# Major sixth

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Musical interval

major sixth 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

In [music theory](/source/Music_theory), a **sixth** is a [musical interval](/source/Interval_(music)) encompassing six note letter names or [staff positions](/source/Staff_position) (see [Interval number](/source/Interval_(music)#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](/source/Semitones). Its smaller counterpart, the [minor sixth](/source/Minor_sixth), spans eight semitones. For example, the interval from C up to the nearest A is a major sixth.

- Audio playback is not supported in your browser. You can [download the audio file](https://upload.wikimedia.org/score/a/r/arisinjonlrf4o6wgyd9hgujvby9eig/arisinjo.mp3).

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](/source/Diminished_sixth) and [augmented sixths](/source/Augmented_sixth) (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](/source/My_Bonnie_Lies_Over_the_Ocean)".[3]

The major sixth is one of the consonances of [common practice](/source/Common_practice) music, along with the [unison](/source/Unison), [octave](/source/Octave), [perfect fifth](/source/Perfect_fifth), major and minor thirds, [minor sixth](/source/Minor_sixth), and (sometimes) the [perfect fourth](/source/Perfect_fourth). In the common practice period, sixths were considered interesting and dynamic consonances along with their [inverses](/source/Inversion_(interval)) the thirds. In [medieval times](/source/Medieval_music), theorists always described them as [Pythagorean](/source/Pythagorean_tuning) 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](/source/Just_intonation), the (5/3) major sixth is classed as a consonance of the [5-limit](/source/Limit_(music)).

A major sixth is also used in transposing music to [E♭](/source/List_of_E-flat_instruments) instruments, like the [alto clarinet](/source/Alto_clarinet), [alto saxophone](/source/Alto_saxophone), E♭ [tuba](/source/Tuba), trumpet, [natural horn](/source/Natural_horn), and [alto horn](/source/Alto_horn) when in E♭, as a written C sounds like E♭ on those instruments.

Assuming close-position [voicings](/source/Voicing_(music)) for the following examples, the major sixth occurs in a first inversion minor [triad](/source/Triad_(music)), 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.

## Frequency proportions

[Major sixth (equal temperament)](https://en.wikipedia.org/wiki/File:Sixth_ET.ogg)

The file plays [middle C](/source/Middle_C), followed by A (a tone 900 cents sharper than C), followed by both tones together.

*Problems playing this file? See [media help](https://en.wikipedia.org/wiki/Help:Media).*

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](/source/Just_intonation), the most common major sixth is the pitch ratio of 5:3 ([play](https://upload.wikimedia.org/wikipedia/commons/transcoded/9/98/Just_major_sixth_on_C.mid/Just_major_sixth_on_C.mid.mp3)[ⓘ](https://en.wikipedia.org/wiki/File:Just_major_sixth_on_C.mid)), approximately 884 cents.

In 12-tone [equal temperament](/source/Equal_temperament), a major sixth is equal to nine [semitones](/source/Semitone), exactly 900 [cents](/source/Cent_(music)), with a frequency ratio of the (9/12) root of 2 over 1.

Pythagorean major sixth [Play](https://upload.wikimedia.org/wikipedia/commons/transcoded/5/5e/Pythagorean_major_sixth_on_C.mid/Pythagorean_major_sixth_on_C.mid.mp3)[ⓘ](https://en.wikipedia.org/wiki/File:Pythagorean_major_sixth_on_C.mid), 3 Pythagorean perfect fifths on C

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 {\displaystyle 702+702+702-1200=906} ). It is the inversion of the [Pythagorean minor third](/source/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](/source/Major_scale) between F and D,[5][*[failed verification](https://en.wikipedia.org/wiki/Wikipedia:Verifiability)*] as well as between C and A, G and E, and D and B. In the [5-limit](/source/5-limit) [justly tuned major scale](/source/Justly_tuned_major_scale), it occurs between the 4th and 2nd degrees (in C major, between F and D). [Play](https://upload.wikimedia.org/wikipedia/commons/transcoded/f/fe/Pythagorean_major_sixth_in_scale.mid/Pythagorean_major_sixth_in_scale.mid.mp3)[ⓘ](https://en.wikipedia.org/wiki/File:Pythagorean_major_sixth_in_scale.mid)

Another major sixth is the 12:7 septimal major sixth or [supermajor sixth](/source/Supermajor_sixth), the inversion of the [septimal minor third](/source/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.

The [septimal](/source/7-limit) major sixth (12/7) is approximated in [53 tone equal temperament](/source/53_tone_equal_temperament) by an interval of 41 steps or 928 [cents](/source/Cent_(music)).

## See also

- [Musical tuning](/source/Musical_tuning)

- [List of meantone intervals](/source/List_of_meantone_intervals)

- [Sixth chord](/source/Sixth_chord)

## References

1. **[^](#cite_ref-1)** Jan Haluska, *The Mathematical Theory of Tone Systems* (New York: Marcel Dekker; London: Momenta; Bratislava: Ister Science, 2004), p.xxiii. [ISBN](/source/ISBN_(identifier)) [978-0-8247-4714-5](https://en.wikipedia.org/wiki/Special:BookSources/978-0-8247-4714-5). Septimal major sixth.

