| 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 |
Inmusic theory, asixth is amusical interval encompassing six note letter names orstaff positions (seeInterval number for more details), and themajor sixth is one of two commonly occurring sixths. It is qualified asmajor because it is the larger of the two. The major sixth spans ninesemitones. Its smaller counterpart, theminor 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 andaugmented 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 ofcommon practice music, along with theunison,octave,perfect fifth, major and minor thirds,minor sixth, and (sometimes) theperfect fourth. In the common practice period, sixths were considered interesting and dynamic consonances along with theirinverses the thirds. Inmedieval times theorists always described them asPythagorean 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. Injust intonation, the (5/3) major sixth is classed as a consonance of the5-limit.
A major sixth is also used in transposing music toE-flat instruments, like thealto clarinet,alto saxophone, E-flattuba, trumpet,natural horn, andalto horn when in E-flat, as a written C sounds like E-flat on those instruments.
Assuming close-positionvoicings for the following examples, the major sixth occurs in a first inversion minortriad, 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.
Theseptimal major sixth (12/7) is approximated in53 tone equal temperament by an interval of 41 steps or 928cents.
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.
Injust intonation, the most common major sixth is the pitch ratio of 5:3 (playⓘ), approximately 884 cents.
In 12-toneequal temperament, a major sixth is equal to ninesemitones, exactly 900cents, with a frequency ratio of the (9/12) root of 2 over 1.
Another major sixth is thePythagorean 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 is the inversion of thePythagorean minor third, and corresponds to the interval between the 27th and the 16th harmonics. The 27:16 Pythagorean major sixth arises in the C Pythagoreanmajor scale between F and D,[5][failed verification] as well as between C and A, G and E, and D and B. In the5-limitjustly tuned major scale, it occurs between the 4th and 2nd degrees (in C major, between F and D).Playⓘ
Another major sixth is the 12:7septimal major sixth orsupermajor sixth, the inversion of theseptimal 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.
Thenineteenth subharmonic is a major sixth, A
= 32/19 = 902.49 cents.
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