Major sixth
Encyclopedia
In classical music
from Western culture
, a sixth is a musical interval encompassing six staff positions (see 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 largest of the two. The major sixth spans nine semitones, its smaller counterpart being the minor sixth
, spanning eight semitones. For example, the interval from C to A is a major sixth, as the note A lies nine semitones above C, and there are six staff positions from C to A. Diminished
and augmented sixth
s span the same number of 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 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 very sharp, to the Pythagorean
major sixth of 27/16. In just intonation
, the 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 and horn (instrument)
when in E-flat as a written C sounds like E-flat on those instruments.
The major sixth commonly occurs between the third
and (upper) root
of minor chord
s. The septimal major sixth is approximated in 53 tone equal temperament by an interval of 41 steps or 928 cents.
most often corresponds to a pitch ratio of 5:3 , or 884 cents, while in 12-tone equal temperament
, a major sixth is equal to nine semitone
s, or 900 cents, 15.641 cent
s higher than the just major sixth and 33 cents lower than the 12:7 septimal major sixth or supermajor sixth of 933 cents.
The Pythagorean major sixth, or 27th harmonic, is 27:16 or 906 cents, constructed from three just perfect fifths (C-A = C-G-D-A = 702+702+702=2106-1200=906).
Classical music
Classical music is the art music produced in, or rooted in, the traditions of Western liturgical and secular music, encompassing a broad period from roughly the 11th century to present times...
from Western culture
Western culture
Western culture, sometimes equated with Western civilization or European civilization, refers to cultures of European origin and is used very broadly to refer to a heritage of social norms, ethical values, traditional customs, religious beliefs, political systems, and specific artifacts and...
, a sixth is a musical interval encompassing six staff positions (see 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 largest of the two. The major sixth spans nine semitones, its smaller counterpart being the minor sixth
Minor sixth
-Subminor sixth:In music, a subminor sixth or septimal sixth is an interval that is noticeably narrower than a minor sixth but noticeably wider than a diminished sixth.The sub-minor sixth is an interval of a 14:9 ratio or alternately 11:7....
, spanning eight semitones. For example, the interval from C to A is a major sixth, as the note A lies nine semitones above C, and there are six staff positions from C to A. Diminished
Diminished sixth
In classical music from Western culture, a diminished sixth is an interval produced by narrowing a minor sixth by a chromatic semitone. For example, the interval from A to F is a minor sixth, eight semitones wide, and both the intervals from A to F, and from A to F are diminished sixths, spanning...
and augmented sixth
Augmented sixth
In classical music from Western culture, an augmented sixth is an interval produced by widening a major sixth by a chromatic semitone. For instance, the interval from C to A is a major sixth, nine semitones wide, and both the intervals from C to A, and from C to A are augmented sixths, spanning...
s span the same number of 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
My Bonnie Lies over the Ocean
"My Bonnie Lies over the Ocean" is a traditional Scottish folk songwhich remains popular in Western culture.-History:The origin of the song is unknown, though it is often suggested that the subject of the song may be...
".
The major sixth is one of consonances of common practice music, along with the unison
Unison
In music, the word unison can be applied in more than one way. In general terms, it may refer to two notes sounding the same pitch, often but not always at the same time; or to the same musical voice being sounded by several voices or instruments together, either at the same pitch or at a distance...
, octave
Octave
In music, an octave is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems"...
, perfect fifth
Perfect fifth
In classical music from Western culture, a fifth is a musical interval encompassing five staff positions , and the perfect fifth is a fifth spanning seven semitones, or in meantone, four diatonic semitones and three chromatic semitones...
, major and minor thirds, minor sixth
Minor sixth
-Subminor sixth:In music, a subminor sixth or septimal sixth is an interval that is noticeably narrower than a minor sixth but noticeably wider than a diminished sixth.The sub-minor sixth is an interval of a 14:9 ratio or alternately 11:7....
and (sometimes) the perfect fourth
Perfect fourth
In classical music from Western culture, a fourth is a musical interval encompassing four staff positions , and the perfect fourth is a fourth spanning five semitones. For example, the ascending interval from C to the next F is a perfect fourth, as the note F lies five semitones above C, and there...
