Notation - Revision history

Vector at 08:32, 28 October 2026

2026-10-28T08:32:58Z

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-There are many different forms of '''musical notation''' in xenharmony. This page will serve as an introduction to some of the concepts found in xenharmonic notation, and some of the more common types. Note that this does not cover [[Naming#Intervals|interval naming]] systems with no notational counterpart. Notation systems are usually designed for consistent tuning systems such as [[Regular temperament|regular temperaments]], or approximately consistent tuning systems.
+Musical notation is any standardized or systematic way of communicating musical information visually. A notation system is generally able to specify [[pitch]] (how high or low notes are), [[rhythm]] (when notes are played), and other information about how to play or sing notes, such as lyrics, slides, techniques, etc. Notation is also often designed to suit [[analysis]] (that is, the understanding of a piece of music through music theory), and therefore tends to also transparently communicate information about harmonic and melodic structures as well.
 In general, a ''notation system'' on this wiki allows for the transcription of musical information such as pitches, note durations, rhythms, etc. Most notation systems here act as extensions or modifications of standard staff notation; however, as this wiki focuses on xenharmony (that is, non-standard intervals), any way of naming and notating pitches (and optionally chords) is generally sufficient to be considered a notation system. A notation system may also include an interval naming system.
-== Introduction ==
+== Introduction: diatonic notation ==
 [[File:Minor.png|thumb|The C minor scale in standard diatonic notation. The notes are C, D, Eb, F, G, Ab, Bb, and C.]]
 ==== Staff ====
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 * 17/16 is a minor second in the Functional Just System and an augmented unison in the Helmholtz-Ellis system; all intervals of 17 are affected by this disparity. It is between the two in terms of size - the minor second is a simpler diatonic interval but it is closer in size to the augmented unison.
 * 14/11 is often conceptualized as a major third (specifically, a neogothic major third), but most notation systems that use formal commas recognize it as an inflected perfect fourth. This is because it is the difference between 11/8 and 7/4 - 11/8 is about as sharp as a perfect fourth can reasonably be, and 7/4 is about as flat as a minor seventh can reasonably be. Therefore, their difference, another perfect fourth, is narrowed considerably. Systems like sagittal notation attempt to accurately capture 14/11's melodic quality, at the cost of sacrificing some stacking logic.

Vector at 04:33, 17 October 2026

2026-10-17T04:33:07Z

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	* Wad Wizard characterizes degrees as positions in a structure (reserving 'points in space' for notes i.e. absolute pitches) and intervals as separations between notes or degrees.		* Wad Wizard characterizes degrees as positions in a structure (reserving 'points in space' for notes i.e. absolute pitches) and intervals as separations between notes or degrees.
	* Vector sees degrees and intervals as fundamentally the same kind of object, with intervals having unambiguous readings as degrees and vice versa when no further context is given.		* Vector sees degrees and intervals as fundamentally the same kind of object, with intervals having unambiguous readings as degrees and vice versa when no further context is given.
	* ~~Intha~~ treats the distinction between the two as analogous to that between points in 2D coordinate space and 2D vectors. Deciding on a "default mode/pitch-set" may be preferable for a functional harmony system, but in modal harmony contexts degrees should ideally be notated as isomorphic to intervals.		* Inthar treats the distinction between the two as analogous to that between points in 2D coordinate space and 2D vectors. Deciding on a "default mode/pitch-set" may be preferable for a functional harmony system, but in modal harmony contexts degrees should ideally be notated as isomorphic to intervals.

	== Microtonal notations ==		== Microtonal notations ==

Inthar: /* Scale degrees vs. intervals */

2026-10-17T03:19:06Z

Scale degrees vs. intervals

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	* Wad Wizard characterizes degrees as positions in a structure (reserving 'points in space' for notes i.e. absolute pitches) and intervals as separations between notes or degrees.		* Wad Wizard characterizes degrees as positions in a structure (reserving 'points in space' for notes i.e. absolute pitches) and intervals as separations between notes or degrees.
	* Vector sees degrees and intervals as fundamentally the same kind of object, with intervals having unambiguous readings as degrees and vice versa when no further context is given.		* Vector sees degrees and intervals as fundamentally the same kind of object, with intervals having unambiguous readings as degrees and vice versa when no further context is given.
	* Intha treats the distinction between the two as analogous to that between points in 2D coordinate space and 2D vectors. Deciding on a "default mode/pitch-set" may be preferable for a functional harmony system, but ~~for describing xen~~ modal harmony, degrees should ideally be notated as isomorphic to intervals.		* Intha treats the distinction between the two as analogous to that between points in 2D coordinate space and 2D vectors. Deciding on a "default mode/pitch-set" may be preferable for a functional harmony system, but in modal harmony contexts degrees should ideally be notated as isomorphic to intervals.

