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Stalefleas

Joined 30 October 2024
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= 22edo chord and interval notation =
 
todo: add a link to kite's 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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|S3 M3
|S3 M3
|CJ+
|CJ+
|C magic minor
|C magic major
|CSv#5
|CSv#5
|-
|-
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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 =
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.
Thus the chord C11 could include the following notes:
C - vE - G - Bb - D - F
However, in 22edo, it is quite likely that we might want the ^11, as it approximates the eleventh harmonic and want the chord that in total approximates the  4:5:6:7:9:11 chord:
C - vE - G - Bb - D - ^F
This could be notated as C9(^11)
Various extended diminished chords can be specified by appending a sixth. If we alternate minor and subminor thirds, we have
C - ^Eb - ^Gb - vBb
since vBb is enharmonically A, we can consider this chord Cd+6, Cdim6. Or, if one prefers, they might opt for the unwieldy Cm^b5(vb7)
We can also add extensions to triads using "add" or by using the comma from Kite notation.
C - vE - G - D
could be written as Cadd9 or C,9
= 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.
C - F - G
would still simply be a Csus4 chord. But of course in 22edo we also have options like
C - ^F - G
which we might write as Csus^4.
While this is not standard practice, one could borrow the convention of writing powerchords with a "5" to notate chords without thirds. So for instance
C - G - vB
might be major or minor depending on the context, but devoid of such a context (or in a situation where specificity is desired) this could be written as a C5M7. Or, one could follow the existing convention of writing this as CM7(no3).
Some chords are difficult to write, for instance, quartal chords like
C - F - Bb
which is often notated as C7sus4, and could be done here. Or, one could opt to write this as Fsus4/C.
Highly complex chords can be notated using polychord notation. For instance
C - Db - E - F - Gb - G - B
could be written as DbS(7)/CS.
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 =
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>
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