Golden ratio

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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.

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.