Logarithmic phi: Difference between revisions

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'''Logarithmic phi''', or 1200*[[Phi|ϕ]] cents = 1941.6 cents (or, octave-reduced, 741.6 cents) is useful as a generator, for example in [[Erv Wilson]]'s "Golden Horagrams".
'''Logarithmic phi''', or 1200*[[Phi|ϕ]] cents = 1941.6 cents (or, octave-reduced, 741.6 cents) is useful as a generator, for example in [[Erv Wilson]]'s "Golden Horagrams". As a frequency relation it is <math>2^{\varphi}</math>, or  <math>2^{\varphi - 1} = 2^{1/\varphi}</math> when octave-reduced.


Logarithmic phi is not to be confused with [[acoustic phi]], which is 833.1¢.
Logarithmic phi is not to be confused with [[acoustic phi]], which is 833.1¢.

Revision as of 12:32, 24 February 2022

Logarithmic phi, or 1200*ϕ cents = 1941.6 cents (or, octave-reduced, 741.6 cents) is useful as a generator, for example in Erv Wilson's "Golden Horagrams". As a frequency relation it is [math]\displaystyle{ 2^{\varphi} }[/math], or [math]\displaystyle{ 2^{\varphi - 1} = 2^{1/\varphi} }[/math] when octave-reduced.

Logarithmic phi is not to be confused with acoustic phi, which is 833.1¢.

See also

The MOS patterns generated by logarithmic phi
Related regular temperaments
Music