Tenney–Euclidean temperament measures: Difference between revisions
m Protected "Tenney-Euclidean temperament measures" ([Edit=Allow only administrators] (indefinite) [Move=Allow only administrators] (indefinite)) |
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Graham Breed defines the simple badness slightly differently, again equivalent to a choice of scaling. This is skipped here because, by that definition, it is easier to find TE complexity and TE error first and multiply them together to get the simple badness. | Graham Breed defines the simple badness slightly differently, again equivalent to a choice of scaling. This is skipped here because, by that definition, it is easier to find TE complexity and TE error first and multiply them together to get the simple badness. | ||
=== Reduction to the Span of a Comma === | |||
It is notable that if M is codimension-1, we may view it as representing [[The dual|the dual]] of a single comma. In this situation, the simple badness happens to reduce to the [[Span|span]] of the comma, up to a constant multiplicative factor, so that the span of any comma can itself be thought of as measuring the complexity relative to the error of the temperament vanishing that comma. | |||
This relationship also holds if TOP is used rather than TE, as the TOP damage associated with tempering some comma n/d is log(n/d)/(n*d), and if we multiply by the complexity n*d, we simply get log(n/d) as our result. | |||
== TE error == | == TE error == | ||