Hey hey everyone,
I'm trying to build an oscillator with continuous analogue waveforms, 
including PWM, triangle-width-modulation and possibly sawtooth-modulation as 
found in many virtual analogue synths. A good example is the Yamaha AN1X 
oscillator architecture, where you can fade from sine to saw and from triangle 
to square. I believe the sine->triangle morph was more of a switch.

Currently the only approach with reasonable CPU demands, that I can find, is 
additive synthesis. The basic waveforms are easily dealt with, but although 
loads of people talk about synthesizing PWM'ed waveshapes with additive 
synthesis, no one actually seems to do it.

Is there a better approach to such an oscillator within Csound?

The reason for it is, to have a basic oscillator, that can be part of a 
completely patch-morphable synthesizer.

I'm grateful for any help! Thank you!

Ta-ta
----
Ffanci
* Homepage: https://freeshell.de/~silvain
* Twitter:  http://twitter.com/ffanci_silvain
* GitHub:   https://github.com/fsilvain

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Did you try vco2? It does triangle -> sawtooth and PWM.
There is a wide range of articles on the topic of bandlimited oscillators, and I expect
all of the designs to be possible to implement using Csound.

========================
Dr Victor Lazzarini
Dean of Arts, Celtic Studies and Philosophy,
Maynooth University,
Maynooth, Co Kildare, Ireland
Tel: 00 353 7086936
Fax: 00 353 1 7086952 

> On 19 Sep 2015, at 12:55, F. Silvain  wrote:
> 
> Hey hey everyone,
> I'm trying to build an oscillator with continuous analogue waveforms, 
> including PWM, triangle-width-modulation and possibly sawtooth-modulation as 
> found in many virtual analogue synths. A good example is the Yamaha AN1X 
> oscillator architecture, where you can fade from sine to saw and from triangle 
> to square. I believe the sine->triangle morph was more of a switch.
> 
> Currently the only approach with reasonable CPU demands, that I can find, is 
> additive synthesis. The basic waveforms are easily dealt with, but although 
> loads of people talk about synthesizing PWM'ed waveshapes with additive 
> synthesis, no one actually seems to do it.
> 
> Is there a better approach to such an oscillator within Csound?
> 
> The reason for it is, to have a basic oscillator, that can be part of a 
> completely patch-morphable synthesizer.
> 
> I'm grateful for any help! Thank you!
> 
> Ta-ta
> ----
> Ffanci
> * Homepage: https://freeshell.de/~silvain
> * Twitter:  http://twitter.com/ffanci_silvain
> * GitHub:   https://github.com/fsilvain
> 
> ------------------------------------------------------------------------------
> _______________________________________________
> Csound-users mailing list
> Csound-users@lists.sourceforge.net
> https://lists.sourceforge.net/lists/listinfo/csound-users
> Send bugs reports to
>        https://github.com/csound/csound/issues
> Discussions of bugs and features can be posted here


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Victor Lazzarini, Sep 19 2015:

> Did you try vco2? It does triangle -> sawtooth and PWM.
Yes, I'm aweare of it. But it doesn't completely satisfy my needs.

> There is a wide range of articles on the topic of bandlimited oscillators, and I expect
> all of the designs to be possible to implement using Csound.
I had a browse through a couple of articles, but haven't found anything to solve the whole puzzle. Either PWM or waveshape morphing.

Especially with Csound in the search term the vco and vco2 opcodes come up of course. :) So I'm lost and can't stomp up the necessary mathematics from scratch to find the road to go.
...

Ta-ta
----
Ffanci
* Homepage: https://freeshell.de/~silvain
* Twitter:  http://twitter.com/ffanci_silvain
* GitHub:   https://github.com/fsilvain

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Perhaps morph between waveform tables?
http://csound.github.io/docs/manual/tabmorph.html

Maybe there is an array-equivalent, so the entire resulting waveform can be held in an array?

Regards,
Anders



> 19 sep 2015 kl. 15:45 skrev F. Silvain :
> 
> Victor Lazzarini, Sep 19 2015:
> 
>> Did you try vco2? It does triangle -> sawtooth and PWM.
> Yes, I'm aweare of it. But it doesn't completely satisfy my needs.
> 
>> There is a wide range of articles on the topic of bandlimited oscillators, and I expect
>> all of the designs to be possible to implement using Csound.
> I had a browse through a couple of articles, but haven't found anything to solve the whole puzzle. Either PWM or waveshape morphing.
> 
> Especially with Csound in the search term the vco and vco2 opcodes come up of course. :) So I'm lost and can't stomp up the necessary mathematics from scratch to find the road to go.
> ...
> 
> Ta-ta
> ----
> Ffanci
> * Homepage: https://freeshell.de/~silvain
> * Twitter:  http://twitter.com/ffanci_silvain
> * GitHub:   https://github.com/fsilvain
> 
> ------------------------------------------------------------------------------
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> Csound-users@lists.sourceforge.net
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> Send bugs reports to
>        https://github.com/csound/csound/issues
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Hey hey,
thank you Victor and Anders for your replies. I believe I found the basics for 
the oscillator, that I need.

