Delta-rational chord: Difference between revisions

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-=== ''p''-norm and ''p''-mean measures ===
-Another possible approach is to view delta signatures as elements of <math>(\mathbb{R}_{>0})^n</math> by fixing the first element as 1 and measure either the <math>L^p</math> distance or the ''p''-mean of the components. While easy to compute, these naive measures are flawed or have unclear or unnatural interpretations, since fixing the first delta is an arbitrary choice.
 == DR and RTT ==
 One may be able to tune a rank-2 regular temperament in such a way that a triad of interest exactly "inherits" its delta signature from a simple JI preimage thereof. This is done by setting up an algebraic equation relating the intervals in the chord to a generator and then solving for the generator that produces proportionally-beating triads. The value to be solved for is the generator's frequency ratio (not its cent value).