Technical data guide for regular temperaments: Difference between revisions
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=== Optimal tuning(s) === | === Optimal tuning(s) === | ||
{{Main|Optimization}} | {{Main|Optimization}} | ||
Tuning ''optimization'' is, essentially, the task of finding a tuning for a given regular temperament that has the lowest error in some way. While many approaches exist to going about this, the most widely used are algorithms based on the ''TE metric'', which weight all intervals in the infinite set available to the temperament by a measure of their complexity, and tune in order to minimize deviation from just across all of them. | |||
It is conventional on the wiki to optimize under the constraint that the octave (or equave) is tuned pure, and therefore that the generator known as the ''period'' is either an exact equave or a fraction thereof. The rational interpretation of the period is depicted as equated to this fraction. However, the other ''generators'' are tuned to inexact values expressed in cents, and appear as rational interpretations equated to these values. Multiple optimization algorithms (most commonly CTE and POTE) may appear; different algorithms have subtle differences and one or the other may be chosen for a specific use. However, optimal tunings are used more often as guidelines for where "good tunings" of a temperament are than as exact ways to tune, and for that purpose the algorithms usually agree sufficiently (aside from extreme exotemperaments and other special cases). | |||
In the future, temperaments may appear with optimal tunings of ''prime harmonics'' (and their deviation from just) in a collapsible table, though this will be merely for the sake of convenience as all tunings of intervals can be derived from the generators and the mapping. | |||
=== Optimal ET sequence === | === Optimal ET sequence === | ||