Golden ratio: Difference between revisions

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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.

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

== 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.

~~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.~~

[[Category:Golden ratio| ]]

[[Category:Theory]]

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 {{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.
+The '''golden ratio''' or '''phi''' (Greek letter <math>\phi</math> / <math>\varphi</math>) may be defined by <math>\frac{a}{b}</math> such that <math>\frac{a}{b} = \frac{a+b}{a}</math>. It follows that <math>\varphi - 1 = 1 / \varphi</math>, and also that <math>\varphi = \frac{1+\sqrt{5}}{2}</math>, or approximately 1.6180339887... <math>\varphi</math> is an irrational number that appears in many branches of mathematics.
 == 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.
-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.
+[[Category:Golden ratio| ]]
+[[Category:Theory]]