Error measures for DR chords: Difference between revisions
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with root real-valued harmonic ''x''. Let <math>D_0 = 0, D_i = \sum_{k=1}^i \delta_k</math> be the delta signature {{nowrap|+δ<sub>1</sub> +δ<sub>2</sub> ... +δ<sub>''n''</sub>}} written cumulatively. | with root real-valued harmonic ''x''. Let <math>D_0 = 0, D_i = \sum_{k=1}^i \delta_k</math> be the delta signature {{nowrap|+δ<sub>1</sub> +δ<sub>2</sub> ... +δ<sub>''n''</sub>}} written cumulatively. | ||
We want to measure the error ''without having to fix any dyad'' (as one might naively fix a dyad and measure errors in the other deltas in relation to the fixed dyad). To do this we solve a least-squares optimization problem: use a root-sum-square objective function and optimize ''x'' (and any free deltas) to minimize that function. | We want to measure the error ''without having to fix any dyad in the target chord'' (as one might naively fix a dyad and measure errors in the other deltas in relation to the fixed dyad). To do this we solve a least-squares optimization problem: use a root-sum-square objective function and optimize ''x'' (and any free deltas) to minimize that function. | ||
== Domain and error model == | == Domain and error model == | ||