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Minor sixth

From Wikipedia, the free encyclopedia
Musical interval
minor sixth
Inversemajor third
Name
Other namesminor hexachord, hexachordon minus, lesser hexachord
Abbreviationm6
Size
Semitones8
Interval class4
Just interval8:5, 128:81, 11:7
Cents
12-Tone equal temperament800
Just intonation814, 792, 782

Inmusic theory, aminor sixth is amusical interval encompassing sixstaff positions (seeInterval number for more details), and is one of two commonly occurring sixths (the other one being themajor sixth). It is qualified asminor because it is the smaller of the two: the minor sixth spans eightsemitones, 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 andaugmented sixths span the same number of staff positions, but consist of a different number of semitones (seven and ten respectively).

Equal temperament

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In 12-toneequal temperament (12-ET), the minor sixth isenharmonically equivalent to theaugmented fifth. It occurs in firstinversion major and dominant seventh chords and second inversion minor chords. It is equal to eightsemitones, i.e. a ratio of 28/12:1 or simplified to 22/3:1 (about 1.587), or 800cents.

Just intonation

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Definition

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Pythagorean minor sixth on CPlay, four Pythagorean perfect fifths.

Injust 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,[1] i.e. 7.82 centsflatter than the 12-ET-minor sixth. This is denoted with a "-" (minus) sign (see figure).
  • In5-limit tuning, a minor sixth most often corresponds to a pitch ratio of 8:5 (play) or 814 cents;[2][3][4] i.e. 13.7 centssharper than the 12-ET-minor sixth.

Consonance

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The minor sixth is one of consonances ofcommon practice music, along with theunison,octave,perfect fifth, major and minor thirds,major sixth and (sometimes) theperfect fourth. In the common practice period, sixths were considered interesting and dynamic consonances along with their inverses the thirds, but inmedieval times they were considered dissonances unusable in a stable final sonority. In that period they were tuned to theflatterPythagorean minor sixth of 128:81. In5-limitjust 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

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Musical interval
subminor sixth
Inversesupermajor third
Name
Abbreviationm6
Size
Semitones8
Interval class4
Just interval14:9[6] or 63:40
Cents
12-Tone equal temperament800
24-Tone equal temperament750
Just intonation765 or 786

In addition, thesubminor sixth, is asubminor interval which includes ratios such as 14:9 and 63:40.[7] of 764.9 cents[8][9] or 786.4 cents respectively.

See also

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References

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  1. ^Benson (2006), p.163.
  2. ^Hermann von Helmholtz and Alexander John Ellis (1912).On the Sensations of Tone as a Physiological Basis for the Theory of Music, p.456.
  3. ^Partch, Harry (1979).Genesis of a Music, p.68.ISBN 0-306-80106-X.
  4. ^Benson, David J. (2006).Music: A Mathematical Offering, p.370.ISBN 0-521-85387-7.
  5. ^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.ISBN 1-894613-32-5. "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)."
  6. ^Haluska, Jan (2003).The Mathematical Theory of Tone Systems, p.xxiii.ISBN 0-8247-4714-3. Septimal minor sixth.
  7. ^Jan Haluska (2003).The Mathematical Theory of Tone Systems, p.xxiii.ISBN 0-8247-4714-3.
  8. ^Duckworth & Fleming (1996).Sound and Light: La Monte Young & Marian Zazeela, p.167.ISBN 0-8387-5346-9.
  9. ^Hewitt, Michael (2000).The Tonal Phoenix, p.137.ISBN 3-922626-96-3.
Twelve-
semitone

(post-Bach
Western)
(Numbers in brackets
are the number of
semitones in the
interval.)
Perfect
Major
Minor
Augmented
Diminished
Compound
Other
tuning
systems
24-tone equal temperament
(Numbers in brackets refer
to fractional semitones.)
Just intonations
(Numbers in brackets
refer to pitch ratios.)
7-limit
Higher-limit
Other
intervals
Groups
Semitones
Quarter tones
Commas
Measurement
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