An Introduction to the Dictionary of Harmonic Functios for 12-equal temperament

HarmonicFunctions titlepageThe Dictionary of Harmonic Functions endeavours to lay out the materials (interval relations, harmonic patterns) for the 12-E.T. tuning system in an elegant as well as practical manner. The relative simplicity of the tuning system, as opposed to the more complex musical cycles of 31 or 53, makes such an inventory manageable. Moreover, the 12 cycle is not dependant on a layout involving the matrix associated with the more complex cycles. Unlike the 19, 31, 43, and 53 cycles which are Prime, the 12 cycle is a Composite System, donating special properties to this much-used framework.

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http://www.siementerpstra.com/writings/Terpstra-HarmonicFunctions12et.pdf