Delta-rational chord: Difference between revisions

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Inthar (talk | contribs)
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== Measuring the error of an approximate fully DR chord ==
== Measuring the error of an approximate fully DR chord ==
=== Least-squares error measures ===
=== Least-squares error measures ===
Say we want the error of a chord 1:''r''<sub>1</sub>:''r''<sub>2</sub>:...:''r''<sub>''n''</sub> (in increasing order) in the linear domain as an approximation to a fully delta-rational chord with signature +δ<sub>1</sub> +δ<sub>2</sub> ... +δ<sub>''n''</sub>, i.e. a chord
Say we want the error of a chord 1:''r''<sub>1</sub>:''r''<sub>2</sub>:...:''r''<sub>''n''</sub> (in increasing order), with ''n'' > 2, in the linear domain as an approximation to a fully delta-rational chord with signature +δ<sub>1</sub> +δ<sub>2</sub> ... +δ<sub>''n''</sub>, i.e. a chord


<math> x : x + \delta_1 : \cdots : x + \sum_{l=1}^n \delta_l </math>
<math> x : x + \delta_1 : \cdots : x + \sum_{l=1}^n \delta_l </math>