music theory Music theory is the study of theoretical frameworks for understanding the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory": The first is the "Elements of music, ...

, a minor sixth is a

musical interval In music theory, an interval is a difference in pitch (music), 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 v ...

encompassing six

staff position In Western musical notation, the staff"staff" in the Collins English Di ...

s (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 har ...

for more details), and is one of two commonly occurring sixths (the other one being the

major sixth In music theory, 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'' because it ...

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

semitone A semitone, also called a minor second, 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 ...

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 Augment or augmentation may refer to: Language *Augment (Indo-European), a syllable added to the beginning of the word in certain Indo-European languages * Augment (Bantu languages), a morpheme that is prefixed to the noun class prefix of nouns ...

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 An equal temperament is a musical temperament or Musical tuning#Tuning systems, tuning system that approximates Just intonation, just intervals by dividing an octave (or other interval) into steps such that the ratio of the frequency, frequencie ...

(12-ET), the minor sixth is

enharmonically equivalent In music, two written notes have enharmonic equivalence if they produce the same pitch but are notated differently. Similarly, written intervals, chords, or key signatures are considered enharmonic if they represent identical pitches that are ...

to the

augmented fifth In Western classical music, 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 from C to G i ...

. It occurs in first

inversion Inversion or inversions may refer to: Arts * ''Inversion'' (artwork), a 2005 temporary sculpture in Houston, Texas * Inversion (music), a term with various meanings in music theory and musical set theory * ''Inversions'' (novel) by Iain M. Bank ...

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

just intonation In music, just intonation or pure intonation is a musical tuning, tuning system in which the space between notes' frequency, frequencies (called interval (music), intervals) is a natural number, whole number ratio, ratio. Intervals spaced in thi ...

multiple definitions of a minor sixth can exist: *In 3-limit tuning, i.e.

Pythagorean tuning Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are determined by choosing a sequence of fifthsBruce Benward and Marilyn Nadine Saker (2003). ''Music: In Theory and Practice'', seventh editi ...

, 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 limit (music)#Odd-limit and prime-limit, 5-odd-limit tuning), is any system for musical tuning, tuning a musical instrument that obtains the frequency of each not ...

, 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 Western classical music, the common practice period (CPP) was the period of about 250 years during which the tonal system was regarded as the only basis for composition. It began when composers' use of the tonal system had clearly superseded ...

music, along with the

unison Unison (stylised as UNISON) is a Great Britain, British trade union. Along with Unite the Union, Unite, Unison is one of the two largest trade unions in the United Kingdom, with over 1.2 million members who work predominantly in public servic ...

octave In music, an octave (: eighth) or perfect octave (sometimes called the diapason) is an interval between two notes, one having twice the frequency of vibration of the other. The octave relationship is a natural phenomenon that has been referr ...

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 f ...

, major and minor thirds,

and (sometimes) the

perfect fourth A fourth is a interval (music), 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 int ...

. 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 5th to the late 15th centuries, similarly to the post-classical period of global history. It began with the fall of the Western Roman Empire and t ...

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 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 not ...

, 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