Odd and Even harmonic distortion

[Rob]

Purpose:
This building block produces harmonic distortion. Either only odd harmonics or both odd and even harmonics are added, controllable by a single knob that adds an amount of even harmonics to the odd harmonics.

The total amount of distortion can be set by a second knob.

Theory of operation:
The harmonics are created by running a signal through a VCA. The gain of the VCA is set to be unity by default, so the control signal that controls the gain is +64 units. To this fixed control signal, named the Bias signal, a small amount of the 'negated quadrature' of the VCA output signal is added. What this does is that on both the positive and the negative peaks of the input signal the gain of the VCA will be reduced to below unity gain. This will compress the peaks slightly and thus produce the odd harmonic distortion. Even harmonics are added by compressing the positive peaks slightly more as the negative peaks.

The reason why the 'quadrature signal' is taken from the output of the VCA is to produce a series of higher harmonics. If the signal was taken from the input of the VCA only the third harmonic would be generated. But now the third harmonic of the output is added to the output signal, which will generate the fifth harmonic to be added to the output signal, which will generate the seventh harmonic, etc. Of course one should read the x-th harmonic of every sinewave partial that is present in the output signal, etc. The amplitude of the harmonic series decreases smoothly, which gives a more grungy sort of distortion than e.g. soft clipping (note: soft clipping is used in the G2 Saturate module).
The even harmonics are created by summing a little of the output signal to the quadrature of the output signal.

The greater the amplitude of the input signal the more pronounced the distortion will be. Harmonic distortion can be quite subtle, in which case it appears to enhance the presence of a sound. In moderate amounts it can be used quite well on vocals. Deeper levels are usually used on strongly resonant filters, the effect gets more pronounced if the GC button on the filter is Off.
This type of distortion also works very well on polyphonic organ sounds, especially in combination with either the frequency shifter used in Doppler mode or Leslie simulators.

The Patch:



The VCA is directly on the input (the Multiply module named 'Input') and the purple signal going into the control input of the VCA module is the modulated Bias signal.
The flow through the green wires shows the control signal feedback loop that modulates the VCA bias signal. The green wire on the output of the VCA first goes through an attenuation module before it is fed into two inputs of a multiply module (named x^2), which produces the quadrature signal. This attenuation is very important as the quadrature signal should not be allowed to hit the headroom and be clipped there. As the headroom is 256 units the multiply module can only accept values below 128 units, as 128 units is arithmetically the value 2 and 2 times 2 is 4, which translates to 256 units or headroom level. If the quadrature would be clipped, the control signal would not be correct anymore. Which gives disastrous results on high level input signals, like clamping the output to the headroom and silencing the circuit. By limiting the signal to below 128 units clamping can never happen and the circuit is stable. Then comes the point where optionally some of the direct signal from the attenuator output can be added to the quadrature signal, to create additional even harmonics.

The following inverting integrator limits the bandwidth of the control signal to 8 kHz, as one would not want higher harmonics to be generated (really!). This also prevents the circuit from possible oscillations at 48kHz, a tendency that is always present in any feedback loop if there is no bandwidth limiting. The integrator is at gain 0.5 to prevent the overall loop from going into selfoscillation mode. Then a mixer defines the amplitude of the signal that is now added to the Bias signal. The Bias is created by using a LevelAdd module.
There are two more LevelAdd modules that correct the final output level in a way that for input waves at standard -64/+64 amplitude level the output signal has roughly the same amplitude.

After the VCA are three more VCA's, which increase the distortion depth. Without these the distortion would be quite subtle, but by routing the output signal of the first VCA through these other VCA's, and controlling them with the same modulated bias signal as the first VCA, the effect is increased. Hint for understanding is that the modulation for these other VCA's is symmetrical around unity gain. So, the overall gain is not affected but the distortive modulation depth is increased fourfold. As these other three VCAs are outside the control feedback loop they cannot force the circuit into an unstable range of operation. So, it is a very convenient solution to increase distortion depth.

Note that the x^2 that modulates another VCA sort of produces the X^3 that generated the third harmonic. Which is the reason why by default only odd harmonics are created. Unless some of the X is added which would produce an x^2 in the VCA, which accounts for the even harmonics. Basically it is all a variation on Chebyshev polynomials, but all in a practical manner.

Variations:
There is one insert point in the patch where other modules can be added to influence the tone. This point is directly on the output of the first VCA before the green signal goes into the attenuation module. It is important to add modules at this point only, as the attenuation will prevent problems in the control feedback loop. An obvious addition is a simple 6dB or 12dB lowpass filter set to e.g. 1.40kHz. This will prevent the build up of harmonics higher as about 3kHz, which gives a warmer, more grungy tone. It will also enhance transients, e.g. the flanks of a sawtooth waveform, as it will slightly delay the compression effect of the distorter. This makes transients come out more pronounced and enhances the presence of the sound in a mix. The bandpass modes of the Multimode and Static filter also work quite well. The peak EQ module however seems to work less well. The FltPhaser and FltComb can do really interesting things, though one should be easy on the Feedback knob on this module. The FltVoice seems less useful and be a bit unpredictable.
Effect modules, delays and shaper modules seem of limited value to be used in the control feedback loop, as in general they interfere too much with the mechanics of the building up of harmonics in the loop. Which for you post-digital 'aestethics of failure' heads should be reason enough to explore that territory.

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HarmonicDistortion.pch2
Description:	Odd and Odd/Even harmonic distortion	Download (listen)
Filename:	HarmonicDistortion.pch2
Filesize:	1.59 KB
Downloaded:	2111 Time(s)

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VariartionHarmonicDistortion.pch2
Description:	Variation on harmonic distortion by inserting some module in the control feedback loop.	Download (listen)
Filename:	VariartionHarmonicDistortion.pch2
Filesize:	1.68 KB
Downloaded:	2054 Time(s)

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[mosc]

This is quite facinating. Thanks, Rob. It's a great patch to hear even and odd distortion so easilly. The explaination is excellent, it teaches about patching and about distortion.

I guess one could use this with very low amounts even harmonic distortion to get that legendary tube sound.

[cebec]

excellent! thanks, Rob... really appreciate the time and effort you've put into these 'lessons'...

[Rob]

[cebec]

oh, i agree with you. i didn't mean 'lesson' in a negative sense at all... a more general sense of the word... to me, your explanations are very insightful, interesting, and educational...great examples of the sort of documentation needed with the building blocks.
furthermore, i have been really into different forms of distortion, lately and your building blocks have been useful.

the first one does look and sound like a tube but the second one, with the filter inserted, can do some really wild stuff!

[Tim Kleinert]

Great stuff!

Interesting: I had arrived at a similar effect when futzing around with DIY-filters, when I, as an experiment, inserted a quadrature (odd harmonic) distorter into the resonance (feedback) gain controller. However, my concoction clamped very easily. Now I understand why.

And what I like most about it is that it isn't just a memoryless distorting transfer function. The feedback is the key. Makes it much more "alive" and organic.

I wondered though: Is there any way to get only even harmonic distortion in this way?

Anyway, thanks alot, Rob! This is so elucidating and it sounds great.

[Rob]

[blue hell]

[Rob]

[mosc]