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]

DECIMAL APPROXIMATION | ||

1:1 | 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 | 2 | Octave |

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See Also

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