Logarithmic phi: Difference between revisions
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{{Infobox Interval | |||
| Ratio = 2^{\varphi} {{=}} 2^{\frac{1+\sqrt{5} }{2} } | |||
| Cents = 1941.640786499874 | |||
| Name = logarithmic phi | |||
}} | |||
'''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''', 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. | ||
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* [http://www.elvenminstrel.com/music/tuning/horagrams/horagram_intro.htm 5- to 9-tone, octave-repeating scales from Wilson's Golden Horagrams of the Scale Tree], by [[David Finnamore]] | * [http://www.elvenminstrel.com/music/tuning/horagrams/horagram_intro.htm 5- to 9-tone, octave-repeating scales from Wilson's Golden Horagrams of the Scale Tree], by [[David Finnamore]] | ||
[[Category:Golden ratio]] | [[Category:Golden ratio]] | ||
Revision as of 17:50, 27 October 2022
| 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 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