Major sixth

Source: Wikipedia, the free encyclopedia.
major sixth
Inverse
minor third
Name
Other namesseptimal major sixth, supermajor sixth, major hexachord, greater hexachord, hexachordon maius
AbbreviationM6
Size
Semitones9
Interval class3
Just interval5:3, 12:7 (septimal), 27:16[1]
Cents
12-Tone equal temperament900
Just intonation884, 933, 906
Major sixth Play
Pythagorean major sixth Play, 3 Pythagorean perfect fifths on C

In music from

semitones. Its smaller counterpart, the minor sixth, spans eight semitones. For example, the interval from C up to the nearest A is a major sixth. It is a sixth because it encompasses six note letter names (C, D, E, F, G, A) and six staff positions. It is a major sixth, not a minor sixth, because the note A lies nine semitones above C. Diminished and augmented sixths
(such as C to A and C to A) span the same number of note letter names and staff positions, but consist of a different number of semitones (seven and ten, respectively).

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 "

My Bonnie Lies Over the Ocean".[3]

The major sixth is one of the consonances of

inverses the thirds. In medieval times theorists always described them as Pythagorean major sixths of 27/16 and therefore considered them dissonances unusable in a stable final sonority. How major sixths actually were sung in the Middle Ages is unknown. In just intonation, the (5/3) major sixth is classed as a consonance of the 5-limit
.

A major sixth is also used in transposing music to

alto horn
when in E-flat, as a written C sounds like E-flat on those instruments.

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

53 tone equal temperament by an interval of 41 steps or 928 cents
.

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 (play), 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,

justly tuned major scale
, it occurs between the 4th and 2nd degrees (in C major, between F and D). Play

Another major sixth is the 12:7 septimal major sixth or

supermajor sixth, the inversion of the septimal minor third, of approximately 933 cents.[4]
The septimal major sixth (12/7) is approximated in 53-tone equal temperament by an interval of 41 steps, giving an actual frequency ratio of the (41/53) root of 2 over 1, approximately 928 cents.

The nineteenth subharmonic is a major sixth, A19U = 32/19 = 902.49 cents.

See also

References

Further reading