10/05/04. edited 02/10/08: The Golden Spiral or Golden Mean or PHI (1.618...) is a decimal approximation* to the ratio of the Fibonacci Series expressed in Whole Numbers. In order of increasing decimal equivalent value, as shown below, the music interval equivalent oscillates between Minor and Major Sixths. As the PHI ratio decreases a musical interval of Enharmonic Sixths is approached save there is no Enharmonic Sixths in standard music and as such cannot actually be reached any more than the approximation can resolve itself. [see 12.20 - PHI]

1:1 Unison
2:3 1.5  Perfect Fifth
5:8 1.6  Minor Sixth
13:21 1.61538... Minor Sixth
-  - Enharmonic Sixth
21:34 1.61904... Major Sixth
8:13 1.625  Major Sixth
3:5 1.6667  Major Sixth
1:2 Octave

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See Also

Golden Mean
Golden Number
Golden Section
Quadrature of the Circle
12.20 - PHI

Created by Dale Pond. Last Modification: Monday October 21, 2019 03:37:13 MDT by dale.