	== Microtonal notations ==		== Microtonal notations ==

Inthar: /* Scale degrees vs. intervals */

2026-10-17T03:18:39Z

Scale degrees vs. intervals

← Older revision		Revision as of 03:18, 17 October 2026
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	* Wad Wizard characterizes degrees as positions in a structure (reserving 'points in space' for notes i.e. absolute pitches) and intervals as separations between notes or degrees.		* Wad Wizard characterizes degrees as positions in a structure (reserving 'points in space' for notes i.e. absolute pitches) and intervals as separations between notes or degrees.
	* Vector sees degrees and intervals as fundamentally the same kind of object, with intervals having unambiguous readings as degrees and vice versa when no further context is given.		* Vector sees degrees and intervals as fundamentally the same kind of object, with intervals having unambiguous readings as degrees and vice versa when no further context is given.
	* Intha treats the distinction between the two as analogous to that between points in 2D coordinate space and 2D vectors. Deciding on a "default mode/pitch-set" may be preferable for a functional harmony system, but for describing xen modal harmony, degrees should ~~preferably~~ be notated as isomorphic to intervals.		* Intha treats the distinction between the two as analogous to that between points in 2D coordinate space and 2D vectors. Deciding on a "default mode/pitch-set" may be preferable for a functional harmony system, but for describing xen modal harmony, degrees should ideally be notated as isomorphic to intervals.

	== Microtonal notations ==		== Microtonal notations ==

Inthar: /* Scale degrees vs. intervals */

2026-10-17T03:18:00Z

Scale degrees vs. intervals

← Older revision		Revision as of 03:18, 17 October 2026
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	* Wad Wizard characterizes degrees as positions in a structure (reserving 'points in space' for notes i.e. absolute pitches) and intervals as separations between notes or degrees.		* Wad Wizard characterizes degrees as positions in a structure (reserving 'points in space' for notes i.e. absolute pitches) and intervals as separations between notes or degrees.
	* Vector sees degrees and intervals as fundamentally the same kind of object, with intervals having unambiguous readings as degrees and vice versa when no further context is given.		* Vector sees degrees and intervals as fundamentally the same kind of object, with intervals having unambiguous readings as degrees and vice versa when no further context is given.
	* Intha treats the distinction between the two as analogous to that between points in 2D coordinate space and 2D vectors. Deciding on a "default mode/pitch-set" may be preferable for a functional harmony system, but for describing xen modal harmony, degrees should be notated as isomorphic to intervals.		* Intha treats the distinction between the two as analogous to that between points in 2D coordinate space and 2D vectors. Deciding on a "default mode/pitch-set" may be preferable for a functional harmony system, but for describing xen modal harmony, degrees should preferably be notated as isomorphic to intervals.

	== Microtonal notations ==		== Microtonal notations ==

Inthar: /* Scale degrees vs. intervals */

2026-10-17T03:17:24Z

Scale degrees vs. intervals

← Older revision		Revision as of 03:17, 17 October 2026
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	* Wad Wizard characterizes degrees as positions in a structure (reserving 'points in space' for notes i.e. absolute pitches) and intervals as separations between notes or degrees.		* Wad Wizard characterizes degrees as positions in a structure (reserving 'points in space' for notes i.e. absolute pitches) and intervals as separations between notes or degrees.
	* Vector sees degrees and intervals as fundamentally the same kind of object, with intervals having unambiguous readings as degrees and vice versa when no further context is given.		* Vector sees degrees and intervals as fundamentally the same kind of object, with intervals having unambiguous readings as degrees and vice versa when no further context is given.
	* Intha treats the distinction between the two as analogous to that between points in 2D coordinate space and 2D vectors. Deciding on a ~~functional~~ "default mode/pitch set" ~~is useful~~ for a functional harmony system, but for describing modal harmony, degrees should be notated as isomorphic to intervals.		* Intha treats the distinction between the two as analogous to that between points in 2D coordinate space and 2D vectors. Deciding on a "default mode/pitch-set" may be preferable for a functional harmony system, but for describing xen modal harmony, degrees should be notated as isomorphic to intervals.

