Tuning map: Difference between revisions
Cmloegcmluin (talk | contribs) "generator map" → "generator tuning map"; I think it's clearer, and there's only one page on the wiki at present that uses either term, and it uses the latter 4 times and the former only once |
Cmloegcmluin (talk | contribs) →Example: update the explanation of the example to fit the tuning map method (one part still was written using ideas from my original erroneous draft of this page that used generator tuning maps with generator count vectors, rather than tuning maps with prime count vectors) |
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So, to answer the question, "how many cents is the approximation of the interval 16/15 in quarter-comma meantone?" we use the dot product to map 16/15's prime count vector {{vector| 4 -1 -1 }} via the tuning map given above, 4×1200.000 + (-1)×1896.578 + (-1)×2786.314 = 117.108 cents. | So, to answer the question, "how many cents is the approximation of the interval 16/15 in quarter-comma meantone?" we use the dot product to map 16/15's prime count vector {{vector| 4 -1 -1 }} via the tuning map given above, 4×1200.000 + (-1)×1896.578 + (-1)×2786.314 = 117.108 cents. | ||
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 1898.446 2788.196 }}. To answer the same question about 16/15 in this tuning of meantone, we | 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 1898.446 2788.196 }}. To answer the same question about 16/15 in this tuning of meantone, we use the same prime count vector, but map it with this different tuning map. So that gives us 4×1201.397 + (-1)×1898.446 + (-1)×2788.196 = 125.931 cents. And that's our answer for TE meantone. | ||
== Cents versus octaves == | == Cents versus octaves == | ||