Golden ratio: Difference between revisions

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The '''golden ratio''' or '''phi''' (Greek letter ~~Φ /~~ φ / ϕ) may be defined by a/b such that a/b = (a+b)/a. It follows that ϕ-1 = 1/ϕ, and also that ϕ = (1+sqrt(5))/2, or approximately 1.6180339887... ϕ is an irrational number that appears in many branches of mathematics.

The '''golden ratio''' or '''phi''' (Greek letter φ / ϕ) may be defined by a/b such that a/b = (a+b)/a. It follows that ϕ-1 = 1/ϕ, and also that ϕ = (1+sqrt(5))/2, or approximately 1.6180339887... ϕ is an irrational number that appears in many branches of mathematics.

~~[http://en.wikipedia.org/wiki/Golden_ratio Wikipedia article on phi]~~

== 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]]. [[Lemba]] is particularly notable for approximating both simply and accurately simultaneously, at a generator + a period for acoustic and 2 generators for logarithmic, making it an excellent choice for experimenting with phi based composition. [[Triforce]] is also essentially based on dividing the 1/3 octave period into logarithmic phi sized fractions.

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-The '''golden ratio''' or '''phi''' (Greek letter Φ / φ / ϕ) may be defined by a/b such that a/b = (a+b)/a. It follows that ϕ-1 = 1/ϕ, and also that ϕ = (1+sqrt(5))/2, or approximately 1.6180339887... ϕ is an irrational number that appears in many branches of mathematics.
+{{Wikipedia}}
+The '''golden ratio''' or '''phi''' (Greek letter φ / ϕ) may be defined by a/b such that a/b = (a+b)/a. It follows that ϕ-1 = 1/ϕ, and also that ϕ = (1+sqrt(5))/2, or approximately 1.6180339887... ϕ is an irrational number that appears in many branches of mathematics.
-[http://en.wikipedia.org/wiki/Golden_ratio Wikipedia article on phi]
 == 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]]. [[Lemba]] is particularly notable for approximating both simply and accurately simultaneously, at a generator + a period for acoustic and 2 generators for logarithmic, making it an excellent choice for experimenting with phi based composition. [[Triforce]] is also essentially based on dividing the 1/3 octave period into logarithmic phi sized fractions.