Minor sixth
Inverse | major third |
---|---|
Name | |
Other names | minor hexachord, hexachordon minus, lesser hexachord |
Abbreviation | m6 |
Size | |
Semitones | 8 |
Interval class | 4 |
Just interval | 8:5, 11:7, 128:81 |
Cents | |
Equal temperament | 800 |
24 equal temperament | 800 |
Just intonation | 814, 782, 792 |
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 is 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).
In equal temperament, the minor sixth is enharmonically equivalent to the augmented fifth. It occurs in first inversion major and dominant seventh chords and second inversion minor chords.
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;^{[1]}^{[2]}^{[3]} in 12-tone equal temperament, a minor sixth is equal to eight semitones, a ratio of 2^{2/3}: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 11:7 undecimal minor sixth is 782.49 cents.^{[4]} (Play (help·info)). In Pythagorean tuning, the minor sixth is the ratio 128:81, or 792.18 cents.^{[5]}
See also the subminor sixth, which includes ratios such as 14:9 and 63:40.^{[6]} of 764.9 cents^{[7]}^{[8]} or 786.4 cents,
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).
Inverse | supermajor third |
---|---|
Name | |
Abbreviation | m6 |
Size | |
Semitones | 8 |
Interval class | 4 |
Just interval | 14:9^{[9]} or 63:40 |
Cents | |
Equal temperament | 800 |
24 equal temperament | 750 |
Just intonation | 765 or 786 |
See also
Sources
- ^ 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.