Diatonic notation - Revision history

Vector at 09:12, 15 March 2026

2026-03-15T09:12:56Z

Vector at 05:04, 4 March 2026

2026-03-04T05:04:47Z

← Older revision		Revision as of 05:04, 4 March 2026
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	=== Melodic antidiatonic notation ===		=== Melodic antidiatonic notation ===
	Antidiatonic systems, if notated with diatonic notation, would have sharps lowering the pitch and flats raising the pitch. Other than that, however, the system remains fully coherent. A quick fix to make the antidiatonic notation intuitive is to swap the meaning of sharp and flat, so that sharp always raises in pitch, and flat always lowers in pitch. So the interval that sounds like a major third would be called a major third, and it would be notated C-E# rather than C-Eb (note that in, say, 16edo, C-E is 300 cents).		Antidiatonic systems, if notated with diatonic notation, would have sharps lowering the pitch and flats raising the pitch, called ''harmonic notation''. Other than that, however, the system remains fully coherent. A quick fix to make the antidiatonic notation intuitive, called ''melodic notation'', is to swap the meaning of sharp and flat, so that sharp always raises in pitch, and flat always lowers in pitch. So the interval that sounds like a major third would be called a major third, and it would be notated C-E# rather than C-Eb (note that in, say, 16edo, C-E is 300 cents).
	{{Cat\|Notation}}		{{Cat\|Notation}}

Vector at 05:03, 4 March 2026

2026-03-04T05:03:07Z

← Older revision		Revision as of 05:03, 4 March 2026
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	=== Neutral diatonic notation ===		=== Neutral diatonic notation ===
	Neutral diatonic notation introduces two new accidentals: semisharp (+ or t) and semiflat (d) to raise and lower by half of a chromatic semitone respectively. This allows the notation of neutral intervals, specifically [[dicot]] intervals. #t is called "sesquisharp" and db is called "sesquiflat".		Neutral diatonic notation introduces two new accidentals: semisharp (+ or t) and semiflat (d) to raise and lower by half of a chromatic semitone respectively. This allows the notation of neutral intervals, specifically [[dicot]] intervals. #t is called "sesquisharp" and db is called "sesquiflat". Interval qualities go ..., sesquidiminished, diminished, semidiminished, perfect (or minor, neutral, major), semiaugmented, augmented, sesquiaugmented, ...

	=== Ups and downs notation ===		=== Ups and downs notation ===

Inthar at 23:19, 14 February 2026

2026-02-14T23:19:16Z

← Older revision		Revision as of 23:19, 14 February 2026
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	==== Modified ups and downs notation ====		==== Modified ups and downs notation ====
	A (non-standard) proposal for the form of ups and downs notation used on Xenharmonic Reference is a slight, but compatible given a modicum of intuition regarding the nature of intervals, alteration of Kite's version of ups and downs notation. The main change is that the basic spine is now neutral diatonic notation, meaning that the "mid" symbol and usage of "mid" is redundant.		A (non-standard) proposal for the form of ups and downs notation used on the Xenharmonic Reference is a slight, but compatible given a modicum of intuition regarding the nature of intervals, alteration of Kite's version of ups and downs notation. The main change is that the basic spine is now neutral diatonic notation, meaning that the "mid" symbol and usage of "mid" is redundant.

	=== Melodic antidiatonic notation ===		=== Melodic antidiatonic notation ===
	Antidiatonic systems, if notated with diatonic notation, would have sharps lowering the pitch and flats raising the pitch. Other than that, however, the system remains fully coherent. A quick fix to make the antidiatonic notation intuitive is to swap the meaning of sharp and flat, so that sharp always raises in pitch, and flat always lowers in pitch. So the interval that sounds like a major third would be called a major third, and it would be notated C-E# rather than C-Eb (note that in, say, 16edo, C-E is 300 cents).		Antidiatonic systems, if notated with diatonic notation, would have sharps lowering the pitch and flats raising the pitch. Other than that, however, the system remains fully coherent. A quick fix to make the antidiatonic notation intuitive is to swap the meaning of sharp and flat, so that sharp always raises in pitch, and flat always lowers in pitch. So the interval that sounds like a major third would be called a major third, and it would be notated C-E# rather than C-Eb (note that in, say, 16edo, C-E is 300 cents).
	{{Cat\|Notation}}		{{Cat\|Notation}}

