Jump to content

Major fourth and minor fifth

Edit links
From Wikipedia, the free encyclopedia

This is an old revision of this page, as edited by Burninthruthesky (talk | contribs) at 12:05, 15 March 2017 (Corrected interval calculation and replaced source with a more reliable one.). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

Major fourth
InverseMinor fifth
Name
Other namesEleventh harmonic
AbbreviationM4
Size
Semitones~5½
Interval class~5½
Just interval11:8
Cents
24-Tone equal temperament550
Just intonation551.32
Minor fifth
InverseMajor fourth
Name
Other namesEleventh subharmonic
Abbreviationm5
Size
Semitones~6½
Interval class~5½
Just interval16:11
Cents
24-Tone equal temperament650
Just intonation648.68
Eleventh harmonic Playⓘ
Just augmented fourth on C Playⓘ and its inverse, the just tritone on C 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

A major fourth (Playⓘ) is the interval between the perfect fourth (500 cents) and the augmented fourth (600 cents) and 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

A minor fifth (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 (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

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ⓘ), 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ⓘ), formed from the perfect fourth and the apotome.[3]

See also

Sources

  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]


Stub icon

This music theory article is a stub. You can help Wikipedia by expanding it.

Retrieved from "https://en.wikipedia.org/w/index.php?title=Major_fourth_and_minor_fifth&oldid=770435560"