Donald Tillman "Palette of Static Waveforms"

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Donald Tillman "Palette of Static Waveforms"

Post by wuff_miggler » Tue May 19, 2020 1:48 am

i just read this artcle by Tillmann - about static waveforms:

http://www.till.com/articles/wavepalette/


i know Doepfer have realised his Trapezoid VCO, but has anyone implemented a design which incorportates the 3 new waveforms he's mentioning here:

*eventooth
*evenangle
*parabolic

Seems interesting - but i wonder - those are possibly achievable with waveshaping and other such modules

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Re: Donald Tillman "Palette of Static Waveforms"

Post by synkrotron » Tue May 19, 2020 2:54 am

An interesting article. Though most of it goes over my head.

I had a listen to the waveforms in the demo application, which was interesting.

I then thought I'd have a mess in Sound Forge to see if I could draw the eventooth and evenangle waveforms.

I think it was a futile attempt. I got close, but it Sound Forge the pencil tool is freehand only... No straight lines or nice curves, no vector stuff. Makes me wonder if there is a waveform graphic package out there that allows you to draw waveforms with a bit more graphic accuracy.

The reason for the Sound Forge experiment is, for the first time in my life (60 soon) I am delving into wavetables and I am looking into using wavetables even for the creation of a static waveform.

I have Distings that are able to read wavetables and I am currently trying to create my own using Sound Forge and its freehand drawing tool. Results are, let's say "interesting" and definitely usable.

Of course, the proper way of doing it would be by using additive synthesis using the formulae as shown in that article.


Anyway, if it sounds like I don't know what I am talking about, you would be correct. I'm just waffling...

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Re: Donald Tillman "Palette of Static Waveforms"

Post by wuff_miggler » Tue May 19, 2020 3:00 am

i agree - the new waveforms are quite interesting , i resonated with the oscillator > filter topology trap too. Like you i dont know the maths either :P

you can draw harmonics (not your own waveforms/wavtables as you want) quite easily in FL Studios Sytrus (which is a bad-ass synth) :D

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Re: Donald Tillman "Palette of Static Waveforms"

Post by synkrotron » Tue May 19, 2020 3:20 am

Seeing as I have six Distings which can create a true sine wave using the B7 algorithm I may have a dabble with mixing all six together to see what I can come up with, sonically speaking. I'm not sure it would be something that I could "play," as such, and I'm thinking more of sampling the output and putting it into something like Iris 2 for playback purposes.

It's about time I got my head around "Harmonic Series" and it keeps me off the streets :mrgreen:

Thanks again for posting that article :tu:

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Re: Donald Tillman "Palette of Static Waveforms"

Post by ricko » Tue May 19, 2020 11:16 pm

Eventooth is a doubly frequency saw plus a sine. So you can construct thus as something like

sine + saw - square

You can construct the even angle from

sine + parabola - tri

But note that the phases of the waves need to be as the diagram shows.

So the only new primary shape you need is the parabola. You could make that with some combination of level shifters and VCA (or perhaps linear-to-expo converter: we would need to figure out exactly what kind of parabola is meant.)

You could also go the other way and have a set richer waves. E.g square - tri.

One thing, though, is that the waves of this pallette are all in the same family of classic waveshapes with only two zero-crossings and aligned phases and unvarying tone. So no harmonic can be louder than the fundamental. So even despite all the hoops, you dont get adventurous tones, just more of the same as the classic shapes (without that being disparaging.) There are other waveshapes (and shapers) that give you completely different families.

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Re: Donald Tillman "Palette of Static Waveforms"

Post by wuff_miggler » Tue May 19, 2020 11:23 pm

ricko wrote:
Tue May 19, 2020 11:16 pm

you dont get adventurous tones, just more of the same as the classic shapes (without that being disparaging.) There are other waveshapes (and shapers) that give you completely different families.

