [[Cassandra]] !! [[Leapday]] !! [[Diaschismic]]
|-
| [[5/4]] || nM3 || nM3 || Sm3 || ~M3
|-
| [[7/4]] || 3SM6 || sm7 || SM6 || 1/2-sm7
|-
|-
| [[5/4]] || nM3 || nM3
| [[11/8]] || 7s5 || 2S4 || S4 || 1/2-sT
|-
|-
| [[7/4]] || sm7 || 3SM6*
| [[13/8]] || || Sm6 || Wm6 || 1/2-sM6
|-
| [[17/16]] || || || 2S1 || ~m2
|}
|}


<nowiki/>* triple-super major 6th
{| 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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