A musical ratio of 5:3.
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's a sixth because it encompasses six note letter names (C, D, E, F, G, A) and six staff positions. It's 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).
A commonly cited example of a melody featuring the major sixth as its opening is "My Bonnie Lies Over the Ocean".
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, but in medieval times they were considered dissonances unusable in a stable final sonority; however in that period they were tuned to the Pythagorean major sixth of 27/16. 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. Wikipedia, Major Sixth
Starting again at C major and A minor and going round by the keys in ♭s, we come first to D minor and F major. The major gets its ♭ fourth from the ♭ sixth of the relative minor; and as the interval between D-E, the major sixth and seventh, must be a 9-comma interval, and its own D-E is only an 8-comma one, it must take the D of A minor, which is a comma lower, and this will correctly show the 9-comma interval between D and E. This is the way of their mutual providing in the region of ♭s; the ♭ sixth of the minor is given to be the ♭ fourth of the relative major; and the comma-lower fourth of the sub-relative minor becomes the correct sixth of the major. The arrows indicate the source from which, and the place to which; the new notes come and go. [Scientific Basis and Build of Music, page 113]
Part 14 - Keelys Mysterious Thirds Sixths and Ninths
Table 14.05 - All phrases in HyperVibes containing the term sixths
12.07 - Keelys Thirds Sixths and Ninths
7.15 - Sixth