XPost: rec.music.gdead, sci.electronics.design   
   From: ksi@koi8.net   
      
   In sci.electronics.design Dick Pierce  wrote:   
   > Arny Krueger wrote:   
   >> "Randy Yates"  wrote in message   
   >> news:BfWdndRN5L09kvLQnZ2dnUVZ_oWdnZ2d@supernews.com   
   >>   
   >>>On 03/02/2011 09:37 PM, David Nebenzahl wrote:   
   >>>   
   >>>>On 3/2/2011 5:09 PM Dick Pierce spake thus:   
   >>>>   
   >>>>   
   >>>>>Arny Krueger wrote:   
   >>>>>   
   >>>>>   
   >>>>>>"Sergey Kubushyn"  wrote in message   
   >>>>>>news:ikkam0$b8$1@speranza.aioe.org   
   >>>>>>   
   >>>>>>>Music is _NOT_ a pure sinusoidal waves and there are   
   >>>>>>>other things like attack, shape etc.   
   >>>>>>   
   >>>>>>Actually, every music wave form can be entirely   
   >>>>>>represented as a collection of enveloped sine wave.   
   >>>>>   
   >>>>>Not even "enveloped" sine waves: simply sine waves.   
   >>   
   >>   
   >>>>Yes. Just what is an "enveloped" sine wave anyway, pray   
   >>>>tell?   
   >>   
   >>   
   >>>Amplitude-modulated.   
   >>   
   >>   
   >> Right.   
   >>   
   >> I would like to hear how one simulates say piano notes by means of just   
   >> linear mixing of continuous sine waves.   
   >   
   > Are you saying that it's not possible? Here, take   
   > my shovel, dig up Mr. Fourier, tell him it's not   
   > possible.   
   >   
   > Take ANY amplitude-modulated waveform. Take it's   
   > Fourier transform. The result is some collection of   
   > continuous sine waves, n'est ce pas?   
   >   
   > Let's look at a simple case: a 1 kHz wave modulated by   
   > a 100 Hz envelope. That's three sine components, whose   
   > relative amplitudes are dependent upon the amount of   
   > modulation: one sitting at 900 Hz, one at 1000 Hz, and   
   > one at 1100 Hz. Y'know, sidebands, and all that?   
   >   
   > Take a more complex waveform with a more complex envelope,   
   > and it's merely an extension of the same thing.   
      
   OK, what is the spectrum of e.g. shattered glass sound or a gunshot? How   
   high it goes when you strike high-hat or ride cymbal? What is the spectral   
   width of even 1KHz square wave? Good analog gear will give you almost   
   undistorted 10KHz square wave. What is the highest sine wave frequency that   
   should be taken into the equation to make that 10KHz square wave to even   
   remotedly resemble the original one?   
      
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