File:DescenteInfinie.ogg

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Equation

${\displaystyle \,s}$ T-periodic on ${\displaystyle \mathbb {R} }$

${\displaystyle \forall t\in \left[0,T\right]}$

${\displaystyle \,s(t)=a(t)\sin \left(\omega (t)t\right)+a(t+T)\sin \left(2\omega (t)t\right)}$

with ${\displaystyle {\begin{cases}{\begin{array}{lcl}a(t)&=&A_{0}{\cfrac {1+\cos \pi {\frac {t}{T}}}{4}}\\\omega (t)&=&2\pi F_{0}{\cfrac {1}{2^{\frac {t}{T}}}}\\F_{0}&=&220\,{\text{Hz}}\\T&=&20\,{\text{s}}\\A_{0}&=&0.7\end{array}}\end{cases}}}$

The same signal is added on a minor chord, on several octaves.

--Gloumouth1 01:39, 10 December 2005 (UTC)

Loop

If you want to have a loop, as T = 20 s, you can crop this sound exactly from 18 s to 38 s.

Another idea

If I (or you) have time, one day, another function which could be programmed and recorded...

${\displaystyle \forall t\in \mathbb {R} \quad s(t)=\sum _{k=-\infty }^{\infty }a_{k}(t)\sin \left(\omega _{k}(t)t\right)}$

with ${\displaystyle {\begin{cases}a_{k}(t)=A_{0}e^{-{\cfrac {\left(k-{\frac {t}{T}}\right)^{2}}{\sigma ^{2}}}}\\\omega _{k}(t)=2\pi F_{0}2^{k-{\frac {t}{T}}}\\A_{0},F_{0},T,\sigma \,{\text{constants}}\end{cases}}}$

--Gloumouth1 17:04, 5 March 2007 (UTC)

en:File:DescenteInfinie.ogg

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Creative Commons Attribution-ShareAlike 3.0 Unported

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inception

9 December 2005

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application/ogg