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 Forum index » Clavia Nord Modular » G2 Building Blocks
Sine Bank
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ian-s



Joined: Apr 01, 2004
Posts: 2575
Location: Auckland, New Zealand
Audio files: 42
G2 patch files: 608

PostPosted: Sun Jul 23, 2006 3:18 am    Post subject: Sine Bank Reply with quote  Mark this post and the followings unread

Someone on the SynthDIY list posted a theory about how the rare Buchla sine bank oscillator might have worked, using just multipliers.
Something like the following…

1 = sine oscillator
2 = 1 * 1
3 = 2 * 1
4 = 2 * 2
5 = 4 * 1 or 3 * 2

I new about the sine frequency doubling trick but have not encountered using the same technique to get all harmonics.
It turns out that odd numbers require some additional work to suppress the fundamental. I don’t fully understand how this works, just trial and error.

The patch includes 8 phase locked, harmonically related sine waves.

BTW, the Buchla module most probably did not work like this, good 4 quadrant multipliers are not cheap in the analogue world.

Edit:24 July
Just noticed that even though the odd numbered waves look ok on the soft scope, there is still some of the lower sideband that I can't cancel out.
The errors get more noticable the higher you go.

Edit:25 July
The errors are only present when using audio oscillator, sine LFO at audio rate is ok Shocked


SineBank.pch2
 Description:
8 sines from 1 osc

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 Filename:  SineBank.pch2
 Filesize:  2.08 KB
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Rob



Joined: Mar 29, 2004
Posts: 580
Location: The Hague/Netherlands/EC
G2 patch files: 109

PostPosted: Tue Jul 25, 2006 6:17 am    Post subject: Re: Sine Bank Reply with quote  Mark this post and the followings unread

g2ian wrote:
Something like the following…

1 = sine oscillator
2 = 1 * 1
3 = 2 * 1
4 = 2 * 2
5 = 4 * 1 or 3 * 2

I new about the sine frequency doubling trick but have not encountered using the same technique to get all harmonics.


It is a long known technique but rarely implemented. E.g. there is a module in the Kyma system that does this. Basically the math is based on Chebyshev polynomials, Hal Chamberlin wrote about it in 1980 in his book 'Musical Applications of Microprocessors'.

Where it gets wrong in your patch is the fifth and seventh harmonics, their amplitudes are twice too high. The fifth harmonic also needs to be inverted.
After these corrections one can e.g. get a nice approximation of a square wave. Note that it is impossible to get the 'graphically correct' shape of a saw as the even harmonics lag in phase in respect with the fundamental and odd harmonics. But it will sound like a saw. Wink

This patch shows the curious behaviour of the LevConv module in Pos mode, as here it happens to multiply by two and then subtract one. Which is exactly what changes the output of the multiplier into the proper second order Chebyshev polynomial "sin^2 * 2 - 1", which is the formula that converts a sinewave with amplitude one into its second harmonic with amplitude one.

Selfmodulating the sine with the 'harmonicised' output works also quite nice, as this thingy doesn't really need a sine as input, any waveform can be used as long as the amplitude is 1. E.g. the ShapeOsc also works nice.


sinebank_187_fix.pch2
 Description:
g2ian's patch with small fix

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 Filename:  sinebank_187_fix.pch2
 Filesize:  2.09 KB
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sinebank_187_fix_mod.pch2
 Description:
g2ian's patch with a small addition to make the fun begin

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 Filename:  sinebank_187_fix_mod.pch2
 Filesize:  2.36 KB
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ian-s



Joined: Apr 01, 2004
Posts: 2575
Location: Auckland, New Zealand
Audio files: 42
G2 patch files: 608

PostPosted: Tue Jul 25, 2006 1:34 pm    Post subject: Reply with quote  Mark this post and the followings unread

Thanks Rob. That Hal Chamberlin book sounds very interesting. I had his "CMOS cookbook".

Any idea why the lower sideband can't be cancelled completely when using the sine from a red signal?
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mosc
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Joined: Jan 31, 2003
Posts: 17618
Location: Allentown, PA
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PostPosted: Thu Jul 27, 2006 8:00 am    Post subject: Re: Sine Bank Reply with quote  Mark this post and the followings unread

Rob wrote:

Selfmodulating the sine with the 'harmonicised' output works also quite nice,

Not only are you a master patcher, but a master of the understatement. Very Happy

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