Delta-rational chord: Difference between revisions
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Then, provided that the positive rational number <math>m/n</math> lies in the image <math>r_{\mathbf{u}, \mathbf{v}}(I),</math> we can solve for <math>g \in I</math> that satisfies <math>r_{\mathbf{u}, \mathbf{v}}(g) = m/n,</math> making the specified chord ('''0''', '''u''', '''v''') a +''n''+''m'' DR chord. | Then, provided that the positive rational number <math>m/n</math> lies in the image <math>r_{\mathbf{u}, \mathbf{v}}(I),</math> we can solve for <math>g \in I</math> that satisfies <math>r_{\mathbf{u}, \mathbf{v}}(g) = m/n,</math> making the specified chord ('''0''', '''u''', '''v''') a +''n''+''m'' DR chord. | ||
The existence of an exact tuning for a delta signature specification is only guaranteed to hold when we only care about a ratio | The existence of an exact tuning for a delta signature specification is only guaranteed to hold when we only care about a ratio between ''two'' terms in the delta signature being exact. If we want to optimize an arbitrary specified delta signature (with some deltas possibly held free), we can use a least-squared-error solution instead to minimize the error. | ||
== DR and RTT == | == DR and RTT == | ||