Major fourth and minor fifth
From Encyclopedia of Microtonality
|Other names||Eleventh harmonic|
|24 equal temperament||550|
|Other names||Eleventh subharmonic|
|24 equal temperament||650|
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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.
|perfect fourth||major fourth||tritone||minor fifth||perfect fifth|
|in C:||F||≊ F||F♯/G♭||≊ G||G|
Major fourth[edit | edit source]
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 (11:8 or 551.32 cents). 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.
Minor fifth[edit | edit source]
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), 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. The tridecimal minor fifth (13:9), or tridecimal tritone, is slightly larger at 636.6 cents.
Other[edit | edit source]
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") is the ratio 25:18, or 568.72 cents (F♯).
- 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)
- 729:512 (F♯++) or 611.73 cents ( Play (help·info)), formed from the perfect fourth and the apotome.
See also[edit | edit source]
Sources[edit | edit source]
- 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.
- Richard Mackenzie Bacon (1821). "Manuscript Work of Francesco Bianchl", The Quarterly Musical Magazine and Review, Volume 3, p.56.
- (1832). The Edinburgh Encyclopaedia, Volume 9, p.249. Joseph Parker. [ISBN unspecified]
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