User:TromboneBoi9: Difference between revisions

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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''.
<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>


==An idea for notation I had ==
==An idea for notation I had ==
Something I noticed in [[Ups and downs notation|regular EDO notation]], relying on Pythagorean names with an extra layer of accidentals, is that the 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 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 making the arrow represent the [[syntonic comma]] instead. 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 anything for EDOs with a syntonic comma less than or equal to one step, of course, but it could have an effect on even "sharper" systems like 37-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]] priority. 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 anything for EDOs with a syntonic comma less than or equal to one step, of course, but it could have an effect on even "sharper" systems like 37-EDO.


For single edosteps, we can instead use a sort of slash-like symbol Bosanquet used in his notation.
The syntonic comma can be represented by a sort of slash-like symbol Bosanquet used in his notation.
 
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]]:
Line 36: Line 40:
|Fb
|Fb
|^Eb
|^Eb
|^D
|/D
|-
|-
|3
|3
|Gbb
|Gbb
|^^Eb
|^^Eb
|^Eb
|/Eb
|-
|-
|4
|4
|Bx
|Bx
|vvD#
|vvD#
|vD#
|\D#
|-
|-
|5
|5
|Cx
|Cx
|vD#
|vD#
|vE
|\E
|-
|-
|6
|6
Line 76: Line 80:
|Abb
|Abb
|^Gb
|^Gb
|^F
|/F
|-
|-
|11
|11
|Bbbb
|Bbbb
|^^Gb
|^^Gb
|^Gb
|/Gb
|-
|-
|12
|12
|Dx
|Dx
|vvF#
|vvF#
|vF#
|\F#
|-
|-
|13
|13
|E#
|E#
|vF#
|vF#
|vG
|\G
|-
|-
|14
|14
Line 111: Line 115:
|Bbb
|Bbb
| ^Ab
| ^Ab
|^G
|/G
|-
|-
|18
|18
|Cbb
|Cbb
|^^Ab
|^^Ab
| ^Ab
| /Ab
|-
|-
| 19
| 19
| Ex
| Ex
|vvG#
|vvG#
|vG#
|\G#
|-
|-
|20
|20
|Fx
|Fx
|vG#
|vG#
| vA
| \A
|-
|-
|21
|21
Line 146: Line 150:
|Cb
|Cb
|^Bb
|^Bb
|^A
|/A
|-
|-
|25
|25
|Dbb
|Dbb
|^^Bb
|^^Bb
|vBb
|\Bb
|-
|-
|26
|26
|F#x
|F#x
|vvA#
|vvA#
|vA#
|\A#
|-
|-
|27
|27
|Gx
|Gx
|vA#
|vA#
|vB
|\B
|-
|-
|28
|28
Line 186: Line 190:
|Ebb
|Ebb
|^Db
|^Db
|^C
|/C
|-
|-
|33
|33
|Fbb
|Fbb
|^^Db
|^^Db
|^Db
|/Db
|-
|-
|34
|34
|Ax
|Ax
|vvC#
|vvC#
|vC#
|\C#
|-
|-
|35
|35
|B#
|B#
|vC#
|vC#
|vD
|\D
|-
|-
|36
|36
Line 213: Line 217:
|D
|D
|}
|}
And for anti-diatonic systems, use '''(''' and ''')''' instead of '''^''' and '''v''', using <u>harmonic notation</u>.
For systems with a negative syntonic comma (most often in anti-diatonic and 7''n''-EDO systems) use ''')''' and '''(''' instead of '''/''' and '''\''', using <u>harmonic notation</u>.


An example in [[13edo|13-EDO]]:
An example in [[13edo|13-EDO]]:
Line 230: Line 234:
|E
|E
|Dx, Ebb
|Dx, Ebb
|E, (C
|E, )C
|-
|-
|2
|2
|Eb
|Eb
| E
| E
|Eb, (D
|Eb, )D
|-
|-
|3
|3
|Fx
|Fx
|Ex, Fb
|Ex, Fb
|(E, )F
|)E, (F
|-
|-
|4
|4
|F#
|F#
|F#
|F#
| F#, )G
| F#, (G
|-
|-
| 5
| 5
|F
|F
|Gb
|Gb
|F, )A
|F, (A
|-
|-
| 6
| 6
|G
|G
|G#
|G#
|G, )B
|G, (B
|-
|-
|7
|7
|A
|A
|Ab
|Ab
|A, (F
|A, )F
|-
|-
|8
|8
|B
|B
| A#
| A#
|B, (G
|B, )G
|-
|-
|9
|9
|Bb
|Bb
|Bb
|Bb
| Bb, (A
| Bb, )A
|-
|-
|10
|10
|Cx
|Cx
|B#
|B#
|(B, )C
|)B, (C
|-
|-
|11
|11
|C#
|C#
|C
|C
|C#, )D
|C#, (D
|-
|-
|12
|12
|C
|C
|Cx, Dbb
|Cx, Dbb
|C, )E
|C, (E
|-
|-
|13
|13

