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Stalefleas

Joined 30 October 2024
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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.  
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.
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 ===
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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.


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.  
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.
For consistency and convenience, all chords are defined on the root of C.
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|+
|+
!Note names
!Note names
!Edosteps
!Interval sizes
!Interval sizes
!Chord label
!Chord label
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|-
|-
|C Eb Gb
|C Eb Gb
|0 5 10
|s3 s3
|s3 s3
|Csb5
|Csb5
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|-
|-
|C Eb ^Gb
|C Eb ^Gb
|0 5 11
|s3 m3
|s3 m3
|Cs^b5
|Cs^b5
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|-
|-
|C ^Eb ^Gb
|C ^Eb ^Gb
|0 6 11
|m3 s3
|m3 s3
|Cdim
|Cdim
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|-
|-
|C Eb vG
|C Eb vG
|0 5 12
|s3 M3
|s3 M3
|Csv5
|Csv5
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|-
|-
|C ^Eb vG
|C ^Eb vG
|0 6 12
|m3 m3
|m3 m3
|Cmv5
|Cmv5
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|-
|-
|C vE vG
|C vE vG
|0 7 12
|M3 s3
|M3 s3
|Cv5
|Cv5
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|-
|-
|C Eb G
|C Eb G
|0 5 13
|s3 S3
|s3 S3
|Cs
|Cs
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|-
|-
|C vEb G
|C vEb G
|0 6 13
|m3 M3
|m3 M3
|Cm
|Cm
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|-
|-
|C vE G
|C vE G
|0 7 13
|M3 m3
|M3 m3
|C
|C
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|-
|-
|C E G
|C E G
|0 8 13
|S3 s3
|S3 s3
|CS
|CS
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|-
|-
|C vEb ^G
|C vEb ^G
|0 6 14
|m3 S3
|m3 S3
|Cm^5
|Cm^5
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|-
|-
|C vE ^G
|C vE ^G
|0 7 14
|M3 M3
|M3 M3
|Caug
|Caug
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|-
|-
|C E ^G
|C E ^G
|0 8 14
|S3 m3
|S3 m3
|CS^5
|CS^5
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|-
|-
|C vE vG#
|C vE vG#
|0 7 15
|M3 S3
|M3 S3
|Cv#5
|Cv#5
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|-
|-
|C E vG#
|C E vG#
|0 8 15
|S3 M3
|S3 M3
|CSv#5
|CSv#5
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|-
|-
|C E G#
|C E G#
|0 8 16
|S3 S3
|S3 S3
|CS#5
|CS#5
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since if this chord were written as D^5, it would be unclear if the root was being modified or the fifth.
since if this chord were written as D^5, it would be unclear if the root was being modified or the fifth.
=== Double-Qualifier Notation ===
In order to avoid using many alterations, we can actually describe every triad based on the quality of its third and the quality of its fifth. Using the interval system above, and the necessary triads, we have seven qualities of fifth: diminished, subminor, minor, perfect, major, supermajor, and augmented. These intervals are 10\22, 11\22, 12\22, 13\22, 14\22, 15\22, and 16\22.
While double-qualifier notation is not immediately obvious, it is quite easy to understand, and is basically interchangeable with classic notation. The advantage to using double-qualifier notation it does not require writing alterations for every type of fifth. In actuality, this is somewhat consistent with 12-edo nomenclature, which usually doesn't explicitly notate altered fifths in chord symbols (except in modern styles like jazz). For instance, the diminished fifth is communicated by the symbol for diminished triad, and the augmented fifth is communicated by the symbol for the augmented triad.
{| class="wikitable"
!Note names
!Edosteps
!Interval sizes
!DQ Label
!DQ spoken name
!Classic label
|-
|C Eb Gb
|0 5 10
|s3 s3
|Csd
|C subminor diminished
|Csb5
|-
|C Eb ^Gb
|0 5 11
|s3 m3
|Css
|C double subminor
|Cs^b5
|-
|C ^Eb ^Gb
|0 6 11
|m3 s3
|Cms
|C minor subminor
|Cdim
|-
|C Eb vG
|0 5 12
|s3 M3
|Csm
|C subminor minor
|Csv5
|-
|C ^Eb vG
|0 6 12
|m3 m3
|Cmm
|C doubleminor
|Cmv5
|-
|C vE vG
|0 7 12
|M3 s3
|CMm
|C major minor
|Cv5
|-
|C Eb G
|0 5 13
|s3 S3
|Cs
|C subminor
|Cs
|-
|C vEb G
|0 6 13
|m3 M3
|Cm
|C minor
|Cm
|-
|C vE G
|0 7 13
|M3 m3
|C
|C (major)
|C
|-
|C E G
|0 8 13
|S3 s3
|CS
|C supermajor
|CS
|-
|C vEb ^G
|0 6 14
|m3 S3
|CmM
|C minor major
|Cm^5
|-
|C vE ^G
|0 7 14
|M3 M3
|CMM
|C double major
|Caug
|-
|C E ^G
|0 8 14
|S3 m3
|CSM
|C supermajor major
|CS^5
|-
|C vE vG#
|0 7 15
|M3 S3
|CMS
|C major supermajor
|Cv#5
|-
|C E vG#
|0 8 15
|S3 M3
|CSS
|C double supermajor
|CSv#5
|-
|C E G#
|0 8 16
|S3 S3
|CSA
|C supermajor augmented
|CS#5
|}
If writing triads, including the 5 is optional. One could opt to include the 5, especially to maintain clarity when writing seventh chords or extended chords (explored in more detail below). For instance, Css could be written as Css5 or Cs(s5).
An advantage to this system is that ups and downs can be used to define alterations beyond fifths and sevenths. A disadvantage is that one must learn the various qualities of the fifth as defined by this system, and the chord names sound very similar. It is also contrary to the usual method of chord qualification, where two qualifiers typically define the quality of the triad and the seventh. For instance, C minor-major is shorthand in 12edo for a minor triad with a major seventh. In this double qualifier system, the same chord should be explicitly called a C minor major-seventh, as opposed to C minor major-fifth.
=== Temperament Notation ===
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