I use adsynt with the harmonics for a sine, saw and a waveform with harmonic 
formula:
harmonic n = 1/n^2

I copy the output of adsynt once. For square/pulse and triangle I invert the 
signal and pass it through vdelay with a maximum length of my basic period. 
For saw I just shift the uninverted copy with the vdelay. That way I get my 
modulation. Now I only need to work out the boring details to properly fade 
between them and Roberta's your mother's partner in law. :)

Ta-ta
----
Ffanci
* Homepage: https://freeshell.de/~silvain
* Twitter:  http://twitter.com/ffanci_silvain
* GitHub:   https://github.com/fsilvain

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I found this question really intriguing.  vco can do triangle -> saw
pretty well since it's using BLIT, and as Victor mentioned, vco2 does
triangle->saw as well. The sine -> saw is curious, which made me think
of FM.  I worked on a small example:

http://csound-notebook.kunstmusik.com/note/136

(Also attached to this email)

The vco and vco2 examples are pretty straightforward, just using a
linseg to sweep through the pulse width to affect triangle/saw-ness.
For sine->saw, I used a single feedback phasor, sort of like doing
feedback with one operator on an FM synth.  I first wrote a phasor UDO
that took in an a-rate phase, but didn't quite get that to sound
right.  Also, since the phasor should be feeding back into itself to
get that sawtooth quality, I figure I could get rid of the delay and
just add the phasor's output to itself, with an adjustment value to
control the "feedback" amount.

The example has the vco, vco2, then PM examples just holding major
3rds and sweeping.  The last example is just something fun I put
together to play octave arpeggiations using a modified PM instrument
that took in a static feedback amount.

The PM instrument (3 and 4) sound pretty good to me and would be very
efficient.  A similar sweeping between different PM or FM settings
could potentially get a nice smooth spectral change at a reasonable
cost. Otherwise, something like VCO would make sense to me to match up
close to analog synths, thinking of how BLITs are basically impulses
generated by a clock, which might match up with how it might have been
done in hardware.

Anyways, all a bit of speculation.  Certainly was fun trying to get
some sweeping sounds, so thanks for asking about that Ffanci! :)

steven


On Sat, Sep 19, 2015 at 8:57 AM, Victor Lazzarini
 wrote:
> Did you try vco2? It does triangle -> sawtooth and PWM.
> There is a wide range of articles on the topic of bandlimited oscillators, and I expect
> all of the designs to be possible to implement using Csound.
>
> ========================
> Dr Victor Lazzarini
> Dean of Arts, Celtic Studies and Philosophy,
> Maynooth University,
> Maynooth, Co Kildare, Ireland
> Tel: 00 353 7086936
> Fax: 00 353 1 7086952
>
>> On 19 Sep 2015, at 12:55, F. Silvain  wrote:
>>
>> Hey hey everyone,
>> I'm trying to build an oscillator with continuous analogue waveforms,
>> including PWM, triangle-width-modulation and possibly sawtooth-modulation as
>> found in many virtual analogue synths. A good example is the Yamaha AN1X
>> oscillator architecture, where you can fade from sine to saw and from triangle
>> to square. I believe the sine->triangle morph was more of a switch.
>>
>> Currently the only approach with reasonable CPU demands, that I can find, is
>> additive synthesis. The basic waveforms are easily dealt with, but although
>> loads of people talk about synthesizing PWM'ed waveshapes with additive
>> synthesis, no one actually seems to do it.
>>
>> Is there a better approach to such an oscillator within Csound?
>>
>> The reason for it is, to have a basic oscillator, that can be part of a
>> completely patch-morphable synthesizer.
>>
>> I'm grateful for any help! Thank you!
>>
>> Ta-ta
>> ----
>> Ffanci
>> * Homepage: https://freeshell.de/~silvain
>> * Twitter:  http://twitter.com/ffanci_silvain
>> * GitHub:   https://github.com/fsilvain
>>
>> ------------------------------------------------------------------------------
>> _______________________________________________
>> Csound-users mailing list
>> Csound-users@lists.sourceforge.net
>> https://lists.sourceforge.net/lists/listinfo/csound-users
>> Send bugs reports to
>>        https://github.com/csound/csound/issues
>> Discussions of bugs and features can be posted here
>
>
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This is not a Csound answer, more of a recipe.

