Tempering out: Difference between revisions
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== Tempering together == | == Tempering together == | ||
Two or more [[chord | Two or more [[chord]]s or intervals are said to be ''tempered together'' if the commas that relate all of their corresponding steps are ''tempered out''. If two chords are tempered together, then the representation of each of those chords in the temperament is identical. | ||
For example, in [[meantone]], which tempers out [[81/80]], the chords [[54:64:81]] (with steps 32/27, 81/64) and [[10:12:15]] (with steps 6/5, 5/4) are tempered together. Since {{nowrap|{{Frac|32|27}}{{dot}}{{Frac|81|80}} {{=}} {{Frac|6|5}}}} and {{nowrap|{{Frac|81|64}} {{=}} {{Frac|5|4}}{{dot}}{{Frac|81|80}}}}, equating 81/80 with 1/1 also equates 32/27 with 6/5, and 81/64 with 5/4. | For example, in [[meantone]], which tempers out [[81/80]], the chords [[54:64:81]] (with steps 32/27, 81/64) and [[10:12:15]] (with steps 6/5, 5/4) are tempered together. Since {{nowrap|{{Frac|32|27}}{{dot}}{{Frac|81|80}} {{=}} {{Frac|6|5}}}} and {{nowrap|{{Frac|81|64}} {{=}} {{Frac|5|4}}{{dot}}{{Frac|81|80}}}}, equating 81/80 with 1/1 also equates 32/27 with 6/5, and 81/64 with 5/4. | ||
== Example == | == Example == | ||
The syntonic comma is 81/80. That is {{sfrac|3<sup>4</sup>|2 | The syntonic comma is 81/80. That is {{sfrac|3<sup>4</sup>|2<sup>4</sup> × 5}} or, in [[monzo]] form, {{monzo| -4 4 -1}}. | ||
19edo tempers out 81/80. (Technically, we should say that 19edo tempers out 81/80 when you use the [[patent val]].) You can see this in several ways: | 19edo tempers out 81/80. (Technically, we should say that 19edo tempers out 81/80 when you use the [[patent val]].) You can see this in several ways: | ||