Interleaving: Difference between revisions
From Xenharmonic Reference
Created page with "A scale is an '''interleaving''' if it is (1) made of multiple copies (called ''strands'') of a smaller scale and (2) ''any two copies'' of the smaller scale are interleaved so that any note of the first copy falls strictly between two notes of the other copy. An interleaving is defined by the choice of strand scale and the choice of the ''polyoffset'': the offset chord that copies of the strand are placed on. For example, the ternary scale blackdye has strand pyth[5] a..." |
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A scale is an '''interleaving''' if it is (1) made of multiple copies (called ''strands'') of a smaller scale and (2) ''any two copies'' of the smaller scale are interleaved so that any note of the first copy falls strictly between two notes of the other copy. | A scale is an '''interleaving''' if it is (1) made of multiple copies (called ''strands'') of a smaller scale and (2) ''any two copies'' of the smaller scale are interleaved so that any note of the first copy falls strictly between two notes of the other copy. | ||
An interleaving is defined by the choice of strand scale and the choice of the ''polyoffset'': the offset chord that copies of the strand are placed on. For example, the ternary scale blackdye has strand pyth[5] and polyoffset 9:10 or 5:9. {{adv|A scale that is a union of multiple copies of a smaller scale ''s'' is an interleaving if and only if no interval of the polyoffset (measured from a given root) falls between the smallest ''k''-step of ''s'' and the largest ''k''-step of ''s' (inclusive) for any ''k'', 1 ≤ k < size of ''s''.}} | An interleaving is defined by the choice of strand scale and the choice of the ''polyoffset'': the offset chord that copies of the strand are placed on. For example, the ternary scale blackdye has strand pyth[5] and polyoffset 9:10 or 5:9. {{adv|A scale that is a union of multiple copies of a smaller scale ''s'' is an interleaving if and only if no interval of the polyoffset (measured from a given root) falls between the smallest ''k''-step of ''s'' and the largest ''k''-step of ''s'' (inclusive) for any ''k'', 1 ≤ k < size of ''s''.}} | ||
[[Category:Scale constructions]] | [[Category:Scale constructions]] | ||
Revision as of 19:30, 17 December 2025
A scale is an interleaving if it is (1) made of multiple copies (called strands) of a smaller scale and (2) any two copies of the smaller scale are interleaved so that any note of the first copy falls strictly between two notes of the other copy.
An interleaving is defined by the choice of strand scale and the choice of the polyoffset: the offset chord that copies of the strand are placed on. For example, the ternary scale blackdye has strand pyth[5] and polyoffset 9:10 or 5:9. A scale that is a union of multiple copies of a smaller scale s is an interleaving if and only if no interval of the polyoffset (measured from a given root) falls between the smallest k-step of s and the largest k-step of s (inclusive) for any k, 1 ≤ k < size of s.