Inthar at 23:00, 14 February 2026

2026-02-14T23:00:30Z

← Older revision		Revision as of 23:00, 14 February 2026
Line 108:		Line 108:

	==== Modified ups and downs notation ====		==== Modified ups and downs notation ====
	A (non-standard) proposal for the form of ups and downs notation used on ~~XenReference~~ is a slight, but compatible given a modicum of intuition regarding the nature of intervals, alteration of Kite's version of ups and downs notation. The main change is that the basic spine is now neutral diatonic notation, meaning that the "mid" symbol and usage of "mid" is redundant.		A (non-standard) proposal for the form of ups and downs notation used on Xenharmonic Reference is a slight, but compatible given a modicum of intuition regarding the nature of intervals, alteration of Kite's version of ups and downs notation. The main change is that the basic spine is now neutral diatonic notation, meaning that the "mid" symbol and usage of "mid" is redundant.

	=== Melodic antidiatonic notation ===		=== Melodic antidiatonic notation ===
	Antidiatonic systems, if notated with diatonic notation, would have sharps lowering the pitch and flats raising the pitch. Other than that, however, the system remains fully coherent. A quick fix to make the antidiatonic notation intuitive is to swap the meaning of sharp and flat, so that sharp always raises in pitch, and flat always lowers in pitch. So the interval that sounds like a major third would be called a major third, and it would be notated C-E# rather than C-Eb (note that in, say, 16edo, C-E is 300 cents).		Antidiatonic systems, if notated with diatonic notation, would have sharps lowering the pitch and flats raising the pitch. Other than that, however, the system remains fully coherent. A quick fix to make the antidiatonic notation intuitive is to swap the meaning of sharp and flat, so that sharp always raises in pitch, and flat always lowers in pitch. So the interval that sounds like a major third would be called a major third, and it would be notated C-E# rather than C-Eb (note that in, say, 16edo, C-E is 300 cents).
	{{Cat\|Notation}}		{{Cat\|Notation}}

Vector at 10:12, 15 January 2026

2026-01-15T10:12:36Z

← Older revision		Revision as of 10:12, 15 January 2026
Line 108:		Line 108:

	==== Modified ups and downs notation ====		==== Modified ups and downs notation ====
	A (non-standard) proposal for the form of ~~'''~~ups and downs notation~~'''~~ used on XenReference is a slight, but compatible given a modicum of intuition regarding the nature of intervals, alteration of Kite's version of ups and downs notation. The main change is that the basic spine is now neutral diatonic notation, meaning that the "mid" symbol and usage of "mid" is redundant.		A (non-standard) proposal for the form of ups and downs notation used on XenReference is a slight, but compatible given a modicum of intuition regarding the nature of intervals, alteration of Kite's version of ups and downs notation. The main change is that the basic spine is now neutral diatonic notation, meaning that the "mid" symbol and usage of "mid" is redundant.

