POTE tuning: Difference between revisions
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Expansion (aka KE tuning, mention Kees optimality) |
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'''POTE tuning''' | '''POTE tuning''' ('''pure-octaves Tenney-Euclidean tuning'''), also known as '''KE tuning''' ('''Kees-Euclidean tuning'''), is a good choice for a standard tuning enforcing a just 2/1 octave. It can be computed from [[TE tuning]] with all primes destretched until 2/1 is just. | ||
== | == Kees optimality == | ||
POTE tuning is alternatively called KE tuning because it is the optimal tuning by Kees metric, that is, it minimizes the squared error of all intervals weighted by [[Kees height]]. | |||
== Computation == | |||
The TE and POTE tuning for a [[mapping|map matrix]] such as M = [{{val|1 0 2 -1}}, {{val|0 5 1 12}}] (the map for 7-limit [[Magic family|magic]], which consists of a linearly independent list of [[val]]s defining magic) can be found as follows: | The TE and POTE tuning for a [[mapping|map matrix]] such as M = [{{val|1 0 2 -1}}, {{val|0 5 1 12}}] (the map for 7-limit [[Magic family|magic]], which consists of a linearly independent list of [[val]]s defining magic) can be found as follows: | ||