Major sixth
Inverse | minor third |
---|---|
Name | |
Other names | septimal major sixth, supermajor sixth, major hexachord, greater hexachord, hexachordon maius |
Abbreviation | M6 |
Size | |
Semitones | 9 |
Interval class | 3 |
Just interval | 5:3, 12:7 (septimal), 27:16[1] |
Cents | |
12-Tone equal temperament | 900 |
Just intonation | 884, 933, 906 |
In music from
The intervals from the tonic (keynote) in an upward direction to the second, to the third, to the sixth, and to the seventh scale degrees (of a major scale are called major.[2]
A commonly cited example of a melody featuring the major sixth as its opening is "
The major sixth is one of the consonances of
A major sixth is also used in transposing music to
Assuming close-position voicings for the following examples, the major sixth occurs in a first inversion minor triad, a second inversion major triad, and either inversion of a diminished triad. It also occurs in the second and third inversions of a dominant seventh chord.
The
Frequency proportions
Many intervals in a various tuning systems qualify to be called "major sixth", sometimes with additional qualifying words in the names. The following examples are sorted by increasing width.
In just intonation, the most common major sixth is the pitch ratio of 5:3 (ⓘ), approximately 884 cents.
In 12-tone equal temperament, a major sixth is equal to nine semitones, exactly 900 cents, with a frequency ratio of the (9/12) root of 2 over 1.
Another major sixth is the Pythagorean major sixth with a ratio of 27:16, approximately 906 cents,
Another major sixth is the 12:7 septimal major sixth or
The nineteenth subharmonic is a major sixth, A = 32/19 = 902.49 cents.
See also
References
- ISBN 978-0-8247-4714-5. Septimal major sixth.
- ISBN 978-0-07-294262-0.
- ISBN 978-0-470-49644-2.
- ^ ISBN 978-1-60206-639-7.
- ^ Oscar Paul, A Manual of Harmony for Use in Music-Schools and Seminaries and for Self-Instruction, trans. Theodore Baker (New York: G. Schirmer, 1885), p. 165.
Further reading
- Duckworth, William (1996). [untitled chapter][ISBN 0-8387-5738-3. [septimal][clarification needed]