You can construct many waveform shapes using cosine wave segments.
If we consider the wave to have 4 parts:
rise - flat(+1) - fall - flat(-1)

"Rise" and "fall" are half cosine sweeps.

Some obvious shapes as % of the wave cycle:
rise=1%, flat=49%, fall=1%, flat=49% : squarewave |¨|_
rise=1%, flat=0, fall=1%, flat=98% : pulse |__
rise=50%, fall=50%, flats=0 : sinewave /\
rise=1%, fall=99% : saw-like wave |\
etc.
You can vary these proportions gradually and get multi-waveform oscil with nice sound.

The trick is to set a hard limit on rise/fall, eg 10 samples (regardless of sample rate).
This means that any square or pulse or saw will decay into a sinewave
at high freqs -- exactly what we need.

The bookkeeping to get stable base freq and waveshape is a little complicated,
esp when feeding it with FM.


I hope to publish code, perhaps a Csound opcode sometime soon-ish.

Haven't actually seen this idea used anywhere - though it's not nearly an "invention",
rather pretty obvious from just looking at the waveforms.
Technically, cosine wave has derivative=0 at phase 0 and PI(rad) for ALL frequencies,
which means you can flip frequency freely at those points and still have a continuous wave.

So, henceforth it shall be considered criminal neglect to have to flick a switch
in a digital synth to change between sine, saw and squarewave.
Due notice.

	-re


PS: The params I use differ slightly from the description above.
Instead of 4 (rise flat fall flat), we just need 2:
Skew: how much to shift from symmetric wave (range +1 to -1 or percentage if you like)
Clip: how much of waveform that should be flat (range 0 to 1)
So,
Skew = 0, Clip = 0: Sinewave (symmetric and no flat part)
Skew = 1, clip = 0: Saw (or skew -1 for left/right saw)
Skew = 0, clip = 1: Squarewave (symmetric but 98% flat)
Skew = 1, clip = 1: Pulse

This needs pictures to explain...


On 2015-09-19 13:55, F. Silvain wrote:
> Hey hey everyone,
> I'm trying to build an oscillator with continuous analogue waveforms,
> including PWM, triangle-width-modulation and possibly sawtooth-modulation as
> found in many virtual analogue synths. A good example is the Yamaha AN1X
> oscillator architecture, where you can fade from sine to saw and from triangle
> to square. I believe the sine->triangle morph was more of a switch.
>
> Currently the only approach with reasonable CPU demands, that I can find, is
> additive synthesis. The basic waveforms are easily dealt with, but although
> loads of people talk about synthesizing PWM'ed waveshapes with additive
> synthesis, no one actually seems to do it.
>
> Is there a better approach to such an oscillator within Csound?
>
> The reason for it is, to have a basic oscillator, that can be part of a
> completely patch-morphable synthesizer.
>
> I'm grateful for any help! Thank you!
>
> Ta-ta
> ----
> Ffanci
> * Homepage: https://freeshell.de/~silvain
> * Twitter:  http://twitter.com/ffanci_silvain
> * GitHub:   https://github.com/fsilvain
>
> ------------------------------------------------------------------------------
> _______________________________________________
> Csound-users mailing list
> Csound-users@lists.sourceforge.net
> https://lists.sourceforge.net/lists/listinfo/csound-users
> Send bugs reports to
>          https://github.com/csound/csound/issues
> Discussions of bugs and features can be posted here
>

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Why do you need adsynt for this? I would have thought GEN 10 would do the job.
========================
Dr Victor Lazzarini
Dean of Arts, Celtic Studies and Philosophy,
Maynooth University,
Maynooth, Co Kildare, Ireland
Tel: 00 353 7086936
Fax: 00 353 1 7086952 

