For sure, I've wanted to build a VCO or DCO that could flexibly control integer harmonics of a fundamental pitch. Like since forever! Whether via a phalanx of digital oscillators; via inverse FFT, with overlap save block samples; an array of oscillators; emulating a Synclavier with later-modern technology; or some clever mastery over the shaping of a comb spectrum.great to see this progressing. and thanks for the audio clips, i like the chaotic stuff!
ive been thinking about the difference between lumped parameter modelling (which is used in both acoustics and electronics) versus the full wave equation. typically you can reduce a system to a single dimension if the length is much greater than its width. for a trombone, this ratio is 1:200, which is definitely good enough. for a 22g wire, 5.6" would give this same ratio, so i think they both can be equally modelled as one dimensional in most cases. a lumped parameter model of a long tube with air gives the air as compressible (capacitor) and the amount of air (tube length) as mass (inductor), so its a resonant system, and the fundamental will come out the same as an LC circuit. but, there is also the issue of operating at greater than a 1/4 wave length (far field approximations), which is very different for acoustics than electronics. i dont have any great conclusions at this point, but im also wondering if the blown pipe analogy is actually all that much better. from the spectrum plots on the flute (page i linked above) the harmonics are no where near pure. there are a few nonlinearities at the openings that shift frequency slightly depending upon the pressure and length.
also, for comb filters (N-tap as mentioned earlier in the thread by uniqview), i found this recently by pugix:
https://pugix.com/synth/cgs-bi-n-tic-filter/
And over enough time, technology has eventually enabled such composite oscillators.
But what if that's musically insufficient? In the technical finessing of such a thing, what if ultimately the tonality turned out pretty boring on it's own: merely an audio rendering which demonstrates a mathematical formalism with a Fourier series ...
What is is then that makes musical sound interesting?
One clue so far is that it's not strictly pure harmonics.
The tone wheel additive synthesis made possible with a Hammond B3 organ is kinda close to a polyphonic harmonic oscillator bank. And I was once greatly inspired by a tone wheel Fourier synthesis science exhibit at the Exploratorium, in San Francisco, California. Like: `Oooh! I need to build one of these.'
But I would argue that the Hammond B3 sound is way, way more than merely adding sine waves together. The dynamics of note onset, and release; the limited dynamic range of any one particular harmonic; distortion as harmonics are mixed; how the player articulates notes legato style; and many other miniature non-linearities that enabled the sound. And! For sure the Leslie rotatining speaker effect
. So, I'm also thinking more toward chaotic system approaches. Note that chaotic does not necessarily mean stochastic, it's more about controlled disequilibrium within bounds. The kind of circuit research and development that Leon Chua has engaged in:
https://en.wikipedia.org/wiki/Chua%27s_circuit
Similarly, as guest points out, the non-linear shifts in frequency that are pressure dependent. Or how a the strings of a piano evolve differently when they are hammered at differing velocities ...
Some amount of imperfection and essential non-linear harmonic behavior seems fairly integral to the enterprise of a Grand Harmonic VCO.
Statistics: Posted by uniqview — Sun Feb 09, 2025 11:12 pm