Delta-rational chord: Difference between revisions
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This error measure is called '''least-squares delta error'''. Least-squares delta error does not depend on whether the chord whose error is being measured is 1:''r''<sub>1</sub>:''r''<sub>2</sub>:...:''r''<sub>''n''</sub> or the same chord linearly shifted to have root α. Unfortunately, this error measure does not form a metric on the set of delta signatures with a fixed number of terms. | This error measure is called '''least-squares delta error'''. Least-squares delta error does not depend on whether the chord whose error is being measured is 1:''r''<sub>1</sub>:''r''<sub>2</sub>:...:''r''<sub>''n''</sub> or the same chord linearly shifted to have root α. Unfortunately, this error measure does not form a metric on the set of delta signatures with a fixed number of terms. | ||
This error measure was found by Inthar with groundfault's help. | |||
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=== Partially DR === | === Partially DR === | ||
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== DR and RTT == | == DR and RTT == | ||
One may be able to tune a rank-2 regular temperament in such a way that a triad of interest exactly "inherits" its delta signature from a simple JI preimage thereof. This is done by setting up an algebraic equation relating the intervals in the chord to a generator and then solving for the generator that produces proportionally-beating triads. The value to be solved for is the generator's frequency ratio (not its cent value). | One may be able to tune a rank-2 regular temperament in such a way that a triad of interest exactly "inherits" its delta signature from a simple JI preimage thereof. This is done by setting up an algebraic equation relating the intervals in the chord to a generator and then solving for the generator that produces proportionally-beating triads. The value to be solved for is the generator's frequency ratio (not its cent value). | ||