In music fromWestern culture,asixthis amusical intervalencompassing six note letter names orstaff positions(seeInterval numberfor more details), and themajor sixthis one of two commonly occurring sixths. It is qualified asmajorbecause 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.Diminishedandaugmented 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).
| 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 |
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 practicemusic, 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 theirinversesthe thirds. Inmedieval timestheorists always described them asPythagoreanmajor 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-flatinstruments, like thealto clarinet,alto saxophone,E-flattuba,trumpet,natural horn,andalto hornwhen in E-flat, as a written C sounds like E-flat on those instruments.
Assuming close-positionvoicingsfor 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.
Theseptimalmajor sixth (12/7) is approximated in53 tone equal temperamentby an interval of 41 steps or 928cents.
Frequency proportions
editMany 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 (), 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 sixthwith 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 scalebetween 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).
Another major sixth is the 12:7septimal major sixthorsupermajor 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 subharmonicis a major sixth, A
= 32/19 = 902.49 cents.
See also
editReferences
edit- ^Jan Haluska,The Mathematical Theory of Tone Systems(New York: Marcel Dekker; London: Momenta; Bratislava: Ister Science, 2004), p.xxiii.ISBN978-0-8247-4714-5.Septimal major sixth.
- ^Bruce Benward and Marilyn Nadine Saker,Music: In Theory and Practice, Vol. I,seventh edition ([full citation needed]2003): p. 52.ISBN978-0-07-294262-0.
- ^Blake Neely,Piano For Dummies,second edition (Hoboken, NJ: Wiley Publishers, 2009), p. 201.ISBN978-0-470-49644-2.
- ^abAlexander J. Ellis, Additions by the translator to Hermann L. F. Von Helmholtz (2007).On the Sensations of Tone,p.456.ISBN978-1-60206-639-7.
- ^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
edit- Duckworth, William (1996). [untitled chapter][verification needed]InSound 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.ISBN9780838753460.Paperback reprint 2006,ISBN0-8387-5738-3.[septimal][clarification needed]