Step pattern product: Difference between revisions
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Once the resulting step pattern has been acquired, one may arbitrarily assign the different types of steps to different relative sizes. Any permutation is possible, such as LLm<sub>1</sub>LLm<sub>2</sub>s, ssLssm<sub>1</sub>m<sub>2</sub>, etc; these scales are all [[sister]]s. | Once the resulting step pattern has been acquired, one may arbitrarily assign the different types of steps to different relative sizes. Any permutation is possible, such as LLm<sub>1</sub>LLm<sub>2</sub>s, ssLssm<sub>1</sub>m<sub>2</sub>, etc; these scales are all [[sister]]s. | ||
== | == Related properties == | ||
* Every [[distributionally even]] ternary scale is the step pattern product of two MOS words. However, the step pattern product of two MOS scales need not be distributionally even. | * Every [[distributionally even]] ternary scale is the step pattern product of two MOS words. However, the step pattern product of two MOS scales (even if ternary) need not be distributionally even. | ||
== Utilization == | == Utilization == | ||
The step pattern product can be used to construct complex scales such as the [[Zarlino]] scale from MOS scales. The Zarlino scale (and its sisters) may be represented by taking the product of ABABABA and AABAAAB, resulting in ABCBABC. | The step pattern product can be used to construct complex scales such as the [[Zarlino]] scale from MOS scales. The Zarlino scale (and its sisters) may be represented by taking the product of ABABABA and AABAAAB, resulting in ABCBABC. | ||
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* [[2a5b * 3a4b]] | * [[2a5b * 3a4b]] | ||
[[Category:Scale]] | [[Category:Scale]] | ||
[[Category:Combinatorics on words]] | [[Category:Combinatorics on words]] | ||