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TromboneBoi9

Joined 2 May 2023
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Currently experimenting with anti-diatonic stuff like EDOs 9, 11, 13, 16, and 23.
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 [[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.


'''[https://akahler.w3spaces.com/ I have a website!!]'''
'''[https://akahler.w3spaces.com/ I have a website!!]'''


== 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.
 
==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.


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.
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.
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|17
|17
|Bbb
|Bbb
|^Ab
| ^Ab
|^G
|^G
|-
|-
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|Cbb
|Cbb
|^^Ab
|^^Ab
|^Ab
| ^Ab
|-
|-
|19
| 19
|Ex
| Ex
|vvG#
|vvG#
|vG#
|vG#
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|Fx
|Fx
|vG#
|vG#
|vA
| vA
|-
|-
|21
|21
|G#
|G#
|G#
| G#
|G#
|G#
|-
|-
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|F#x
|F#x
|vvA#
|vvA#
|^A#
|vA#
|-
|-
|27
|27
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|-
|-
|28
|28
|A#
| A#
|A#
|A#
|A#
|A#
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|2
|2
|Eb
|Eb
|E
| E
|Eb, (D
|Eb, (D
|-
|-
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|F#
|F#
|F#
|F#
|F#, )G
| F#, )G
|-
|-
|5
| 5
|F
|F
|Gb
|Gb
|F, )A
|F, )A
|-
|-
|6
| 6
|G
|G
|G#
|G#
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|8
|8
|B
|B
|A#
| A#
|B, (G
|B, (G
|-
|-
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|Bb
|Bb
|Bb
|Bb
|Bb, (A
| Bb, (A
|-
|-
|10
|10
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''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.''
''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 ==
== Cloudy scales==
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.
I don't know about you, but I love the seventh harmonic. These [[MOS scale|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 [[26edo|26-EDO]]; it approximates the whole of 26-EDO when extended to a 5L21s MOS, which I dub '''''Cumulus Alpha Holo'''''.


=== Cumulus Alpha ===
''That's right. We're comparing JI to EDOs instead of the other way around.''
'''''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"
{| class="wikitable mw-collapsible"
!Steps
! Steps
!Ratio
!Ratio
!Cents
!Cents
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|0
|0
|-
|-
|1
| 1
|16807/16384
| 16807/16384
|43.130
|43.130
|1
|1
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|}
|}


=== Cumulus Beta ===
===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.
'''''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, with a mean difference of about 0.409 cents, proving 9-EDO's place as an exceptional 7-limit approximation.
{| class="wikitable mw-collapsible"
{| class="wikitable mw-collapsible"
!Steps
!Steps
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!9-EDO Difference
!9-EDO Difference
|-
|-
|0
| 0
|1/1
|1/1
|0.000
|0.000
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|}
|}


=== Cumulus Gamma ===
===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.
'''''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 7 cents, with a mean difference of 3.199 cents.
{| class="wikitable mw-collapsible"
{| class="wikitable mw-collapsible"
!Steps
!Steps
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