[sdiy] harmonic generator & megaloopers

[mark verbos]

Grant Richter wrote:

>>Now you lost me. What is a windowing function?
>>
>
>Here's how I understand it, maybe some of the math guru's can straighten me
>out. A continuous time Fourier transform of a sine wave has a discrete peak
>at one point as long a the sine wave goes from negative infinity to positive
>infinity. If there is a discontinuity (the sine wave is not infinite in
>duration), that discontinuity itself has harmonic content and the transform
>is no longer a single discrete peak.
>
>In the digital world, using sampled data, a non-windowed function shows
>"bleeding" (rounding at the bottom) between the frequency bins of the
>transform. By windowing the function (multiplying by another function that
>changes the edges) we reduce bleeding in the frequency bins and make the
>transform more "discrete" looking.
>
>It seems something like that should also apply to a continuous time
>transform. Changes in the shape of the discontinuity (edges of the window)
>should appear in the output of the transform and change the short term
>harmonic spectra.
>
>The only time I have seen this mentioned is Electronotes #45 Page 21
>"Transform methods in musical engineering" where Bernie talks about how the
>Fourier series fails for gated sine waves. But he does not say what does
>happens exactly, or why fading in a sine wave vs. gating it removes the
>clicks mathematically.
>
wouldn't that suggest that the sine wave should be synched to the note 
start? That way beginning of a note is always comming from a zero point. 
Then the click that results from a short attack would be eliminated. 
Assuming that the abrupt jump to the zero state doesn't cause a click at 
the end of the previous note ;)

>
>
>>My new obsession is the Buchla 248. With a bigger one, you could have a
>>synth with no other control modules. This one doing ALL the sequencing,
>>enveloping (AD,AR,ADSR or multistage), LFOing and combinations of these.
>>
>
>Doctor Mabuse and I have been discussing this as part of the "Envelooper"
>research. If you consider a sequencer as triggering an envelope on each
>stage, then an envelope becomes a "microsequence" inside of the
>"macrosequence" generated by the sequencer.
>
>Up to this point, the envelope generator progression has been functioning
>asynchronously with the sequencer. That is the ADSR states proceed as
>dictated by the time settings, not the sequencer clock. We have built some
>envelopes that use the least significant bits of the sequence counter and
>used those to control the ADSR states. So the sequencer is also the envelope
>generator for "synchronous" envelopes.
>
>The MARF uses a PWM crossfade function to generate continuous lines from
>discrete steps. Taking a very large counter, the LSBs can be used to
>generate a ramp for controlling the PWM crossfade between levels. So a large
>counter, DAC, comparators and CMOS logic could be used to generate the main
>sequence, ADSR, and LFO all synchronously locked together. The ramp times
>would adjust them selves automatically with the master clock.
>
wo. cool.

mark

>