Xenharmonic Wiki

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 [[EDO|EDOs]], free [[Just intonation|JI]], and various [[Musical notation|notations]].


Currently experimenting with anti-diatonic stuff like EDOs 9, 11, 13, 16, and 23.
Here's [https://tilde.town/~tromboneboi9/ my website], it's got various things from photos to web-apps as well as scales I've designed.


'''[https://akahler.w3spaces.com/ I have a website!!]'''
Here's [https://tromboneboi9.github.io my GitHub page], where I might put various web-apps and web development projects.


== An idea for notation I had ==
I also exist on the [https://discord.com/invite/FSF5JFT XA Discord], currently under the alias ''Sir Semiflat''.
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 temperaments is no longer the closest the EDO has to 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.
<!--
== Xenharmonic Discography ==
As of mid-November 2024 (non-comprehensive)


In essence, instead of solely relying on Pythaogrean 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.
* '''''Torn Gamelan''''' for solo piano in [[31edo]], 2023
* '''''Apollo's Broken Piano''''' for solo piano in [[7-limit|7-limit just intonation]], 2023
* '''''Chicago Olēka''''' for rock band in [[19edo]], 2023
* '''''A Harmonization of a Microtonal Etude''''' for string quartet in [[24edo]], 2024
-->


For single edosteps, we can instead use a sort of slash-like symbol Bosanquet used in his notation, and perhaps stack them on top of each other to use less horizontal space.
== Pages I've contributed to ==


Here's a full example in [[37edo|37-EDO]]:
* [[Harmonic Scale]]
{| class="wikitable mw-collapsible"
* [[HEJI]]
!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#
|vD#
|-
|5
|Cx
|vD#
|vE
|-
|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#
|vF#
|-
|13
|E#
|vF#
|vG
|-
|14
|F#
|F#
|F#
|-
|15
|G
|G
|G
|-
|16
|Ab
|Ab
|Ab
|-
|17
|Bbb
|^Ab
|^G
|-
|18
|Cbb
|^^Ab
|^Ab
|-
|19
|Ex
|vvG#
|vG#
|-
|20
|Fx
|vG#
|vA
|-
|21
|G#
|G#
|G#
|-
|22
|A
|A
|A
|-
|23
|Bb
|Bb
|Bb
|-
|24
|Cb
|^Bb
|^A
|-
|25
|Dbb
|^^Bb
|vBb
|-
|26
|F#x
|vvA#
|^A#
|-
|27
|Gx
|vA#
|vB
|-
|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#
|vC#
|-
|35
|B#
|vC#
|vD
|-
|36
|C#
|C#
|C#
|-
|37
|D
|D
|D
|}
And for anti-diatonic systems, use '''(''' and ''')''' instead of '''^''' and '''v''', using <u>harmonic notation</u>.


An example in [[13edo|13-EDO]]:
== Subpages ==
{| 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
|}
''I have also devised custom accidentals for quartertones 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 ==
{{Special:PrefixIndex/User:TromboneBoi9/}}
I don't know about you, but I love the seventh harmonic. These 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 [[26edo|26-EDO]]; it approximates the whole of 26-EDO when extended to a 5L21s MOS, which I dub '''''Cumulus Alpha Holo'''''.
{| class="wikitable mw-collapsible"
!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. It approximates all intervals of [[9edo|9-EDO]] within a cent, proving 9-EDO's place as an exceptional 7-limit approximation.
{| class="wikitable mw-collapsible"
!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 [[11edo|11-EDO]] within 10 cents.
{| class="wikitable mw-collapsible"
!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
|}
Retrieved from "https://en.xen.wiki/w/User:TromboneBoi9"