# Major fourth and minor fifth

Inverse | Minor fifth |
---|---|

Name | |

Other names | Eleventh harmonic |

Abbreviation | M4 |

Size | |

Semitones | ~5½ |

Interval class | ~5½ |

Just interval | 11:8 |

Cents | |

24 equal temperament | 550 |

Just intonation | 551.32 |

Inverse | Major fourth |
---|---|

Name | |

Other names | Eleventh subharmonic |

Abbreviation | m5 |

Size | |

Semitones | ~6½ |

Interval class | ~5½ |

Just interval | 16:11 |

Cents | |

24 equal temperament | 650 |

Just intonation | 648.68 |

In music, **major fourth** and **minor fifth** are intervals from the quarter tone scale, named by Ivan Wyschnegradsky to describe the tones surrounding the tritone (F♯/G♭) found in the more familiar twelve tone scale.^{[1]}

perfect fourth | major fourth | tritone | minor fifth | perfect fifth | |
---|---|---|---|---|---|

in C: | F | ≊ F | F♯/G♭ | ≊ G | G |

## Major fourth[edit]

A major fourth ( Play (help·info)) is the interval that lies midway between the perfect fourth (500 cents) and the augmented fourth (600 cents) and is thus 550 cents (F). It inverts to a minor fifth. Wyschnegradsky considered it a good approximation of the eleventh harmonic^{[1]} (11:8 or 551.32 cents).^{[2]} A narrower undecimal major fourth is found at 537 cents (the ratio 15:11). 31 equal temperament has an interval of 542 cents, which lies in between the two types of undecimal major fourth.

The term may also be applied to the "comma-deficient major fourth" (or "chromatic major fourth"^{[3]}), which is the ratio 25:18, or 568.72 cents (F♯).^{[4]}

## Minor fifth[edit]

A minor fifth ( Play (help·info)) is the interval midway between the diminished fifth (600 cents) and the perfect fifth (700 cents) and thus 650 cents (G). It inverts to a major fourth. It approximates the eleventh subharmonic (G↓), 16:11 (648.68 cents).

The term may also be applied to the ratio 64:45 (G♭-) or 609.77 cents ( Play (help·info)), formed from the perfect fourth (4/3 = 498.04) and the major semitone (16/15 = 111.73),^{[3]} which is sharp of the G♭ tritone. The "comma-redundant minor fifth" has the ratio 36:25 (G♭), or 631.28 cents, and is formed from two minor thirds.^{[4]} The tridecimal minor fifth (13:9), or tridecimal tritone, is slightly larger at 636.6 cents.

## Other[edit]

The term major fourth may also be applied to the follow, as minor fifth may be applied to their inversions (in the sense of augmented and diminished):

- The "comma-deficient major fourth" (or "chromatic major fourth"
^{[3]}) is the ratio 25:18, or 568.72 cents (F♯).^{[4]} - 45:32 (F♯+) or 590.22 cents ( Play (help·info)), formed from the major third (5/4 = 386.31) and the major tone (9/8 = 203.91) or two major tones (9:8) and one minor tone (10:9)
^{[3]} - 729:512 (F♯++) or 611.73 cents ( Play (help·info)), formed from the perfect fourth and the apotome.
^{[3]}

## See also[edit]

## Sources[edit]

- ^
^{a}^{b}Skinner, Miles Leigh (2007).*Toward a Quarter-tone Syntax: Analyses of Selected Works by Blackwood, Haba, Ives, and Wyschnegradsky*, p.25. ProQuest. ISBN 9780542998478. **^**Benson, Dave (2007-01-01).*Music: A Mathematical Offering*. Cambridge University Press. p. 370. ISBN 9780521853873.- ^
^{a}^{b}^{c}^{d}^{e}Richard Mackenzie Bacon (1821). "Manuscript Work of Francesco Bianchl",*The Quarterly Musical Magazine and Review*, Volume 3, p.56. - ^
^{a}^{b}^{c}(1832).*The Edinburgh Encyclopaedia*, Volume 9, p.249. Joseph Parker. [ISBN unspecified]

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