For my initial foray into to Pd, I'd like to make a simple tremolo circuit. This would be using a LFO (0–20Hz) that oscillates any frequency with varying degrees of amplitude modulation from full volume down to zero decibels (i.e. a totally on then off sound, producing a harsh staccato sound). Does a schematic for this patch exist somewhere, or could anyone provide guidance?

Many thanks!

Hi Silas,

Have a look on this patch I prepared for you: Amp-modulation.pd

If you need help explaining the logic behind the patch, just let me know.

Take care,
Gilberto

Thanks Gilberto! That's really just fantastic. Yes, I may have questions later, but this allows me to run the experiment I desire successfully. It's greatly appreciated.

Essentially, I had taken an online introductory course in Digital Sound Design, taught by professor/composer Steve Everett where he'd described sidebands in a way that portrayed them, under certain conditions, as an artifact of our hearing, i.e. not really occurring but rather something which our brains construct. Basically, he seemed to say that an LFO oscillating the amplitude of a sine wave at a rate of 1-20 times per sec, would produce tremolo as expected, however, once the rate increased above 20 times per sec, sidebands were emerge that weren't actually there, but rather were our brains way of interpreting the information. To test this, I thought I try a hard tremelo in Pd, as my first foray with PureData. Any thoughts?

Hi Silas,

Have a look on these two patches I prepared:

1.pd
2.pd

The first shows the difference between adding and multiplying audio signals, as well as the effect of sidebands when the carrier frequency is very high. The second allows you to control the carrier frequency value, so you can see and listen to the results.

I do have problems when people say that some acoustic effects are actually not there and that it is all in our brains. The same is said about the beating effect (when you play two close frequencies such as 440 Hz and 440.5 Hz and you generate a tremolo effect with the rate of their difference), but just as with the sidebands on my second example above, not only you can listen to the effect but you also can see it in a spectrogram. With a heavy beating scenario like the one I described in this paragraph, we see the fast frequency inside of an oscillating envelope: that is, we clearly see two frequencies, and our brain listen to both - so what is constructed here? It is more than clear to me that we are all born with FFT-capable devices (normally called auditory system, but that is a much less fancy name!) which are able to get the most convoluted oscillating mass of air and decode each single frequency in that mess. But I digress...

I hope some of this will help. Take care,
Gilberto

ya sidebands can be derived mathematically, to question their existence outside of our minds is pretty existential, like not believing in math's usefulness.
One of the ways I personally like to think of sidebands is a convolution of a cosine wave with another cosine wave in the frequency domain. (in the frequency domain cosine waves are 2 infinitely narrow points with equal negative and positive portions, each of 1/2 of the amplitude of the time domain cosine wave). When you multiply a signal by another signal in the time domain it corresponds to convolution in the frequency domain and visa-versa. Therefore when you multiply 2 cosine waves together the result will be the convolution of their frequency domain graphs, those infinitely narrow points.
To explore the difference between ring and amplitude modulation consider this:
amplitude modulation is when you multiply a signal by a cosine wave that is only positive, like going back and forth between 0 and 1. In the frequency domain this is like having a cosine wave (2 infinitely narrow points in the frequency domain) at 1/2 amplitude and a DC component (infinitely narrow point at 0) at 1/2 amplitude. That is why when you use amplitude modulation some of the original signal remains in the output: when the dc portion is convolved with the signal it leaves some of the original signal.
For ring modulation, the modulating wave is going between -1 and 1 usually (or some scalar of -1 and 1). So in the frequency domain this is just a normal cosine wave without any dc, and when this is convolved with another cosine wave the result is like amplitude modulation but without any of the original signal left

I think what your professor was probably referring to was the limits of human hearing perception: although the sidebands do exist below 20 hz humans can not hear them as distinct frequencies and only perceive the changes in amplitude. when they go over 20 hz they are in the audible range.

so in reality it's the opposite of what your professor said I guess

A detailed and helpful explanation, Gilberto – thanks so much. The professor's overly simplified comments on the emergence of sidebands described in terms of our brain tricking us was perhaps not the ideal way to convey the idea. He almost certainly did not mean it to be interpreted quite the way it came across to me, but provided ample opportunity for it. You know, I was certain as well that the sidebands would be evident in a spectrogram, clearly visible and measurable.

And contrary to his explanation that audible sidebands begin to emerge above low freq. oscillations of 20 cycles per sec, I very clearly hear them as low as 15, maybe 13 cycles per sec when oscillating a 170Hz sine wave. At 15 cycles, one distinctly perceives a major 3rd above the fundamental. But I'm curious, what change would I need to make to the patch in order to have the tone rather than oscillate, switch on and off, hard, from 0 amplitude to full on? Would the sidebands sound the same?

The patches are a good starting point on my end. It seems something like the "binaural beats" phenomenon can be recreated here – but in this basic Pd patch, this is not aurally 3-dimensional (how complex would adding dimensionality be? Quite, I'd imagine).

Perhaps this is what you're demonstrating already, but can the spectrogram here be compartmentalized into revealing, in separate spectrograms, the fundamental in one, and the sidebands in another? Are sidebands another form of harmonics or distinct and separate?

Kind regards,
Silas

Hi Silas,

Sorry for my late reply, I left this thread opened in a tab but I lost track of it. I just replied to another user asking a question about the same subjects we are talking here. This is the thread, maybe you'd like to have a look on it as well: http://forum.pdpatchrepo.info/topic/8743/help-to-understang-ringmodulation/2

Take care,
Gilberto