Tempering out: Difference between revisions
add related term “tempering together”, which was already widely used but not specifically defined throughout the wiki |
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== Tempering together == | == Tempering together == | ||
Two or more [[chord|chords]] 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. | Two or more [[chord|chords]] 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 {{Frac|32|27}}{{dot}}{{Frac|81|80}} = {{Frac|6|5}} and {{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 {{Frac|32|27}}{{dot}}{{Frac|81|80}} = {{Frac|6|5}} and {{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. | ||