View source for Distance model

[[Image:Diminished scales on Db, D, and Eb.PNG|thumb|right|300px|1:2 distance models on E{{music|flat}}, D, and D{{music|flat}}. Also known as octatonic scales.]]
[[Image:'Ode-to-Napoleon' hexachord.png|thumb|right|300px|[["Ode-to-Napoleon" hexachord]]<ref>[[David Lewin|Lewin, David]] (1959). "Re: Intervallic Relations Between Two Collections of Notes". ''Journal of Music Theory'' 3, no. 2 (November 1959): 298–301. p.300.</ref> in [[set (music)|prime form]]<ref name="Toorn">Van den Toorn, Pieter C. (1996). ''Music, Politics, and the Academy'', p.128-29. {{ISBN|0-520-20116-7}}.</ref> {{audio|'Ode-to-Napoleon' hexachord.mid|Play}}. It is also [[Ernő Lendvai]]'s "1:3 Model" scale and one of [[Milton Babbitt]]'s six all-combinatorial hexachord "source sets".<ref name="Toorn"/>]]

In [[music]] a '''distance model''' is the alternation of two different [[Interval (music)|intervals]] to create a non-diatonic [[musical mode]] such as the 1:3 distance model, the alternation of [[semitone]]s and [[minor third]]s: C-E{{music|flat}}-E-G-A{{music|flat}}-B-C.  This scale is also an example of [[polymodal chromaticism]] as it includes both the [[Tonic (music)|tonic]] and [[Dominant (music)|dominant]] as well as "'two of the most typical degrees from both major and minor' (E and B, E{{music|flat}} and A{{music|flat}}, respectively) ([Kárpáti 1975] p.132)".<ref>Kárpáti, János (1975). ''Bartók's String Quartets'', p.132. Translated by Fred MacNicol. Budapest: Corvina Press. Cited in Wilson 1992.</ref><ref>Wilson, Paul (1992). ''The Music of Béla Bartók'', p.&nbsp;8-9. {{ISBN|0-300-05111-5}}.</ref>

The most common distance model is the 1:2, also known as the [[octatonic scale]] ([[Forte number|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.<ref>Wilson (1992), p.&nbsp;25-26.</ref> Set type 4-9 has also been referred to as a "Z-Cell."<ref>{{cite web | url=http://openmusictheory.com/atonal.html | title=Analyzing atonal music }}</ref>

==See also==
*[[Generated collection]]

==References==
{{reflist}}

{{Atonality}}
{{Scales}}

[[Category:Modes (music)]]


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