Tuning map: Difference between revisions
Cmloegcmluin (talk | contribs) →With respect to the JIP: again update explanation to reflect the difference between tuning map and generator tuning map |
Cmloegcmluin (talk | contribs) →Example: clarify difference between generator tuning map and tuning map |
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== Example == | == Example == | ||
Consider meantone temperament, with the mapping {{ket|{{map| 1 1 0 }} {{map| 0 1 4 }} }}. Temperaments, as represented by mappings, remain abstract; while this mapping does convey that the generators are ~2/1 and ~3/2, it does not specify exact tunings for those approximations. One example tuning would be quarter-comma meantone, where the octave is pure and the perfect fifth is 5<sup>1/4</sup>; this gives a generator tuning map of {{map| 1200.000 696.578 }}. | Consider meantone temperament, with the mapping {{ket|{{map| 1 1 0 }} {{map| 0 1 4 }} }}. Temperaments, as represented by mappings, remain abstract; while this mapping does convey that the generators are ~2/1 and ~3/2, it does not specify exact tunings for those approximations. One example tuning would be quarter-comma meantone, where the octave is pure and the perfect fifth is 5<sup>1/4</sup>; this gives a '''generator tuning map''' of {{map| 1200.000 696.578 }}. The generator tuning map is like a tuning map, but each entry gives the size in cents or octaves of a different [[generator]], rather than of a formal prime. | ||
From the generator tuning map G and the temperament mapping V, we can obtain the tuning map T: | |||
<math> | <math> | ||