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{{Short description|Ten note musical scale}}
] ]
½-½-1-½-½'''<nowiki>|</nowiki>'''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}}]] ½–½–1–½–½<nowiki>|</nowiki>½–½–1–½–½"<ref>] (2018). '''', p. 43. Fennica Gehrman. {{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 ] exist, 10-1—10-6: A '''decatonic scale''' is a ten ] ]. If the notes are ordered, a decatonic set has 3,628,800 permutations,<ref>] (2011). '''', p. 2. Mel Bay. {{ISBN|9781610656207}}.</ref> however, in ] only six unordered ten note ] exist, 10-1—10-6:
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#{{audio|10-1 (chromatic) decachord on C.mid|Play 0,1,2,3,4,5,6,7,8,9}} (missing t & e) #{{audio|10-1 (chromatic) decachord on C.mid|Play 10-1}} (all pitch classes but t & e)
#{{audio|10-2 decachord on C.mid|Play 0,1,2,3,4,5,6,7,8,t}} (missing 9 & e) #{{audio|10-2 decachord on C.mid|Play 10-2}} (all but 9 & e)
#{{audio|10-3 decachord on C.mid|Play 0,1,2,3,4,5,6,7,9,t}} (missing 8 & e) #{{audio|10-3 decachord on C.mid|Play 10-3}} (all but 8 & e)
#{{audio|10-4 decachord on C.mid|Play 0,1,2,3,4,5,6,8,9,t}} (missing 7 & e) #{{audio|10-4 decachord on C.mid|Play 10-4}} (all but 7 & e)
#{{audio|10-5 decachord on C.mid|Play 0,1,2,3,4,5,7,8,9,t}} (missing 6 & e) #{{audio|10-5 decachord on C.mid|Play 10-5}} (all but 6 & e)
#{{audio|10-6 decachord on C.mid|Play 0,1,2,3,4,6,7,8,9,t}} (missing 5 & e) #{{audio|10-6 decachord on C.mid|Play 10-6}} (all but 5 & e)
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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 ] 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 {{music|b}}2 {{music|natural}}2 {{music|b}}3 {{music|natural}}3 {{music|#}}4 {{music|natural}}5 {{music|b}}6 {{music|natural}}6 {{music|b}}7," and thus spelled, on C, as C, D{{music|b}}, D{{music|natural}}, E{{music|b}}, E{{music|natural}}, F{{music|#}}, G, A{{music|b}}, A{{music|natural}}, B{{music|b}}.<ref name="Dziuba">Dziuba, Mark (2014). '''', p.48. Alfred Music. {{ISBN|9781470625757}}.</ref> This is a mode of ]'s seventh ]; it has six transpositions, like the tritone, and five modes (the same pitch classes with C, D{{music|b}}, D, E{{music|b}}, or E taken as the first ] or tonic). This allows a ] to be built upon the ] and a ], and allows the tonic chord to have an ] ], ], and ] ].<ref name="Dziuba"/> However, ] containing more than seven notes become increasingly similar to each other.<ref name="HansonHoward33">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."</ref> 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 ] 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 {{music|b}}2 {{music|natural}}2 {{music|b}}3 {{music|natural}}3 {{music|#}}4 {{music|natural}}5 {{music|b}}6 {{music|natural}}6 {{music|b}}7," and thus spelled, on C, as C, D{{music|b}}, D{{music|natural}}, E{{music|b}}, E{{music|natural}}, F{{music|#}}, G, A{{music|b}}, A{{music|natural}}, B{{music|b}}.<ref name="Dziuba">Dziuba, Mark (2014). '''', p. 48. Alfred Music. {{ISBN|9781470625757}}.</ref> This is a mode of ]'s seventh ]; it has six transpositions, like the tritone, and five modes (the same pitch classes with C, D{{music|b}}, D, E{{music|b}}, or E taken as the first ] or tonic). This allows a ] to be built upon the ] and a ], and allows the tonic chord to have an ] ], ], and ] ].<ref name="Dziuba"/> However, ] containing more than seven notes become increasingly similar to each other.<ref>]. (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 {{em|new}} intervals can be added." "On the other hand, as sonorities are projected beyond the six-tone series they tend to lose their individuality. {{em|All}} seven-tone series, for example, contain {{em|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."</ref>

A decatonic scale that has been used or considered by ] and ] in ] ] is 1/1, 12/11, 32/27, 9/7, 4/3, 132/91, 3/2, 18/11, 16/9, 176/91, and 2/1.<ref>Just Intonation Network (2002). '''', p. 17. Just Intonation Network: San Francisco.</ref> {{audio|13-limit just decatonic scale on C.mid|Play}}


==References== ==References==

Latest revision as of 00:15, 1 April 2023

Ten note musical scale
Four-semitone tritone scale Play
Symmetrical decatonic scale: "symmetric pattern ½–½–1–½–½|½–½–1–½–½" Play

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 sets exist, 10-1—10-6:

  1. Play 10-1 (all pitch classes but t & e)
  2. Play 10-2 (all but 9 & e)
  3. Play 10-3 (all but 8 & e)
  4. Play 10-4 (all but 7 & e)
  5. Play 10-5 (all but 6 & e)
  6. Play 10-6 (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 Play
Dominant seventh raised ninth vs. dominant seventh split third chord. Play

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♭. 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.

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. Play

References

  1. ^ 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. 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 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.
Musical scales (list)
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