Diatonic notation - Revision history

Vector at 23:58, 10 May 2026

2026-05-10T23:58:30Z

← Older revision		Revision as of 23:58, 10 May 2026
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	Transpositions may be written explicitly, i.e. "1\11 higher than written", at the top of the score or at a key change. This avoids having to write in difficult-to-notate microtonal keys.		Transpositions may be written explicitly, i.e. "1\11 higher than written", at the top of the score or at a key change. This avoids having to write in difficult-to-notate microtonal keys.

	The EDO which a score is played in may be written explicitly, i.e. "53edo".		The EDO which a score is played in may be written explicitly, i.e. "53edo". If an edo has multiple diatonic scales, or if an arbitrary diatonic scale is warranted, it may be specified by using the generator tuning, e.g. "54edo, diatonic fifth = 31\54", or "Non-edo mos tuning, diatonic fifth = 696.2144 cents".
	[[File:DM alt.png\|thumb\|"ALT" notation for specifying a MODMOS. Note that this uses ups and downs notation, with the symbols used for diamond-MOS.]]		[[File:DM alt.png\|thumb\|"ALT" notation for specifying a MODMOS. Note that this uses ups and downs notation, with the symbols used for diamond-MOS.]]
	Key signatures may feature non-MOS alterations, placed after a vertical dotted line labelled "ALT" below it.		Key signatures may feature non-MOS alterations, placed after a vertical dotted line labelled "ALT" below it.

Vector at 23:56, 10 May 2026

2026-05-10T23:56:00Z

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 == Extensions ==
 === Neutral diatonic notation ===
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 === 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 ~ and called "mid" (e.g. neutral 3rd, neutral 4th = ~3, ~4).
+''Main article: [[Ups and downs notation]]''
 ==== Modified ups and downs notation ====

Vector at 00:41, 30 April 2026

2026-04-30T00:41:31Z

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	'''Diatonic notation''' or '''chain-of-fifths notation''' is the standard notation system in Western music. 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.		'''Diatonic notation''' or '''chain-of-fifths notation''' is the generalization of the standard notation system for 12edo in Western music that aligns with its historical usage to notate meantone or Pythagorean temperaments with greater than 12 notes. 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.

	== Basic concepts ==		== Basic concepts ==

Vector at 02:47, 7 April 2026

2026-04-07T02:47:10Z

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	The MOS diatonic scale is generated by a chain of 7 notes separated by fifths, with the chain of fifths being ... d5 - m2 - m6 - m3 - m7 - P4 - P1 - P5 - M2 - M6 - M3 - M7 - A4 ..., and continuing with augmented and diminished intervals in their respective directions infinitely (in the case of a rank-2 tuning) or until the circle closes (in the case of an equal temperament).		The MOS diatonic scale is generated by a chain of 7 notes separated by fifths, with the chain of fifths being ... d5 - m2 - m6 - m3 - m7 - P4 - P1 - P5 - M2 - M6 - M3 - M7 - A4 ..., and continuing with augmented and diminished intervals in their respective directions infinitely (in the case of a rank-2 tuning) or until the circle closes (in the case of an equal temperament).

	This means that the accidentals # and b replace a note with the note 7 fifths in one direction or another on the chain of fifths, with the interval at 7 fifths being the augmented unison or chromatic semitone. (Note that in the general case, this is not equal to the diatonic semitone found as the small step of the diatonic scale. Additionally, sharp and flat do not always inflect by a single edostep; in fact, it is rare that they do so.) Additionally, the tunings of the intervals in a diatonic scale can vary significantly based on the tuning of the fifth used to create it. For example, a fifth tuned to 715 cents generates a major third of 460 cents, while a fifth tuned to 690 cents generates a major third of 360 cents, which is a difference of a whole semitone. Therefore, the primary compromise of the MOS diatonic scale is that the same label (say, "major third") can refer to wildly different intervals depending on the system. The tuning of a diatonic interval can be determined by stacking the corresponding fifth the necessary number of times (for example, the major third in 17edo is 424 cents, because the fifth of 706 cents stacks four times to 2824 cents, which results in 424 cents after octave-reducing) However, ultimately, this ends up being better than the alternatives in practice.		This means that the accidentals # and b replace a note with the note 7 fifths in one direction or another on the chain of fifths, with the interval at 7 fifths being the augmented unison or chromatic semitone. (Note that in the general case, this is not equal to the diatonic semitone found as the small step of the diatonic scale. Additionally, sharp and flat do not always inflect by a single edostep; in fact, it is rare that they do so.) Additionally, the tunings of the intervals in a diatonic scale can vary significantly based on the tuning of the fifth used to create it. For example, a fifth tuned to 715 cents generates a major third of 460 cents, while a fifth tuned to 690 cents generates a major third of 360 cents, which is a difference of a whole semitone. Therefore, the primary compromise of the MOS diatonic scale is that the same label (say, "major third") can refer to wildly different intervals depending on the system. The tuning of a diatonic interval can be determined by stacking the corresponding fifth the necessary number of times (for example, the major third in 17edo is 424 cents, because the fifth of 706 cents stacks four times to 2824 cents, which results in 424 cents after octave-reducing) However, ultimately, this ends up being better than the alternatives in practice. (As a shortcut in mental arithmetic, you may use only the difference between the fifth and 12edo's fifth - 64 = 24, therefore a 706c fifth generates a 424c major third; similarly, 44=16, therefore a 696c fifth (700-4) generates a 384c major third (400-16).)

	This idea of scale sensitivity to generator tuning is the fundamental idea behind [[monocot]] temperaments (such as [[meantone]] and [[archy]]), and more generally of [[regular temperament]] theory as a whole.		This idea of scale sensitivity to generator tuning is the fundamental idea behind [[monocot]] temperaments (such as [[meantone]] and [[archy]]), and more generally of [[regular temperament]] theory as a whole.

Vector at 09:12, 15 March 2026

2026-03-15T09:12:56Z

Show changes

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}}