	=== Melodic antidiatonic notation ===		=== Melodic antidiatonic notation ===
	Antidiatonic systems, if notated with diatonic notation, would have sharps lowering the pitch and flats raising the pitch. Other than that, however, the system remains fully coherent. A quick fix to make the antidiatonic notation intuitive is to swap the meaning of sharp and flat, so that sharp always raises in pitch, and flat always lowers in pitch. So the interval that sounds like a major third would be called a major third, and it would be notated C-E# rather than C-Eb (note that in, say, 16edo, C-E is 300 cents).		Antidiatonic systems, if notated with diatonic notation, would have sharps lowering the pitch and flats raising the pitch. Other than that, however, the system remains fully coherent. A quick fix to make the antidiatonic notation intuitive is to swap the meaning of sharp and flat, so that sharp always raises in pitch, and flat always lowers in pitch. So the interval that sounds like a major third would be called a major third, and it would be notated C-E# rather than C-Eb (note that in, say, 16edo, C-E is 300 cents).
	{{Cat\|Notation}}		{{Cat\|Notation}}

Vector at 10:12, 15 January 2026

2026-01-15T10:12:20Z

← Older revision		Revision as of 10:12, 15 January 2026
Line 97:		Line 97:

	=== Ups and downs notation ===		=== Ups and downs notation ===
	Ups and downs notation allows edos to be easily notated by providing the up (^) and down (v) accidentals to raise and lower by a single edostep. For example, in 29edo, the 372c interval is often used as a [[classical major third]], and can be notated C-vE (a "downmajor third") instead of notating it as a diminished fourth (C-Fb), which would otherwise be necessary. Note that ups and downs always go before notes and interval names. Neutral intervals are notated with the symbol ~ (e.g. neutral 3rd, neutral 4th = ~3, ~4).		Ups and downs notation allows edos to be easily notated by providing the up (^) and down (v) accidentals to raise and lower by a single edostep. For example, in 29edo, the 372c interval is often used as a [[classical major third]], and can be notated C-vE (a "downmajor third") instead of notating it as a diminished fourth (C-Fb), which would otherwise be necessary. Note that ups and downs always go before notes and interval names. Neutral intervals are notated with the symbol ~ and called "mid" (e.g. neutral 3rd, neutral 4th = ~3, ~4).

			Any sharp, flat, or arrow cancels any previous ones, meaning that an arrow by itself implies a natural sign.

	The up and down arrows may also be used to notate steps smaller than a chromatic semitone in rank-2 systems. For example, the generator of [[porcupine]], a submajor second of about 160c, may be notated C-vD.		The up and down arrows may also be used to notate steps smaller than a chromatic semitone in rank-2 systems. For example, the generator of [[porcupine]], a submajor second of about 160c, may be notated C-vD.

			When using ups and downs, Roman numerals should always be uppercase, alterations are enclosed in parentheses, and additions never are. Alterations always come last in the chord name. "a" and "d" are used for augmented and diminished.

			Read the [https://en.xen.wiki/w/Kite%27s_ups_and_downs_notation ups and downs] page on the XenWiki for more information.

			==== Modified ups and downs notation ====
			A (non-standard) proposal for the form of '''ups and downs notation''' used on XenReference is a slight, but compatible given a modicum of intuition regarding the nature of intervals, alteration of Kite's version of ups and downs notation. The main change is that the basic spine is now neutral diatonic notation, meaning that the "mid" symbol and usage of "mid" is redundant.

	=== Melodic antidiatonic notation ===		=== Melodic antidiatonic notation ===
	Antidiatonic systems, if notated with diatonic notation, would have sharps lowering the pitch and flats raising the pitch. Other than that, however, the system remains fully coherent. A quick fix to make the antidiatonic notation intuitive is to swap the meaning of sharp and flat, so that sharp always raises in pitch, and flat always lowers in pitch. So the interval that sounds like a major third would be called a major third, and it would be notated C-E# rather than C-Eb (note that in, say, 16edo, C-E is 300 cents).		Antidiatonic systems, if notated with diatonic notation, would have sharps lowering the pitch and flats raising the pitch. Other than that, however, the system remains fully coherent. A quick fix to make the antidiatonic notation intuitive is to swap the meaning of sharp and flat, so that sharp always raises in pitch, and flat always lowers in pitch. So the interval that sounds like a major third would be called a major third, and it would be notated C-E# rather than C-Eb (note that in, say, 16edo, C-E is 300 cents).
	{{Cat\|Notation}}		{{Cat\|Notation}}

