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TromboneBoi9

Joined 2 May 2023
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Hello! My name is Andrew and I like screwing around with xenharmony, especially notation.
Hello! My name is Andrew and I like screwing around with xenharmony, especially EDOs, JI, and various notations.


''Check it out, I have a website! [https://tilde.town/~tromboneboi9/ Here she is!]''
''[https://tilde.town/~tromboneboi9/ Here's my website]...if you could call it that.''


I also exist on the [https://discord.com/invite/FSF5JFT XA Discord], currently under the alias ''Sir Semiflat''.
I also exist on the [https://discord.com/invite/FSF5JFT XA Discord], currently under the alias ''Sir Semiflat''.
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At some point I plan to make a piece similar to [[wikipedia:Twelve_Microtonal_Etudes_for_Electronic_Music_Media|Easley Blackwood's 12 Etudes]] or [https://aaronandrewhunt.bandcamp.com/album/the-equal-tempered-keyboard Aaron Andrew Hunt's Equal-Tempered Keyboard], an "album" experimenting with a range of different EDO systems.
At some point I plan to make a piece similar to [[wikipedia:Twelve_Microtonal_Etudes_for_Electronic_Music_Media|Easley Blackwood's 12 Etudes]] or [https://aaronandrewhunt.bandcamp.com/album/the-equal-tempered-keyboard Aaron Andrew Hunt's Equal-Tempered Keyboard], an "album" experimenting with a range of different EDO systems.


<u>Keep in mind that I have constantly been making changes to this page, so I could have made a lot of mistakes here.</u>
<u>Keep in mind that I have been making regular changes to this page, so I could have made a lot of mistakes here.</u>


==An idea for notation I had ==
==Extended Ups and Downs ==
Something I noticed in [[Ups and downs notation|regular EDO notation]], relying on [[Pythagorean]] names with an extra layer of accidentals, is that the [[81/64|Pythagorean major third]] in a lot of EDO systems doesn't match the [[5/4|just major third 5/4]]. So, with some thought from Just Intonation notations, I came up with something that I think might be promising.
Something I noticed in [[Ups and downs notation|regular EDO notation]]--relying on [[Pythagorean]] names with an extra layer of accidentals--is that the [[81/64|Pythagorean major third]] in a lot of EDO systems doesn't match the [[5/4|just major third 5/4]]. So, with some thought from Just Intonation notations, I came up with something that I think might be promising.


In essence, instead of solely relying on Pythagorean names and arrows for edosteps in between (which can get unwieldy in larger EDOs, e.g. [[72edo#Intervals|72-EDO]]), I considered giving the [[syntonic comma]] a single symbol instead. That way you can emphasize the [[5-limit]] in your compositions more easily, and it will stay that way when directly read in a different EDO.
In essence, instead of solely relying on Pythagorean names and arrows for edosteps in between (which can get unwieldy in larger EDOs, e.g. [[72edo#Intervals|72-EDO]]), I considered giving the [[syntonic comma]] a single symbol instead. That way you can emphasize the [[5-limit]] in your compositions more easily, and it will stay that way when directly read in a different EDO.
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If your EDO has a different pitch for the just major third and the Pythagorean major third, then of course, it has a syntonic comma that hasn't been tempered out. This won't change much notation-wise for EDOs with a syntonic comma of 0 or 1 step, of course, but it could have an effect on even "sharper" systems like 37-EDO with a larger comma.
If your EDO has a different pitch for the just major third and the Pythagorean major third, then of course, it has a syntonic comma that hasn't been tempered out. This won't change much notation-wise for EDOs with a syntonic comma of 0 or 1 step, of course, but it could have an effect on even "sharper" systems like 37-EDO with a larger comma.


The syntonic comma can be represented by slashes: '''/''' and '''\'''. Single edosteps are still notated with arrows: '''^''' and '''v'''.
The syntonic comma can be represented by slashes: '''/''' (pitch up) and '''\''' (pitch down). Single edosteps are still notated with arrows: '''^''' and '''v'''.


Here's a full example in [[37edo|37-EDO]]:
Here's a full example in [[37edo|37-EDO]] where the syntonic comma is 2 steps large:
{| class="wikitable mw-collapsible"
{| class="wikitable mw-collapsible"
!Steps
!Steps
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|D
|D
|}
|}
For systems with a negative syntonic comma (most often in sub-meantone systems), use ''')''' and '''(''' instead of '''/''' and '''\'''.
For systems with a negative syntonic comma (most often in sub-meantone systems), use ''')''' (pitch up) and '''(''' (pitch down) instead of '''/''' and '''\'''.


Use <u>harmonic notation</u> for anti-diatonic systems.
For anti-diatonic systems, the meantone-favoring flat and sharp symbols are not recommended, but use <u>harmonic notation</u> should they be needed.