Rick
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i was thinking that too - but didnt voice it perhaps as i thought - maybe i dont know enough to be correct

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Re: Donald Tillman "Palette of Static Waveforms"

Post by Revok » Tue May 19, 2020 11:57 pm

The Befaco Even VCO has a shape similar to the eventooth.

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Re: Donald Tillman "Palette of Static Waveforms"

Post by wuff_miggler » Wed May 20, 2020 12:10 am

Revok wrote:
Tue May 19, 2020 11:57 pm
The Befaco Even VCO has a shape similar to the eventooth.
not sure if tillman or vedder :P
thanks for heads up Revok

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Re: Donald Tillman "Palette of Static Waveforms"

Post by cptnal » Wed May 20, 2020 3:40 am

Jason from Instruo describes an Easter egg in the Cš-L overview video, which is pretty much the eventooth waveform. I think it's multiply a sine and a DC-offset square. Should be achievable with basic modules, but I've yet to try it.



(The Easter egg is a few minutes from the end.)

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Re: Donald Tillman "Palette of Static Waveforms"

Post by wuff_miggler » Wed May 20, 2020 3:51 am

cptnal wrote:
Wed May 20, 2020 3:40 am
I think it's multiply a sine and a DC-offset square. Should be achievable with basic modules, but I've yet to try it.

that's exactly what i was thinking... not experienced enough to be confident tho !
thx cptnal

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Re: Donald Tillman "Palette of Static Waveforms"

Post by KSS » Wed May 20, 2020 4:17 am

What Don T calls parabola was described in an old Polyphony magazine as "Hyper-triangular" and was promoted as a better way to modulate phasers and flangers compared to a triangle or sine.

Here's some discussion on its creation and use: https://www.diystompboxes.com/smfforum/ ... opic=302.0

RG Keen's post in that thread is very good.

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Re: Donald Tillman "Palette of Static Waveforms"

Post by cptnal » Wed May 20, 2020 6:29 am

wuff_miggler wrote:
Wed May 20, 2020 3:51 am
cptnal wrote:
Wed May 20, 2020 3:40 am
I think it's multiply a sine and a DC-offset square. Should be achievable with basic modules, but I've yet to try it.

that's exactly what i was thinking... not experienced enough to be confident tho !
thx cptnal
Update: What Jason actually says is multiply the sine with a rectified version of the square. Which puzzles me since a rectified square is a continuous voltage. There's obviously some additional voodoo in that multiply circuit that he's not divulging. I was able to get part way (try rectifying and offsetting the sine instead), but it's worth exploring in any case for the things you find along the way. Just don't beat yourself up about not getting there. :cloud:

Edit: "A rectified square is a continuous voltage" Is it though? Not if it's been offset. So the rectification is a red herring, as is his slightly offset square. The trick is to offset the square completely-and-then-some into the positive domain, ring modulate that with a sine, and you're golden. :party:

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Re: Donald Tillman "Palette of Static Waveforms"

Post by jorg » Wed May 20, 2020 12:00 pm

wuff_miggler wrote:
Wed May 20, 2020 12:10 am
Revok wrote:
Tue May 19, 2020 11:57 pm
The Befaco Even VCO has a shape similar to the eventooth.
not sure if tillman or vedder :P
thanks for heads up Revok
No, Vedder did "Evensaw"

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Re: Donald Tillman "Palette of Static Waveforms"

Post by wuff_miggler » Wed May 20, 2020 3:53 pm

jorg wrote:
Wed May 20, 2020 12:00 pm
wuff_miggler wrote:
Wed May 20, 2020 12:10 am
Revok wrote:
Tue May 19, 2020 11:57 pm
The Befaco Even VCO has a shape similar to the eventooth.
not sure if tillman or vedder :P
thanks for heads up Revok
No, Vedder did "Evensaw"
very good!

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Re: Donald Tillman "Palette of Static Waveforms"

Post by jdontillman » Thu May 21, 2020 2:38 am

I'm here if you have any questions.

