Constrained tuning: Difference between revisions
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'''Constrained tunings''' are tuning [[optimization]] techniques using the constraint of some purely tuned intervals (i.e. [[eigenmonzo]]s). '''CTE tuning''' ('''constrained Tenney-Euclidean tuning''') is the most typical instance. It has a more sophisticated variant, '''CTWE tuning''' ('''constrained Tenney-Weil-Euclidean tuning'''). These two tunings will be the focus of this article. Otherwise normed tunings can be defined and computed analogously. | '''Constrained tunings''' are tuning [[optimization]] techniques using the constraint of some purely tuned intervals (i.e. [[eigenmonzo]]s, or unchanged-intervals). '''CTE tuning''' ('''constrained Tenney-Euclidean tuning''') is the most typical instance. It has a more sophisticated variant, '''CTWE tuning''' ('''constrained Tenney-Weil-Euclidean tuning'''). These two tunings will be the focus of this article. Otherwise normed tunings can be defined and computed analogously. | ||
All constrained tunings are standard temperament optimization problems. Specifically, as [[TE tuning]] can be viewed as a [[Wikipedia: Least squares|least squares problem]], CTE tuning can be viewed as an equality-constrained least squares problem. | All constrained tunings are standard temperament optimization problems. Specifically, as [[TE tuning]] can be viewed as a [[Wikipedia: Least squares|least squares problem]], CTE tuning can be viewed as an equality-constrained least squares problem. | ||