Tuning system: Difference between revisions

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 == Concrete and abstract systems ==
-A very basic distinction among tuning systems is between concrete and abstract systems. A '''concrete system''' defines exact intervals between all of its possible notes. Examples include untempered just intonation and equal tunings. An "abstract tuning system" doesn't refer to a concrete tuning, but to a set of "characteristics" or "rules" that a concrete tuning can have. For example, any regular tuning that follows the rule that ~3/2^4 = ~5/1 is a tuning of [[meantone]] temperament; if you change the rule to ~3/2^4 = ~36/7, then the same tuning can be treated as a tuning of [[archy]] temperament.
+A very basic distinction among tuning systems is between concrete and abstract systems. A concrete system defines exact intervals between all of its possible notes. Examples include untempered just intonation and equal tunings. An abstract system is a set of characteristics or rules that a concrete tuning can have. For example, any regular tuning that follows the rule that ~(3/2)<sup>4</sup> = ~5/1 is a tuning of [[meantone]] temperament; if you change the rule to ~(3/2)<sup>4</sup> = ~36/7, then the same tuning can be treated as a tuning of [[archy]] temperament.
 Analogous definitions exist for [[scale]]s.
 == Open and closed systems ==