	== Microtonal notations ==		== Microtonal notations ==

Inthar: /* Scale degrees vs. intervals */

2026-10-17T03:16:37Z

Scale degrees vs. intervals

← Older revision		Revision as of 03:16, 17 October 2026
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	* Wad Wizard characterizes degrees as positions in a structure (reserving 'points in space' for notes i.e. absolute pitches) and intervals as separations between notes or degrees.		* Wad Wizard characterizes degrees as positions in a structure (reserving 'points in space' for notes i.e. absolute pitches) and intervals as separations between notes or degrees.
	* Vector sees degrees and intervals as fundamentally the same kind of object, with intervals having unambiguous readings as degrees and vice versa when no further context is given.		* Vector sees degrees and intervals as fundamentally the same kind of object, with intervals having unambiguous readings as degrees and vice versa when no further context is given.
	* ~~Inthar~~ treats the distinction between the two as analogous to that between points in 2D coordinate space and 2D vectors.		* Intha treats the distinction between the two as analogous to that between points in 2D coordinate space and 2D vectors. Deciding on a functional "default mode/pitch set" is useful for a functional harmony system, but for describing modal harmony, degrees should be notated as isomorphic to intervals.

	== Microtonal notations ==		== Microtonal notations ==

Vector at 03:16, 26 September 2026

2026-09-26T03:16:10Z

← Older revision		Revision as of 03:16, 26 September 2026
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	===== Etymology =====		===== Etymology =====
	Keys in Western music are usually each associated with a mode and transposition of the diatonic scale, the latter of which the key signature specifies.[[File:5555.png\|thumb\|201x201px\|A key signature using FJS accidentals to specify the 5-limit zarlino scale in C major. D, E, A, and B are flattened by a syntonic comma.]]		Keys in Western music are usually each associated with a mode (major = Ionian, minor ~= Aeolian) and transposition of the diatonic scale, the latter of which the key signature specifies. For instance, a key signature of F# implies G major or E minor, due to G Ionian being G A B C D E F# and E Aeolian being E F# G A B C D. [[File:5555.png\|thumb\|201x201px\|A key signature using FJS accidentals to specify the 5-limit zarlino scale in C major. D, E, A, and B are flattened by a syntonic comma.]]

	==== Note symbols ====		==== Note symbols ====
	While not directly pitch- or interval-related, an important consideration in standard notation is that note duration is represented by differences in symbol shape, rather than by physical size, which allows the precise reading of durations.		While not directly pitch- or interval-related, an important consideration in standard notation is that note duration is represented by differences in symbol shape, rather than by physical size, which allows the precise reading of durations, so if you're designing a notation system around using symbol shape for inflections or other pitch-related meanings, that needs to be accounted for.

	=== Annotations ===		=== Annotations ===
	Figured bass is a prominent form of notation accompanying a standard score that indicates what notes and/or chords to play, most commonly used for analytical clarity, especially where performers are expected to improvise. It utilizes the numbers 1 through 7 to indicate the degrees of a scale. One notable constraint of figured bass is that the symbols for degrees must be singular digits or letters, disallowing constructions like "1/2" and "15"; this makes it rather painful to generalize to microtonal scales while keeping numeric indices for intuition. One system works around this by utilizing the letters of the Greek alphabet, which allow for 24 distinct degrees to be notated. Another option is to utilize alternative systems to figured bass, such as placing chord symbols above the score.		Figured bass is a prominent form of notation accompanying a standard score that indicates what notes and/or chords to play, most commonly used for analytical clarity, especially where performers are expected to improvise. It utilizes the numbers 1 through 7 to indicate the degrees of a scale. One notable constraint of figured bass is that to avoid compromising any ease of readability, the symbols for degrees must be singular digits or letters, disallowing constructions like "1/2" and "15"; this makes it rather painful to generalize to microtonal scales while keeping numeric indices for intuition. One system works around this by utilizing the letters of the Greek alphabet, which allow for 24 distinct degrees to be notated. Another option is to utilize alternative systems to figured bass, such as placing chord symbols above the score.

