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Distance model

From Wikipedia, the free encyclopedia
1:2 distance models on E, D, and D. Also known as octatonic scales.
"Ode-to-Napoleon" hexachord[1] inprime form[2]Play. It is alsoErnő Lendvai's "1:3 Model" scale and one ofMilton Babbitt's six all-combinatorial hexachord "source sets".[2]

Inmusic adistance model is the alternation of two differentintervals to create a non-diatonicmusical mode such as the 1:3 distance model, the alternation ofsemitones andminor thirds: C-E-E-G-A-B-C. This scale is also an example ofpolymodal chromaticism as it includes both thetonic anddominant as well as "'two of the most typical degrees from both major and minor' (E and B, E and A, respectively) ([Kárpáti 1975] p.132)".[3][4]

The most common distance model is the 1:2, also known as theoctatonic scale (set type 8-28), followed by 1:3 and 1:5, also known as set type 4-9, which is a subset of the 1:2 model.[5] Set type 4-9 has also been referred to as a "Z-Cell."[6]

See also

[edit]

References

[edit]
  1. ^Lewin, David (1959). "Re: Intervallic Relations Between Two Collections of Notes".Journal of Music Theory 3, no. 2 (November 1959): 298–301. p.300.
  2. ^abVan den Toorn, Pieter C. (1996).Music, Politics, and the Academy, p.128-29.ISBN 0-520-20116-7.
  3. ^Kárpáti, János (1975).Bartók's String Quartets, p.132. Translated by Fred MacNicol. Budapest: Corvina Press. Cited in Wilson 1992.
  4. ^Wilson, Paul (1992).The Music of Béla Bartók, p. 8-9.ISBN 0-300-05111-5.
  5. ^Wilson (1992), p. 25-26.
  6. ^"Analyzing atonal music".
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