Inthar: /* Melodic antidiatonic notation */

2025-12-23T17:02:01Z

Melodic antidiatonic notation

← Older revision		Revision as of 17:02, 23 December 2025
Line 103:		Line 103:
	=== Melodic antidiatonic notation ===		=== Melodic antidiatonic notation ===
	Antidiatonic systems, if notated with diatonic notation, would have sharps lowering the pitch and flats raising the pitch. Other than that, however, the system remains fully coherent. A quick fix to make the antidiatonic notation intuitive is to swap the meaning of sharp and flat, so that sharp always raises in pitch, and flat always lowers in pitch. So the interval that sounds like a major third would be called a major third, and it would be notated C-E# rather than C-Eb (note that in, say, 16edo, C-E is 300 cents).		Antidiatonic systems, if notated with diatonic notation, would have sharps lowering the pitch and flats raising the pitch. Other than that, however, the system remains fully coherent. A quick fix to make the antidiatonic notation intuitive is to swap the meaning of sharp and flat, so that sharp always raises in pitch, and flat always lowers in pitch. So the interval that sounds like a major third would be called a major third, and it would be notated C-E# rather than C-Eb (note that in, say, 16edo, C-E is 300 cents).
			{{Cat\|Notation}}

Vector at 01:28, 19 December 2025

2025-12-19T01:28:47Z

← Older revision		Revision as of 01:28, 19 December 2025
Line 2:		Line 2:

	Diatonic notation uses the 7 [[Notation#Nominals\|nominals]] (C, D, E, F, G, A, B) to form the C [[Scale quality\|major scale]], and the [[Notation#Accidentals\|accidentals]] (#, b) to raise and lower by a [[chromatic semitone]] respectively. Note that a chromatic semitone is the difference between a [[diatonic major second]] and a [[diatonic semitone]], and is in general not equal to a diatonic semitone, so, for example, C# and Db are in general not the same note.		Diatonic notation uses the 7 [[Notation#Nominals\|nominals]] (C, D, E, F, G, A, B) to form the C [[Scale quality\|major scale]], and the [[Notation#Accidentals\|accidentals]] (#, b) to raise and lower by a [[chromatic semitone]] respectively. Note that a chromatic semitone is the difference between a [[diatonic major second]] and a [[diatonic semitone]], and is in general not equal to a diatonic semitone, so, for example, C# and Db are in general not the same note.

			== Stacking intervals ==
			The result of stacking two diatonic intervals can be determined by consulting this [[isomorphic]] table. Each step down is a major second, and each step to the right is a chromatic semitone. Add the two intervals as vectors from P1, and the result is the proper notation for the interval formed by stacking them.
			{\| class="wikitable"
			\|+Monocot isomorphic table
			! colspan="1" rowspan="2" \|Degree
			! colspan="7" rowspan="1" \|Quality
			\|-
			!-3
			!-2
			!-1
			!0
			!1
			!2
			!3
			\|-
			!1sn
			\|4d1
			\|3d1
			\|dd1
			\|d1
			\|'''<u>P1</u>'''
			\|A1
			\|AA1
			\|-
			!2nd
			\|3d2
			\|dd2
			\|d2
			\|'''m2'''
			\|'''M2'''
			\|A2
			\|AA2
			\|-
			!3rd
			\|3d3
			\|dd3
			\|d3
			\|'''m3'''
			\|'''M3'''
			\|A3
			\|AA3
			\|-
			!4th
			\|3d4
			\|dd4
			\|d4
			\|'''P4'''
			\|A4
			\|AA4
			\|3A4
			\|-
			!5th
			\|3d5
			\|dd5
			\|d5
			\|'''P5'''
			\|A5
			\|AA5
			\|3A5
			\|-
			!6th
			\|dd6
			\|d6
			\|'''m6'''
			\|'''M6'''
			\|A6
			\|AA6
			\|3A6
			\|-
			!7th
			\|dd7
			\|d7
			\|'''m7'''
			\|'''M7'''
			\|A7
			\|AA7
			\|3A7
			\|-
			!8ve
			\|dd8
			\|d8
			\|'''<u>P8</u>'''
			\|A8
			\|AA8
			\|3A8
			\|4A8
			\|}

