Xenharmonic Wiki

User:Zhenlige/Chromatic notation: Difference between revisions

← Older edit
VisualWikitext
Zhenlige (talk | contribs)
autopatrolled
318 edits
Zhenlige (talk | contribs)
autopatrolled
318 edits
 
(7 intermediate revisions by the same user not shown)
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]]
Line 21: Line 21:
|-
|-
| 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]]
|-
|-
Line 27: Line 27:
|-
|-
| 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]] ||
|-
|-
Line 33: Line 33:
|-
|-
| 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]] ||
|-
|-
Line 39: Line 39:
|-
|-
| 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]]
|-
|-
Line 63: Line 63:
|-
|-
| 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]]
|-
|-
Line 69: Line 69:
|-
|-
| 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]] ||
|-
|-
Line 75: Line 75:
|-
|-
| 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]] ||
|-
|-
Line 81: Line 81:
|-
|-
| 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]]
|-
|-
Line 91: Line 91:
|}
|}


The 12edo diatonic 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 perfect - super major - super minor - double super perfect….
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 103: Line 103:
| '''ε''' || E♭
| '''ε''' || E♭
|-
|-
| ↑ε || D♯
| ^ε || D♯
|-
|-
| '''E''' || '''E'''
| '''E''' || '''E'''
Line 111: Line 111:
| '''γ''' || G♭
| '''γ''' || G♭
|-
|-
| ↑γ || F♯
| ^γ || F♯
|-
|-
| '''G''' || '''G'''
| '''G''' || '''G'''
Line 117: Line 117:
| '''α''' || A♭
| '''α''' || A♭
|-
|-
| ↑α || G♯
| ^α || G♯
|-
|-
| '''A''' || '''A'''
| '''A''' || '''A'''
Line 123: Line 123:
| '''β''' || B♭
| '''β''' || B♭
|-
|-
| ↑β || A♯
| ^β || A♯
|-
|-
| '''B''' || '''B'''
| '''B''' || '''B'''
Line 131: Line 131:
| '''δ''' || D♭
| '''δ''' || D♭
|-
|-
| ↑δ || C♯
| ^δ || C♯
|-
|-
| '''D''' || '''D'''
| '''D''' || '''D'''
Line 140: Line 140:


== Applications ==
== Applications ==
The chromatic notation is useful for notating temperaments which require many fifths to get some primes, making diatonic notation very unintuitive. 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 !! [[Ponta]] !! [[Cassandra]] !! [[Leapday]]
! Interval !! [[Ponta]] !! [[Cassandra]] !! [[Leapday]] !! [[Diaschismic]]
|-
|-
| [[5/4]] || nM3 || nM3 || Sm3
| [[5/4]] || nM3 || nM3 || Sm3 || ~M3
|-
|-
| [[7/4]] || 3SM6 || sm7 || SM6
| [[7/4]] || 3SM6 || sm7 || SM6 || 1/2-sm7
|-
|-
| [[11/8]] || 7s5 || 2S4 || S4
| [[11/8]] || 7s5 || 2S4 || S4 || 1/2-sT
|-
|-
| [[13/8]] || || Sm6 || Wm6
| [[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
|}
|}
Retrieved from "https://en.xen.wiki/w/User:Zhenlige/Chromatic_notation"