Distributional evenness: Difference between revisions
Tags: Mobile edit Mobile web edit |
Tags: Mobile edit Mobile web edit |
||
| Line 9: | Line 9: | ||
Using this definition, an ''r''-ary scale word in ''x''<sub>1</sub>, ..., ''x''<sub>''r''</sub> is DE if and only if for every ''i'' ∈ {1, ..., ''r''}, the binary scale obtained by equating all step sizes except ''x''<sub>''i''</sub> is DE. This shows that distributionally even scales over ''r'' letters are a subset of [[product word]]s of ''r'' − 1 MOS scales, which can be thought of as temperament-agnostic [[Fokker block]]s. | Using this definition, an ''r''-ary scale word in ''x''<sub>1</sub>, ..., ''x''<sub>''r''</sub> is DE if and only if for every ''i'' ∈ {1, ..., ''r''}, the binary scale obtained by equating all step sizes except ''x''<sub>''i''</sub> is DE. This shows that distributionally even scales over ''r'' letters are a subset of [[product word]]s of ''r'' − 1 MOS scales, which can be thought of as temperament-agnostic [[Fokker block]]s. | ||
All DE scales in this extended sense are also [[billiard scales]].<ref>Sano, S., Miyoshi, N., & Kataoka, R. (2004). m-Balanced words: A generalization of balanced words. Theoretical computer science, 314(1-2), 97-120.</ref> | All DE scales in this extended sense are also [[billiard scales]].<ref>Sano, S., Miyoshi, N., & Kataoka, R. (2004). m-Balanced words: A generalization of balanced words. Theoretical computer science, 314(1-2), 97-120.</ref> (Sano et al. call this property ''strongly balanced''.) | ||
== Related topics == | == Related topics == | ||