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." > > > > > > > > > _______________________________________________ > dupswapdrop: music-dsp mailing list > music-dsp@music.columbia.edu > https://lists.columbia.edu/mailman/listinfo/music-dsp >
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