-- Don

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Re: Donald Tillman "Palette of Static Waveforms"

Post by jdontillman » Thu May 21, 2020 3:03 am

ricko wrote:
Tue May 19, 2020 11:16 pm
One thing, though, is that the waves of this pallette are all in the same family of classic waveshapes with only two zero-crossings and aligned phases and unvarying tone.
I've never heard of this "family of classic waveshapes with only two zero-crossings and aligned phases and unvarying tone".

If you look closely you'll see that the eventooth waveform has four zero-crossings per cycle. That said, I don't see how it's an issue as our sense of hearing cannot actually detect zero-crossings.

"Aligned phases" is a very nice feature for audio signals. It means that when you mix waveforms together you'll have a more intuitive understanding of the result.

I think it's weird that phase alignment is a concept that's been mostly ignored in the synth world. It's like someone said, "we delivered the waveforms, so we're done, what more could you possibly want? Don't answer that." Check out VCO2 in the classic ARP2600; it has four waveforms, sine, square, triangle, and sawtooth. And the fundamental components of those waveforms hit all four quadrature phases; 0, 90, 180, and 270 degrees. None of them are in phase. So mixing the waveforms makes no sense at all.

"Unvarying tone" is what static waveforms are. I'm a big fan of varying the tone, but this article is limited to the domain of static waveforms.

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Re: Donald Tillman "Palette of Static Waveforms"

Post by KSS » Thu May 21, 2020 5:12 am

jdontillman wrote:
Thu May 21, 2020 3:03 am
So mixing the waveforms makes no sense at all.
??
Do you mean makes no logically reasoned sense prior to mixing? That the result of mixing is not as easily discerned as it would be if they were phase aligned?

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Re: Donald Tillman "Palette of Static Waveforms"

Post by jdontillman » Thu May 21, 2020 5:34 pm

KSS wrote:
Thu May 21, 2020 5:12 am
jdontillman wrote:
Thu May 21, 2020 3:03 am
So mixing the waveforms makes no sense at all.
??
Do you mean makes no logically reasoned sense prior to mixing? That the result of mixing is not as easily discerned as it would be if they were phase aligned?
Yes.

For the last 50-something years, we've learned about the four basic audio waveforms and their harmonic content. So what happens if you mix those waveforms together? Well that depends. It depends on 1., the phase of the fundamental component of each waveform, and 2. the phases of the harmonics of each waveform.

If two waveforms have their fundamental components in phase, those will add together nicely when you mix them. If the fundamental components are out of phase, they'll subtract and null out at some point in the middle. If they're 90 degrees apart, the fundamental components will add a little bit, regardless of whether you add them or subtract them in the mix. So that's wildly different behavior.

And from the player's point of view, they'll have no idea what it will do unless they went over the schematics of the oscillator.

That same issues applies to the harmonics.

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Re: Donald Tillman "Palette of Static Waveforms"

Post by KSS » Thu May 21, 2020 10:00 pm

Don, Can you share a graphic of the classic four basic waveforms phase aligned?

Or mark the points to be aligned on an unaligned chart? Like you mentioned of VCO2 of the 2600.

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Re: Donald Tillman "Palette of Static Waveforms"

Post by jdontillman » Fri May 22, 2020 1:38 am

The main graphic in my article is phase correct. That is, 1, the fundamental components are all in phase, and 2. the maximum number of harmonics are in phase with those fundamentals.

On the ARP2600 VCO, the fundamental components of the sawtooth and triangle are 90 degrees apart, the sawtooth and square are 180 degrees apart, and the triangle and sine are 180 degrees apart. So that's all four quadrature phases.

I'm not intending to rag on the ARP2600. It's just an iconic example I'm very familiar with. I don't know of a single VCO (other than my own) that has phase correct waveforms.

It seems that nobody has paid attention to the phase. Or if they do, they tend to set up the phases for purposes of modulation as opposed to audio.

Some really large fraction of the VCOs out there, I'd guess over 90%, have a sawtooth core. And if the VCO has a sawtooth core, and derives the triangle by running the sawtooth through an absolute value circuit, than the triangle with be 90 degrees out of phase with the sawtooth. The 90 degree point of the triangle corresponds to the 0 degree point of the sawtooth.

