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

[cheater cheater]

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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