music theory Music theory is the study of theoretical frameworks for understanding the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory": The first is the "Elements of music, ...

, 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 In music theory, a minor sixth is a musical interval encompassing six staff positions (see Interval number for more details), and is one of two commonly occurring sixths (the other one being the major sixth). It is qualified as ''minor'' bec ...

, 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 sixth In music, an augmented sixth () is an Interval (music), interval produced by Augmentation (music), widening a major sixth by a chromatic semitone.Benward & Saker (2003). ''Music: In Theory and Practice, Vol. I'', p.54. . Specific example of an ...

s (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). A commonly cited example of a melody featuring the major sixth as its opening is " My Bonnie Lies Over the Ocean".Blake Neely, ''Piano For Dummies'', second edition (Hoboken, NJ: Wiley Publishers, 2009), p. 201. . The major sixth is one of the consonances of common practice music, along with the

unison Unison (stylised as UNISON) is a Great Britain, British trade union. Along with Unite the Union, Unite, Unison is one of the two largest trade unions in the United Kingdom, with over 1.2 million members who work predominantly in public servic ...

octave In music, an octave (: eighth) or perfect octave (sometimes called the diapason) is an interval between two notes, one having twice the frequency of vibration of the other. The octave relationship is a natural phenomenon that has been referr ...

perfect fifth In music theory, a perfect fifth is the Interval (music), musical interval corresponding to a pair of pitch (music), pitches with a frequency ratio of 3:2, or very nearly so. In classical music from Western culture, a fifth is the interval f ...

, major and minor thirds,

, and (sometimes) the

perfect fourth A fourth is a interval (music), musical interval encompassing four staff positions in the music notation of Western culture, and a perfect fourth () is the fourth spanning five semitones (half steps, or half tones). For example, the ascending int ...

. 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. How major sixths actually were sung in the Middle Ages is unknown. In

just intonation In music, just intonation or pure intonation is a musical tuning, tuning system in which the space between notes' frequency, frequencies (called interval (music), intervals) is a natural number, whole number ratio, ratio. Intervals spaced in thi ...

, 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 The alto saxophone is a member of the saxophone family of woodwind instruments. Saxophones were invented by Belgians, Belgian instrument designer Adolphe Sax in the 1840s and patented in 1846. The alto saxophone is pitched in the key of E♭ ( ...

, E-flat

tuba The tuba (; ) is the largest and lowest-pitched musical instrument in the brass instrument, brass family. As with all brass instruments, the sound is produced by lip vibrationa buzzinto a mouthpiece (brass), mouthpiece. It first appeared in th ...

, 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

, the most common major sixth is the pitch ratio of 5:3 (), approximately 884 cents. In 12-tone

equal temperament An equal temperament is a musical temperament or Musical tuning#Tuning systems, tuning system that approximates Just intonation, just intervals by dividing an octave (or other interval) into steps such that the ratio of the frequency, frequencie ...

, 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, 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 the Pythagorean minor third, and corresponds to the interval between the 27th and the 16th harmonics. The 27:16 Pythagorean major sixth arises in the C Pythagorean

major scale The major scale (or Ionian mode) is one of the most commonly used musical scales, especially in Western music. It is one of the diatonic scales. Like many musical scales, it is made up of seven notes: the eighth duplicates the first at doubl ...

between F and D,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. as well as between C and A, G and E, and D and B. In the 5-limit justly tuned major scale, it occurs between the 4th and 2nd degrees (in C major, between F and D). Another major sixth is the 12:7 septimal major sixth or supermajor sixth, the inversion of the

septimal minor third Septimal may refer to: *Septimal chromatic semitone, the interval 21:20, about 84.47 cents *Septimal comma, a small musical interval in just intonation divisible by 7 *Septimal diatonic semitone, the interval 15:14, about 119.44 cents *S ...

, of approximately 933 cents.Alexander J. Ellis, Additions by the translator to Hermann L. F. Von Helmholtz (2007). ''On the Sensations of Tone'', p.456. . 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.

Frequency proportions

See also

References

Further reading