Logarithmic phi: Difference between revisions
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| Name = logarithmic phi | | Name = logarithmic phi | ||
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'''Logarithmic phi''', or 1200*[[Phi|<math>\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>2^{\varphi}</math>, or <math>2^{\varphi - 1} = 2^{1/\varphi}</math> when octave-reduced.Logarithmic phi is notable for being the most difficult interval to approximate by [[EDO]]s, and as such an "equal division of logarithmic phi" [[nonoctave]] tuning would minimize pseudo-octaves. | '''Logarithmic phi''', or 1200*[[Phi|<math>\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>2^{\varphi}</math>, or <math>2^{\varphi - 1} = 2^{1/\varphi}</math> when octave-reduced. Logarithmic phi is notable for being the most difficult interval to approximate by [[EDO]]s, and as such an "equal division of logarithmic phi" [[nonoctave]] tuning would minimize pseudo-octaves. | ||
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 08:37, 8 April 2023
| Interval information |
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 an "equal division of logarithmic phi" nonoctave tuning would minimize pseudo-octaves.
Logarithmic phi is not to be confused with acoustic phi, which is 833.1¢.
See also
- Generating a scale through successive divisions of the octave by the Golden Ratio
- Golden meantone
- Metallic MOS
- The MOS patterns generated by logarithmic phi
- Related regular temperaments
- Music