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Stalefleas: /* Temperament Notation */

2025-11-08T10:58:31Z

Temperament Notation

← Older revision		Revision as of 10:58, 8 November 2025
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	\|S3 M3		\|S3 M3
	\|CJ+		\|CJ+
	\|C magic ~~minor~~		\|C magic major
	\|CSv#5		\|CSv#5
	\|-		\|-

Stalefleas: formatting

2025-09-28T02:47:15Z

formatting

← Older revision		Revision as of 02:47, 28 September 2025
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	todo: add a link to kite's notation		todo: add a link to kite's notation

	= 22edo chord notation =		== 22edo chord notation ==
	The following ideas have been formed out as part of the first Tuning of the Year project (for year 2025), hereafter referred to as TOTY. The focus of the original TOTY was 22edo, which was voted on by the Xenharmonic Alliance discord.		The following ideas have been formed out as part of the first Tuning of the Year project (for year 2025), hereafter referred to as TOTY. The focus of the original TOTY was 22edo, which was voted on by the Xenharmonic Alliance discord.

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	Including ups and downs notation, we have at least four distinct methods of identifying chords in 22edo. These methods are all comprehensive, meaning one can reasonably identify any chord just as well as one can identify chords in 12edo using standard chord labels. In sum, we have ups and downs notation, classic notation, double-qualifier notation, and temperament notation.		Including ups and downs notation, we have at least four distinct methods of identifying chords in 22edo. These methods are all comprehensive, meaning one can reasonably identify any chord just as well as one can identify chords in 12edo using standard chord labels. In sum, we have ups and downs notation, classic notation, double-qualifier notation, and temperament notation.

	== Intervals ==		= Intervals =
	Using a "sounds-like" system of interval naming, we can identify 22edo as having the following intervals:		Using a "sounds-like" system of interval naming, we can identify 22edo as having the following intervals:
	{\| class="wikitable"		{\| class="wikitable"
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	While obviously, there is some subjectivity here, and the possibility of an even more refined perspective. But this seems good enough to talk about 22edo in a way that is intuitive to what we are hearing.		While obviously, there is some subjectivity here, and the possibility of an even more refined perspective. But this seems good enough to talk about 22edo in a way that is intuitive to what we are hearing.

	== Triads ==		= Triads =
	In order to communicate the chords of 22edo, it is necessary to identify the names of the tertian triads. Adding sevenths to our triads gives us many practical chords that will be used by most composers and musicians. Adding our standard modifications to these, adding the sevenths, and alterations, gives us a complete system with which to name any chord. Here a triad is defined explicitly as a tertian triad, being a chord made out of two stacked thirds. Only the subminor, minor, major, and supermajor thirds (5\22, 6\22, 7\22, 8\22) are considered.		In order to communicate the chords of 22edo, it is necessary to identify the names of the tertian triads. Adding sevenths to our triads gives us many practical chords that will be used by most composers and musicians. Adding our standard modifications to these, adding the sevenths, and alterations, gives us a complete system with which to name any chord. Here a triad is defined explicitly as a tertian triad, being a chord made out of two stacked thirds. Only the subminor, minor, major, and supermajor thirds (5\22, 6\22, 7\22, 8\22) are considered.

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	\|}		\|}

	== Seventh Chords ==		= Seventh Chords =
	Notating seventh chords is fairly straightforward. One simply identifies the type of triad in their preferred system, and appends the quality of the seventh.		Notating seventh chords is fairly straightforward. One simply identifies the type of triad in their preferred system, and appends the quality of the seventh.

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	Disambiguation is not necessary for all chords, but defaulting to using it could lead to greater consistency in notation.		Disambiguation is not necessary for all chords, but defaulting to using it could lead to greater consistency in notation.

