The Yamaha AN1x Synthesizer mailing list

> I read (a fairly scholarly) paper on modular synthesis for the 
Nord
> Micro Modular and it said unequivocally that digital oscillators 
have
> more energy above 10,000 Hz than their analog counterparts 
============================
Here's part of the article that I was referencing:

http://www.cim.mcgill.ca/%7Eclark/nordmodularbook/nm_oscillator.html

> "Rob Hordijk has developed a very nice sounding "analog" style 
filter. His filter avoids the "buzzy" sound produced by many digital 
resonant filters. The buzziness arises because digital oscillators 
contain a relatively large amount of energy above 10kHz. Most analog 
oscillators have less energy in this region, as the analog circuitry 
itself filters part of it away. Imagine a sawtooth set to 200 Hz, 
therefore having overtones 200 Hz apart from each other. This means 
that in the area between 10 kHz and 20 kHz there are 50 overtones 
present, all crowded together within a single octave! When using, 
for example, 3 slightly detuned oscillators you're talking about 3 * 
50 = 150 overtones all in that one high octave, and all phasing fast 
with each other. The amplitudes of these overtones are very small, 
but there are a lot of them and very high sounds are perceived quite 
well, so there is a distinct buzz in the high. If the cutoff 
frequency is set to this area the buzziness is increased even more 
at high resonance levels. The resonance band of a 12 dB filter is a 
bit broader than that of a 24 dB filter, so the 12 dB filter suffers 
a bit more from the buzz. 

The problem with this buzz is that it can mess up those other sounds 
that have by nature lots of energy in the same band, notably hihats 
and cymbals and some dipthongs in the vocals. Thus it is a good 
practice to filter everything above 10kHz away from all instruments 
when there are hihats and cymbals in the rhythm track, or if you use 
vocals from someone with a clear voice. Otherwise these hihats and 
the s's and t's will drown in the high of the other instruments. Its 
even worse if the 10kHz+ area gets in a reverb with a very bright 
tail. That will start to produce lots of noise. 

For most synth sounds, especially strings, its not the 10kHz+ area 
which is important, but the area between 3.5kHz and 10 kHz. So 
filtering away all above 10kHz but slightly emphasizing the 3.5 to 8 
kHz area greatly improves the warmth and depth of stringsounds. A 
single 6 dB LP filter set to 10kHz won't do the job, the cutoff 
frequency should be set to 2.5 kHz or less to effectively remove the 
buzz. Even the cutoff frequency of a 24 dB filter should be set to 
something like 5kHz. But in both cases you would also lose part of 
the important 3.5 to 8 kHz area. The most useful solution is to use 
a dipfilter with a notch around 12 kHz. 

The filter is composed of two 12 dB filters that are cascaded to get 
a 24 dB filter. On the first filter a little bit of the HP output is 
mixed to the LP output. This is tuned by a MasterOsc module. As it 
apparently needs some bizarre overexponential control to get 
everything right, the grey signal is raised to the power of two and 
mixed with the grey signal to control the amount of HP. This creates 
a notch at the top end of the spectrum, which does three things: 

1) it attenuates the very high end, making the filter less "buzzy ". 
2) it reduces the resonance at the top end of the spectrum relative 
to the rest of the spectrum, especially at high resonance settings. 
This also makes the sound less buzzy. 
3) the notch increases the filter slope slightly. 

The messing about with that grey signal is just to keep the notch at 
the right place, which is tuned to taste by ear. 

The second 12dB filter increases the filter cutoff slope to 24 dB. 
The feedback from the LP output of the second filter increases the 
bottom end of the spectrum, giving the sound a little bit more guts. 

This filter can give good analog bass sounds with even a single 
sawtooth oscillator. "