A fan, Fleck, asked me for details about how the audio output works. I was feeling especially rambly that night, so I wrote the Great American Novel in reply. As this might be of interest to others, I thought I'd also put it here.
Note that whenever I refer to a "faster clock", I'm referring to the fact that he's trying to get it to run on an ATtiny13A, which has a 9.7 MHz internal oscillator as opposed to the 8 MHz one in the ATtiny9 I used.
On 10.06.2013 13:43, Fleck wrote:
big problem for now is that I don't understand - how sounds are made! Maybe you could point out some links/manuals/tutorials where I can learn step by step - how do I create 440Hz for example sq.wave and triangle or sine wave notes... Cause I don't get it, timer int runs 37500 times a second, far beyond ear limits, so... What we do to hear sound?
Hah, that's actually something I can explain!
The basic idea (you probably already figured this out) is that I generate the sound using PWM; similar to how you would dim a LED, just with a faster changing output value.
It's correct that I set up the timer to run at 32K PWM periods per second (37,5K on your chip), which would correspond to a sample rate of 32 kHz if I were to change the sample value (OCR0A) after each PWM period.
Now, I do not intend to run at that high a sample rate, nor do I have enough processing power to generate that many samples in real time, so I divide the sampling rate by four simply by only changing OCR0A every four PWM periods. This gives me a sample rate of 8 kHz, with a theoretical Nyquist frequency of 4 kHz.
Why am I not just running a slower PWM, you ask? Well, the main reason is that the PWM, being essentially a square wave, introduces its own set of distortions and overtones. The faster I run the PWM, the higher up (and therefore out of the audible range) my overtones. If I ran the PWM at normal 8 kHz, it would cause a constant, high-pitched beep all over the music.
Another arguable advantage of this technique is that this very basic sample rate conversion (if you want to call it that), using a simple step function, introduces all kinds of aliasing harmonics. While normally unwanted, this aliasing is what gives the Noiseplug its treble-rich sound although it's only producing samples at 8 kHz. This is also why the C prototype version sounds so dull compared to the actual plug -- it's missing the aliasing because the 8kHz are properly upsampled to whatever the soundcard can output and are put through the card's reconstruction filter.
For the details, please take a look at the very basic framework code from the commit I linked to: https://github.com/dop3j0e/noiseplug/commit/62c720ab1bfa62de564a630cafb3bb62ce006703
As you can see, the interrupt routine does nothing but increment int_ctr modulo 4. The main loop below sleeps until int_ctr reaches zero, then starts computing a new sample and outputs it to OCR0A when it's done. This makes sure that every four interrupts, a new sample is generated.
Also, there's a 24-bit loop counter, i, that increments on each sample. This is the basic system time that drives most of the song. The test code in the framework simply uses the second byte of that counter to generate the next sample, which gives you a sawtooth wave that increments every 256 samples, wrapping back to zero every 64K samples. You might notice that this gives you a frequency of 1/8 Hz ;) So you won't hear anything, but if you hook up your scope to the PWM pin, you should be able to actually see a PWM wave that's slowly incrementing with a period of 8 seconds (less with your higher clock frequency).
I used a scope for debugging a lot; you'll notice the two instructions setting and clearing bit two of PORTB, before and after the sample calculation. This is pure debug code so I could see on my scope how long my sample generation code was taking.
As for generating actual square or triangle waves, lft's seminar might be a good start: http://www.linusakesson.net/music/elements/index.php
The oscillators in the Noiseplug are simple 16-bit accumulators. I choose which note they play by choosing the value I add to them each sample. I generate the sample by shifting and masking the accumulator values -- a good example is the voice_bass() function in the C prototype:
unsigned char ret = ((bassosc >> 8) & 0x7F) + ((flangeosc >> 8) & 0x7F);
I have two oscillators, slightly detuned for a flanger effect. I take the almost-highest seven bits of the accumulators for a sample value, giving me a nice sawtooth wave. Taking bits near the MSB gives me slowly changing values, and shifting by eight means I can just take the upper byte of the two-byte value instead of shifting.
For a square wave, I just pick a single bit from the oscillator and choose a sample value of zero or non-zero based on that bit:
return (arp_osc & (1 << 12)) ? 0 : 35;
I can tune the voice in octaves by simply changing which bit to pick.
As for what value to add for a C, C#, D and so on, I used a table of basic note frequencies and converted them using a spreadsheet -- see win/nodes.ods in the Github repo for that. Column B is the note frequency in Hz, C is the corresponding period in samples, based on my sample rate of 8 kHz. In D, I multiplied the periods with 2 or 4 to pitch them down one or two octaves respectively, giving me a two-octave scale. In column E, finally, I get my "how much to add to the accumulator" value by asking: "If I had an accumulator that wraps after 16K, how much would I have to add per sample to make it wrap every N samples?". I could have gotten there much easier had I known from the start what I was doing, but there you have it =)
Hint: As your clock is running faster, try changing the 8K in the formulas for column C to 9375. That should give you the Noiseplug's original pitch back.
Guess in which table in the firmware these note values ended up ;)
That's all, hope it helps! Joachim
 Note that even that sample rate would give you a Nyquist frequency of 16 kHz, which is actually within the audible range.
 In the final version, I reserved three registers solely for i because I was running out of RAM, so you won't find any explicit memory location called "i" there.