---------------------------- 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&rsquo;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&rsquo;t consider that the error of a 
> &ldquo;naive&rdquo; oscillator becomes increasingly smaller for lower 
> frequencies. Of course, it&rsquo;s waveform specific, so that&rsquo;s why I 
> suggested bigger tables. (Side comment: If you get big enough tables, you 
> could
choose to skip linear interpolation altogether&mdash;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&rsquo;t a waveform. I guess some people only consider the basic 
synth waves as &ldquo;waveforms&rdquo;. :-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 
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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