	=== Scale degrees vs. intervals ===		=== Scale degrees vs. intervals ===
	A scale degree refers to a note defined by an offset from the tonal center, tonic, or otherwise a fixed reference point that does not change throughout a song or section. Scale degrees are conventionally notated by specifying alterations from the degrees of the characteristic scale. Intervals are the offsets themselves, which may be applied either to the tonal center (specifying a scale degree) or to any other pitch. Intervals are notated with qualities such as major or minor, so that "m3" ("minor third") is an interval while "b3" ("flat three") is a degree. Note that outside of major and minor/sharp and flat, additional accidentals tend to share their names with qualities.		A scale degree refers to a note defined by an offset from the tonal center, tonic, or otherwise a fixed reference point that does not change throughout a song or section. Scale degrees are conventionally notated by specifying alterations from the degrees of the characteristic scale (that is, the scale degree a minor third above the tonal center in diatonic, where Ionian is the characteristic scale, is b3). Intervals are the offsets themselves, which may be applied either to the tonal center (specifying a scale degree) or to any other pitch. Intervals are notated with qualities such as major or minor, so that "m3" ("minor third") is an interval while "b3" ("flat three") is a degree. Note that outside of major and minor/sharp and flat, additional accidentals tend to share their names with qualities.

	However, note that this is somewhat disputed:		However, note that this is somewhat disputed:
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	* Unque characterizes scale degrees as "points in space" and intervals as "types of motion within that space", characterizing pitch space relative to the tonal center as a form of "secondary absolute" space.		* Unque characterizes scale degrees as "points in space" and intervals as "types of motion within that space", characterizing pitch space relative to the tonal center as a form of "secondary absolute" space.
	* Wad Wizard characterizes degrees as positions in a structure (reserving 'points in space' for notes i.e. absolute pitches) and intervals as separations between notes or degrees.		* Wad Wizard characterizes degrees as positions in a structure (reserving 'points in space' for notes i.e. absolute pitches) and intervals as separations between notes or degrees.
	* Vector sees degrees and intervals as fundamentally the same kind of object, with intervals having unambiguous readings as degrees and vice versa.		* Vector sees degrees and intervals as fundamentally the same kind of object, with intervals having unambiguous readings as degrees and vice versa when no further context is given.
	* Inthar treats the distinction between the two as analogous to that between points in 2D coordinate space and 2D vectors.		* Inthar treats the distinction between the two as analogous to that between points in 2D coordinate space and 2D vectors.

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	=== Diatonic notation ===		=== Diatonic notation ===
	[[Diatonic notation\|This page]] covers commonly accepted extensions to standard diatonic notation used in microtonality. The 7 nominals C, D, E, F, G, A, B form the C major scale, and # and b raise and lower notes by a chroma.		[[Diatonic notation\|This page]] covers commonly accepted extensions to standard diatonic notation used in microtonality. The 7 nominals C, D, E, F, G, A, B form the C major scale, and # and b raise and lower notes by a chroma. Accidentals apply to the portion of the measure after the place where the accidental appears.

	=== KISS notation ===		=== KISS notation ===
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	==== Diamond-MOS notation ====		==== Diamond-MOS notation ====
	Diamond-MOS notation aims to disambiguate itself from diatonic notation by using different nominals (from J onwards), different accidentals (& = #, @ = b), and a custom clef system that makes it visually apparent where J is in different octaves on the staff and what MOS is being used.		Diamond-MOS notation aims to disambiguate itself from diatonic notation by using different nominals (from J onwards), different accidentals (& = #, @ = b), and a custom clef system that makes it visually apparent where J is in different octaves on the staff and what MOS is being used. The accessibility features of Diamond-MOS notation may be applied to other notation systems.

	=== Just notation systems ===		=== Just notation systems ===
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	==== Color notation ====		==== Color notation ====
	Color notation is a notation system that uses a series of syllables to notate just intervals, fully replacing the standard interval qualities. An interval's degree is determined from its mapping to ~~24edo~~.		Color notation is a notation system that uses a series of syllables to notate just intervals, fully replacing the standard interval qualities. An interval's degree is determined from its mapping to 12edo.
	{\| class="wikitable"		{\| class="wikitable"
	\|+		\|+

