Tuning system: Difference between revisions

Concrete and abstract systems: rework and focus on the principles since the examples were too specific and anecdotal
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== Concrete and abstract systems ==
== 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 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.  
A very basic distinction among tuning systems is between concrete and abstract systems. A concrete tuning system defines exact intervals between all of its possible notes. Examples include untempered just intonation and equal tunings. An abstract tuning system has at least one variable interval, often constrained to preserve certain important properties. In other words, an abstract system is a set of concrete systems that have some characteristics or follow some rules. Depending on the characteristics or rules being considered, a concrete tuning system may be part of multiple abstract tuning systems. The most notable class of abstract systems is the regular temperaments.  


Analogous definitions exist for [[scale]]s.
Analogous definitions exist for [[scale]]s.