Constrained tuning: Difference between revisions
Created page with "The '''CTE tuning''' ('''constrained Tenney-Eclidean tuning''') is TE tuning under the constraints of some purely tuned intervals (i.e. eigenmonzos). While the TE tuni..." |
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The '''CTE tuning''' ('''constrained Tenney- | The '''CTE tuning''' ('''constrained Tenney-Euclidean tuning''') is [[TE tuning]] under the constraints of some purely tuned intervals (i.e. [[eigenmonzo]]s). While the TE tuning can be viewed as a [[Wikipedia: Least squares|least squares problem]], the CTE tuning can be viewed as an equality-constrained least squares problem. For a rank-''r'' temperament, specifying ''m'' eigenmonzos will yield ''r'' - ''m'' [[Wikipedia: Degrees of freedom|degrees of freedom]] to be optimized. | ||
The most significant form of CTE tuning is pure-octave constrained. For higher-rank temperaments, it may make sense to add multiple constraints, such as the pure-{2, 3} CTE tuning. | The most significant form of CTE tuning is pure-octave constrained. For higher-rank temperaments, it may make sense to add multiple constraints, such as the pure-{2, 3} CTE tuning. | ||