[sdiy] Wave terrain synthesis (was Re: Generating acyclicwaveforms?)

cheater cheater cheater00 at gmail.com
Wed Mar 24 21:39:53 CET 2010 

On Wed, Mar 24, 2010 at 21:29, Jerry Gray-Eskue <jerryge at cableone.net> wrote:
> A rather broad assumption considering that the only prerequisite for this
> form is an interest in DIY Synths.
> I am sure there are several people here that understood what you stated, but
> I suspect that there are several more that are interested in your comments,
> and if they were was a bit more verbose English explanation of your concepts
> more of us would benefit from your expertise.

I guess you're right. I can only invite everyone who reads this to
pick up and read an introductory linear algebra/calculus book for
technical university students that covers complex and linear algebra,
discrete mathematics, classical calculus and multivariate calculus.
This is infinitely useful in understanding sound synthesis, be it
analog or digital.

Unfortunately the mathematics above can't be explained to the layman
in less than ten paragraphs at which point it becomes pointless, but
if you read the first paragraphs of definition for these terms you
should be able to understand everything:

- parametrized curve
- vector perpendicular to a curve
- vector parallel to a curve
- derivative of a vector

Cheers
D.

P.S. in the previous post I should have said 'phase' not 'phasor' of course :-)


>
>
>
>
> -----Original Message-----
> From: cheater cheater [mailto:cheater00 at gmail.com]
> Sent: Wednesday, March 24, 2010 2:22 PM
> To: Jerry Gray-Eskue
> Cc: synth-diy at dropmix.xs4all.nl
> Subject: Re: [sdiy] Wave terrain synthesis (was Re: Generating
> acyclicwaveforms?)
>
>
> I assumed everyone here knew analytic geometry.
>
> D.
>
> On Wed, Mar 24, 2010 at 20:22, Jerry Gray-Eskue <jerryge at cableone.net>
> wrote:
>> And a little subspace distortion....;)
>>
>> -----Original Message-----
>> From: synth-diy-bounces at dropmix.xs4all.nl
>> [mailto:synth-diy-bounces at dropmix.xs4all.nl]On Behalf Of Tom Wiltshire
>> Sent: Wednesday, March 24, 2010 1:45 PM
>> To: cheater cheater
>> Cc: synth-diy at dropmix.xs4all.nl
>> Subject: Re: [sdiy] Wave terrain synthesis (was Re: Generating
>> acyclicwaveforms?)
>>
>>
>> Hehe, you *must* be making that up! Just add more dilithium crystals!
>>
>> T.
>>
>> On 24 Mar 2010, at 18:32, cheater cheater wrote:
>>
>>> Actually it's some sort of generalization of both at the same time.
>>>
>>> If you have a trajectory C_1(phi) : [0, 1] -> R^2 over which the
>>> terrain is scanned then translating it by a vector by doing C_2(phi) =
>>> (C_{1,x}(phi) + L_x, C_{2,x}(phi) + L_y) (where L is a certain vector
>>> and (x,y) signifies a vector in R^2) will work just like a wavetable
>>> index scan in the part of the trajectory that is perpendicular to the
>>> vector L, and will work like pitch bending in the part of the
>>> trajectory that is parallel to the vector if dL/dt is a non-zero
>>> constant.
>>>
>>> Changing the function C_1(phi) or the phasor function from phi(x) = x
>>> to something different will work like PM.
>>>
>>> D.
>>>
>>> On Wed, Mar 24, 2010 at 11:23, Tom Wiltshire
>>> <tom at electricdruid.net> wrote:
>>>> I find it very interesting that this technique makes similar
>>>> sounds to FM,
>>>> since in my mind it is more closely related to wavetable synthesis
>>>> than
>>>> either of the nonlinear techniques you mention (waveshaping and
>>>> FM). I can
>>>> completely imagine that it is difficult to control or predict what
>>>> you'll
>>>> get out. Experimentation is good, but sometimes you're aiming for
>>>> something
>>>> particular and it would be nice to be able to get closer.
>>>>
>>>> Thanks very much for a practical report on this.
>>>>
>>>> T.
>>>>
>>>> On 24 Mar 2010, at 03:46, Scott Nordlund wrote:
>>>>
>>>>>
>>>>>> Simon Brouwer wrote:
>>>>>>>
>>>>>>> I see two other ways:
>>>>>>> - using wavetables (very long ones)
>>>>>>
>>>>>> I'd discounted wavetables just because they would have to be
>>>>>> very long,
>>>>>> but memory is cheap, so why not.
>>>>>>
>>>>>> What about Wave Terrain synthesis? Is there an sdiy implementation
>>>>>> anywhere? Load up a 2-d matrix with a surface of choice and then
>>>>>> read
>>>>>> linear subsections. Altering the start and end coordinates over
>>>>>> time to
>>>>>> vary the output waveform.
>>>>>>
>>>>>> -Dave
>>>>>
>>>>> I've tried wave terrain synthesis in Pure Data.  It's neat to
>>>>> think about,
>>>>> but the results I've gotten aren't drastically different from FM or
>>>>> waveshaping or similar things (you could kind of consider
>>>>> waveshaping and
>>>>> FM to be subsets of wave terrain).  My implementation scanned a
>>>>> surface
>>>>> (defined by an arbitrary equation, F(x,y)) with a sort of
>>>>> lissajous figure
>>>>> that could be scaled, rotated, offset, etc.  To get something decent
>>>>> sounding, I limited the surface and modulation to continuous,
>>>>> bounded
>>>>> functions (lots of sin, cos, atan).  A surface with
>>>>> discontinuities or
>>>>> singularities isn't going to sound so great.
>>>>>
>>>>> Anyway, yes, there's plenty of room for inharmonics and animated and
>>>>> complex sounding things, and it's nice that any of the inputs can
>>>>> be used
>>>>> with envelopes or slow or fast modulation or whatever, but
>>>>> there's also
>>>>> a lot of unintuitive messing about to avoid sudden and
>>>>> "unmusical" timbral
>>>>> changes, or just to generally come up with something interesting.
>>>>>
>>>>> The end result resembles something that might be more easily
>>>>> obtained from
>>>>> FM/waveshaping with arbitrary waveforms.  In fact that might be a
>>>>> better
>>>>> approach, because it's difficult to make an equation for an
>>>>> interesting
>>>>> surface.
>>>>>
>>>>> I'm not saying it's not interesting or potentially rewarding, but
>>>>> it's not
>>>>> the revelation that I'd hoped for.  Imagine FM with several added
>>>>> layers
>>>>> of confusion and obfuscation and you won't be too far off.
>>>>>
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