Western classical music Classical music generally refers to the art music of the Western world, considered to be distinct from Western folk music or popular music traditions. It is sometimes distinguished as Western classical music, as the term "classical music" ...

, a minor sixth is a musical interval encompassing six 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 is one of two commonly occurring sixths (the other one being the

major sixth In music from Western culture, a sixth is a musical interval encompassing six note letter names or staff positions (see Interval number for more details), and the major sixth is one of two commonly occurring sixths. It is qualified as ''major ...

). It is qualified as ''minor'' because it is the smaller of the two: the minor sixth spans eight

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, the major sixth nine. For example, the interval from A to F is a minor sixth, as the note F lies eight semitones above A, and there are six staff positions from A to F. Diminished and augmented sixths span the same number of staff positions, but consist of a different number of semitones (seven and ten respectively).

Equal temperament

In 12-tone equal temperament (12-ET), the minor sixth is

enharmonically equivalent In modern musical notation and tuning, an enharmonic equivalent is a note, interval, or key signature that is equivalent to some other note, interval, or key signature but "spelled", or named differently. The enharmonic spelling of a written n ...

to the

augmented fifth In classical music from Western culture, an augmented fifth () is an interval produced by widening a perfect fifth by a chromatic semitone.Benward & Saker (2003). ''Music: In Theory and Practice, Vol. I'', p.54. . For instance, the interval f ...

. It occurs in first inversion major and dominant seventh chords and second inversion minor chords. It is equal to eight

s, i.e. a ratio of 2^8/12:1 or simplified to 2^2/3:1 (about 1.587), or 800 cents.

Just temperament

Definition

In just intonation multiple definitions of a minor sixth can exist: *In 3-limit tuning, i.e. Pythagorean tuning, the minor sixth is the ratio 128:81, or 792.18 cents, i.e. 7.82 cents ''flatter'' than the 12-ET-minor sixth. This is denoted with a "-" (minus) sign (see figure). *In

5-limit tuning 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 minor sixth most often corresponds to a pitch ratio of 8:5 () or 814 cents;Hermann von Helmholtz and Alexander John Ellis (1912). ''On the Sensations of Tone as a Physiological Basis for the Theory of Music'', p.456.Partch, Harry (1979). ''

Genesis of a Music ''Genesis of a Music'' is a book first published in 1949 by microtonal composer Harry Partch (1901–1974). Partch first presents a polemic against both equal temperament and the long history of stagnation in the teaching of music; according ...

'', p.68. .Benson, David J. (2006). ''Music: A Mathematical Offering'', p.370. . i.e. 13.7 cents ''sharper'' than the 12-ET-minor sixth. *In 11-limit tuning, the 11:7 () undecimal minor sixth is 782.49 cents.International Institute for Advanced Studies in Systems Research and Cybernetics (2003). ''Systems Research in the Arts'': Music, Environmental Design, and the Choreography of Space, Volume 5, p.18. . "The proportion 11:7, obtained by isolating one 35° angle from its complement within the 90° quadrant, similarly corresponds to an undecimal minor sixth (782.5 cents)."

Consonance

The minor sixth is one of 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,

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, but 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 ...

they were considered dissonances unusable in a stable final sonority. In that period they were tuned to the ''flatter''

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 ...

minor sixth of 128:81. In 5-limit just intonation, the minor sixth of 8:5 is classed as a consonance. Any note will only appear in major scales from any of its minor sixth major scale notes (for example, C is the minor sixth note from E and E will only appear in C, D, E, F, G, A and B major scales).

Subminor sixth

In addition, the subminor sixth, is a subminor interval which includes ratios such as 14:9 and 63:40.Jan Haluska (2003). ''The Mathematical Theory of Tone Systems'', p.xxiii. . of 764.9 centsDuckworth & Fleming (1996). ''Sound and Light: La Monte Young & Marian Zazeela'', p.167. .Hewitt, Michael (2000). ''The Tonal Phoenix'', p.137. . or 786.4 cents respectively.

References