Major sixth

In music from Western culture, a sixth is a musical interval encompassing six note letter names or staff positions (see Interval number for more details), and the major sixth is one of two commonly occurring sixths. It is qualified as major because it is the larger of the two. The major sixth spans nine 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]

major sixth
Inverseminor 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
Equal temperament900
Just intonation884, 933, 906
Major sixth Play 
Pythagorean major sixth Play , 3 Pythagorean perfect fifths on C.

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 common practice music, along with the unison, octave, perfect fifth, major and minor thirds, minor sixth, and (sometimes) the perfect fourth. In the common practice period, sixths were considered interesting and dynamic consonances along with their 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. We cannot know how major sixths actually were sung in the Middle Ages. 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 E-flat instruments, like the alto clarinet, alto saxophone, E-flat tuba, trumpet, natural horn, and 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 septimal major sixth (12/7) is approximated in 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,[4] called "Pythagorean" because it can be constructed from three just perfect fifths (C-A = C-G-D-A = 702+702+702-1200=906). It corresponds to the interval between the 27th and the 16th harmonics. The 27:16 Pythagorean major sixth arises in the C Pythagorean major scale between F and D,[5] as well as between C and A, G and E, and D and B.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, A = 32/19 = 902.49 cents.

See also

Sources
  1. Jan Haluska, The Mathematical Theory of Tone Systems (New York: Marcel Dekker; London: Momenta; Bratislava: Ister Science, 2004), p.xxiii. ISBN 978-0-8247-4714-5. Septimal major sixth.
  2. Bruce Benward and Marilyn Nadine Saker, Music: In Theory and Practice, Vol. I, seventh edition ( 2003): p. 52. ISBN 978-0-07-294262-0.
  3. Blake Neely, Piano For Dummies, second edition (Hoboken, NJ: Wiley Publishers, 2009), p. 201. ISBN 978-0-470-49644-2.
  4. Alexander J. Ellis, Additions by the translator to Hermann L. F. Von Helmholtz (2007). On the Sensations of Tone, p.456. ISBN 978-1-60206-639-7.
  5. 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] In Sound and Light: La Monte Young, Marian Zazeela, edited by William Duckworth and Richard Fleming, p. 167. Bucknell Review 40, no. 1. Lewisburg [Pa.]: Bucknell University Press; London and Cranbury, NJ: Associated University Presses. ISBN 9780838753460. Paperback reprint 2006, ISBN 0-8387-5738-3. [septimal]
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