# Diminished sixth

### From Encyclopedia of Microtonality

Inverse | augmented third |
---|---|

Name | |

Other names | - |

Abbreviation |
d6^{[1]} |

Size | |

Semitones | 7 |

Interval class | 5 |

Just interval |
192:125,^{[2]} 32:21,49:32 |

Cents | |

Equal temperament | 700 |

24 equal temperament | 700 |

Just intonation | 743 |

In classical music from Western culture, a **diminished sixth** ( Play (help·info)) is an interval produced by narrowing a minor sixth by a chromatic semitone.^{[1]}^{[3]} For example, the interval from A to F is a minor sixth, eight semitones wide, and both the intervals from A♯ to F, and from A to F♭ are diminished sixths, spanning seven semitones. Being diminished, it is considered a dissonant interval,^{[4]} despite being equivalent to an interval known for its consonance.

Its inversion is the augmented third, and its enharmonic equivalent is the perfect fifth.

## Wolf fifth[edit | edit source]

A severely dissonant diminished sixth is observed when the instrument is tuned using a Pythagorean or a meantone temperament tuning system. Typically, this is the interval between G♯ and E♭. Since it seems to howl like a wolf (because of the beating), and since it is meant to be the enharmonic equivalent to a fifth, this interval is called the wolf fifth. Notice that a justly tuned fifth is the most consonant interval after the perfect unison and the perfect octave.

## Sources[edit | edit source]

- ↑
^{1.0}^{1.1}Benward & Saker (2003).*Music: In Theory and Practice, Vol. I*, p.54. ISBN 978-0-07-294262-0. Specific example of an d6 not given but general example of minor intervals described. - ↑ Haluska, Jan (2003).
*The Mathematical Theory of Tone Systems*, p.xxvi. ISBN 0-8247-4714-3. Classic diminished sixth. - ↑ Hoffmann, F.A. (1881).
*Music: Its Theory & Practice*, p.89-90. Thurgate & Sons. Digitized Aug 16, 2007. - ↑ Benward & Saker (2003), p.92.

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