[sdiy] Interesting article on top octave generators.

[Richie Burnett]

In "DSP land" you can use Chebyshev polynomials of the first kind to 
multiply the frequency of a sine-wave by an integer...

https://en.wikipedia.org/wiki/Chebyshev_polynomials#First_kind

So, if you have a sine-wave at f and want another sine-wave at 3f you can 
"wave-shape" it using the T3(x) function in that table.  This can be quicker 
than running another NCO at 3f and another (interpolated) LUT to convert 
it's phase-angle to a sine-wave, provided your processor is quick at maths. 
The f and 3f waveforms are guaranteed to be "phase locked", if that is what 
you're after.  If you don't want them phase locked then running a bunch of 
"Magic circle" algorithms is probably the quickest way to get a load of 
sine-waves at arbitrary frequencies.

Real tone-wheels don't generate pure sine-waves though (>.<)

-Richie,


-----Original Message----- 
From: Tom Wiltshire
Sent: Friday, December 27, 2024 11:48 PM
To: Roman
Cc: synth-diy at synth-diy org
Subject: Re: [sdiy] Interesting article on top octave generators.

I think the tonewheel "n/m" thing is actually quite a bit harder to do. The 
obvious way would be an NCO, since that gives you the fractional divider 
structure, the n/m, but then you have a problem with jitter, which is not 
something the gearwheels in the original generator have to deal with. With 
rotating gears, you can multiply a frequency *up* or *down* by whatever 
tooth-ratio you like, within reason. Since in that situation you might be 
after sinewaves instead of squares, perhaps some kind of 
pulse-density-modulated sine output would be ok. Yes, there'd be some small 
amount of jitter, but after the PDM is filtered, it might well be inaudible.
It's actually a situation where DSP with a fairly low sample rate is more 
than acceptable, since we're only producing sinewaves and the highest sine 
frequency in the Hammond organ isn't that high - just under 6KHz. Hence a 
fairly modest DSP running at even a 20KHz sample rate could generate the 
sines with no aliasing.


The classic divide-down TOG can be done without jitter since it's always a 
whole number of master clock pulses. With the original chips running at 
about 2MHz, there's enough time to calculate the outputs on a basic 
processor going somewhat faster (20MHz, 32MHz, whatever).

I completely agree that RPi2040 is massive overkill even for a 12-note TOG, 
let alone six. It's been done on an AVR, so there's really no need for such 
heavy firepower!




On 27 Dec 2024, at 14:06, Roman via Synth-diy <synth-diy at synth-diy.org> 
wrote:


Following that route - why not make TOG replacement which produses exact 
frequencies of tonewheels, or better yet, switchable frequencies of every 
historical or another weird scales?
Frankly, using RP2040 for 6 tone TOG is not so impressive to make video 
about it. Microcontroller based TOG replacements are available for decades 
now.


Roman



---- Użytkownik Tom Wiltshire napisał ----


.
>
>
> I agree that it does seem a bit crazy to replace some basic logic with a 
> whole uP, but the arguments for doing it are pretty convincing. Doing 
> twelve 9-bit dividers in hardware is going to be a lot of chips, whereas 
> the uP is only one. That makes it much easier to fit inside whatever it is 
> you're fixing. And it's cheaper - a boardful of simple logic costs *more* 
> than a processor these days because of the economies of scale. It *is* 
> crazy to use a million transistors when 10,000 would do, but when they all 
> come on one chip and costs pennies, it starts to make a lot of sense.
>
>
> It terms of the technological limitations, all of the uP-based divider 
> solutions I've seen are pretty much exact clones and just as limited as 
> the original chips! They certainly keep the original division ratios and 
> consequent frequency error.
>
>
> There are a few original divider chips out there, but the people that have 
> them want $30 a chip or worse for them. $1 processor wins over that every 
> time.
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