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ian-s
Joined: Apr 01, 2004 Posts: 2669 Location: Auckland, New Zealand
Audio files: 42
G2 patch files: 626
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Rob
Joined: Mar 29, 2004 Posts: 580 Location: The Hague/Netherlands/EC
G2 patch files: 109
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Posted: Tue Jul 25, 2006 6:17 am Post subject:
Re: Sine Bank |
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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.
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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.
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.
Description: |
g2ian's patch with small fix |
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sinebank_187_fix.pch2 |
Filesize: |
2.09 KB |
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1463 Time(s) |
Description: |
g2ian's patch with a small addition to make the fun begin |
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Download |
Filename: |
sinebank_187_fix_mod.pch2 |
Filesize: |
2.36 KB |
Downloaded: |
1563 Time(s) |
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ian-s
Joined: Apr 01, 2004 Posts: 2669 Location: Auckland, New Zealand
Audio files: 42
G2 patch files: 626
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Posted: Tue Jul 25, 2006 1:34 pm Post subject:
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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
Site Admin
Joined: Jan 31, 2003 Posts: 18198 Location: Durham, NC
Audio files: 213
G2 patch files: 60
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Posted: Thu Jul 27, 2006 8:00 am Post subject:
Re: Sine Bank |
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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. _________________ --Howard
my music and other stuff |
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