Chorus-Ensemble vibrato wave shape

[scg]

This is minor, and may be user error, but it's just something I'm curious about.

The interface and documentation for the Chorus-Ensemble effect indicate that the 'Shape' control interpolates between a sine wave and a triangle wave. It seems though that it's actually a square wave, not a triangle wave. You can hear this, and also see it by using Tuner in histogram mode.

I'm using Live 11.2.10 and macOS 12.6.3. Is this a bug or error in the interface and documentation? Or am I missing something?

[[jur]]

According to the devs, it's really a triangle wave, but the square that you hear somehow is an acoustic illusion (i never took the time to understand why!).

[scg]

That's...interesting! Given that you're a forum moderator and you're saying this comes straight from the developers, I can't really argue. But, I'm somewhat perplexed, for the following reasons:

If I set up Wavetable with pitch modulated by its own LFO with a triangle wave, I get what I'd expect a triangle wave to sound like, and Tuner shows a triangle pattern. If I instead use Chorus-Ensemble in triangle mode, it's clearly more like a square, both audibly and according to Tuner.

If it were purely an acoustic illusion, I'd expect it to occur with any triangle-wave modulation of pitch, but that's not the case - I only observe it with Chorus-Ensemble. Also, the fact that Tuner shows a square(-ish) wave suggests it's not just a subjective perception issue.

It occurred to me that maybe it's not an acoustic illusion, but rather a side-effect of whatever algorithm Chorus-Ensemble is using. But, if I try Waves SoundShifter with triangle-wave modulation, it's a completely smooth triangle, so it doesn't seem like a given that pitch-shifting would cause this.

Again, can't argue with the developers, but for the moment at least I'm skeptical that there's actually nothing else going on here other than perceptual error, so any further illumination anyone can provide will be welcome!

[yur2die4]

This one is a tricky one.

The important thing to note is that this effect ‘modulates’ the frequency, rather than ‘sets’ the frequency. If you’re taking a source (since it is an effect in real-time rather than a tone generator) and increasing frequency at a steady rate, referencing the buffer, you will sort of ‘catch up’ to the source, but then you decrease and you lag from the source. Abruptly switching gears, and with the modulation being a steady amount, I can see how there can be times where it could result in more of a square appearance in pitch modulation.

I played around a bit, and this thing is really difficult to get predictable results from. At higher speeds it seems to work sort of as expected. At slower speeds it feels like there might be slew issues or a limit of buffer length.

FOR a comparison, I played with using the Delay effect set to Pitch using the maxforlive LFO device to change either Time or the Percent offset of time. And I could get much more dramatic results which is fun. I could also sometimes emulate the square behavior by using a Triangle. But one aspect that makes this modulation Different is that I’m working in amounts in relation to the time settings offered in the Delay effect. So I get slightly skewed sines etc.

But yeah. In some ways I feel like you’re onto something. I also feel like there is a use for having a square result. If you need a workaround, try using the Delay effects. As an added note, in this exploration I also had to hunt down the OG Chorus to play with. I feel it’s a shame that it is hidden now, as it does do some cool things (particularly at high mod rates). I used to use it as a makeshift Vibrato effect in fact.

[scg]

Thanks to you both for the great replies. (I'd upvote you if I could! But I gather this forum doesn't have that feature.)

yur2die4, thanks for your detailed reply. To be clear, this issue doesn't have any practical impact - it's just something I'm curious about.

It does seem like it could be a result of the algorithm being used, but what puzzles me about that is that the sine wave produces a completely smooth pitch oscillation, and a triangle wave is similar to a sine wave in shape, so it seems like its results shouldn't be that different. But, a triangle wave does 'abruptly switch gears', as you alluded to, so maybe that has something to do with it.

Also, I notice now that the vibrato amplitude scales with the rate (e.g. higher rate means higher amplitude). That may or may not mean anything, but it might be a hint as to what sort of algorithm is being used.

Again, no practical impact, just an oddity. But, I remain curious as to what's actually going on under the hood here.

Thanks again for the replies.

[yur2die4]

A big difference between triangle and sine is that a triangle is linear and a sine is flip flopping between exponential and logarithmic. But yeah, also that transition type at the peaks.

I’m not 100% sure how to interpret the result. Or if these results are what were intended by design (like, the devs claim it is indeed a triangle, but is the result of this in fact what they were aiming for?) I’m roughly acquainted with deriving functional changes in graphs but with relationship to the frequency domain of audio, and the given buffering amounts, all that stuff is over my head heheh.

