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, 128:81, 11:7 |
Cents | |
12-Tone equal temperament | 800 |
Just intonation | 814, 792, 782 |
In
staff positions (see Interval number for more details), and is one of two commonly occurring sixths (the other one being the major sixth). 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 respectively).
Equal temperament
In 12-tone
enharmonically equivalent to the augmented fifth. It occurs in first inversion major and dominant seventh chords and second inversion minor chords. It is equal to eight semitones, i.e. a ratio of 28/12:1 or simplified to 22/3:1 (about 1.587), or 800 cents
.
Just temperament
Definition
In just intonation multiple definitions of a minor sixth can exist:
- In 3-limit tuning, i.e. Pythagorean tuning, the minor sixth is the ratio 128:81, or 792.18 cents,[1] i.e. 7.82 cents flatter than the 12-ET-minor sixth. This is denoted with a "-" (minus) sign (see figure).
- In i.e. 13.7 cents sharper than the 12-ET-minor sixth.
- In
Consonance
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. In that period they were tuned to the flatter Pythagorean minor sixth of 128:81. In 5-limit just intonation
, the minor sixth of 8:5 is classed as a consonance.
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).
Subminor sixth
supermajor third | |
---|---|
Name | |
Abbreviation | m6 |
Size | |
Semitones | 8 |
Interval class | 4 |
Just interval | 14:9[6] or 63:40 |
Cents | |
12-Tone equal temperament | 800 |
24-Tone equal temperament | 750 |
Just intonation | 765 or 786 |
In addition, the subminor sixth, is a
or 786.4 cents respectively.See also
- Musical tuning
- List of meantone intervals
- Sixth chord
- 833 cents scale (golden ratio = 833.09 cents)
References
- ^ Benson (2006), p.163.
- ^ Hermann von Helmholtz and Alexander John Ellis (1912). On the Sensations of Tone as a Physiological Basis for the Theory of Music, p.456.
- ISBN 0-306-80106-X.
- ISBN 0-521-85387-7.
- 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)."
- ISBN 0-8247-4714-3. Septimal minor sixth.
- ISBN 0-8247-4714-3.
- ISBN 0-8387-5346-9.
- ISBN 3-922626-96-3.