Delta-rational chord: Difference between revisions
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# When all dyads are linearly related, equivalently when the chord has a delta signature with all entries integers, we call the chord ''fully delta-rational'' (FDR) or ''linear''. | # When all dyads are linearly related, equivalently when the chord has a delta signature with all entries integers, we call the chord ''fully delta-rational'' (FDR) or ''linear''. | ||
# A chord that has a delta signature with all entries +1 is called ''[[isoharmonic chord|isodifferential]]''. | # A chord that has a delta signature with all entries +1 is called ''[[isoharmonic chord|isodifferential]]''. | ||
Due to the aforementioned equivalence of delta signatures under scaling, delta signatures of ''n'' terms are really elements of a projective space <math>\mathbb{R}\mathbf{P}^{n-1}</math>, specifically in the image of the all-positive orthant. | |||
In practice these terms can loosely refer to approximations of mathematically exact PDR and FDR chords, for example in [[edo]] tunings. | In practice these terms can loosely refer to approximations of mathematically exact PDR and FDR chords, for example in [[edo]] tunings. | ||