1. **[^](#cite_ref-2)** Bruce Benward and Marilyn Nadine Saker, *Music: In Theory and Practice, Vol. I*, seventh edition ([*[full citation needed](https://en.wikipedia.org/wiki/Wikipedia:Citing_sources#What_information_to_include)*] 2003): p. 52. [ISBN](/source/ISBN_(identifier)) [978-0-07-294262-0](https://en.wikipedia.org/wiki/Special:BookSources/978-0-07-294262-0).

1. **[^](#cite_ref-Neely_3-0)** Blake Neely, *Piano For Dummies*, second edition (Hoboken, NJ: Wiley Publishers, 2009), p. 201. [ISBN](/source/ISBN_(identifier)) [978-0-470-49644-2](https://en.wikipedia.org/wiki/Special:BookSources/978-0-470-49644-2).

1. ^ [***a***](#cite_ref-Helmholtz-Ellis_4-0) [***b***](#cite_ref-Helmholtz-Ellis_4-1) Alexander J. Ellis, Additions by the translator to Hermann L. F. Von Helmholtz (2007). *On the Sensations of Tone*, p.456. [ISBN](/source/ISBN_(identifier)) [978-1-60206-639-7](https://en.wikipedia.org/wiki/Special:BookSources/978-1-60206-639-7).

1. **[^](#cite_ref-5)** Oscar Paul, *[A Manual of Harmony for Use in Music-Schools and Seminaries and for Self-Instruction](https://books.google.com/books?id=4WEJAQAAMAAJ&q=musical+interval+%22pythagorean+major+third%22)*, trans. Theodore Baker (New York: G. Schirmer, 1885), p. 165.

## Further reading

- Duckworth, William (1996). [untitled chapter][*[verification needed](https://en.wikipedia.org/wiki/Wikipedia:Verifiability)*] 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; Cranbury, NJ / London: Associated University Presses. [ISBN](/source/ISBN_(identifier)) [9780838753460](https://en.wikipedia.org/wiki/Special:BookSources/9780838753460). Paperback reprint 2006, [ISBN](/source/ISBN_(identifier)) [0-8387-5738-3](https://en.wikipedia.org/wiki/Special:BookSources/0-8387-5738-3). [septimal][*[clarification needed](https://en.wikipedia.org/wiki/Wikipedia:Please_clarify)*]

v t e Intervals Twelve- semitone (post-Bach Western) (Numbers in brackets are the number of semitones in the interval.) Perfect unison (0) fourth (5) fifth (7) octave (12) Major second (2) third (4) sixth (9) seventh (11) Minor second (1) third (3) sixth (8) seventh (10) Augmented unison (1) second (3) third (5) fourth (6) fifth (8) sixth (10) seventh (12) octave (13) Diminished unison (−1) second (0) third (2) fourth (4) fifth (6) sixth (7) seventh (9) octave (11) Compound ninth (13 or 14) tenth (15 or 16) eleventh (17) twelfth (19) thirteenth (20 or 21) fourteenth (22 or 23) fifteenth (24) Other tuning systems 24-tone equal temperament (Numbers in brackets refer to fractional semitones.) Neutral quarter tone (1⁄2) second (1+1⁄2) third (3+1⁄2) major fourth (5+1⁄2) minor fifth (6+1⁄2) sixth (8+1⁄2) seventh (10+1⁄2) Just intonations (Numbers in brackets refer to pitch ratios.) 7-limit septimal quarter tone (36:35) septimal third tone (28:27) septimal chromatic semitone (21:20) septimal diatonic semitone (15:14) supermajor second (8:7) subminor third (7:6) supermajor third (9:7) subminor fifth (7:5) supermajor fourth (10:7) subminor seventh (7:4) Higher-limit minor diatonic semitone (17-limit) Other intervals Groups Microtone 5-limit Comma Pseudo-octave Pythagorean interval Subminor and supermajor Semitones Pythagorean limma Pythagorean apotome Major limma Quarter tones Quarter tone Septimal quarter tone Undecimal quarter tone Commas Pythagorean comma (23.5 cents) Syntonic comma (21.5 cents) Holdrian comma (22.6 cents) Septimal comma (27.3 cents) Lesser diesis (41.1 cents) Greater diesis (62.6 cents) Septimal diesis (35.7 cents) Diaschisma (19.5 cents) Semicomma (10.1 cents) Septimal semicomma (13.8 cents) Kleisma (8.1 cents) Septimal kleisma (7.7 cents) Schisma (1.95 cents) Breedsma (0.72 cents) Ragisma (0.4 cents) Measurement Cent Centitone Millioctave Savart Others Wolf Ditone Semiditone Secor Incomposite interval List of pitch intervals

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Adapted from the Wikipedia article [Major sixth](https://en.wikipedia.org/wiki/Major_sixth) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Major_sixth?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.