User:Akselai: Difference between revisions
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<math>\displaystyle \lVert M \rVert_\text{RMS}' = \sqrt {\frac{\operatorname{det} (VV^\mathsf{T})}{C(n, r)}} = \frac {\lVert M \rVert_2}{\sqrt {C(n, r)}}</math> | <math>\displaystyle \lVert M \rVert_\text{RMS}' = \sqrt {\frac{\operatorname{det} (VV^\mathsf{T})}{C(n, r)}} = \frac {\lVert M \rVert_2}{\sqrt {C(n, r)}}</math> | ||
where <math>n</math> is the number of primes in the subgroup, <math>r</math> is the rank of the temperament. | where <math>n</math> is the number of primes in the subgroup, <math>r</math> is the rank of the temperament. | ||
= Current contributions = | |||
[[Fractal scale]] | |||
= Ideas and thoughts = | |||
[[User:Akselai/RES comma]] | |||
Revision as of 15:24, 21 January 2024
Pure mathematician interested in tuning. TODO: put my tuning scripts here. (There is a GitHub page by my name, there should be something soon.)
Some formulas for testing:
RTT and zeta: If [math]\displaystyle{ s\gt 1 }[/math], then [math]\displaystyle{ \displaystyle \sum_{\text{prime }p \geq 1} \frac{\Vert x \log p \Vert}{p^s} \lt \infty }[/math].
L^2 norm: [math]\displaystyle{ \displaystyle \lVert M \rVert_2 = \sqrt {\operatorname{det} (VV^\mathsf{T})} }[/math]
(Standard) RMS norm: [math]\displaystyle{ \displaystyle \lVert M \rVert_\text{RMS}' = \sqrt {\frac{\operatorname{det} (VV^\mathsf{T})}{C(n, r)}} = \frac {\lVert M \rVert_2}{\sqrt {C(n, r)}} }[/math] where [math]\displaystyle{ n }[/math] is the number of primes in the subgroup, [math]\displaystyle{ r }[/math] is the rank of the temperament.