Delta-rational chord: Difference between revisions
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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> | ||