|Other names||minor hexachord, hexachordon minus, lesser hexachord|
|Just interval||8:5 or 11:7|
|24 equal temperament||800|
|Just intonation||814 or 782|
In classical music from Western culture, a sixth is a musical interval encompassing six staff positions (see Interval number for more details), and the minor sixth is one of two commonly occurring sixths. It is qualified as minor because it the smaller of the two: the minor sixth spans eight semitones, the major sixth nine. For example, the interval from A to F is a minor sixth, as the note F lies eight semitones above A, and there are six staff positions from A to F. Diminished and augmented sixths span the same number of staff positions, but consist of a different number of semitones (seven and ten).
A minor sixth in just intonation most often corresponds to a pitch ratio of 8:5 or 1.6:1 ( play (help·info)) of 814 cents; in 12-tone equal temperament, a minor sixth is equal to eight semitones, a ratio of 22/3:1 (about 1.587), or 800 cents, 13.7 cents smaller. The ratios of both major and minor sixths are corresponding numbers of the Fibonacci sequence, 5 and 8 for a minor sixth and 3 and 5 for a major.
The minor sixth is one of consonances of common practice music, along with the unison, octave, perfect fifth, major and minor thirds, major sixth and (sometimes) the perfect fourth. In the common practice period, sixths were considered interesting and dynamic consonances along with their inverses the thirds, but in medieval times they were considered dissonances unusable in a stable final sonority; however in that period they were tuned very flat, to the Pythagorean minor sixth of 128/81. In just intonation, the minor sixth is classed as a consonance of the 5-limit.
Any note will only appear in major scales from any of its minor sixth major scale notes (for example, C is the minor sixth note from E and E will only appear in C, D, E, F, G, A and B major scales).
|Just interval||14:9 or 63:40|
|24 equal temperament||750|
|Just intonation||765 or 786|
- Hermann von Helmholtz and Alexander John Ellis (1912). On the Sensations of Tone as a Physiological Basis for the Theory of Music, p.456.
- Partch, Harry (1979). Genesis of a Music, p.68. ISBN 0-306-80106-X.
- Benson, David J. (2006). Music: A Mathematical Offering, p.370. ISBN 0-521-85387-7.
- International Institute for Advanced Studies in Systems Research and Cybernetics (2003). Systems Research in the Arts: Music, Environmental Design, and the Choreography of Space, Volume 5, p.18. ISBN 1-894613-32-5. "The proportion 11:7, obtained by isolating one 35° angle from its complement within the 90° quadrant, similarly corresponds to an undecimal minor sixth (782.5 cents)."
- Benson (2006), p.163.
- Jan Haluska (2003). The Mathematical Theory of Tone Systems, p.xxiii. ISBN 0-8247-4714-3.
- Duckworth & Fleming (1996). Sound and Light: La Monte Young & Marian Zazeela, p.167. ISBN 0-8387-5346-9.
- Hewitt, Michael (2000). The Tonal Phoenix, p.137. ISBN 3-922626-96-3.
- Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxiii. ISBN 0-8247-4714-3. Septimal minor sixth.
- John Fonville. "Ben Johnston's Extended Just Intonation- A Guide for Interpreters", p.122, Perspectives of New Music, Vol. 29, No. 2 (Summer, 1991), pp. 106–137.
- Royal Society (Great Britain) (1880, digitized Feb 26, 2008). Proceedings of the Royal Society of London, Volume 30, p.531. Harvard University.
- Society of Arts (Great Britain) (1877, digitized Nov 19, 2009). Journal of the Society of Arts, Volume 25, p.670. The Society.
- Andrew Horner, Lydia Ayres (2002). Cooking with Csound: Woodwind and Brass Recipes, p.131. ISBN 0-89579-507-8.