Tenney–Euclidean temperament measures: Difference between revisions
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By Graham Breed's definition, TE error may be accessed via [[Tenney–Euclidean tuning|TE tuning map]]. If ''T''<sub>''W''</sub> is the Tenney-weighted tuning map, then the TE error ''G'' can be found by | By Graham Breed's definition, TE error may be accessed via [[Tenney–Euclidean tuning|TE tuning map]]. If ''T''<sub>''W''</sub> is the Tenney-weighted tuning map, then the TE error ''G'' can be found by | ||
$$ | |||
\begin{align} | \begin{align} | ||
G &= \norm{T_W - J_W}_\text{RMS} \\ | G &= \norm{T_W - J_W}_\text{RMS} \\ | ||
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&= \sqrt{J_W(V_W^+ V_W - I)(V_W^+ V_W - I)^\mathsf{T} J_W^\mathsf{T}/n} | &= \sqrt{J_W(V_W^+ V_W - I)(V_W^+ V_W - I)^\mathsf{T} J_W^\mathsf{T}/n} | ||
\end{align} | \end{align} | ||
$$ | |||
If ''T''<sub>''W''</sub> is denominated in cents, then ''J''<sub>''W''</sub> should be also, so that {{nowrap|''J''<sub>''W''</sub> {{=}} {{val| 1200 1200 … 1200 }}}}. Here {{nowrap|''T''<sub>''W''</sub> − ''J''<sub>''W''</sub>}} is the list of weighted errors of each prime harmonic. | If ''T''<sub>''W''</sub> is denominated in cents, then ''J''<sub>''W''</sub> should be also, so that {{nowrap|''J''<sub>''W''</sub> {{=}} {{val| 1200 1200 … 1200 }}}}. Here {{nowrap|''T''<sub>''W''</sub> − ''J''<sub>''W''</sub>}} is the list of weighted errors of each prime harmonic. | ||