[scg]

Points well taken about the differences in the waves. I doubt it's purely an acoustic illusion for reasons already mentioned, but it's still not obvious to me why it behaves the way it does. I guess it'll remain a mystery for now

[NF2K]

Yeah I just checked with a sine wave as audio source and it does indeed jump between two pitches when Vibrato mode's Shape is a triangle. This reminds me of Phase Modulation vs Frequency Modulation - if you modulate a sine carrier by a slow triangle modulator in Operator you will get the same two-tone sound. I wonder if that's what's going on / if it's intentional

[scg]

Yeah, FM produces similar results, which may be a hint as to what Chorus-Ensemble is doing, just as you suggest. So it seems to be a result of how the modulation is implemented (which is maybe what the developers meant by 'acoustic illusion').

[[jur]]

(which is maybe what the developers meant by 'acoustic illusion').

I wrote "acoustic illusion" in a hurry, that's probably not the best description as I'm not sure this is purely psycho-acoustic. The device is modelling some analog unit and there's an interplay of modulations that produces this surprising result.
I'll ask the devs for the proper explanation and will let you know all about this mystery!

[NF2K]

Yeah, FM produces similar results, which may be a hint as to what Chorus-Ensemble is doing, just as you suggest. So it seems to be a result of how the modulation is implemented (which is maybe what the developers meant by 'acoustic illusion').

Just to clarify: Operator, as with most "FM" software synths, actually uses Phase Modulation instead of Frequency Modulation. In Phase Modulation, the slope of the modulator waveform determines the pitch. A triangle wave has only two linear slopes, so it results in the carrier (and in this case, the signal being fed into Chorus-Ensemble's Vibrato) being flip-flopped between two pitches. I learned this from the following video: https://youtu.be/GNebO-yqeVI?t=357

Though I still don't understand why the Live devs would choose this form of modulation vs actual pitch modulation for this

[scg]

I wrote "acoustic illusion" in a hurry, that's probably not the best description as I'm not sure this is purely psycho-acoustic. The device is modelling some analog unit and there's an interplay of modulations that produces this surprising result.

Got it - that makes more sense.

I'll ask the devs for the proper explanation and will let you know all about this mystery!

If you can get any more information out of them, it'd be interesting to know!

Just to clarify: Operator, as with most "FM" software synths, actually uses Phase Modulation instead of Frequency Modulation. In Phase Modulation, the slope of the modulator waveform determines the pitch. A triangle wave has only two linear slopes, so it results in the carrier (and in this case, the signal being fed into Chorus-Ensemble's Vibrato) being flip-flopped between two pitches. I learned this from the following video: https://youtu.be/GNebO-yqeVI?t=357

Interesting information - thanks. Seems like that's probably the explanation for the behavior.

[Synthbuilder]

It does seem like it could be a result of the algorithm being used, but what puzzles me about that is that the sine wave produces a completely smooth pitch oscillation, and a triangle wave is similar to a sine wave in shape, so it seems like its results shouldn't be that different.

It's related to rate of change. So the perceived pitch caused by a modulated delay is partly determined by the first derivative of the modulation waveform. The rate of change of a sine wave is also a sine wave shape albeit one that is shifted in phase. So a small amount of sine wave modulation in delay time sounds similar to the sine wave modulation of pitch.

A triangle waveform is two straight lines, one going up followed by one going down and so on. The first derivative of this, that is the rate of change, is a constant positive value for the up bit and a constant negative value for the down bit. The first derivative of a triangle wave therefore looks like a square wave. So modulating a delay with a triangle wave sounds like an oscillator whose pitch is being modulated by a square wave.

It is more complex than that when the modulation amount is large. This is because we are modulating delay time and frequency is proportional to the reciprocal of time.

[scg]

It's related to rate of change. So the perceived pitch caused by a modulated delay is partly determined by the first derivative of the modulation waveform. The rate of change of a sine wave is also a sine wave shape albeit one that is shifted in phase. So a small amount of sine wave modulation in delay time sounds similar to the sine wave modulation of pitch.

A triangle waveform is two straight lines, one going up followed by one going down and so on. The first derivative of this, that is the rate of change, is a constant positive value for the up bit and a constant negative value for the down bit. The first derivative of a triangle wave therefore looks like a square wave. So modulating a delay with a triangle wave sounds like an oscillator whose pitch is being modulated by a square wave.

It is more complex than that when the modulation amount is large. This is because we are modulating delay time and frequency is proportional to the reciprocal of time.

Yup, that's all clear now (some good explanations along these same lines were offered earlier in the thread). Thanks for the additional clarification though. In any case, it seems clear now why it behaves as it does.

[[jur]]

Hey all, here's a little explanation I got from the mastermind behind the device:

"Imagine you're recording sound to a tape and reading it out at a later point, with a read-head that can be moved a little to the left and right, alongside the tape. The modulation signal we have in Chorus would then literally control that position. A sine wave would therefore lead to a movement of the readout head that varies in speed, while a triangle wave leads to a movement of the readout-position at a constant speed, which just leads to a temporary constant pitch change, for the time the modulation goes up- or downwards along the waveform”