Inverse | Minor fifth |
---|---|
Name | |
Other names | Eleventh harmonic |
Abbreviation | M4 |
Size | |
Semitones | ~5½ |
Interval class | ~5½ |
Just interval | 11:8 |
Cents | |
24-Tone 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-Tone equal temperament | 650 |
Just intonation | 648.68 |
In music, the major fourth and minor fifth, also known as the paramajor fourth and paraminor 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] as shown in the table below:
perfect fourth | (para)major fourth | tritone | (para)minor fifth | perfect fifth | |
---|---|---|---|---|---|
in C: | F | ≊ F |
F♯/G♭ | ≊ G |
G |
in cents: | 500 | 550 | 600 | 650 | 700 |
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Transcription
Major fourth
A major fourth (ⓘ) is the interval that lies midway between the perfect fourth (500 cents) and the augmented fourth (600 cents) and is thus 550 cents (F
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
A minor fifth (ⓘ) is the interval midway between the diminished fifth (600 cents) and the perfect fifth (700 cents) and thus 650 cents (G
The term may also be applied to the ratio 64:45 (G♭-) or 609.77 cents (ⓘ), 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 (ⓘ), 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 (ⓘ), formed from the perfect fourth and the apotome.[3]
See also
References
- ^ 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]