[sdiy] Additive Synthesis questions

[cheater cheater]

On Thu, Apr 8, 2010 at 20:54, David G. Dixon <dixon at interchange.ubc.ca> wrote:
>> If I was going to make an analogue additive synthesizer, is there a simple
>> way of building a sine wave oscillator with just a few parts that aren't
>> some expensive special function chips?
>>
>> What would be a good number of sine waves for analogue additive synthesis?
>> 4, 7, as many as can be crammed on a panel?
>
> First, bear in mind that I know NOTHING about this, but I'm also interested
> in it (for later).  (Care to read on...?)
>
> For generating lots of low-cost sine waves, why not simply filter square
> waves?  The square waves can be generated in harmonic ratios off of a single
> VCO with dividers, and then a dedicated filter (BP with some Q, perhaps?)
> could be stuck on each square output.  As long as each filter tracks the
> frequency of each input square wave, you should get a decent sine wave.

I wonder if there's a simple way to do that. It feels complicated and
unreliable.

> Otherwise, a single expo current source divided into many different triangle
> cores which are then shaped into sines.  You could do each tricore/sine
> shaper with an LM13700 (one for the integrator, one for the sine shaper), a
> TL072 (ditto), one capacitor (for the integrator), two 2N3904s (for the
> schmitt trigger), two trimmers (for the sine shaper), and about 14
> resistors.  If you're clever, the whole thing could be mounted on a PCB
> about 2" x 1", a collection of which could then be plugged into a master
> control board with the expo converter and the routing transistors/resistors
> on it.  Each sine board would cost less than $5.

Yes, that's what I'd do too if I wanted to go all analog additive.

> However, getting the exact
> frequency ratios might be a challenge (but perhaps this would be part of the
> charm?).

Yes, it would!



> I think that anything else (excluding digital) would be prohibitive in terms
> of parts volume and board complexity, if not actual cost.

One thing more that's halfway digital, halfway analog is to use the
cheapest PIC available that can produce good enough sine output. It
can do the frequency, the partial level, and other stuff, all in
digital. Then you create an 8-bit buss onto which you put 8-bit
parallel output of all PICs. The digital outputs of each pic get mixed
together bit by bit and then we use an R/2R DAC at the end of that - I
think it should still work with such a signal, what do you guys think?

Or if it's not much more expensive, then just use a part with onboard DAC.

Richard,

> Additive really needs to be smart to be interesting. Mashing together the partials is the easy part. Giving the partials something interesting to do over the duration of a note is the only way to make additive stand out from other synthesis options.

Yes. If a system is too complex, giving control over every single part
of it is too atomic - you want to have control over parameters that
change the whole system at once. For example, a parameter that
uniformly changes the phase, or frequency, of each partial in some
specific way. Just exploring different possible algorithms (and
therefore different possible intervals between partials) can keep you
busy for a lifetime.

Another thing is microsequencing. You input a sequence into your VCO,
and it somehow applies a generalized version to each harmonic,
altering the pitch, or the amplitude, or the waveform. That's one
thing that lets the c64 make very lush sounds.

Yet another thing is filtering, but in a different way than
LPF/HPF/etc. In mathematics a filter is something that throws away
items that are too far from the ideal value. For example you can have
a filter that you put integers through, and it filters away prime
numbers throwing away non-prime numbers. Similarly a lot of crazy
filters could be defined on such a vco. A simple example is cutting
off partials from the top to the bottom, taking out the partial
numbered 15, then 14, and so on. But that's simple. Another thing you
could do is start 'throwing away' partials that are too far from the
harmonic series. First throw away the furthest one, then another one,
and so on. Yet another thing you could do is make the harmonic series
'attract' the partials: at maximum, the partials are at the harmonic
frequency nearest to their 'basic' frequency setting. As you turn down
this setting the partials slowly return to their 'basic' frequency.
Exploring the possible algorithms here could take a *lot* of time and
could be very fun.

Generally it doesn't pay off to allow people to control single
partials, or even groups of partials. If you want single partials,
then use a VCO with a single waveform. If you want two groups of
partials, just use two additive VCOs.

> Ideally you really want to be able to do resynthesis - pulling sounds apart automatically, and reconstituting them with additive+effects. (Random or organised frequency+time+amplitude modulation, stretching/squashing the overtones, and so on.)
>
> 24 partials is a bare minimum, 32 is better, 64 is better still, but not so much better that it's worth going insane over an implementation if resources are scarce.

I dunno, I've had fun with my 15-harmonic model. It did sound
low-passed, but that was character rather than defect.. It definitely
did not sound 'empty' or 'plain'.

Ingo,
> I've read in several postings here that harmonic ratios as required in
> additive synthesis (or created by a vibrating string) can be created by
> frequency division. Or am I misunderstanding?
>
> But, but, but..
> It cannot be done that way. For additive synthesis you need frequencies f,
> 2f, 3f, 4f, 5f and so on. With a frequency divider you'll get f, f/2, f/3,
> f/4, f/5...
> This is very different. Even if you start with a fairly high master
> frequency, say 60f, you only get f, 2f, ... 6f. 7f doesnt work, you would
> need 420f as a master frequency then.
>
> Am I missing the point?

No, you're right.

Although, it might be possible to alias the signal, and invert the
whole thing! In that case the frequencies will be f, 2f, 3f, ..., 7f
again, I think - might be wrong though, got no time to check the maths
at this point.

Cheers
D.