In Western classical music, a minor sixth is a

musical interval 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 ...

encompassing six

staff position In Western musical notation, the staff (US and UK)"staff" in the Collins ...

s (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 ''minor'' because it is the smaller of the two: the minor sixth spans eight semitones, 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 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 ...

(12-ET), the minor sixth is enharmonically equivalent to the augmented fifth. It occurs in first inversion major and dominant seventh chords and second inversion minor chords. It is equal to eight semitones, i.e. a ratio of 2^8/12:1 or simplified to 2^2/3:1 (about 1.587), or 800

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 * ...

Just temperament

Definition

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 ...

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 based on the ratio 3:2.Bruce Benward and Marilyn Nadine Saker (2003). ''Music: In Theory and Practice'', seventh edition, 2 vols. (Boston: Mc ...

, 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'', 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 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 ''limit'' was introduced by Harry Partch, who used it to give ...

, 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 music, along with the unison,

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, major 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. In that period they were tuned to the ''flatter'' Pythagorean 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 note ...

, 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 In music, a subminor interval is an interval that is noticeably wider than a diminished interval but noticeably narrower than a minor interval. It is found in between a minor and diminished interval, thus making it below, or subminor to, the min ...

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