| Revision as of 01:42, 23 January 2020 editHyacinth (talk | contribs)176,976 edits thumb|upright=1.75|Symmetrical decatonic scale<ref>Rechberger, Herman (2018). '''', p.43. Fennica Gehrman Ltd. {{ISBN|9789525489286}}.</ref> {{audio|Symmetrical four-semitone tritone scale on C.mid|Play}}← Previous edit | Revision as of 01:45, 23 January 2020 edit undoHyacinth (talk | contribs)176,976 editsm →top: "symmetric pattern ½-½-1-½-½|½-½-1-½-½"Next edit → | ||
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| '', p.43. Fennica Gehrman Ltd. {{ISBN|9789525489286}}.</ref> {{audio|Symmetrical four-semitone tritone scale on C.mid|Play}}]] | ½-½-1-½-½|½-½-1-½-½"<ref>Rechberger, Herman (2018). '''', p.43. Fennica Gehrman Ltd. {{ISBN|9789525489286}}.</ref> {{audio|Symmetrical four-semitone tritone scale on C.mid|Play}}]] | ||
| A '''decatonic scale''' is a ten ] ]. If the notes are ordered, a decatonic set has 3,628,800 permutations,<ref>Wyble, Jimmy (2011). '''', p.2. Mel Bay. {{ISBN|9781610656207}}.</ref> however, in ] only six unordered ten note set exists, 10-1—10-6: | A '''decatonic scale''' is a ten ] ]. If the notes are ordered, a decatonic set has 3,628,800 permutations,<ref>Wyble, Jimmy (2011). '''', p.2. Mel Bay. {{ISBN|9781610656207}}.</ref> however, in ] only six unordered ten note set exists, 10-1—10-6: | ||
Revision as of 01:45, 23 January 2020
A decatonic scale is a ten note musical scale. If the notes are ordered, a decatonic set has 3,628,800 permutations, however, in twelve tone equal temperament only six unordered ten note set exists, 10-1—10-6:
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.
The four-semitone tritone scale 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♭. 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. However, pitch sets containing more than seven notes become increasingly similar to each other.
References
- ^ Dziuba, Mark (2014). The Ultimate Guitar Scale Bible: 130 Useful Scales for Improvisation, p.48. Alfred Music. ISBN 9781470625757.
- 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.
- Wyble, Jimmy (2011). Concepts for the Classical and Jazz Guitar, p.2. Mel Bay. ISBN 9781610656207.
- Hanson, Howard. (1960) Harmonic Materials of Modern Music, p. 33. New York: Appleton-Century-Crofts. LOC 58-8138. "When the projection 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."
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