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Re: Donald Tillman "Palette of Static Waveforms"

Post by KSS » Fri May 22, 2020 2:47 am

Thank you Don.

One of my favorite mods to a 2600 -I call it SawToo- is Bernie's EN animator on VCO1. But only the phase shift component, like 1/4 of a Doepfer A-137-2
http://www.doepfer.de/a1372.htm

i've written often about the importance of mixers, and pointed out how the classics have facilitated easy Osc WF mixing. CP3's just below the moog VCO group, Polyfusion's same arrangement, 1004P of a 2500 and the VCF mixer of the 2600.

I would dearly love to have a phase 'shifter' module like the SawToo that was accurate for Triangles and Sines. Square too, but for those PWM can be manipulated. A phase re-alignnent tool. Call it ShiPHIt. Can you design us one? Please.

While we're on the subject of unexplored items we've inexplicably accepted for half a century, plain PWM is another on my list. We get the single comparator on the core WF; tri or saw. There's so much more!

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Re: Donald Tillman "Palette of Static Waveforms"

Post by KSS » Fri May 22, 2020 3:07 am

Here's the 1004 from the 2500. The sine is actually inverted from what's shown here on some 1004 modules. An inverter was added to reduce core loading. PWM operating only on the tri-core, so expanding equally from center only. In an unmodded Osc. ;)
edit: another mod -selectively- removes the bias from the ramp and pulse.
You do not have the required permissions to view the files attached to this post.

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Re: Donald Tillman "Palette of Static Waveforms"

Post by ricko » Fri May 22, 2020 8:28 am

jdontillman wrote:
Thu May 21, 2020 3:03 am

If you look closely you'll see that the eventooth waveform has four zero-crossings per cycle. That said, I don't see how it's an issue as our sense of hearing cannot actually detect zero-crossings.

"Aligned phases" is a very nice feature for audio signals. It means that when you mix waveforms together you'll have a more intuitive understanding of the result.

I think it's weird that phase alignment is a concept that's been mostly ignored in the synth world. It's like someone said, "we delivered the waveforms, so we're done, what more could you possibly want? Don't answer that." Check out VCO2 in the classic ARP2600; it has four waveforms, sine, square, triangle, and sawtooth. And the fundamental components of those waveforms hit all four quadrature phases; 0, 90, 180, and 270 degrees. None of them are in phase. So mixing the waveforms makes no sense at all.
Oops, what I meant to say was that if you have a waveshape with only two zero-crossings, then the fundamental must be louder than any harmonics. (Not that all waves where the the fundamental is louder have only two zero crossings, as you mention disproved by the eventooth.)

Yes I think dividing waveshapes into families helps understand the limits to the kinds of sounds they can achieve, and to see the gaps in current offerings. I think Don is right about the current pallette of waveshapes being unnecessarily limited, but I think his suggestions dont scratch the surface.

The non-exclusive families I see are:

1. Classic static phase-aligned two-zero-crossing
-saw, sine, tri, square

2. As 1. yet with variable mark/space
- variable width pulses (with the leading edge fixed if derived from saw, or decreasing in phase with the width if derived from triangle, or increading in phase with width if like the ARP ProSoloist pulses and my fricko ProPulse module), or the saw-to-half-saw modulation of the Polymoog Polycom cards, or the "self modulation" on some VCOs

3. As 2. but where the mark portion (the wave) is fixed duration and the space varies
- eg the Variophon, my fricko Blip! module, the Bergatrofon woodwind waveshaper, the SH-3A "saw" to an extent.