Vector at 07:25, 30 April 2026

2026-04-30T07:25:49Z

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	Note that the words "sharp" and "flat" in alterations (and the symbols "#" and "b") are more specific than the adjectives sharp and flat as used in regards to tuning: the former refer to a fixed alteration by the chroma of mosdiatonic, which often generalizes outside diatonic (e.g. Bohlen-Pierce, KISS) to the moschroma in general, while the latter just mean "higher in pitch/distance" and "lower in pitch/distance", functioning as a generalization from the alignment of # and b with a single edostep in 12edo. More at [[Notation/Generalizations of sharp and flat]].		Note that the words "sharp" and "flat" in alterations (and the symbols "#" and "b") are more specific than the adjectives sharp and flat as used in regards to tuning: the former refer to a fixed alteration by the chroma of mosdiatonic, which often generalizes outside diatonic (e.g. Bohlen-Pierce, KISS) to the moschroma in general, while the latter just mean "higher in pitch/distance" and "lower in pitch/distance", functioning as a generalization from the alignment of # and b with a single edostep in 12edo. More at [[Notation/Generalizations of sharp and flat]].

			===== Etymology =====
			"Accident" originally referred to something non-essential or incidental, so an "accidental" represented a note that was non-essential to the key being played in.

	==== Key signatures ====		==== Key signatures ====
	A key signature is a set of accidentals placed at the beginning of the sheet music that apply to the whole piece and serve as the "default" accidentals to apply to staff positions. These accidentals also apply to notes separated by octaves from their position, which is not true of other accidentals. In general, there are only about 15 key signatures in use (based on the circle of fifths) representing the various transpositions of the diatonic scale. However, key signatures are theoretically possible for any set of defined alterations from the base notes of the characteristic scale, so that (for instance) one could specify a non-MOS diatonic scale with alterations to the standard version. (Note that otherwise, accidentals work normally, so that if the key signature specifies C#, placing a b accidental before a C note will read as Cb, not C (which is what the natural accidental is used for).[[File:5555.png\|thumb\|201x201px\|A key signature using FJS accidentals to specify the 5-limit zarlino scale in C major. D, E, A, and B are flattened by a syntonic comma.]]		A key signature is a set of accidentals placed at the beginning of the sheet music that apply to the whole piece and serve as the "default" accidentals to apply to staff positions. These accidentals also apply to notes separated by octaves from their position, which is not true of other accidentals. In general, there are only about 15 key signatures in use (based on the circle of fifths) representing the various transpositions of the diatonic scale. However, key signatures are theoretically possible for any set of defined alterations from the base notes of the characteristic scale, so that (for instance) one could specify a non-MOS diatonic scale with alterations to the standard version. (Note that otherwise, accidentals work normally, so that if the key signature specifies C#, placing a b accidental before a C note will read as Cb, not C (which is what the natural accidental is used for).) However, it is important to note that people usually only read the number of sharps or flats in the key signature to determine the scale, so scales other than diatonic modes are somewhat awkward to write and read as key signatures.

			===== Etymology =====
			Keys in Western music are usually each associated with a mode and transposition of the diatonic scale, the latter of which the key signature specifies.[[File:5555.png\|thumb\|201x201px\|A key signature using FJS accidentals to specify the 5-limit zarlino scale in C major. D, E, A, and B are flattened by a syntonic comma.]]

	==== Note symbols ====		==== Note symbols ====

Vector at 07:18, 30 April 2026

2026-04-30T07:18:06Z

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	\|-		\|-
	!Other notes		!Other notes
	\|All formal commas are derived systematically. Each prime harmonic is inflected from the simplest Pythagorean interval within 54.1 cents (or 57.8 cents).		\|All formal commas are derived systematically. Each prime harmonic is inflected from the simplest Pythagorean interval within a semiaugmented unison (56.8 cents) (or, as originally described, 65/63 (54.1 cents)).
	\|More aesthetically pleasing than FJS in certain contexts and more widely supported, however its symbol choices are very unintuitive and arbitrary.		\|More aesthetically pleasing than FJS in certain contexts and more widely supported, however its symbol choices are very unintuitive and arbitrary.
	\|Similar to FJS, but includes "dicot" intervals for more intuitive notation of neutral intervals. Each prime harmonic is inflected from the simplest Pythagorean or neutral interval within 33.4 cents.		\|Similar to FJS, but includes "dicot" intervals for more intuitive notation of neutral intervals. Each prime harmonic is inflected from the simplest Pythagorean or neutral interval within 33.4 cents.