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TromboneBoi9

Joined 2 May 2023
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==Extended Ups and Downs ==
==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.
See [[User:TromboneBoi9/Extended Ups and Downs]]
 
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.
 
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: '''/''' (pitch up) and '''\''' (pitch down). Single edosteps are still notated with arrows: '''^''' and '''v'''.
 
Here's a full example in [[37edo|37-EDO]] where the syntonic comma is 2 steps large:
{| class="wikitable mw-collapsible"
!Steps
!Pythagorean notation
!Old notation
!New notation
|-
|0
|D
|D
|D
|-
|1
|Eb
|Eb
|Eb
|-
|2
|Fb
|^Eb
|/D
|-
|3
|Gbb
|^^Eb
|/Eb
|-
|4
|Bx
|vvD#
|\D#
|-
|5
|Cx
|vD#
|\E
|-
|6
|D#
|D#
|D#
|-
|7
|E
|E
|E
|-
|8
|F
|F
|F
|-
|9
|Gb
|Gb
|Gb
|-
|10
|Abb
|^Gb
|/F
|-
|11
|Bbbb
|^^Gb
|/Gb
|-
|12
|Dx
|vvF#
|\F#
|-
|13
|E#
|vF#
|\G
|-
|14
|F#
|F#
|F#
|-
|15
|G
|G
|G
|-
|16
|Ab
|Ab
|Ab
|-
|17
|Bbb
| ^Ab
|/G
|-
|18
|Cbb
|^^Ab
| /Ab
|-
| 19
| Ex
|vvG#
|\G#
|-
|20
|Fx
|vG#
| \A
|-
|21
|G#
| G#
|G#
|-
|22
|A
|A
|A
|-
|23
|Bb
|Bb
|Bb
|-
|24
|Cb
|^Bb
|/A
|-
|25
|Dbb
|^^Bb
|\Bb
|-
|26
|F#x
|vvA#
|\A#
|-
|27
|Gx
|vA#
|\B
|-
|28
| A#
|A#
|A#
|-
|29
|B
|B
|B
|-
|30
|C
|C
|C
|-
|31
|Db
|Db
|Db
|-
|32
|Ebb
|^Db
|/C
|-
|33
|Fbb
|^^Db
|/Db
|-
|34
|Ax
|vvC#
|\C#
|-
|35
|B#
|vC#
|\D
|-
|36
|C#
|C#
|C#
|-
|37
|D
|D
|D
|}
For systems with a negative syntonic comma (most often in sub-meantone systems), use ''')''' (pitch up) and '''(''' (pitch down) instead of '''/''' and '''\'''.
 
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|13b-EDO]] where the syntonic comma is -2 steps (technically):
{| class="wikitable mw-collapsible"
!Steps
!Pythagorean/old notation
!26-EDO Subset
!New notation
|-
|0
|D
|D
|D
|-
|1
|E
|Dx, Ebb
|E, )C
|-
|2
|Eb
| E
|Eb, )D
|-
|3
|Fx
|Ex, Fb
|)E, (F
|-
|4
|F#
|F#
| F#, (G
|-
| 5
|F
|Gb
|F, (A
|-
| 6
|G
|G#
|G, (B
|-
|7
|A
|Ab
|A, )F
|-
|8
|B
| A#
|B, )G
|-
|9
|Bb
|Bb
| Bb, )A
|-
|10
|Cx
|B#
|)B, (C
|-
|11
|C#
|C
|C#, (D
|-
|12
|C
|Cx, Dbb
|C, (E
|-
|13
|D
|D
|D
|}
For systems with describable quarter tones, you can optionally use ad-lib quarter tone notation. Though for many systems ([[10edo|10]], [[17edo|17]], [[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]] with '''+''' for a quartertone sharp and '''d''' for a quartertone flat:
{| 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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