The above image shows the waveshaper in the Roland SH-3A synthesizer. It provides square, pulse and quasi-sawtooth waveforms in each of 5 footages, which are simultaneously available and mixable.
The square waves come from an organ divider chip, LM3216. Additionally the 8' pitch is also available as a pulse width modulated waveform, with an on/off switch as part of the rate control (labelled 8' CHORUS).
The sawtooth waves are generated from each square wave by a capacitor, resistor and diode circuit similar to those found in string ensembles. The capacitor and resistor form a differentiator (high pass filter) and the diode allows only positive going spikes through. However, whereas in a string ensemble each capacitor and resistor combination is selected for that particular key, here each footage's circuit must cover the full range of the synthesizer oscillator, which is 5 1/2 octaves (3 1/2 octave keyboard plus two extra transpose octaves), not including any frequency modulations.
This explains the thinness of the sawtooth tone generated by these circuits. The harmonic spectrum varies across the range of the instrument because the cutoff frequencies of the differentiators remain fixed while the frequencies produced by the oscillator vary. At the lower end of the synthesizer's range the differentiators remove most of the fundamental in the sawtooth tones.
Whereas the 32', 16' and 4' pulse waves are generated by diode combinations of the square wave footages, the 8' and 2' pulse waves use a transistor circuit to generate a fixed pulse from the differentiator waveform coming from the sawtooth circuits. In the case of 2' I believe this was done because there were no higher frequency footages available (e.g. 1', 1/2') to use the diode method. In the case of 8', the pulse and sawtooth waveforms are derived from a signal which may be a square wave or may be a PWM wave.
Again, the problem with this approach is that the differentiator time constants remain fixed across the range of the synthesizer oscillator, and so the 8' and 2' pulse waves get thinner at lower frequencies.
The 32', 16' and 4' pulse waves, on the other hand, maintain their mark-space ratio across the range of oscillator frequencies, and hence sound much more musically pleasing to me. The 32' and 16' footages are 12.5% (1/8) pulse waves, whereas the 4' footage is a 25% (1/4) pulse wave. Both of these are useful, indeed they feature heavily in the music of the 2A03 processor / sound chip from the Nintendo Famicom / NES. It would be interesting to try modifying the SH-3A waveshaper circuit to provide 12.5% and 25% pulse waveforms at each of the 32', 16' and 8' footages. Additionally, 32' and 16' 6.25% (1/16) and 32' 3.125% (1/32) pulse waves would also be possible.