	== Extended chords ==		= Extended chords =
	Following the convention of 12edo notation, we have qualifiers for both triads and sevenths. In 22edo these have been described above. To add additional extensions, we can also follow the example provided by standard notation. All extensions will be assumed to be mos-diatonic (super-pythagorean) unless otherwise qualified. So, seconds are supermajor by default, fourths are perfect, and sixths are supermajor.		Following the convention of 12edo notation, we have qualifiers for both triads and sevenths. In 22edo these have been described above. To add additional extensions, we can also follow the example provided by standard notation. All extensions will be assumed to be mos-diatonic (super-pythagorean) unless otherwise qualified. So, seconds are supermajor by default, fourths are perfect, and sixths are supermajor.

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	could be written as Cadd9 or C,9		could be written as Cadd9 or C,9

	== Non-tertian chords ==		= Non-tertian chords =
	Of course, any chord that exists in 12edo can still be expressed in 22edo. We have many non-tertian triads including suspended chords, chords with no thirds, chords with no fifths, etc. We can adopt the same conventions from standard chord notation and apply them to 22edo.		Of course, any chord that exists in 12edo can still be expressed in 22edo. We have many non-tertian triads including suspended chords, chords with no thirds, chords with no fifths, etc. We can adopt the same conventions from standard chord notation and apply them to 22edo.

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	Of course, there are instances where notating a chord might be difficult, if there are large clusters of notes, for instance. Non-standard labels might need to be referred to or invented. Or, once could simply use standard sheet music notation, which can express any number of notes with absolute clarity.		Of course, there are instances where notating a chord might be difficult, if there are large clusters of notes, for instance. Non-standard labels might need to be referred to or invented. Or, once could simply use standard sheet music notation, which can express any number of notes with absolute clarity.

	== Additional resources ==		= Additional resources =
	Video of the tertian triads of 22edo:		Video of the tertian triads of 22edo:

	https://www.youtube.com/watch?v=fMeRlKlreV8		https://www.youtube.com/watch?v=fMeRlKlreV8

	== Contributors ==		= Contributors =

	Official members of TOTY 2025, as identified by their discord handles at the time:<blockquote>Nick Vuci (project lead)		Official members of TOTY 2025, as identified by their discord handles at the time:<blockquote>Nick Vuci (project lead)

Stalefleas: okkk

2025-09-27T15:01:45Z

okkk

← Older revision		Revision as of 15:01, 27 September 2025
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	Of course, there are instances where notating a chord might be difficult, if there are large clusters of notes, for instance. Non-standard labels might need to be referred to or invented. Or, once could simply use standard sheet music notation, which can express any number of notes with absolute clarity.		Of course, there are instances where notating a chord might be difficult, if there are large clusters of notes, for instance. Non-standard labels might need to be referred to or invented. Or, once could simply use standard sheet music notation, which can express any number of notes with absolute clarity.

			== Additional resources ==
			Video of the tertian triads of 22edo:

			https://www.youtube.com/watch?v=fMeRlKlreV8

	== Contributors ==		== Contributors ==
			Official members of TOTY 2025, as identified by their discord handles at the time:<blockquote>Nick Vuci (project lead)

			stalefleas (project lead)

			Sevish

			pailiaq

			maily

			Wrenharmonic

			Domin

			Ebooone

			bartonius

			Colonizor48

			ground

			x e n o [ i ] n d e x

			dogwithabome

			YoVariable

			54edo Pajara

			CompactStar

			Samikata

			MidnightBlue

			j87j]oi:bu

			recentlymaterialized

			MR. LEAKY 666

			Romeolz

			don page commata

			The Universe of Music

			Alexei</blockquote>

Stalefleas: yes

2025-09-27T14:49:37Z

yes

@@ Line 1: / Line 1: @@
 [this page is still in progress]
-= 22edo chord and interval notation =
 The following ideas have been formed out as part of the first Tuning of the Year project (for year 2025), hereafter referred to as TOTY. The focus of the original TOTY was 22edo, which was voted on by the Xenharmonic Alliance discord.
@@ Line 12: / Line 15: @@
 Including ups and downs notation, we have at least four distinct methods of identifying chords in 22edo. These methods are all comprehensive, meaning one can reasonably identify any chord just as well as one can identify chords in 12edo using standard chord labels. In sum, we have ups and downs notation, classic notation, double-qualifier notation, and temperament notation.
-=== Intervals ===
+== Intervals ==
 Using a "sounds-like" system of interval naming, we can identify 22edo as having the following intervals:
 {| class="wikitable"
@@ Line 788: / Line 791: @@
 Disambiguation is not necessary for all chords, but defaulting to using it could lead to greater consistency in notation.

