Delta-rational chord: Difference between revisions
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Let ''a'' and ''b'' be positive integers and suppose {{nowrap|gcd(''a'', ''b'') {{=}} 1}}. Let {{nowrap|''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, {{nowrap|'''0''' (unison) < '''u''' < '''v'''}}. Let '''p''', '''g''' be a basis formally representing the MOS scale's period and generator. Write | Let ''a'' and ''b'' be positive integers and suppose {{nowrap|gcd(''a'', ''b'') {{=}} 1}}. Let {{nowrap|''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, {{nowrap|'''0''' (unison) < '''u''' < '''v'''}}. Let '''p''', '''g''' be a basis formally representing the MOS scale's period and generator. Write | ||
<math>\begin{ | <math>\begin{aligned} | ||
\mathbf{u} &= u_p \mathbf{p} + u_g \mathbf{g} \\ | \mathbf{u} &= u_p \mathbf{p} + u_g \mathbf{g} \\ | ||
\mathbf{v} &= v_p \mathbf{p} + v_g \mathbf{g} | \mathbf{v} &= v_p \mathbf{p} + v_g \mathbf{g} | ||
\end{ | \end{aligned} | ||
</math> | </math> | ||