4. As 1 but where you can sweep from a single shape to fit more repeats of the shape:
- eg oscillator synch, frequency doublers, - for sine/tri a Buchla wavefolder, for a saw my fricko Rasp module, for pulses the Ian Fritz 5-pulser

5. As 1 (etc) but with some other number of zero-crossing:
- e.g. Don Tillman's eventooth, my fricko Shell waveshaper produces waves with 4 or 6 zero crossings (so it readily produces waves with a lower harmonic louder than the fundamental, like many notes on many physical instruments)

6. Waves with non-harmonic partials.
- e.g. ring modulators, frequency shifters, subharmonics through BP filters like the Trautonium (or my VST Neumuxturtrautonium), soft synch "locking".
A builder of my fricko Splice Combiner module sent me an interesting variant on this a couple of weeks ago: one VCO provides the harmonics below about 900Hz, but the partials above 900Hz came from a VCO tuned a pythagorean major third below the first: so in the upper partial, every fourth harmonic is the expected frequency, so they "fit", but there are four intermediate sines nit at integer multiples of the nominal frequency, instead of the expected three: sounded like a saw but denser.

7. Waves with clear register behaviour, so that the harmonic selection is dependent on the general note frequency but without substantial variation between neighbouting notes:
- coarse EQ, my fricko Blip! waveshaper, fricko Prism combiner, fricko Splice combiner, (distinct ftom KCV mod of waveshape)

8. Waves with a sharp variation in harmonics between neighbouring notes.
- E.g using resonators or comb filters or EQ or string filters (like fricko Vox H resonator) but with some feedback to waveshaping.

Some of these can be patched, kinda, if you have the right modules, but it is extra work to end up with wapeshapes and behaviours that should be the start for exploration not the exhaustion point.

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Last edited by ricko on Fri May 22, 2020 8:36 am, edited 2 times in total.

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Re: Donald Tillman "Palette of Static Waveforms"

Post by EATyourGUITAR » Fri May 22, 2020 8:31 am

I don't want to discredit Don. I think he does good work. I wouldn't want him to stop publishing articles. but I think he fills the role that Steven Hawking did. very popular with the lay people but there is an enormous body of work done by the massive math and science community that is not targeted towards lay people. first of all I was already doing this with serum. so was everyone that has serum. the new waveforms he proposes are a very narrow subset of all the possible waveforms that fit his arbitrary harmonic classifications. He ventures beyond the accepted concept of odd & even harmonics into a new territory of mellow and bright! clearly this is a perceptive model he invented on his own without perceptive model research. while it is likely not completely without merit, he is using his subjective perception of the qualitative differences in sounds that he can hear based on no accepted standard. the language uses itself to define itself. otherwise it is not defined.

why do we need phase alignment to 0 for all partials? why does he use SIN alignment on some formulas and COS for others? answer, because it looks cool. he is a simple man. he likes traditional synthesizer waveforms. He wants to find mathematical formulas for pre-existing sounds. that does not mean that he invented those sounds. he only invented one possible way to create them through mathematical synthesis. since he wrote the mathematical formula for saw tooth then why does he not claim to have invented the saw tooth? the logic falls apart.
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Re: Donald Tillman "Palette of Static Waveforms"

Post by ricko » Fri May 22, 2020 9:46 am

EATyourGUITAR wrote:
Fri May 22, 2020 8:31 am
I don't want to discredit Don. I think he does good work. I wouldn't want him to stop publishing articles. but I think he fills the role that Steven Hawking did.
Gosh Don, you are only a popularizer like that simplistic hack Steven Hawking!

I am trying to remember a post where the writer was simultaneously so sneering, incorrect (where does Don claim to have invented these waveforms or say that he only likes static waves etc?) and foolish (the pseudo-science babble about perceptual models, spare us!) Probably I have done as bad, mind you, but I hope I would have apologized after realizing. He could have made his point (which, to the extent that it was that there are more interesting waveforms possible, and that research has provided much new information that can feed in, I agree with, but I expect instrument physics rather than neuroscience is a better place to start) better with more actual respect not the insincere disclaimer.

Rick

B.t.w. Is a forum on modular synths really the place for promoting commercial VSTs? ... Seems like a hard sell. In what universe is "Go digital" an answer to "Are there extra possibilities for analog?"

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