User:TromboneBoi9: Difference between revisions

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Hello! My name is Andrew and I like screwing around with xenharmony, especially [[EDO|EDOs]], [[Just intonation|JI]], and various [[Musical notation|notations]].
Hello! My name is Andrew and I like screwing around with xenharmony, especially [[EDO|EDOs]], free [[Just intonation|JI]], and various [[Musical notation|notations]].


''[https://tilde.town/~tromboneboi9/ Here's my website]...if you could call it that.''
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.
 
Here's [https://tromboneboi9.github.io my GitHub page], where I might put various web-apps and web development projects.


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''.
 
<!--
== Xenharmonic Discography ==
== Xenharmonic Discography ==
As of mid-April 2024 (non-comprehensive)
As of mid-November 2024 (non-comprehensive)
 
=== Completed works ===


* '''''Torn Gamelan''''' for solo piano in [[31edo]], 2023
* '''''Torn Gamelan''''' for solo piano in [[31edo]], 2023
Line 14: Line 14:
* '''''Chicago Olēka''''' for rock band in [[19edo]], 2023
* '''''Chicago Olēka''''' for rock band in [[19edo]], 2023
* '''''A Harmonization of a Microtonal Etude''''' for string quartet in [[24edo]], 2024
* '''''A Harmonization of a Microtonal Etude''''' for string quartet in [[24edo]], 2024
* '''''Adagio con demenza''''' for solo piano in [[16edo]], 2023
-->
 
=== Incompleted works ===
 
* '''''Keyboard Suite in 20-equal Tuning''''' for solo keyboard in [[20edo]]
* '''''Treated Four by Four''''' for solo piano in [[16edo]]
 
==Extended Ups and Downs ==
See [[User:TromboneBoi9/Extended Ups and Downs]]
 
== Scales n' Stuff==
 
=== Website ===
I have some scales ready in Scala format on my website [https://tilde.town/~tromboneboi9/scales.html here].
 
=== "Drewnian" Scale System ===
I recently developed an eleven-tone scale system, similar to Western theory in construction but by no means similar in sound. I like to think it's what Wstern tonality would look like if the [[7/4]] was prioritized over the [[5/4]].
 
It involves two scales, each built with a seven-based [[tetrachord]]. One is built with a [[8/7]], 8/7, [[49/48]] tetrachord, generating the "major" intervals; and the other is built with a 49/48, 8/7, 8/7 tetrachord, generating the "minor" intervals. As a result, the scale has very large major seconds and very small minor seconds.
 
{| class="wikitable"
!Degree!!Name!!Ratio!!Cents
|-
|0||P1||1/1||0.000
|-
|1||m2||49/48||35.697
|-
|2||M2||8/7||231.174
|-
|3||m3||7/6||266.871
|-
|4||M3||64/49||462.348
|-
|5||P4||4/3||498.045
|-
|6||P5||3/2||701.955
|-
|7||m6||49/32||737.652
|-
|8||M6||12/7||933.129
|-
|9||m7||7/4||968.826
|-
|10||M7||96/49||1164.303
|-
|11||P8||2/1||1200.000
|}
 
The intent with these weird [[superpyth]]-like constructions is to make [[5-EDO]]-like scales with some [[49/48|extra small intervals]] for spice.
 
It's very easily possible to map this scale to a 12-tone keyboard, in fact it is by design a mimicry of Western tonality. However, there is no tritone. For this interval you can either use the eleventh harmonic [[11/8]], a septimal whole tone below the "minor sixth". or a septimal whole tone above the "major third".
 
=== Enneatonic scale in JI ===
[[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:
 
In 19-tone, 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, measuring around 950.978 cents. What would that sound like?
{| class="wikitable"
!Degree
!Ratio
!Decimal
!Cents
|-
|1
|1/1
|1.0000
|0.000
|-
|2
|9/8
|1.1250
|203.910
|-
|3
|81/64
|1.2656
|407.820
|-
|4
|3√3/4
|1.2990
|452.933
|-
|5
|27√3/32
|1.4614
|656.843
|-
|6
|3/2
|1.5000
|701.955
|-
|7
|27/16
|1.6875
|905.865
|-
|8
|√3/1
|1.7321
|950.978
|-
|9
|9√3/8
|1.9486
|1154.888
|-
|10
|2/1
|2.0000
|1200.000
|}
But of course Saga wasn't looking for a √3 interval, he meant to use the [[7/4|harmonic (subminor) seventh]]. The two intervals are rather close though: the seventh is about 17.848 cents sharper.
 
Using harmonic sevenths of 968.826 cents:
{| class="wikitable"
!Degree
!Ratio
!Decimal
!Cents
|-
|1
|1/1
|1.0000
|0.000
|-
|2
|9/8
|1.1250
|203.910
|-
|3
|81/64
|1.2656
|407.820
|-
|4
|21/16
|1.3125
|470.781
|-
|5
|189/128
|1.4766
|674.691
|-
|6
|3/2
|1.5000
|701.955
|-
|7
|27/16
|1.6875
|905.865
|-
|8
|7/4
|1.7500
|968.826
|-
|9
|63/32
|1.9486
|1172.736
|-
|10
|2/1
|2.0000
|1200.000
|}
Using harmonic sevenths inverted around the third harmonic, or just [[12/7|supermajor sixths (12/7)]], of 933.129 cents:
{| class="wikitable"
!Degree
!Ratio
!Decimal
!Cents
|-
|1
|1/1
|1.0000
|0.000
|-
|2
|9/8
|1.1250
|203.910
|-
|3
|81/64
|1.2656
|407.820
|-
|4
|9/7
|1.2857
|435.084
|-
|5
|81/56
|1.4464
|638.9941
|-
|6
|3/2
|1.5000
|701.955
|-
|7
|27/16
|1.6875
|905.865
|-
|8
|12/7
|1.7143
|933.129
|-
|9
|27/14
|1.9286
|1137.039
|-
|10
|2/1
|2.0000
|1200.000
|}
 
== Irrational HEJI Extensions ==
I've heard [[Golden ratio|phi]] is somewhat useful 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?
 
===Commas===
 
====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 81ϕ/128, about 40.9103 cents. I dub this interval the '''Golden quartertone'''.


====Pi====
== Pages I've contributed to ==
The ratio π/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 256/81π, about 10.3846 cents. I dub this interval the '''Circular comma'''.


====Euler's constant====
* [[Harmonic Scale]]
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'''.
* [[HEJI]]


===Notation===
== Subpages ==
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.
{{Special:PrefixIndex/User:TromboneBoi9/}}

Latest revision as of 03:11, 17 June 2025

Hello! My name is Andrew and I like screwing around with xenharmony, especially EDOs, free JI, and various notations.

Here's my website, it's got various things from photos to web-apps as well as scales I've designed.

Here's my GitHub page, where I might put various web-apps and web development projects.

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

Pages I've contributed to

Subpages

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