Logarithmic phi

Interval information

Expression

[math]\displaystyle{ 2^{\varphi} = 2^{\frac{1+\sqrt{5} } {2} } }[/math]

Size in cents

1941.641¢

Name

logarithmic phi

Logarithmic phi, or 1200*[math]\displaystyle{ \varphi }[/math] 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 notable for being the most difficult interval to approximate by EDOs, and as such a "small equal division of logarithmic phi" nonoctave tuning would minimize pseudo-octaves. With or without pseudo-octaves, an "equal division of logarithmic phi" nonoctave tuning forms an Intense Phrygian-Subpental Aeolian mode.

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

Logarithmic phi

See also