Logarithmic phi
Jump to navigation
Jump to search
| Expression | [math]2^{\varphi} = 2^{\frac{1+\sqrt{5} } {2} }[/math] |
| Size in cents | 1941.6408¢ |
| Name | logarithmic phi |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.3665 bits |
Logarithmic phi, or 1200*[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 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¢.
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
- Father temperament
- Aurora temperament
- Triforce divides an 1/3 octave period into logarithmic-phi-sized fractions.
- Music