User:Zhenlige/Chromatic notation - Revision history

Zhenlige: /* Intervals */

2026-02-20T11:21:41Z

Intervals

← Older revision		Revision as of 11:21, 20 February 2026
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	\|}		\|}

	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 ~~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 ==

Zhenlige: /* Applications */

2026-02-19T19:39:14Z

Applications

← Older revision		Revision as of 19:39, 19 February 2026
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	== Applications ==		== 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~~. 12edo diatonic based 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]] !! [[Diaschismic]]		! Interval !! [[Ponta]] !! [[Cassandra]] !! [[Leapday]] !! [[Diaschismic]]
	\|-		\|-
	\| [[5/4]] \|\| nM3 \|\| nM3 \|\| Sm3 \|\| ~M3		\| [[5/4]] \|\| nM3 \|\| nM3 \|\| Sm3 \|\| ~M3
	\|-		\|-
	\| [[7/4]] \|\| 3SM6 \|\| sm7 \|\| SM6 \|\| 1/2-~~SM2~~		\| [[7/4]] \|\| 3SM6 \|\| sm7 \|\| SM6 \|\| 1/2-sm7
	\|-		\|-
	\| [[11/8]] \|\| 7s5 \|\| 2S4 \|\| S4 \|\| 1/2-sT		\| [[11/8]] \|\| 7s5 \|\| 2S4 \|\| S4 \|\| 1/2-sT
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	\|-		\|-
	\| [[17/16]] \|\| \|\| \|\| 2S1 \|\| ~m2		\| [[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
	\|}		\|}

Zhenlige: /* Applications */

2026-02-19T19:13:36Z

Applications

← Older revision		Revision as of 19:13, 19 February 2026
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 based 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. 12edo diatonic based names are used in the table below.

	{\| class="wikitable"		{\| class="wikitable"

Zhenlige: /* Applications */

2026-02-19T19:11:16Z

Applications

← Older revision		Revision as of 19:11, 19 February 2026
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	{\| class="wikitable"		{\| class="wikitable"
	\|+		\|+
	! 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-SM2
	\|-		\|-
	\| [[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
	\|}		\|}

Zhenlige: /* Applications */

2026-02-19T19:03:20Z

Applications

← Older revision		Revision as of 19:03, 19 February 2026
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 which require many fifths to get some primes, making diatonic notation very unintuitive. 12edo diatonic based names are used in the table below.

	{\| class="wikitable"		{\| class="wikitable"

Zhenlige: /* Intervals */

2026-02-19T19:03:08Z

Intervals

← Older revision		Revision as of 19:03, 19 February 2026
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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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	\|}		\|}

	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 perfect - super major - super minor - double super perfect….

	== Note names ==		== Note names ==

Zhenlige: /* Intervals */

2026-02-19T19:01:40Z

Intervals

← Older revision		Revision as of 19:01, 19 February 2026
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	! 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]]

Zhenlige: /* Note names */

2026-02-19T19:00:04Z

Note names

← Older revision		Revision as of 19:00, 19 February 2026
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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'''

Zhenlige: /* Intervals */

2026-02-19T18:59:13Z

Intervals

← Older revision		Revision as of 18:59, 19 February 2026
Line 2:		Line 2:

	== 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.
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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 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….

	== Note names ==		== Note names ==

Zhenlige: /* Applications */

2026-02-19T18:41:47Z

Applications

← Older revision		Revision as of 18:41, 19 February 2026
Line 138:		Line 138:

	== 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 which require many fifths to get some primes, making diatonic notation very unintuitive. 12edo diatonic names are used in the table below.

	{\| class="wikitable"		{\| class="wikitable"
	\|+		\|+
	! Interval !! [[~~Pontiac~~]] !! [[~~Garibaldi~~]]		! Interval !! [[Ponta]] !! [[Cassandra]] !! [[Leapday]]
	\|-		\|-
	\| [[5/4]] \|\| nM3 \|\| nM3		\| [[5/4]] \|\| nM3 \|\| nM3 \|\| Sm3
	\|-		\|-
	\| [[7/4]] \|\| sm7 \|\| 3SM6*		\| [[7/4]] \|\| 3SM6 \|\| sm7 \|\| SM6
			\|-
			\| [[11/8]] \|\| 7s5 \|\| 2S4 \|\| S4
			\|-
			\| [[13/8]] \|\| \|\| Sm6 \|\| Wm6
	\|}		\|}

	~~<nowiki/>* triple-super major 6th~~