Major fourth and minor fifth

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Major fourth
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
Minor fifth
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
Eleventh harmonic About this sound Play 
Just augmented fourth on C About this sound Play  and its inverse, the just tritone on C About this sound Play 

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 ≊ Fhalf sharp F/G ≊ Ghalf flat G

Major fourth[edit]

A major fourth (About this sound Play ) is the interval that lies midway between the perfect fourth (500 cents) and the augmented fourth (600 cents) and is thus 550 cents (Fhalf sharp). 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]) is the ratio 25:18, or 568.72 cents (F).[4]

Minor fifth[edit]

A minor fifth (About this sound Play ) is the interval between the diminished fifth (600 cents) and the perfect fifth (700 cents) and thus 650 cents (Ghalf flat). 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 (About this sound Play ), 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 (About this sound Play ), 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 (About this sound Play ), formed from the perfect fourth and the apotome.[3]

See also[edit]

Sources[edit]

  1. ^ 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.
  2. ^ Benson, Dave (2007-01-01). Music: A Mathematical Offering. Cambridge University Press. p. 370. ISBN 9780521853873. 
  3. ^ a b c d e Richard Mackenzie Bacon (1821). "Manuscript Work of Francesco Bianchl", The Quarterly Musical Magazine and Review, Volume 3, p.56.
  4. ^ a b c (1832). The Edinburgh Encyclopaedia, Volume 9, p.249. Joseph Parker. [ISBN unspecified]