> On 19 Sep 2015, at 19:00, F. Silvain  wrote:
> 
> Hey hey,
> thank you Victor and Anders for your replies. I believe I found the basics for 
> the oscillator, that I need.
> 
> I use adsynt with the harmonics for a sine, saw and a waveform with harmonic 
> formula:
> harmonic n = 1/n^2
> 
> I copy the output of adsynt once. For square/pulse and triangle I invert the 
> signal and pass it through vdelay with a maximum length of my basic period. 
> For saw I just shift the uninverted copy with the vdelay. That way I get my 
> modulation. Now I only need to work out the boring details to properly fade 
> between them and Roberta's your mother's partner in law. :)
> 
> Ta-ta
> ----
> Ffanci
> * Homepage: https://freeshell.de/~silvain
> * Twitter:  http://twitter.com/ffanci_silvain
> * GitHub:   https://github.com/fsilvain
> 
> ------------------------------------------------------------------------------
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> Csound-users mailing list
> Csound-users@lists.sourceforge.net
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>        https://github.com/csound/csound/issues
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Victor Lazzarini, Sep 19 2015:

> Why do you need adsynt for this? I would have thought GEN 10 would do the job.
I used adsynt to morph the spectrum and not blend the waves in the wavetable way.

Thank you Rasmus, for your very interesting idea.

Steven, your code is also interesting. Not what I was looking for. But I'm interested in your arpeggiator and will look at it more closely VERY soon!
...

Ta-ta
----
Ffanci
* Homepage: https://freeshell.de/~silvain
* Twitter:  http://twitter.com/ffanci_silvain
* GitHub:   https://github.com/fsilvain

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I have some papers on the subject if you’re interested

http://eprints.maynoothuniversity.ie/4104/1/VL_New_perspectives.pdf
http://eprints.maynoothuniversity.ie/4693/1/VL_synthesis%20of%20resonance.pdf

Regards
========================
Dr Victor Lazzarini
Dean of Arts, Celtic Studies and Philosophy,
Maynooth University,
Maynooth, Co Kildare, Ireland
Tel: 00 353 7086936
Fax: 00 353 1 7086952 

> On 19 Sep 2015, at 20:37, F. Silvain  wrote:
> 
> Victor Lazzarini, Sep 19 2015:
> 
>> Why do you need adsynt for this? I would have thought GEN 10 would do the job.
> I used adsynt to morph the spectrum and not blend the waves in the wavetable way.
> 
> Thank you Rasmus, for your very interesting idea.
> 
> Steven, your code is also interesting. Not what I was looking for. But I'm interested in your arpeggiator and will look at it more closely VERY soon!
> ...
> 
> Ta-ta
> ----
> Ffanci
> * Homepage: https://freeshell.de/~silvain
> * Twitter:  http://twitter.com/ffanci_silvain
> * GitHub:   https://github.com/fsilvain
> 
> ------------------------------------------------------------------------------
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Sure thing, I'll be curious to hear what you end up developing.

Just as a sidenote, I realized I messed up the phase modulation and
forgot to add in an extra tablei (pasted below, also updated at
http://csound-notebook.kunstmusik.com/note/136)

The new version modulates correctly, but doesn't get much of a
sawtooth sound, IMO.  Anyways, thought it worth noting for the sake of
correctness.

steven


instr 3 ; sine -> saw
;setksmps 1

ipch = cps2pch(p4,12)
iamp = ampdbfs(p5)
ifeedback = p6

aenv linsegr 0, 0.01, 1, 0.01, .9, .3, 0

;aphs = aphasor(ipch, afeedback)
aphs = phasor:a(ipch)
amod = tablei:a(aphs, 1, 1)
aphs = aphs + (amod * ifeedback)
aout = tablei:a(aphs, 1, 1, 0, 1)
;afeedback = aphs * ifeedback

aout = aout * aenv * iamp
aout moogladder aout, 2000, .2
outs aout, aout
endin

On Sat, Sep 19, 2015 at 3:37 PM, F. Silvain  wrote:
> Victor Lazzarini, Sep 19 2015:
>
>> Why do you need adsynt for this? I would have thought GEN 10 would do the job.
> I used adsynt to morph the spectrum and not blend the waves in the wavetable way.
>
> Thank you Rasmus, for your very interesting idea.
>
> Steven, your code is also interesting. Not what I was looking for. But I'm interested in your arpeggiator and will look at it more closely VERY soon!
> ...
>
> Ta-ta
> ----
> Ffanci
> * Homepage: https://freeshell.de/~silvain
> * Twitter:  http://twitter.com/ffanci_silvain
> * GitHub:   https://github.com/fsilvain
>
> ------------------------------------------------------------------------------
> _______________________________________________
> Csound-users mailing list
> Csound-users@lists.sourceforge.net
> https://lists.sourceforge.net/lists/listinfo/csound-users
> Send bugs reports to
>         https://github.com/csound/csound/issues
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