Delta-rational chord: Difference between revisions
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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. | ||
=== Finding a tuning of a MOS scale with an exact DR chord === | |||
Let ''a'', ''b'' be positive integers and suppose gcd(''a'', ''b'') = 1. Let ''E'' > 1 be the frequency ratio of the equave. Consider a MOS ''a'''''L'''''b'''''s'''{{angbr|''E''}} with generator range <math>I \subseteq (1, \sqrt{E})</math> (in the linear frequency domain), and consider a pair ('''u''', '''v''') of notes from the root of a given triad in the MOS, '''0''' (unison) < '''u''' < '''v'''. Let '''p''', '''g''' be a basis formally representing the MOS scale's period and generator. Write | Let ''a'', ''b'' be positive integers and suppose gcd(''a'', ''b'') = 1. Let ''E'' > 1 be the frequency ratio of the equave. Consider a MOS ''a'''''L'''''b'''''s'''{{angbr|''E''}} with generator range <math>I \subseteq (1, \sqrt{E})</math> (in the linear frequency domain), and consider a pair ('''u''', '''v''') of notes from the root of a given triad in the MOS, '''0''' (unison) < '''u''' < '''v'''. Let '''p''', '''g''' be a basis formally representing the MOS scale's period and generator. Write | ||