	== Extensions ==		== Extensions ==

Vector: Created page with "'''Diatonic notation''' or '''chain-of-fifths notation''' is the standard notation system in Western music, which notates systems that are octave-periodic and generated by a (just or tempered) perfect fifth. Many tuning systems may be notated this way. EDOs can be notated using unmodified diatonic notation if they contain a single chain of fifths that generates a diatonic scale. For example, 23edo cannot be notated with standard diatonic notation because it d..."

2025-12-13T07:30:34Z

Created page with "'''Diatonic notation''' or '''chain-of-fifths notation''' is the standard notation system in Western music, which notates systems that are octave-periodic and generated by a (just or tempered) perfect fifth. Many tuning systems may be notated this way. EDOs can be notated using unmodified diatonic notation if they contain a single chain of fifths that generates a diatonic scale. For example, 23edo cannot be notated with standard diatonic notation because it d..."

New page

'''Diatonic notation''' or '''chain-of-fifths notation''' is the standard notation system in Western music, which notates systems that are [[octave]]-periodic and generated by a (just or tempered) [[3/2|perfect fifth]]. Many tuning systems may be notated this way. EDOs can be notated using unmodified diatonic notation if they contain a single chain of fifths that generates a diatonic scale. For example, 23edo cannot be notated with standard diatonic notation because it does not have a diatonic scale, and 24edo cannot be notated with standard diatonic notation because it has two distinct chains of fifths.

Diatonic notation uses the 7 [[Notation#Nominals|nominals]] (C, D, E, F, G, A, B) to form the C [[Scale quality|major scale]], and the [[Notation#Accidentals|accidentals]] (#, b) to raise and lower by a [[chromatic semitone]] respectively. Note that a chromatic semitone is the difference between a [[diatonic major second]] and a [[diatonic semitone]], and is in general not equal to a diatonic semitone, so, for example, C# and Db are in general not the same note.

== Extensions ==

=== Neutral diatonic notation ===
Neutral diatonic notation introduces two new accidentals: semisharp (+ or t) and semiflat (d) to raise and lower by half of a chromatic semitone respectively. This allows the notation of neutral intervals, specifically [[dicot]] intervals. #t is called "sesquisharp" and db is called "sesquiflat".

=== Ups and downs notation ===
Ups and downs notation allows edos to be easily notated by providing the up (^) and down (v) accidentals to raise and lower by a single edostep. For example, in 29edo, the 372c interval is often used as a [[classical major third]], and can be notated C-vE (a "downmajor third") instead of notating it as a diminished fourth (C-Fb), which would otherwise be necessary. Note that ups and downs always go before notes and interval names. Neutral intervals are notated with the symbol ~ (e.g. neutral 3rd, neutral 4th = ~3, ~4).

The up and down arrows may also be used to notate steps smaller than a chromatic semitone in rank-2 systems. For example, the generator of [[porcupine]], a submajor second of about 160c, may be notated C-vD.

=== Melodic antidiatonic notation ===
Antidiatonic systems, if notated with diatonic notation, would have sharps lowering the pitch and flats raising the pitch. Other than that, however, the system remains fully coherent. A quick fix to make the antidiatonic notation intuitive is to swap the meaning of sharp and flat, so that sharp always raises in pitch, and flat always lowers in pitch. So the interval that sounds like a major third would be called a major third, and it would be notated C-E# rather than C-Eb (note that in, say, 16edo, C-E is 300 cents).