The Logic Off Topic list

>"All" you have to do is find some way of, for example, representing pi 
>accurately in a digital filter ... which by its very definition is going to 
>be somewhat limited in its capabilities given that the synthesizer with the 
>ability to represent pi accurately has yet to be created (far as I know 
>none of them have the infinite memory required to represent pi with the 
>required degree of accuracy).

Thats what double precision floating point is for. 64 bits or 128 bits 
will get you pretty accurate estimate - certainly good enough so no one 
can hear any difference. I have the Maple program on my computer and I 
can give you as many digits of Pi as you like. You want 1,000 digits of 
Pi? (it only takes a second) - if you want 5 or 10,000 digits, just le me 
know
 
Pi == 
3.1415926535897932384626433832795028841971693993751058209749445923078164062
862089986280348253421170679821480865132823066470938446095505822317253594081
284811174502841027019385211055596446229489549303819644288109756659334461284
756482337867831652712019091456485669234603486104543266482133936072602491412
737245870066063155881748815209209628292540917153643678925903600113305305488
204665213841469519415116094330572703657595919530921861173819326117931051185
480744623799627495673518857527248912279381830119491298336733624406566430860
213949463952247371907021798609437027705392171762931767523846748184676694051
320005681271452635608277857713427577896091736371787214684409012249534301465
495853710507922796892589235420199561121290219608640344181598136297747713099
605187072113499999983729780499510597317328160963185950244594553469083026425
223082533446850352619311881710100031378387528865875332083814206171776691473
035982534904287554687311595628638823537875937519577818577805321712268066130
01927876611195909216420199

>>Real analog devices are pretty noisy actually.
>So are digital ones. Lots of squealing and stuff. Then you've got all that 
>Nyquist palaver. Etc etc etc. No Shangri-La there, sadly. Pretty good though.

There is a simple point which you keep avoiding.

Case 1.
Peter Gabriel sings 
 ----> mic -> preamp -> A/D converter -> digital file

Play back 
digital file ---> D/A converter ---> amplifier ---> speakers


Case 2
Mathematical numbers are used to create a sound
 .......  digital file

Play back 
digital file ---> D/A converter ---> amplifier ---> speakers

There may be noise going out in both cases, but there is bunch of noise 
going on the first case only. And analog synths produce a lot of noise!!!




>>The digital analog synths sound source was
>>purely mathematical.
>And ... so was the sample purely mathematical. A sample is not a real 
>recording, it is merely a collection of numbers that is supposed to 
>represent a wave form. But ... so also is 'a sine wave', within the same 
>digital domain, merely a collection of numbers that is supposed to 
>represent a waveform. Both are thrown at converters in order to produce a 
>sound. Can't see the difference myself. But I accept that you do.


Do you like to argue just for the sake of arguing or do you actually 
believe this?