Stalefleas: /* Temperament Notation */

2025-09-27T14:24:05Z

Temperament Notation

Show changes

Stalefleas: still writing this article

2025-09-27T13:13:40Z

still writing this article

Show changes

Stalefleas: started this page

2025-09-27T12:48:14Z

started this page

New page

[this page is still in progress]

= 22edo chord and interval notation =
The following ideas have been formed out as part of the first Tuning of the Year project (for year 2025), hereafter referred to as TOTY. The focus of the original TOTY was 22edo, which was voted on by the Xenharmonic Alliance discord.

Our objective was to flesh out 22edo music theory, arrive at a deeper understanding, and provide resources to help beginners learn how to think about and play in 22edo. The most rigorous work in this tuning had already been accomplished. Ups and downs notation sufficiently identifies the notes and chords, and the most important chords have already been identified and labelled.

Most of our work was in assessing our overall impressions of the tuning, discovering what language was available to discuss harmonies in this tuning, and to check existing nomenclature against our intuitive grasp of what things sound like. Ultimately we arrived at a nomenclature that explains 22edo in terms of how it sounds, as opposed to how it conforms to the logic of the pythagorean circle of fifths. Note names have been unaltered, but some chord and interval names have been altered and potentially refined.

When TOTY began, there was one existing system of chord nomenclature that covers 22edo, Kite Giedraitis' ups and down notation. Most of us were unfamiliar with the naming convention of this system. In developing our own systems of nomenclature, Kite reached out to us with information on his existing system.

Including ups and downs notation, we have at least four distinct methods of identifying chords in 22edo. These methods are all comprehensive, meaning one can reasonably identify any chord just as well as one can identify chords in 12edo using standard chord labels. In sum, we have ups and downs notation, classic notation, double qualifier notation, and temperament notation.

=== Intervals ===
Using a "sounds-like" system of interval naming, we can identify 22edo as having the following intervals:
{| class="wikitable"
|+
!edosteps
!symbol
!spoken name
!size (in cents)
|-
|1\22
|s2
|subminor second
|54.5
|-
|2\22
|m2
|minor second
|109.1
|-
|3\22
|n2
|neutral second
|163.6
|-
|4\22
|M2
|major second
|218.2
|-
|5\22
|s3
|subminor third
|272.7
|-
|6\22
|m3
|minor third
|327.3
|-
|7\22
|M3
|major third
|381.8
|-
|8\22
|S3
|supermajor third
|436.4
|-
|9\22
|p4
|perfect fourth
|490.9
|-
|10\22
|M4
|major fourth
|545.5
|-
|11\22
|S4/s5
|supermajor fourth
subminor fifth
|600
|-
|12\22
|m5
|minor fifth
|654.5
|-
|13\22
|P5
|perfect fifth
|709.1
|-
|14\22
|s6
|subminor sixth
|763.6
|-
|15\22
|m6
|minor sixth
|818.2
|-
|16\22
|M6
|major sixth
|872.7
|-
|17\22
|S6
|supermajor sixth
|927.3
|-
|18\22
|m7
|minor seventh
|981.8
|-
|19\22
|n7
|neutral seventh
|1036.4
|-
|20\22
|M7
|major seventh
|1090.9
|-
|21\22
|S7
|supermajor seventh
|1145.5
|-
|22\22
|p8
|octave
|1200
|}
Note that this is contrary to the established convention of referring to the 6\22 interval as the "upminor" and the 7\22 interval as the "downmajor". Generally speaking, we felt that these intervals simply sound like minor and major intervals, respectively. Also, their lesser and greater counterparts, 5\22 and 8\22, which are labelled on the 22edo page as "minor" and "major," sound more like subminor and supermajor intervals. The nearest LCJI approximations to these two intervals, 7/6 (266.8c) and 9/7 (435c) are typically defined as subminor and supermajor.

