Diamond tradeoff: Difference between revisions
Cmloegcmluin (talk | contribs) →Example: better matrix formatting (in particular right-alignment) |
Cmloegcmluin (talk | contribs) →Example: explain edge case |
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We now have our generator sizes that give us pure consonances in the tonality diamond: 701.955¢, 696.578¢, and 694.786¢. The minimum of those is 694.786¢ and the maximum is 701.955¢, so that's our diamond tradeoff range. Anywhere inside that range, we are making at least one of our diamond consonances purer; outside it, we're making them all less pure. | We now have our generator sizes that give us pure consonances in the tonality diamond: 701.955¢, 696.578¢, and 694.786¢. The minimum of those is 694.786¢ and the maximum is 701.955¢, so that's our diamond tradeoff range. Anywhere inside that range, we are making at least one of our diamond consonances purer; outside it, we're making them all less pure. | ||
This method works as long as you do not choose for your unchanged intervals any intervals that are separated by commas of the temperament. In that case, <math>MU</math> will come out singular, that is, determinant 0, with no inverse, which is math's way of telling you that there's no way to not change both intervals when one of them must be tempered to the other. For example, you couldn't set both 3/2 and 40/27 to be unchanged intervals of meantone, because they're off from each other by 81/80. But then again, you wouldn't try to do something weird like that in the first place, would you. | |||
== See also == | == See also == | ||