User:TromboneBoi9: Difference between revisions

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

[I've had to make some ~~changes--I~~ do not have a website anymore, but soon enough I will have a new one.]

I've had to make some changes—I do not have a website anymore, but soon enough I will have a new one.

I also exist on the [https://discord.com/invite/FSF5JFT XA Discord], currently under the alias ''Sir Semiflat''.

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.

~~(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>

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====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'''.

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====

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'''.

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====

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'''.

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===

@@ Line 1: / Line 1: @@
 Hello! My name is Andrew and I like screwing around with xenharmony, especially notation.
-[I've had to make some changes--I do not have a website anymore, but soon enough I will have a new one.]
+I've had to make some changes—I do not have a website anymore, but soon enough I will have a new one.
 I also exist on the [https://discord.com/invite/FSF5JFT XA Discord], currently under the alias ''Sir Semiflat''.
 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.
-(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>
@@ Line 567: / Line 565: @@
 ====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'''.
+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====
-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'''.
+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====
-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'''.
+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===