| Author |
Message |
Antimon
Joined: Jan 18, 2005
Posts: 4145
Location: Sweden
Audio files: 371
G2 patch files: 100
|
|
|
Back to top
|
|
 |
Frostburn
Joined: Dec 12, 2007
Posts: 255
Location: Finland
Audio files: 9
|
 Posted: Sat Mar 15, 2008 10:13 am Post subject:
|
  |
|
Yeah. It's actually supposed to do that.
It's called frequency warping.
Here's a little background:
A sawtooth wave like any periodic waveform is in a mathematical sense composed of harmonics. Sine waves playing at a base frequency and it's integer multiples.
The thing with sawtooth and square wave especially is that they are very sharp and it means that their harmonics stay strong well beyond the limits of human hearing.
The problem arises because you cannot produce those high frequencies with the samplerates we use. The harmonics climb to nyquist (frequency of half the sampling rate) and then start descending back towards zero. This sounds awful. You can verify the effect yourself by playing a sinewave sweep that goes up in frequency endlessly. After getting really high it will start comming back down, reaches zero and starts going up again.
What we need to do is cut the harmonics off at nyquist. Luckily ChucK comes with BlitSaw (bandlimited sawtooth wave) that does this.
| Code: | BlitSaw c => dac;
0.5 => c.gain;
while (true) {
for (0 => int y; y < 8; y++) {
Std.mtof(y*16 + 8) => c.freq;
0 => c.harmonics; //Let ChucK calculate how many harmonics we need
500::ms => now;
}
} |
Try BlitSquare too!
_________________
To boldly go where no man has bothered to go before. |
|
|
Back to top
|
|
|
Antimon
Joined: Jan 18, 2005
Posts: 4145
Location: Sweden
Audio files: 371
G2 patch files: 100
|
| Posted: Sat Mar 15, 2008 10:44 am Post subject:
|
|
|
Aha - thanks a lot for that very fast and informative reply!  I even see that I delved into stuff mentioned in your signature! A new topic that I didn't know about.
I'm actually not completely in the clear because I was running into this when I was messing about with CurveTable. I've always been intrigued by "drawing your own waveform" kind of synthesis, and was hoping that I could make some interesting timbres with this. Maybe you're not really supposed to work with waveforms this way... drawing curves with sharp edges will always get you into these frequency warping issues maybe?
/Stefan
_________________
Antimon's Window
@soundcloud @Flattr home - you can't explain music |
|
|
Back to top
|
|
|
kijjaz
Joined: Sep 20, 2004
Posts: 765
Location: bangkok, thailand
Audio files: 4
|
| Posted: Sat Mar 15, 2008 11:10 am Post subject:
|
|
|
If you really need the sound but at the same time want to lower the warping,
you may want to work with a higher sample rate..
so if your soundcard / audio interface support that, you can try and hear out. |
|
|
Back to top
|
|
|
Kassen
Janitor
Joined: Jul 06, 2004
Posts: 7678
Location: The Hague, NL
G2 patch files: 3
|
| Posted: Sat Mar 15, 2008 11:18 am Post subject:
|
|
|
| Antimon wrote: | drawing curves with sharp edges will always get you into these frequency warping issues maybe?
|
Typically, yes. Unless the module is anti-aliased, I fear.
So, the way to go would be a higher sample rate, then filtering and down sampling. Of course this means calculating what sample-rate would be sufficient for a given curve... which may be hard...
I tend to go by ear for stuff like that.
_________________
Kassen |
|
|
Back to top
|
|
|
Antimon
Joined: Jan 18, 2005
Posts: 4145
Location: Sweden
Audio files: 371
G2 patch files: 100
|
| Posted: Sat Mar 15, 2008 11:45 am Post subject:
|
|
|
OK, thanks guys. Moving the points around a bit and changing curvature might help in a CurveTable I guess. I'll see where I'll go.
/Stefan
_________________
Antimon's Window
@soundcloud @Flattr home - you can't explain music |
|
|
Back to top
|
|
|
dewdrop_world
Joined: Aug 28, 2006
Posts: 858
Location: Guangzhou, China
Audio files: 4
|
| Posted: Sat Mar 15, 2008 12:27 pm Post subject:
|
|
|
Someone should implement band-limited oscillators, then. Band-Limited Impulse Trains: http://www.musicdsp.org/archive.php?classid=1#90
SuperCollider has them (Saw, Pulse etc.) and they rock. They're a bit more cpu-hungry than the non-band-limited versions (LFSaw, LFPulse) but sound great over the whole frequency range.
I've also used wavetable synthesis where you interpolate between adjacent buffers. In pseudocode:
| Code: |
numberOfBuffers = 8;
lowMidi = 48 (midi note num) / 12 (notes per octave);
buffers = Buffer[numberOfBuffers];
for(i = 0; i < numberOfBuffers; i++) {
base = (i + lowMidi) * 12;
numHarmonics = int (20000 / midiToCps(base));
for(j = 0; j < numHarmonics; j++) {
add harmonic to buffers[i] with amplitude 1/(j+1)
}
} |
Then, you can map the frequency onto the right fractional buffer number -- log2(freq / basefreq) / log2(topfreq / basefreq) * (numberOfBuffers-1) -- or, to remove a division, (log2(freq) - log2(basefreq)) / (log2(topfreq) - log2(basefreq)).
