rbj wrote:
>i, personally, would rather see a consistent method used throughout the
MIDI keyboard range

If you squint at it hard enough, you can maybe convince yourself that the
naive sawtooth generator is just a memory optimization for low-frequency
wavetable entries. I mean, it does a perfect job at DC right? :]

On Sun, Aug 5, 2018 at 4:27 PM, robert bristow-johnson <
r...@audioimagination.com> wrote:

> ---------------------------- Original Message ----------------------------
> Subject: Re: [music-dsp] Antialiased OSC
> From: "Nigel Redmon" <earle...@earlevel.com>
> Date: Sun, August 5, 2018 1:30 pm
> To: music-dsp@music.columbia.edu
> --------------------------------------------------------------------------
> > Yes, that’s a good way, not only for LFO but for that rare time you want
> to sweep down into the nether regions to show off.
> i, personally, would rather see a consistent method used throughout the
> MIDI keyboard range; high notes or low.  it's hard to gracefully transition
> from one method to a totally different method while the note sweeps.  like
> what if portamento is turned on?  the only way to clicklessly jump from
> wavetable to a "naive" sawtooth would be to crossfade.  but crossfading to
> a wavetable richer in harmonics is already built in.  and what if the
> "classic" waveform wasn't a saw but something else?  more general?
> > I think a lot of people don’t consider that the error of a “naive”
> oscillator becomes increasingly smaller for lower frequencies. Of course,
> it’s waveform specific, so that’s why I suggested bigger tables. (Side
> comment: If you get big enough tables, you could choose to skip linear
> interpolation altogether—at constant table size, the higher frequency
> octave/whatever tables, where it matters more, will be progressively more
> oversampled anyway.)
> well, Duane Wise and i visited this drop-sample vs. linear vs. various
> different cubic splines (Lagrange, Hermite...) a couple decades ago.  for
> really high quality audio (not the same as an electronic musical
> instrument), i had been able to show that, for 120 dB S/N, 512x
> oversampling is sufficient for linear interpolation but 512K is what is
> needed for drop sample.  even relaxing those standards, choosing to forgo
> linear interpolation for drop-sample "interpolation" might require bigger
> wavetables than you might wanna pay for.  for the general wavetable synth
> (or NCO or DDS or whatever you wanna call this LUT thing, including just
> sample playback) i would never recommend interpolation cruder than linear.
> Nigel, i remember your code didn't require big tables and you could have
> each wavetable a different size (i think you had the accumulated phase be a
> float between 0 and 1 and that was scaled to the wavetable size, right?)
> but then that might mean you have to do better interpolation than linear,
> if you want it clean.
> > Funny thing I found in writing the wavetable articles. One soft synth
> developer dismissed the whole idea of wavetables (in favor of minBLEPs,
> etc.). When I pointed out that wavetables allow any waveform, he said the
> other methods did too. I questioned that assertion by giving an example of
> a wavetable with a few arbitrary harmonics. He countered that it wasn’t a
> waveform. I guess some people only consider the basic synth waves as
> “waveforms”. :-D
> >
> i've had arguments like this with other Kurzweil people while i worked
> there a decade ago (still such a waste when you consider how good and how
> much work they put into their sample-playback, looping, and interpolation
> hardware, only a small modification was needed to make it into a decent
> wavetable synth with morphing).
> for me, a "waveform" is any quasi-periodic function.  A note from any
> decently harmonic instrument; piano, fiddle, a plucked guitar, oboe,
> trumpet, flute, all of those can be done with wavetable synthesis (and
> most, maybe all, of them can be limited to 127 harmonics allowing archived
> wavetables to be as small as 256).
> these are the two necessary ingredients to wavetable synthesis:
> quasi-periodic note (that means it can be represented as a Fourier series
> with slowly-changing Fourier coefficients) and bandlimited.  if it's
> quasi-periodic and bandlimited it can be done with wavetable synthesis.  to
> me, for someone to argue against that, means to me that they are arguing
> against Fourier and Shannon.
> there is a straight-forward way of pitch tracking the sampled note from
> attack to release, and from that slowly-changing period information, there
> is a straight-forward way to sample it to 256 points per cycle and
> converting each adjacent cycle into a wavetable.  that's a lotta redundant
> data and most of the wavetables (nearly all of them) can be culled with the
> assumption that the wavetables surviving the culling process will be
> linearly cross-faded from one to the next.
> and if several notes (say up and down the keyboard) are sampled, there is
> a way to align the wavetables (before culling) between the different notes
> to be phase aligned.  then, say you have a split every half octave, the
> note at E-flat can be a mix of the wavetables for C below and F# above.
> it's like the F# is pitched down 3 semitones and the C is pitched up 3
> semitones and the Eb is a phase-aligned mix of the two.  this can be done
> with any harmonic or quasi-periodic instrument, even a piano (but maybe you
> will need more than 2 splits per octave).
> > Hard sync is another topic...
> hard sync is sorta hard, but still very doable with wavetable (and
> morphing along one dimension) as long as one is willing to put a lotta
> memory into it.  each incremental change in the slave/master frequency
> ratio (which is a timbre control) will require a separate wavetable to
> cross-fade into and out.
> --
> r b-j                         r...@audioimagination.com
> "Imagination is more important than knowledge."
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