User:Akselai

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.

Current contributions

Fractal scale

Ideas and thoughts

User:Akselai/RES comma User:Akselai/Quasi-modal construction of fractal scales