One can see that there is some inconsistency in qualities across the intervals. Seconds and sevenths are defined as minor, neutral, major, and supermajor, while thirds and sixths are defined as subminor, minor, major, and supermajor. This simply seems more accurate to the sound. Note that symmetry is still preserved across the tritone.

While obviously, there is some subjectivity here, and the possibility of an even more refined perspective. But this seems good enough to talk about 22edo in a way that is intuitive to what we are hearing.

== Triads ==
In order to communicate the chords of 22edo, it is necessary to identify the names of the tertian triads. Adding sevenths to our triads gives us many practical chords that will be used by most composers and musicians. Adding our standard modifications to these, adding the sevenths, and alterations, gives us a complete system with which to name any chord. Here a triad is defined explicitly as a tertian triad, being a chord made out of two stacked thirds. Only the subminor, minor, major, and supermajor thirds (5\22, 6\22, 7\22, 8\22) are considered.

There are (at least) four comprehensive systems for naming chords in 22edo: ups and downs notation, classic notation, double qualifier notation, and temperament notation. Ups and downs notation adheres to pythagorean logic in naming all chords and intervals, and is oldest and most established of the four. TOTY was not involved in its inception. The other three were created in tandem, and are quite closely related.

For consistency and convenience, all chords are defined on the root of C.

=== Classic Notation ===
The classic notation system is intended to be intuitive and clear. Chord labels are very similar to 12edo chord symbols. With the exception of ups and downs, which are standard accidentals in many microtonal systems, no new chord symbols are introduced.

Many tertian triads in 22edo have altered fifths. In classic notation, the alteration is spelled out explicitly. The chord C - E - vG would be spelled as a CS(v5).

The tertian triads in classic notation would be spelled thusly:
{| class="wikitable"
|+
!Note names
!Interval sizes
!Chord label
!Spoken name
|-
|C Eb Gb
|s3 s3
|Csb5
|C subdiminished
|-
|C Eb ^Gb
|s3 m3
|Cs^b5
|C subminor up-flat five
|-
|C ^Eb ^Gb
|m3 s3
|Cdim
|C diminished
|-
|C Eb vG
|s3 M3
|Csv5
|C subminor down five
|-
|C ^Eb vG
|m3 m3
|Cmv5
|C minor down five
|-
|C vE vG
|M3 s3
|Cv5
|C down-five
|-
|C Eb G
|s3 S3
|Cs
|C subminor
|-
|C vEb G
|m3 M3
|Cm
|C minor
|-
|C vE G
|M3 m3
|C
|C (major)
|-
|C E G
|S3 s3
|CS
|C supermajor
|-
|C vEb ^G
|m3 S3
|Cm^5
|C minor up five
|-
|C vE ^G
|M3 M3
|Caug
|C augmented
|-
|C E ^G
|S3 m3
|CS^5
|C supermajor up five
|-
|C vE vG#
|M3 S3
|Cv#5
|C down-sharp five
|-
|C E vG#
|S3 M3
|CSv#5
|C supermajor down-sharp five
|-
|C E G#
|S3 S3
|CS#5
|C supermajor sharp five
|}
In this system, chords are quite clear. For maximum clarity, one could also opt to call the diminished chord "C minor up-flat five" and call the augmented chord "C major up five".

While the chord labels can be completely unambiguous written in this way, many people do not write ups and downs before the note they modify. In this case, it would be necessary to include the alterations of the fifth either in parenthesis or otherwise demarcated. However, it's quite clean if ups and downs are written before the note they modify. For instance, written correctly, ^D - F# ^A would be written as:

^D5

or written without respect to this convention:

D^(5)

since if this chord were written as D^5, it would be unclear if the root was being modified or the fifth.