Golden ratio: Difference between revisions

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== Musical applications ==

The golden ratio can be used as a frequency multiplier or as a pitch fraction; in the former case it is known as [[acoustic phi]] and in the latter case it is known as [[logarithmic phi]]. These two versions of phi have completely different musical applications which can be read about in detail on their separate pages. [[Lemba]] is a notable [[regular temperament]] for approximating both ~~versions of~~ phi simultaneously, requiring only two of its [[generators]] for logarithmic phi, and only one each of its generator and [[period]] for acoustic phi.

The golden ratio can be used as a frequency multiplier or as a pitch fraction; in the former case it is known as [[acoustic phi]] and in the latter case it is known as [[logarithmic phi]]. These two versions of phi have completely different musical applications which can be read about in detail on their separate pages. A third interval, the [[phith root of phi]] ([math]\displaystyle{ \sqrt[\varphi]{\varphi} }[/math]), acts as a bridge between the two: it divides acoustic phi logarithmically by phi, enabling golden MOS scales with acoustic phi as the equave.

[[Lemba]] is a notable [[regular temperament]] for approximating both acoustic and logarithmic phi simultaneously, requiring only two of its [[generators]] for logarithmic phi, and only one each of its generator and [[period]] for acoustic phi.

== Compositions based on the golden ratio ==

* ''[[Star Nursery]]'' - [[Sean Archibald]] (2021)

* ''[[Abyss]]'' - [[T.C. Edwards]] (2024)

== External links ==

* [https://sevish.com/2017/golden-ratio-music-interval/ The Golden Ratio as a musical interval] by [[Sevish]]

* [http://tonalsoft.com/enc/p/phi.aspx Phi Φ / phi φ] on [[Tonalsoft Encyclopedia]]

[[Category:Golden ratio]]

[[Category:Irrational intervals]]

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 == Musical applications ==
-The golden ratio can be used as a frequency multiplier or as a pitch fraction; in the former case it is known as [[acoustic phi]] and in the latter case it is known as [[logarithmic phi]]. These two versions of phi have completely different musical applications which can be read about in detail on their separate pages. [[Lemba]] is a notable [[regular temperament]] for approximating both versions of phi simultaneously, requiring only two of its [[generators]] for logarithmic phi, and only one each of its generator and [[period]] for acoustic phi.
+The golden ratio can be used as a frequency multiplier or as a pitch fraction; in the former case it is known as [[acoustic phi]] and in the latter case it is known as [[logarithmic phi]]. These two versions of phi have completely different musical applications which can be read about in detail on their separate pages. A third interval, the [[phith root of phi]] ([math]\displaystyle{ \sqrt[\varphi]{\varphi} }[/math]), acts as a bridge between the two: it divides acoustic phi logarithmically by phi, enabling golden MOS scales with acoustic phi as the equave.
+[[Lemba]] is a notable [[regular temperament]] for approximating both acoustic and logarithmic phi simultaneously, requiring only two of its [[generators]] for logarithmic phi, and only one each of its generator and [[period]] for acoustic phi.
+== Compositions based on the golden ratio ==
+* ''[[Star Nursery]]'' - [[Sean Archibald]] (2021)
+* ''[[Abyss]]'' - [[T.C. Edwards]] (2024)
 == External links ==
+* [https://sevish.com/2017/golden-ratio-music-interval/ The Golden Ratio as a musical interval] by [[Sevish]]
 * [http://tonalsoft.com/enc/p/phi.aspx Phi Φ / phi φ] on [[Tonalsoft Encyclopedia]]
 [[Category:Golden ratio]]
 [[Category:Irrational intervals]]