Diamond tradeoff: Difference between revisions
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For each of these three diamond consonances, we want to find what generator is required in order that this pitch remains pure after tempering, or in other words, that it is an unchanged interval (sometimes called an [[eigenmonzo]]). And we want to know this for the situation where octaves are pure. | For each of these three diamond consonances, we want to find what generator is required in order that this pitch remains pure after tempering, or in other words, that it is an unchanged interval (sometimes called an [[eigenmonzo]]). And we want to know this for the situation where octaves are pure. | ||
Let's do it for 4/3 first. So, we prepare a matrix out of these two unchanged, 2/1 and 4/3, and call it <span><math>U</math></span>: | Let's do it for 4/3 first. So, we prepare a matrix out of these two unchanged intervals, 2/1 and 4/3, and call it <span><math>U</math></span>: | ||
<math> | <math> | ||