An example in [[13edo|13-EDO]]:
An example in [[13edo|13-EDO]] where the syntonic comma is -2 steps (technically):
{| class="wikitable mw-collapsible"
{| class="wikitable mw-collapsible"
!Steps
!Steps
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|D
|D
|}
|}
For systems with describable quarter tones, you can optionally use quarter tone notation. Though for many systems ([[24edo|24]], [[31edo|31]]), the syntonic comma notation makes it redundant; perhaps it could be of use in larger systems like [[41edo|41]], [[48edo|48]], or [[72edo|72]].
For systems with describable quarter tones, you can optionally use ad-lib quarter tone notation. Though for many systems ([[24edo|24]], [[31edo|31]]), the syntonic comma notation makes it redundant; perhaps it could be of use in larger systems like [[41edo|41]], [[48edo|48]], or [[72edo|72]].
 
An example in [[41edo|41-EDO]]:
{| class="wikitable mw-collapsible"
!Steps
!Pythagorean Notation
!Old Notation
!New Notation
!With Quartertones
|-
|0
|D
|D
|D
|D
|-
|1
|Cx
|^D
|/D
|/D
|-
|2
|Fbb
|^^D, vEb
|\Eb
|D+
|-
|3
|Eb
|vD#, Eb
|Eb
|Eb
|-
|4
|D#
|D#, ^Eb
|D#
|D#
|-
|5
|C#x
|^D#, vvE
|/D#
|Ed
|-
|6
|Fb
|vE
|\E
|\E
|-
|7
|E
|E
|E
|E
|-
|8
|Dx
|^E
|/E
|Fd
|-
|9
|Gbb
|vF
|\F
|E+
|-
|10
|F
|F
|F
|F
|-
|11
|E#
|^F
|/F
|/F
|-
|12
|Abbb
|^^F, vGb
|\Gb
|F+
|-
|13
|Gb
|vF#, Gb
|Gb
|Gb
|-
|14
|F#
|F#, ^Gb
|F#
|F#
|-
|15
|Ex
|^F#, vvG
|/F#
|Gd
|-
|16
|Abb
|vG
|\G
|\G
|-
|17
|G
|G
|G
|G
|-
|18
|Fx
|^G
|/G
|/G
|-
|19
|Bbbb
|^^G, vAb
|\Ab
|G+
|-
|20
|Ab
|vG#, Ab
|Ab
|Ab
|-
|21
|G#
|G#, ^Ab
|G#
|G#
|-
|22
|F#x
|^G#, vvA
|/G#
|Ad
|-
|23
|Bbb
|vA
|\A
|\A
|-
|24
|A
|A
|A
|A
|-
|25
|Gx
|^A
|/A
|/A
|-
|26
|Cbb
|^^A, vBb
|\Bb
|A+
|-
|27
|Bb
|vA#, Bb
|Bb
|Bb
|-
|28
|A#
|A#, ^Bb
|A#
|A#
|-
|29
|G#x
|^A#, vvB
|/A#
|Bd
|-
|30
|Cb
|vB
|\B
|\B
|-
|31
|B
|B
|B
|B
|-
|32
|Ax
|^B
|/B
|Cd
|-
|33
|Dbb
|vC
|\C
|B+
|-
|34
|C
|C
|C
|C
|-
|35
|B#
|^C
|/C
|/C
|-
|36
|Ebbb
|^^C, vDb
|\Db
|C+
|-
|37
|Db
|vC#, Db
|Db
|Db
|-
|38
|C#
|C#, ^Db
|C#
|C#
|-
|39
|Bx
|C#^, vvD
|/C#
|Dd
|-
|40
|Ebb
|vD
|\D
|\D
|-
|41
|D
|D
|D
|D
|}


== Scales n' Stuff==
== Scales n' Stuff==
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[[User:SupahstarSaga|Supahstar Saga]] described a scale in [[19-EDO]] in his [https://www.youtube.com/playlist?list=PLha3CFvr8SzwlDpGL9MrJcoN8xOHyowsw ''Exploring 19-TET'' YouTube series] called the Enneatonic scale:
[[User:SupahstarSaga|Supahstar Saga]] described a scale in [[19-EDO]] in his [https://www.youtube.com/playlist?list=PLha3CFvr8SzwlDpGL9MrJcoN8xOHyowsw ''Exploring 19-TET'' YouTube series] called the Enneatonic scale:


Since the third harmonic is an even number of steps in 19 (30 steps), splitting evenly into two harmonic (subminor) sevenths. If you take a major pentatonic scale, put a harmonic seventh in between each fifth, and reduce the whole scale into an octave, you get a nine-tone scale somewhat similar to the [[wikipedia:Double_harmonic_scale|double harmonic scale]] in 12.
In 19-tone, the third harmonic is an even number of steps in 19 (30 steps), splitting evenly into two harmonic (subminor) sevenths. If you take a major pentatonic scale, put a harmonic seventh in between each fifth, and reduce the whole scale into an octave, you get a nine-tone scale somewhat similar to the [[wikipedia:Double_harmonic_scale|double harmonic scale]] in 12.


My thought was, if you use pure 3-limit Just Intonation, you can split the third harmonic into two "ratios" of √3, measuring around 950.978 cents. What would that sound like?
My thought was, if you use pure 3-limit Just Intonation, you can split the third harmonic into two "ratios" of √3, measuring around 950.978 cents. What would that sound like?
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