Edϕ: Difference between revisions
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Add Music section, starting with Bryan Deister's ''12edΦ improv'' (2026) |
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Various equal divisions of the octave have close approximations of [[acoustic phi]], or <math>φ</math>, ≈833.090296357¢. | Various equal divisions of the octave have close approximations of [[acoustic phi]], or <math>φ</math>, ≈833.090296357¢. | ||
If the <math>m^{th}</math> step of <math>n</math><span> | If the <math>m^{th}</math> step of <math>n</math><span>edo is a close approximation of <math>φ</math>, the <math>n^{th}</math> step of <math>m</math><span>ed<math>φ</math> will be a close approximation of 2. | ||
For example, the 7th step of | For example, the 7th step of [[10edo]] is 840¢, and the 10th step of 7ed<math>φ</math> is ≈1190.128995¢. | ||
As another example, the 9th step of | As another example, the 9th step of [[13edo]] is ≈830.7692308¢, and the 13th step of [[9edϕ|9ed<math>φ</math>]] is ≈1203.35265¢. | ||
Such <math>m</math><span>ed<math>φ</math> are interesting as variants of their respective <math>n</math><span>ed<math>2</math><span>, introducing some combination tone powers. | Such <math>m</math><span>ed<math>φ</math> are interesting as variants of their respective <math>n</math><span>ed<math>2</math><span>, introducing some combination tone powers. | ||
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cet46.scl 18 18th root of phi, Walter O´Connell (1993) | cet46.scl 18 18th root of phi, Walter O´Connell (1993) | ||
== Music == | |||
; [[Bryan Deister]] | |||
* [https://www.youtube.com/shorts/JrGYILddm64 ''12edΦ improv''] (2026) | |||
== See also == | |||
* [[EDe]] | |||
* [[Acoustic pi]] | |||
* [[User:Eliora/Phi to the phi]] | |||
[[Category:Golden ratio]] | [[Category:Golden ratio]] | ||
{{todo|inline=1|improve synopsis|improve readability}} | |||