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How can I synthesize something like a droning string, something like a tanpura. The main effect that I can't seem to get roughly periodic tambre variation over time. I tried using a phaser on some triangle waves, but that didn't where I wanted.
Ultimately, I'll try to construct a patch in pure data, but I'm more interested in understanding the synthesis components/approach than a specific implementation.
Although it is a drone or single harmony, the timbre here is rich, and the depth comes from the range of harmonics. Further depth here seems to come from the tones of D5 chord (D + A). Drones like this are not often a single note, but quite an array of harmonics - which lends itself to the experimentation of blending fundamentally different notes for a rich texture.
To synthesize this you'd benefit a lot from using Wavetable, Additive or even FM synthesis, since you will need to produce a lot of harmonics. Additive will be the most direct way since you can hear the tone being approached more directly, with every harmonic you add. Generally though, a Sawtooth wave would be a good foundation, perhaps with some distortion or notch filters. In contrast, triangle waves (used as oscillators) are too dull with few harmonics, and also hollow sounding because they are only odd harmonics (comparable with wind instruments).
If you try using a phaser, you might influence too much of the spectrum at a time, and at too distinct frequencies. The spectrum here changes very subtly, so I would suggest a slight detuning overall, but only once you are happy with the main wave spectrum.
The character of the Tanpura has a strong (glissando-like) variation in the upper harmonics, which it comes through between 2600hz-4700hz. You could add this by experimenting with FM synthesis: starting with a sine oscillator with the FM index ramping down. To narrow the bandwidth, a fixed band-pass filter would isolate those frequencies better.
A fantastic synth I suggest trying is Absynth 5 by Native Instruments. It features all these kinds of synthesis in one, as well as a wave-morph (see the video from 5 minutes) feature, which allows morphing between two digital waveforms.
In wave morph, the user can specify anchor points to morph between on the waveforms themselves. Over time, the waves are harmonically linked as a percentage. When this morphing (percentage) itself is modulated, certain partials of the wave begin to trace around the spectrum in that similar glissando-like fashion, which are often the same partials of the wave being excited in a different way.
Overall though it will definitely take some in-depth experimentation in synthesis, since it is not exactly a simple tone, like most instruments. I think this contributes to why the Tanpura is designed for drones.
At around 4:31 here Leon Dewan gets whats sounds to me like droning string sounds with (what he describes as) a wave-folding synthesis approach. I haven't been able to test it, but, based on his verbal description, he is chaining three steps of:
1) Starting with a signal (the initial source is a pure sine wave) 2) asymmetrically clipping it, reflecting the signal about the clipping threshold, 3) Dynamically varying where the clipping level is (alternately, he's keeping the clip fixed, but adding a bias to the input signal).
The modulation rates on the clipping of the different stages are different, which is what gives the sonic effect of different overtones coming into and going out of the foreground.
