Septimal tritone
A septimal tritone is a tritone (about one half of an octave) that involves the factor seven. There are two that are inverses. The lesser septimal tritone (also Huygens' tritone) is the musical interval with ratio 7:5 (582.51 cents). The greater septimal tritone (also Euler's tritone), is an interval with ratio 10:7[2] (617.49 cents). They are also known as the sub-fifth and super-fourth, or subminor fifth and supermajor fourth, respectively.[3][4]
The 7:5 interval (diminished fifth) is equal to a 6:5 minor third plus a 7:6 subminor third.
The 10:7 interval (augmented fourth) is equal to a 5:4 major third plus a 8:7 supermajor second, or a 9:7 supermajor third plus a 10:9 major second.
The difference between these two is the septimal sixth tone (50:49, 34.98 cents) Audio file "Septimal sixth-tone on C.mid" not found.
The lesser septimal tritone is the most consonant tritone when measured by combination tones, harmonic entropy, and period length.[5]
Sources
- ↑ 1.0 1.1 Fonville, John. "Ben Johnston's Extended Just Intonation- A Guide for Interpreters", p.121-122, Perspectives of New Music, Vol. 29, No. 2 (Summer, 1991), pp. 106-137.
- ↑ Partch, Harry (1979). Genesis of a Music, p.68. ISBN 0-306-80106-X.
- ↑ Society of Arts (Great Britain) (1877, digitized Nov 19, 2009). Journal of the Society of Arts, Volume 25, p.670. The Society.
- ↑ Royal Society (Great Britain) (1880, digitized Feb 26, 2008). Proceedings of the Royal Society of London, Volume 30, p.531. Harvard University.
- ↑ "An unorthodox look at consonance", The Bohlen-Pierce Site.
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