From Mark Kolmar Sent Sat, May 13th 1995, 01:55
From Mark Kolmar Sent Sat, May 13th 1995, 01:55
I hope you will take my comments on digital equipment in the spirit they are intended. I admire the passion which some people on this list feel for their analog synthesizers. I did not join this mailing list to tout the benefits of digital synths or to knock analog synths. I'm dissatisfied with commercial synthesizers and the decisions that designers and engineers have been making. I came to analogue heaven first to try to figure out where to obtain a true ring mod, and low-pass resonant filter, and move in the direction of a modular. I stayed to learn more about the particulars of different models of synthesizers, and possibly help determine which one(s) (if any) I wanted to buy. I'm disheartened at the cost of the level of MIDI->CV I'd need for what I'd have in mind. Add enough modules to make the project worthwhile (the inexpensive ones from Doepfer even) and we'd already be in for over $2000, for one voice -- but oh what a voice that would be! On Fri, 12 May 1995, Don Tillman wrote: > Mark Kolmar stated that it is possible _IN THEORY_ and it sure _IS_ > possible to come _AS_CLOSE_AS_ONE_WANTS_TO_. Or perhaps I slept > through my entire education. > > Not exactly; he said "Digital synthesis in theory can do anything that > can be done with analogue synthesis". I will stand behind my original words, and the slightly different connotation of the paraphrased version. Nothing about FM synthesis, for example, is inherently digital. A wave modulates the frequency of another. The -implementation- of this method of synthesis however has been exclusively digital (to my knowledge). You can criticize the method--FM can be difficult. You can criticize the interface--I'd much rather have all the parms in front of me than have to dig through menus, too. But let's not confuse the separate issues of methods of synthesis, implementation and interface. > My remark was inspired by the comment: "Ring modulation, waveshaping, > amplitude modulation, distortion, anything related to phase shifting, > etc., are relatively easy to implement digitally." Ring Mod: Represent the waveforms as series of floating-point numbers between -1 and +1. Multiply the numbers together. Waveshaping: Remap values in the original waveform to new values in a lookup table. Lookup table formed by a polynomial function: y = v1 * (x ^ a) + v2 * (x ^ b) + v3 * (x ^ c) . . . where a, b, c are the frequency ratios (if integers, then harmonics) and v(x) are the relative amplitudes. Pitch shift of an octave is then achieved by y = x ^ 2. LPF: In ten words or less, "make the bumps and spikes on the waveform smaller". Resonance? Don't ask me... > Except for phase > shifting, these are all nonlinear operations that will create new > frequency components outside the spectrum and alias up a storm in the > usual annoying way. Getting around this is one of many very difficult > problems. Why pretend they don't exist? The posting suggested that > improvements in D/A converters and wider datapaths will fix the > situation, and this simply isn't true. I fully acknowledge the problem of aliasing distortion. Frequencies over 1/2 the sampling rate or under 0 will "fold over" and go 180 degrees out of phase. I am not a DSP programmer so I frankly don't know how one deals with this problem. I suppose one would have to detect and eliminate these frequencies during calculation. (One possible approach for the high end could be to increase the sample rate during calculation, apply a low-pass filter to the result, and then convert back.) Before you say "quantization error", allow me to briefly put this in perspective. You already know all this, I'm just repeating it: A digital representation of a sound is like a big piece of graph paper. For one second of audio on one channel of a CD, this piece of graph paper would be 44,100 x 65,536. Let's assume that after our calculations the least significant bit is always wrong due to rounding errors. This is 0.003% distortion. This is the -worst- that can happen before D/A conversion (which is where the real trouble starts). In contrast, I just shelled out a good chunk of money for a pre-amp & power-amp spec-ed at 0.03% THD. A cassette at normal operating levels adds 1-3% distortion. Vinyl is similar. I'd say a starting point for attempting to simulate the behavior (coloration, etc.) of an analog circuit (assuming you would want to) is the realization that the analog circuit (amplifier, synth, tape, etc.) is progressively "maxing-out" more and more as the levels increase. Therefore any attempt at a digital simulation of analog distortion, for instance, must do considerably more than just chop the waveform.