The related scale for a given spectrum is found by drawing the dissonance curve and locating the minima. The complementary problem of finding a spectrum for a given scale is not as simple, since there is no single “best” spectrum for a given scale. But it is often possible to find “locally best” spectra which can be specified as the solution to a certain constrained optimization problem. For some kinds of scales, such as n-tet, properties of the dissonance curves can be exploited to directly solve the problem. A general “symbolic method” for constructing related spectra works well for scales built from a small number of successive intervals.
KeywordsConstrain Optimization Problem Scale Interval Harmonic Spectrum Simple Scale Scale Step
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