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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 notation.


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!!]'''


(Just wrote what I plan to be the first "song" of the aforementioned new piece, in [[5edo|5-EDO]]. I'm gonna call the whole thing "'''Clavier du ciel'''", ''clavier from the heavens''.)
I also exist on the [https://discord.com/invite/FSF5JFT XA Discord], currently under the alias ''Sir Semiflat''.


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


I also exist on the [https://discord.com/invite/FSF5JFT XA Discord], currently under the alias ''Sir Semiflat''.
(Update: Progress has started! It will be named "'''A Solo Spectrum Clavier'''".)


<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 constantly been making changes to this page, so I could have made a lot of mistakes here.</u>
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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 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]].


== Cloudy scales==
== Scales n' Stuff==
 
=== Cumulus scales ===
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.
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====
'''''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''''' 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'''''.


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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. Amazingly, it approximates all intervals of [[9edo|9-EDO]] within a cent, with a mean difference of about 0.409 cents.
'''''Cumulus Beta''''' is an 4L5s MOS with [[7/6]] as the generator and [[2/1]] as the period. Amazingly, it approximates all intervals of [[9edo|9-EDO]] within a cent, with a mean difference of about 0.409 cents.
{| class="wikitable mw-collapsible"
{| class="wikitable mw-collapsible"
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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 7 cents, with a mean difference of 3.199 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"
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|0.000
|0.000
|}
|}
=== Blues scale in 10-EDO ===
I kinda like the '''3 1 1 1 2 2''' scale in 10-EDO, it works alright as a Blues scale. I think the second degree (3\10) is a bit sharper than it should, in fact a lot of intervals are "stretched out" in comparison to the Blues scale in 12, but before I didn't have very many scales in 10 under my belt except for the equipentatonic scale.
I dunno, I stick to theory more often than I should; I use ''theoretical'' diatonic intervals/scales more often than intervals/scales that actually ''sound'' diatonic. Luckily I've been experimenting with 14-EDO recently, and I think it's good territory to fix that.
=== Enneatonic scale in "3-limit" ===
[[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.
My thought was, if you use pure 3-limit Just Intonation, you can split the third harmonic into two "ratios" of √3. What would that sound like?
{| class="wikitable"
!Degree
!Ratio
!Cents
|-
|1
|1/1
|0.000
|-
|2
|9/8
|203.910
|-
|3
|81/64
|407.820
|-
|4
|3√3/4
|452.933
|-
|5
|27√3/32
|656.843
|-
|6
|3/2
|701.955
|-
|7
|27/16
|905.865
|-
|8
|√3/1
|950.978
|-
|9
|9√3/8
|1154.888
|-
|10
|2/1
|1200.000
|}
== Irrational HEJI Extensions ==
I've heard [[Golden ratio|phi]] is somewhat usefu in xen areas, as well as other popular irrational numbers, so what would it look like if I extended [[Helmholtz-Ellis notation|HEJI]] (my go-to Just Intonation notation) to support these numbers like factors?
=== Comma ===
==== Golden Ratio ====
The ratio [[Acoustic phi|phi]] adds up to 833.0903 cents, a sharp minor sixth. The Pythagorean minor sixth is [[128/81]], about 792.1800 cents. This leaves a comma of (81*phi)/128, about 40.9103 cents. I dub this interval the '''Golden quartertone'''.
==== Pi ====
The ratio pi/2 adds up to 781.7954 cents, an okay minor sixth. The Pythagorean minor sixth is [[128/81]], about 792.1800 cents. This leaves a comma of 256/(81*pi), about 10.3846 cents. I dub this interval the '''Circular comma'''.
==== Euler's constant ====
The ratio e/2 adds up to 531.2340 cents, a pretty sharp fourth. The Pythagorean perfect fourth is, of course, [[4/3]], 498.0450 cents. This leaves a comma of (3*e)/8, about 33.1890 cents. I dub this interval the '''Eulerian comma'''.
=== Notation ===
For the golden quartertone, I plan to use the symbol Blackwood used in his microtonal notation, because it already resembles a phi symbol (ϕ). For pi, I designed a symbol similar to [https://en.xen.wiki/images/c/cf/Sagittal_sharp_kao.png the 55-comma symbol in Sagittal], but the "arrowhead" is replaced with a circular cap, making the symbol resemble a ''J'' with an extra shaft.
I'm yet to design a symbol for e.
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