Delta-rational chord: Difference between revisions
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== Least-squares error == | == Least-squares error == | ||
=== Fully DR === | |||
The idea motivating least-squares 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 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> | ||
}} (where the delta signature is written based on the chord written to have root 1), i.e. a chord | }} (where the delta signature is written based on the chord written to have root 1), i.e. a chord | ||
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This error measure is called the ''least-squares error''. This error measure does not form a metric on the set of delta signatures with a fixed number of terms, since it is not symmetric. | This error measure is called the ''least-squares error''. This error measure does not form a metric on the set of delta signatures with a fixed number of terms, since it is not symmetric. | ||
=== Partially DR === | |||
== DR triads in small edos == | == DR triads in small edos == | ||