Constrained tuning: Difference between revisions

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== Versus CTWE and POTE tuning ==

Consider the fact that TE tuning does not treat divisive ratios as more important than multiplicative ratios – 5/3 and 15/1 are taken as equally important, for example. To address that, a skew on the space may be introduced, resulting in TWE tuning. Constraining the equave to pure on top of TWE gives CTWE aka KE tuning. POTE works as a quick approximation to CTWE. As POTE destretches the equave, it keeps the angle in the tuning space unchanged, and thus sacrifices multiplicative ratios for divisive ratios. On the contrary, CTE sticks to the original design book of TE as its result remains TE optimal.

Consider the fact that TE tuning does not treat divisive ratios as more important than multiplicative ratios – 5/3 and 15/1 are taken as equally important, for example. To address that, a skew on the space may be introduced, resulting in [[TWE tuning]]. Constraining the equave to pure on top of TWE gives CTWE aka KE tuning. POTE works as a quick approximation to CTWE. As POTE destretches the equave, it keeps the angle in the tuning space unchanged, and thus sacrifices multiplicative ratios for divisive ratios. On the contrary, CTE sticks to the original design book of TE as its result remains TE optimal.

These tunings can be very different from each other. Take 7-limit meantone as an example. The POTE [[tuning map]] is a little bit flatter than [[quarter-comma meantone]], with all the primes tuned flat:

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 == Versus CTWE and POTE tuning ==
-Consider the fact that TE tuning does not treat divisive ratios as more important than multiplicative ratios – 5/3 and 15/1 are taken as equally important, for example. To address that, a skew on the space may be introduced, resulting in TWE tuning. Constraining the equave to pure on top of TWE gives CTWE aka KE tuning. POTE works as a quick approximation to CTWE. As POTE destretches the equave, it keeps the angle in the tuning space unchanged, and thus sacrifices multiplicative ratios for divisive ratios. On the contrary, CTE sticks to the original design book of TE as its result remains TE optimal.
+Consider the fact that TE tuning does not treat divisive ratios as more important than multiplicative ratios – 5/3 and 15/1 are taken as equally important, for example. To address that, a skew on the space may be introduced, resulting in [[TWE tuning]]. Constraining the equave to pure on top of TWE gives CTWE aka KE tuning. POTE works as a quick approximation to CTWE. As POTE destretches the equave, it keeps the angle in the tuning space unchanged, and thus sacrifices multiplicative ratios for divisive ratios. On the contrary, CTE sticks to the original design book of TE as its result remains TE optimal.
 These tunings can be very different from each other. Take 7-limit meantone as an example. The POTE [[tuning map]] is a little bit flatter than [[quarter-comma meantone]], with all the primes tuned flat: