Delta-rational chord: Difference between revisions
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== Least-squares error == | == Least-squares error == | ||
Least-squares linear error (here linear means "in frequency space, not pitch space") is a proposed error measure for approximations to DR chords. | Least-squares linear error (here linear means "in frequency space, not pitch space") is a proposed error measure for approximations to DR chords. It has the advantage of not fixing a particular interval in the chord. However, like any other numerical measure of concordance or error, you should take it with a grain of salt. | ||
=== Fully DR === | === Fully DR === | ||
The idea motivating least-squares linear error on a chord as an approximation to a given delta signature is the following: 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 {{nowrap|''n'' > 1}}, in the linear domain as an approximation to a fully delta-rational chord with signature {{nowrap|+δ<sub>1</sub> +δ<sub>2</sub> ... +δ<sub>''n''</sub> | The idea motivating least-squares linear error on a chord as an approximation to a given delta signature is the following: 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 {{nowrap|''n'' > 1}}, in the linear domain as an approximation to a fully delta-rational chord with signature {{nowrap|+δ<sub>1</sub> +δ<sub>2</sub> ... +δ<sub>''n''</sub> | ||