Then interpolate:
float b = (log2(freq) - log2(basefreq)) / (log2(topfreq) - log2(basefreq));
int bInt = (int) trunc(b);
WavetableOscillator(bInt) * (bInt - b + 1)
+ WaveTableOscillator(bInt+1) * (b - bInt)
Hope that's not too unclear... I'm trying to extract the basic idea from SuperCollider code I've been using for years.
James
_________________
ddw online: http://www.dewdrop-world.net
sc3 online: http://supercollider.sourceforge.net |
|
|
Back to top
|
|
|
Antimon
Joined: Jan 18, 2005
Posts: 4145
Location: Sweden
Audio files: 371
G2 patch files: 100
|
| Posted: Sat Mar 15, 2008 1:11 pm Post subject:
|
|
|
Another newbie question: what, exactly, does Blit do? What's the difference between it and BlitSaw?
/Stefan
_________________
Antimon's Window
@soundcloud @Flattr home - you can't explain music |
|
|
Back to top
|
|
|
Frostburn
Joined: Dec 12, 2007
Posts: 255
Location: Finland
Audio files: 9
|
| Posted: Sat Mar 15, 2008 2:24 pm Post subject:
|
|
|
| Antimon wrote: | | Another newbie question: what, exactly, does Blit do? |
Blit is short for band limited oscillator. It produces a set of harmonics with equal gains.
The two patches bellow sound the same but if you look at the waveforms they're completely different!
Human hearing isn't phase aware so it doesn't matter how the harmonics are related to each other in phase as long as their relative gains are the same.
Blit is useful when you want to do timbre manipulation with filters. Blit is what is called spectrally flat so it doesn't impinge any additional characteristic to the sound.
| Code: | 220.0 => float freq;
//Try the Blit:
Blit b => dac;
freq => b.freq;
10 => b.harmonics;
second => now;
b =< dac;
second => now;
//Let's make a Blit ourselves:
SinOsc harmonic[10];
float k;
for(0 => int i; i < harmonic.cap(); i++){
harmonic[i] => dac;
i+1 => k; //This is the index of the harmonic
freq*k => harmonic[i].freq;
0.1 => harmonic[i].gain;
}
second => now; |
| Quote: | | What's the difference between it and BlitSaw? |
The difference is that Blit produces harmonics with equal gains and BlitSaw weights them according to the alternating harmonic series. That is the kth partial is weighted ( -(-1)^k )/k.
So the first sinewave has a weight 1.0.
the second -0.5
the third 0.33333...
the fourth -0.25
and so on....
BlitSquare skips over every even harmonic. It's odd in spectrum.
_________________
To boldly go where no man has bothered to go before. |
|
|
Back to top
|
|
|
Frostburn
Joined: Dec 12, 2007
Posts: 255
Location: Finland
Audio files: 9
|
| Posted: Sat Mar 15, 2008 2:39 pm Post subject:
|
|
|
| dewdrop_world wrote: | | I've also used wavetable synthesis where you interpolate between adjacent buffers... |
Funny you mention that. Because it's exactly what I did with my FourierPool. It can be found in the Instrument library I just posted on the other thread.
It's based on IFFT (Inverse Fast Fourier Transform) that is an UAna (Unit Analyser) in chuck.
The basic idea is to place sinewave partials in to the discrete frequency bins using linear interpolation for fractional bin values.
It almost has it all. It's perfectly band limited by definition (assuming you use the best settings to eliminate artifacts), allows precise control over the timbre (assuming you are a float function wizard), but it's not especially fast.
_________________
To boldly go where no man has bothered to go before. |
|
|
Back to top
|
|
|
Inventor
Stream Operator
Joined: Oct 13, 2007
Posts: 6221
Location: near Austin, Tx, USA
Audio files: 267
|
| Posted: Sat Mar 15, 2008 3:08 pm Post subject:
|
|
|
| Quote: | | Human hearing isn't phase aware so it doesn't matter how the harmonics are related to each other in phase as long as their relative gains are the same. |
That's a great thing to know, Frostburn, I always thought the phase mattered. Looking forward to hearing some additive synthesis tunes. |
|
|
Back to top
|
|
|
Antimon
Joined: Jan 18, 2005
Posts: 4145
Location: Sweden
Audio files: 371
G2 patch files: 100
|
| Posted: Sat Mar 15, 2008 4:48 pm Post subject:
|
|
|
| Frostburn wrote: | | Antimon wrote: | | Another newbie question: what, exactly, does Blit do? |
Blit is short for band limited oscillator. It produces a set of harmonics with equal gains.
[...]
|
Thanks for that great explanation.  I knew a bit about saws being the sum of a series of harmonics, but I've never learned the details.
/Stefan
_________________
Antimon's Window
@soundcloud @Flattr home - you can't explain music |
|
|
Back to top
|
|
|
Frostburn
Joined: Dec 12, 2007
Posts: 255
Location: Finland
Audio files: 9
|
| Posted: Sun Mar 16, 2008 1:03 pm Post subject:
|
|
|
| Inventor wrote: | | That's a great thing to know, Frostburn, I always thought the phase mattered. Looking forward to hearing some additive synthesis tunes. |
For a single sound source it's harmonic phase relations aren't audible. (well maybe a little but it's not much)
They still make a difference when you mix different sources together, especially if distortion is involved.
_________________
To boldly go where no man has bothered to go before. |
|
|
Back to top
|
|
|
|
Forum index » DIY Hardware and Software » ChucK programming language
FAQ
Calendar
Search
Memberlist
Usergroups
Register
Profile
Log in to check your private messages
Log in
Chat Room
