This is a waveshaper that converts a sawtooth input to a triangle waveform. As with many waveshapers, this one copies input imperfections to it's output. Slow reset times and nonlinear ramps will show up as glitches and nonlinear triangle ramps. Sonically, the imperfections do not cause a problem because they are constant and repeatable for each wave cycle. This means that whatever the distortion, the timbre is constant for a given pitch.
Comparing the input sawtooth sound to the resulting "triangle" output, I hear a very much sinewave like sound, with much less harmonic content than the sawtooth.
The 'soft clipped triangle' output looks like a sine approximation on an o'scope, and has a sine-like, flutey sound.
The circuit works as follows:
The three gates at the bottom create a square wave where the square toggles when the ramp reaches about +V/2. Three gates were used to make sure the signal is rectangular and at logic levels. The last inverter in this chain is used to provide an inverted copy of the logic signal. The two gates at the left/top provide two copies of the saw signal, one inverted, the other noninverted. The square logic signals (inv. and noninv.) are applied to the gate terminals of the two P MOSFET transistors (the N transistors are not used). This arrangement causes the two transistors to alternately allow either the saw or inverted saw to be connected to the buffer amp. The buffer amp returns some gain because the method used here effectively halves the saw amplitude. The second buffer amp is expected to distort. MOSFET gates used in 'linear' mode distort by soft clipping the input. The soft clipping then converts the triangle at it's input to an approximation of a sinewave, rounded tops with spline shaped ('S') sides.
The whole circuit is built of one 4069 and one 4007. Only the two N transistors are not used.
Please note that I use the word 'triangle' loosely. The sound will be triangle-like, but won't look perfect on a scope. The same is true of the sine-like output. I've added some capacitors to do a little low pass filtering which improved the waveforms, but they will not be perfect.