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 ha ...

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 In Western classical music, 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 ''mi ...

, 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 classical music from Western culture, an augmented sixth () is an interval produced by widening a major sixth by a chromatic semitone.Benward & Saker (2003). ''Music: In Theory and Practice, Vol. I'', p.54. . Specific example of an A6 not g ...

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 "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 evolutio ...

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 In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been refer ...

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 fro ...

, major and minor thirds,

, 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 a ...

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 In music, just intonation or pure intonation is the tuning of musical intervals Interval may refer to: Mathematics and physics * Interval (mathematics), a range of numbers ** Partially ordered set#Intervals, its generalization from numbers to ...

, the (5/3) major sixth is classed as a consonance of the

5-limit Five-limit tuning, 5-limit tuning, or 5-prime-limit tuning (not to be confused with 5-odd-limit tuning), is any system for tuning a musical instrument that obtains the frequency of each note by multiplying the frequency of a given reference note ...

. A major sixth is also used in transposing music to E-flat instruments, like the

alto clarinet The alto clarinet is a woodwind instrument of the clarinet family. It is a transposing instrument pitched in the key of E, though instruments in F have been made. In size it lies between the soprano clarinet and the bass clarinet. It bears a grea ...

alto saxophone The alto saxophone is a member of the saxophone family of woodwind instruments. Saxophones were invented by Belgian instrument designer Adolphe Sax in the 1840s and patented in 1846. The alto saxophone is pitched in E, smaller than the B tenor ...

, 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 flug ...

when in E-flat, as a written C sounds like E-flat on those instruments. Assuming close-position

voicings ''Voicings'' was the last recording by the Minneapolis jazz vocal group Rio Nido. The album was one of the early recordings to feature live "direct to digital" recording techniques. Track listing # "Northern Lights" (D. Karr, L. Ball) # "I'm ...

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 tuning system, which approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, wh ...

, 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

cent Cent may refer to: Currency * Cent (currency), a one-hundredth subdivision of several units of currency * Penny (Canadian coin), a Canadian coin removed from circulation in 2013 * 1 cent (Dutch coin), a Dutch coin minted between 1941 and 1944 * ...

s, 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 In music theory, a minor third is a musical interval that encompasses three half steps, or semitones. Staff notation represents the minor third as encompassing three staff positions (see: interval number). The minor third is one of two common ...

, 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 i ...

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

justly tuned major scale Ptolemy's intense diatonic scale, also known as the Ptolemaic sequence, justly tuned major scale, Ptolemy's tense diatonic scale, or the syntonous (or syntonic) diatonic scale, is a musical tuning, tuning for the diatonic scale proposed by Ptole ...

, 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.

Frequency proportions

See also

References

Further reading