Complexity: Difference between revisions
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In tuning, '''complexity''' is... | In tuning, '''complexity''' is a characteristic of [[temperament]]s, which 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. | |||
Some specific, mathematically rigorous definitions of "complexity" are... | |||
* [[Graham complexity]] | |||
* [[Generator complexity]] | |||
* [[Tenney-Euclidean_temperament_measures#TE Complexity|TE complexity]] | |||
* [[Tenney-Euclidean_metrics#Temperamental complexity|Temperamental complexity]] | |||
* [[Benedetti height]]</li></ul> | |||
==See also== | ==See also== | ||
* [http://en.wikipedia.org/wiki/Complexity http://en.wikipedia.org/wiki/Complexity] | |||
[[Category: | [[Category:complexity]] | ||
Revision as of 00:03, 21 September 2018
In tuning, complexity is a characteristic of temperaments, which 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 generators 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 EDOs) cannot have low error, and very low error temperaments (e.g. microtemperaments 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.
Some specific, mathematically rigorous definitions of "complexity" are...