In music from
Western culture
Leonardo da Vinci's ''Vitruvian Man''. Based on the correlations of ideal Body proportions">human proportions with geometry described by the ancient Roman architect Vitruvius in Book III of his treatise ''De architectura''.
image:Plato Pio-Cle ...
, a sixth is a
musical interval encompassing six note letter names or
staff positions (see
Interval number
In music theory, an interval is a difference in pitch between two sounds.
An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or h ...
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
A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically.
It is defined as the interval between two adjacent no ...
. 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 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 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).
A commonly cited example of a melody featuring the major sixth as its opening is "
My Bonnie Lies Over the Ocean
"My Bonnie Lies over the Ocean", or simply "My Bonnie", is a traditional Scottish folk song that is popular in Western culture. It is listed in Roud Folk Song Index as No. 1422. The song has been recorded by numerous artists since the beginning of ...
".
[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
In European art music, the common-practice period is the era of the tonal system. Most of its features persisted from the mid-Baroque period through the Classical and Romantic periods, roughly from 1650 to 1900. There was much stylistic evoluti ...
music, along with the
unison
In music, unison is two or more musical parts that sound either the same pitch or pitches separated by intervals of one or more octaves, usually at the same time. ''Rhythmic unison'' is another term for homorhythm.
Definition
Unison or per ...
,
octave,
perfect fifth, major and minor thirds,
minor sixth, and (sometimes) the
perfect fourth
A fourth is a 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 interval from C to ...
. In the common practice period, sixths were considered interesting and dynamic consonances along with their
inverses the thirds. In
medieval times
In the history of Europe, the Middle Ages or medieval period lasted approximately from the late 5th to the late 15th centuries, similar to the post-classical period of global history. It began with the fall of the Western Roman Empire an ...
theorists always described them as
Pythagorean
Pythagorean, meaning of or pertaining to the ancient Ionian mathematician, philosopher, and music theorist Pythagoras, may refer to:
Philosophy
* Pythagoreanism, the esoteric and metaphysical beliefs purported to have been held by Pythagoras
* Ne ...
major sixths of 27/16 and therefore considered them dissonances unusable in a stable final sonority. We cannot know how major sixths actually were sung in the Middle Ages. 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
The tuba (; ) is the lowest-pitched musical instrument in the brass family. As with all brass instruments, the sound is produced by lip vibrationa buzzinto a mouthpiece. It first appeared in the mid-19th century, making it one of the ne ...
, trumpet,
natural horn
The natural horn is a musical instrument that is the predecessor to the modern-day (French) horn (differentiated by its lack of valves). Throughout the seventeenth and eighteenth century the natural horn evolved as a separation from the trump ...
, and
alto horn
The tenor horn (British English; alto horn in American English, Althorn in Germany; occasionally referred to as E horn) is a brass instrument in the saxhorn family and is usually pitched in E. It has a bore that is mostly conical, like the flu ...
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
just intonation, the most common major sixth is the pitch ratio of 5:3 (), approximately 884 cents.
In 12-tone
equal temperament, a major sixth is equal to nine
semitone
A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically.
It is defined as the interval between two adjacent no ...
s, 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 double ...
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
In music, the septimal minor third, also called the subminor third (e.g., by Ellis), is the musical interval exactly or approximately equal to a 7/6 ratio of frequencies. In terms of cents, it is 267 cents, a quartertone of size 36/35 flatter ...
, 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.
See also
*
Musical tuning
*
List of meantone intervals
The following is a list of intervals of extended meantone temperament. These intervals constitute the standard vocabulary of intervals for the Western common practice era. Here 12-EDO refers to the size of the interval in 12 equal divisions of th ...
*
Sixth chord
The term ''sixth chord'' refers to two different kinds of chord, the first in classical music and the second in modern popular music.
The original meaning of the term is a ''chord in first inversion'', in other words with its third in the bass a ...
References
Further reading
*Duckworth, William (1996).
ntitled chapterIn ''Sound and Light: La Monte Young, Marian Zazeela'', edited by William Duckworth and Richard Fleming, p. 167. Bucknell Review 40, no. 1. Lewisburg
a. Bucknell University Press; London and Cranbury, NJ: Associated University Presses. . Paperback reprint 2006, .
eptimal!--What the heck is this here for?-->
{{DEFAULTSORT:Major Sixth
Major intervals
Sixths (music)