Revision as of 13:25, 24 May 2023

Hello! My name is Andrew and I like screwing around with xenharmony, especially notation.

Currently experimenting with anti-diatonic stuff like EDOs 9, 11, 13, 16, and 23.

At some point I plan to make a piece similar to Easley Blackwood's 12 Etudes or Aaron Andrew Hunt's Equal-Tempered Keyboard, an "album" experimenting with a range of different EDO systems.

I have a website!!

I also exist on the XA Discord, currently under the alias Sir Semiflat.

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

An idea for notation I had

Something I noticed in regular EDO notation, relying on Pythagorean names with an extra layer of accidentals, is that the Pythagorean major third in a lot of EDO systems doesn't match the 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. 72-EDO), I considered giving the syntonic comma priority. 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 anything for EDOs with a syntonic comma less than or equal to one step, of course, but it could have an effect on even "sharper" systems like 37-EDO.

The syntonic comma can be represented by a sort of slash-like symbol Bosanquet used in his notation.

Single edosteps are still notated with arrows: ^ and v.

Here's a full example in 37-EDO:

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 anti-diatonic and 7n-EDO systems) use ) and ( instead of / and \, using harmonic notation.

An example in 13-EDO:

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

I have also devised custom accidentals for quarter tones in both diatonic and anti-diatonic systems, but the image uploading process is being weird so I'll have to figure that out at some point.

Cloudy scales

I don't know about you, but I love the seventh harmonic. These MOS scales are named after the cloudy comma, and use different 7-limit intervals for generators.

Cumulus Alpha

Cumulus Alpha is a 5L6s MOS with 7/4 as the generator and 2/1 as the period. This appears to approximate a subset of 26-EDO; it approximates the whole of 26-EDO when extended to a 5L21s MOS, which I dub Cumulus Alpha Holo.

That's right. We're comparing JI to EDOs instead of the other way around.

Steps Ratio Cents Approx. 26-EDO Degree
0 1/1 0.000 0
1 16807/16384 43.130 1
2 8/7 231.174 5
3 2401/2048 275.304 6
4 64/49 462.348 10
5 343/256 506.478 11
6 512/343 693.522 15
7 49/32 737.652 16
8 4096/2401 924.696 20
9 7/4 968.826 21
10 32768/16807 1155.870 25
11 2/1 1200.000 26

Cumulus Beta

Cumulus Beta is an 4L5s MOS with 7/6 as the generator and 2/1 as the period. Amazingly, it approximates all intervals of 9-EDO within a cent, with a mean difference of about 0.409 cents.

Steps Ratio Cents 9-EDO Difference
0 1/1 0.000 0.000
1 2592/2401 132.516 -0.817
2 7/6 266.871 0.204
3 432/343 399.387 -0.613
4 49/36 533.742 0.409
5 72/49 666.258 -0.409
6 343/216 800.613 0.613
7 12/7 933.129 -0.204
8 2401/1296 1067.484 0.817
9 7/4 1200.000 0.000

Cumulus Gamma

Cumulus Gamma is an 3L8s MOS with 9/7 as the generator and 2/1 as the period. It approximates all intervals of 11-EDO within 7 cents, with a mean difference of 3.199 cents.

Steps Ratio Cents 11-EDO Difference
0 1/1 0.000 0.000
1 729/686 105.252 3.839
2 67228/59049 224.580 -6.398
3 98/81 329.832 -2.559
4 9/7 435.084 1.280
5 6561/4802 540.336 5.119
6 9604/6561 659.664 -5.119
7 14/9 764.916 -1.280
8 81/49 870.168 2.559
9 59049/33614 975.420 6.398
10 1372/729 1094.748 -3.839
11 2/1 1200.000 0.000
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