Decatonic scale

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Four-semitone tritone scale[1] About this soundPlay (help·info)
Symmetrical decatonic scale: "symmetric pattern [between steps] ½-½-1-½-½|½-½-1-½-½"[2] About this soundPlay (help·info)

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:

  1. About this soundPlay 10-1 (help·info) (all pitch classes but t & e)
  2. About this soundPlay 10-2 (help·info) (all but 9 & e)
  3. About this soundPlay 10-3 (help·info) (all but 8 & e)
  4. About this soundPlay 10-4 (help·info) (all but 7 & e)
  5. About this soundPlay 10-5 (help·info) (all but 6 & e)
  6. About this soundPlay 10-6 (help·info) (all but 5 & e)

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.

Four-semitone tritone scale/Messiaen's 7th mode About this soundPlay (help·info)
Dominant seventh raised ninth vs. dominant seventh split third chord. About this soundPlay (help·info)

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 ♭2 ♮2 ♭3 ♮3 ♯4 ♮5 ♭6 ♮6 ♭7," and thus spelled, on C, as C, D♭, D♮, E♭, E♮, F♯, G, A♭, A♮, B♭.[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, D♭, D, E♭, 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] About this soundPlay (help·info)

References[]

  1. ^ Jump up to: a b c Dziuba, Mark (2014). The Ultimate Guitar Scale Bible: 130 Useful Scales for Improvisation, p.48. Alfred Music. ISBN 9781470625757.
  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 Ltd. ISBN 9789525489286.
  3. ^ Wyble, Jimmy (2011). Concepts for the Classical and Jazz Guitar, p.2. Mel Bay. ISBN 9781610656207.
  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 new intervals can be added." "On the other hand, as sonorities are projected beyond the six-tone series they tend to lose their individuality. All seven-tone series, for example, contain all 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, CA.
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