Английская Википедия:Decatonic scale

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Шаблон:Short description

Файл:Four-semitone tritone scale on C.png
Four-semitone tritone scale[1] Шаблон:Audio
Файл:Symmetrical four-semitone tritone scale on C.png
Symmetrical decatonic scale: "symmetric pattern [between steps] ½–½–1–½–½|½–½–1–½–½"[2] Шаблон:Audio

A decatonic scale is a ten note musical scale. If the notes are ordered, a decatonic set has 3,628,800 permutations,[3] however, in twelve tone equal temperament only six unordered ten note sets exist, 10-1—10-6: Шаблон:Div col

  1. Шаблон:Audio (all pitch classes but t & e)
  2. Шаблон:Audio (all but 9 & e)
  3. Шаблон:Audio (all but 8 & e)
  4. Шаблон:Audio (all but 7 & e)
  5. Шаблон:Audio (all but 6 & e)
  6. Шаблон:Audio (all but 5 & e)

Шаблон:Div col end

Given that two of the notes from the chromatic scale are missing and only two whole tones are possible, all 10-note scales are cohemitonic scales.

Файл:MOLT 7.png
Four-semitone tritone scale/Messiaen's 7th mode Шаблон:Audio
Файл:Dominant seventh raised ninth vs dominant seventh split third chord.png
Dominant seventh raised ninth vs. dominant seventh split third chord. Шаблон:Audio

The four-semitone tritone scale (set 10-6) is a decatonic scale consisting of four semitones, a whole tone, four semitones, and a whole tone (four semitones a tritone apart): 0,1,2,3,4,6,7,8,9,10. This may be related to the seven notes of the diatonic scale as, "1 Шаблон:Music2 Шаблон:Music2 Шаблон:Music3 Шаблон:Music3 Шаблон:Music4 Шаблон:Music5 Шаблон:Music6 Шаблон:Music6 Шаблон:Music7," and thus spelled, on C, as C, DШаблон:Music, DШаблон:Music, EШаблон:Music, EШаблон:Music, FШаблон:Music, G, AШаблон:Music, AШаблон:Music, BШаблон:Music.[1] This is a mode of Olivier Messiaen's seventh mode of limited transposition; it has six transpositions, like the tritone, and five modes (the same pitch classes with C, DШаблон:Music, D, EШаблон:Music, or E taken as the first scale step or tonic). This allows a dominant seventh chord to be built upon the tonic and a seventh sharp nine chord, and allows the tonic chord to have an altered ninth, eleventh, and thirteenth factors.[1] However, pitch sets containing more than seven notes become increasingly similar to each other.[4]

A decatonic scale that has been used or considered by Kyle Gann and La Monte Young in 13-limit just intonation is 1/1, 12/11, 32/27, 9/7, 4/3, 132/91, 3/2, 18/11, 16/9, 176/91, and 2/1.[5] Шаблон:Audio

References

Шаблон:Reflist

Шаблон:Scales

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  1. ↑ 1,0 1,1 1,2 Dziuba, Mark (2014). The Ultimate Guitar Scale Bible: 130 Useful Scales for Improvisation, p. 48. Alfred Music. Шаблон:ISBN.
  2. ↑ Rechberger, Herman (2018). Scales and Modes Around the World: The complete guide to the scales and modes of the world, p. 43. Fennica Gehrman. Шаблон:ISBN.
  3. ↑ Wyble, Jimmy (2011). Concepts for the Classical and Jazz Guitar, p. 2. Mel Bay. Шаблон:ISBN.
  4. ↑ Hanson, Howard. (1960) Harmonic Materials of Modern Music, p. 33. New York: Appleton-Century-Crofts. LOC 58-8138. "When the projection [of the perfect fifth] is carried beyond seven tones, no Шаблон:Em intervals can be added." "On the other hand, as sonorities are projected beyond the six-tone series they tend to lose their individuality. Шаблон:Em seven-tone series, for example, contain Шаблон:Em of the six basic intervals, and difference in their proportion decreases as additional tones are added ... Such patterns tend to lose their identity, producing a monochromatic effect with its accompanying lack of the essential element of contrast."
  5. ↑ Just Intonation Network (2002). 1/1: The Quarterly Journal of the Just Intonation Network, Volume 11, p. 17. Just Intonation Network: San Francisco.
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