. In the common practice period, sixths were considered interesting and dynamic consonances along with their inverses the thirds, but in medieval times
Medieval music
Medieval music is Western music written during the Middle Ages. This era begins with the fall of the Roman Empire and ends sometime in the early fifteenth century...
they were considered dissonances unusable in a stable final sonority; however in that period they were tuned very sharp, to the Pythagorean
Pythagorean tuning
Pythagorean tuning is a system of musical tuning in which the frequency relationships of all intervals are based on the ratio 3:2. This interval is chosen because it is one of the most consonant...
major sixth of 27/16. In just intonation
Just intonation
In music, just intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Any interval tuned in this way is called a just interval. The two notes in any just interval are members of the same harmonic series...
, the major sixth is classed as a consonance of the 5-limit
Limit (music)
In music theory, limit or harmonic limit is a way of characterizing the harmony found in a piece or genre of music, or the harmonies that can be made using a particular scale. The term was introduced by Harry Partch, who used it to give an upper bound on the complexity of harmony; hence the name...
.
A major sixth is also used in transposing music to E-flat
E-flat
E-flat may refer to:* E♭ * E-flat major* E-flat minor* E-flat tuning, on a guitar...
instruments, like the alto clarinet
Alto clarinet
The alto clarinet is a wind instrument of the clarinet family. It is a transposing instrument pitched in the key of E, though instruments in F have been made. It is sometimes known as a tenor clarinet; this name especially is applied to the instrument in F...
, alto saxophone
Alto saxophone
The alto saxophone is a member of the saxophone family of woodwind instruments invented by Belgian instrument designer Adolphe Sax in 1841. It is smaller than the tenor but larger than the soprano, and is the type most used in classical compositions...
, E-flat tuba
Tuba
The tuba is the largest and lowest-pitched brass instrument. Sound is produced by vibrating or "buzzing" the lips into a large cupped mouthpiece. It is one of the most recent additions to the modern symphony orchestra, first appearing in the mid-19th century, when it largely replaced the...
, trumpet and horn (instrument)
Horn (instrument)
The horn is a brass instrument consisting of about of tubing wrapped into a coil with a flared bell. A musician who plays the horn is called a horn player ....
when in E-flat as a written C sounds like E-flat on those instruments.
The major sixth commonly occurs between the third
Third
Third may refer to:*3 , such as the 3rd of something -see also Ordinal number *Fraction , such as 1/3*1/60 of a second, or 1/3,600 of a minute *Third World, economically underdeveloped nations...
and (upper) root
Root (chord)
In music theory, the root of a chord is the note or pitch upon which a triadic chord is built. For example, the root of the major triad C-E-G is C....
of minor chord
Minor chord
In music theory, a minor chord is a chord having a root, a minor third, and a perfect fifth.When a chord has these three notes alone, it is called a minor triad....
s. The septimal major sixth is approximated in 53 tone equal temperament by an interval of 41 steps or 928 cents.
Frequency proportions
A major sixth in just intonationJust intonation
In music, just intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Any interval tuned in this way is called a just interval. The two notes in any just interval are members of the same harmonic series...
most often corresponds to a pitch ratio of 5:3 , or 884 cents, while in 12-tone equal temperament
Equal temperament
An equal temperament is a musical temperament, or a system of tuning, in which every pair of adjacent notes has an identical frequency ratio. As pitch is perceived roughly as the logarithm of frequency, this means that the perceived "distance" from every note to its nearest neighbor is the same for...
, a major sixth is equal to nine semitone
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....
s, or 900 cents, 15.641 cent
Cent (music)
The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each...
s higher than the just major sixth and 33 cents lower than the 12:7 septimal major sixth or supermajor sixth of 933 cents.
The Pythagorean major sixth, or 27th harmonic, is 27:16 or 906 cents, constructed from three just perfect fifths (C-A = C-G-D-A = 702+702+702=2106-1200=906).
Further reading
- Duckworth, William (2009). Sound and Light: La Monte Young, Marian Zazeela, p. 167. ISBN 0838757383. [septimal]