Complexity: Difference between revisions

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Being a characteristic of [[temperament]]s, complexity can be used to evaluate and compare them. Generally speaking, if a temperament has high complexity, that means that interesting pitches (e.g. ones [[consonant]] with each other) are many [[generator]]s apart, so useful scales tend to have many notes. If a temperament has low complexity, fewer generators are required, and scales with fewer notes are more likely to be useful.

Complexity and [[error]] are both usually treated as undesirable characteristics, but there is a trade-off between them in that very low complexity temperaments (e.g. small [[edo]]s) ~~cannot~~ have low error, and very low error temperaments (e.g. [[microtemperament]]s or [[JI]] itself) ~~cannot~~ have low complexity. [[Badness]] is a way to combine complexity and error such that a search for low-badness temperaments yields results with a particularly good trade-off between complexity and error.

Complexity and [[error]] are both usually treated as undesirable characteristics, but there is a trade-off between them in that very low complexity temperaments (e.g. small [[edo]]s) typically do not have low error, and very low error temperaments (e.g. [[microtemperament]]s or [[JI]] itself) typically do not have low complexity. [[Badness]] is a way to combine complexity and error such that a search for low-badness temperaments yields results with a particularly good trade-off between complexity and error.

== Complexity of an interval in a temperament ==

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 Being a characteristic of [[temperament]]s, complexity can be used to evaluate and compare them. Generally speaking, if a temperament has high complexity, that means that interesting pitches (e.g. ones [[consonant]] with each other) are many [[generator]]s apart, so useful scales tend to have many notes. If a temperament has low complexity, fewer generators are required, and scales with fewer notes are more likely to be useful.
-Complexity and [[error]] are both usually treated as undesirable characteristics, but there is a trade-off between them in that very low complexity temperaments (e.g. small [[edo]]s) cannot have low error, and very low error temperaments (e.g. [[microtemperament]]s or [[JI]] itself) cannot have low complexity. [[Badness]] is a way to combine complexity and error such that a search for low-badness temperaments yields results with a particularly good trade-off between complexity and error.
+Complexity and [[error]] are both usually treated as undesirable characteristics, but there is a trade-off between them in that very low complexity temperaments (e.g. small [[edo]]s) typically do not have low error, and very low error temperaments (e.g. [[microtemperament]]s or [[JI]] itself) typically do not have low complexity. [[Badness]] is a way to combine complexity and error such that a search for low-badness temperaments yields results with a particularly good trade-off between complexity and error.
 == Complexity of an interval in a temperament ==