Tuning map: Difference between revisions
Cmloegcmluin (talk | contribs) Created page with "A '''tuning map''' represents the tuning of a regular temperament. It takes a vector representation of an interval as input and outputs its pitch, usually measured in cent..." |
Cmloegcmluin (talk | contribs) →Example: fix typo |
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But now we need to know how many cents each ~2/1 and each ~3/2 map to, and the tuning map is what answers that question. So we take this {{vector|3 -5}} and dot product it in turn with the tuning map {{map|1200 696.578}}, which gives us 3·1200 + -5·696.578 = 117.110. So that's our answer! | But now we need to know how many cents each ~2/1 and each ~3/2 map to, and the tuning map is what answers that question. So we take this {{vector|3 -5}} and dot product it in turn with the tuning map {{map|1200 696.578}}, which gives us 3·1200 + -5·696.578 = 117.110. So that's our answer! | ||
Another example tuning for meantone would be the [[TE tuning]], which is the default that [http://x31eq.com/temper|Graham Breed's popular RTT web tool] provides. This gives us a tuning map of {{map|1201.397 | Another example tuning for meantone would be the [[TE tuning]], which is the default that [http://x31eq.com/temper|Graham Breed's popular RTT web tool] provides. This gives us a tuning map of {{map|1201.397 695.652}} (when we take the octave complement of the generator so that it matches our mapping). To answer the same question about 16/15 in this tuning of meantone, we can use the same generator count vector we already found; the {{vector|3 -5}} part is the same in any tuning of meantone. All we need to do now is map that with this different tuning map. So that gives us 3·1201.397 + -5·695.652 = 125.931. So that's our answer for TE meantone. | ||
== Cents versus octaves == | == Cents versus octaves == | ||