Appendix A: Sample rates deep dive

"But why don't most sample trackers let you record and play at the highest sample rates the hardware can support? Why are they limited to 28603Hz (PAL) and 28867Hz (NTSC), rather than say 55Khz or higher? After all, most samplers' bundled sampling programs could do that!", we hear you ask. Well, there are a couple of things going on here.

Firstly, those figures of 28603Hz (28.6Khz) and 28867Hz (28.8Khz) are important because while the theoretical maximum sample rate of Paula (ie the rate at which its PWM output can switch on and off) is about 31Khz, there are some limitations imposed by the chipset internals of the Amiga - detailed on page 260, Appendix A of the Amiga Hardware Reference Manual if you want to dive even deeper. Each Paula channel's playback frequency is derived from the system's clock speed (not the CPU clock, but the master clock from which all custom chips and the CPU derive their speeds) which is 3546895Hz on PAL systems and 3579545Hz on NTSC systems. This clock speed is divided by a value from a look-up table of 'periods' - ie PWM interrupt intervals - which correspond with the desired audio playback sample rate. What do PAL and NTSC have to do with it? More on that later.

It is possible to play back audio data at sample rates higher than those practical limits, and most trackers have a few entries in their note period look-up tables that correspond to such rates (generally A-3, A#3 and B-3), but you should expect results to be unpredictable and probably way out of tune with notes further down the scale. That doesn't mean they're useless - those notes and their commensurate high quality can still be useful for unpitched stuff like snares or hi-hats, or even for melodic/harmonic content that never needs to change pitch, but if your channel effects ever raise the pitch (vibrato or arpeggio for example) then horrible things will probably happen to your ears. And if not yours, then probably somebody else's when they listen to your module on a different system. On a PAL machine, A-3 is 27.928Khz and A#3, a semitone up, is 29.557Khz; the aforementioned practical limit falls between these semitones, so your realistic upper limit when tracking should be A-3, and perhaps even G-3 to be safe.

Secondly, those references to PAL and NTSC timing remind us that everything about the Amiga's custom chip architecture, and the rates at which those custom chips' DMA runs, is linked to video display timing. It's an ideological relic of the Amiga's time, and it's why the system was so great at what it did. So if you've used sampler carts in the past, especially with their bundled sampling programs, you'll remember that it was possible to record and play back EXTREMELY high-quality audio - in sample rate terms, at least. But you'll also remember that the screen went blank or froze both when recording and replaying in these high quality modes. And even in Protracker the screen goes blank when doing the actual recording (not monitoring) of a sample.

Each Paula channel gets one DMA slot per horizontal display scanline, so to monitor (without recording) incoming sampler audio, most programs can continue to update their graphics while playing back that incoming sound and doing some basic analysis on the signal to display waveform scopes or VU meters. But in order to record, including at rates higher than our 'limit', the screenmode has to be changed to one that performs horizontal scans at a rate which allows Paula DMA access at a higher frequency. To play back these samples, programs like TechnoSound Turbo, MegaloSound, MasterSound etc. also need to change their display modes and blank/freeze their screens because playback in the program's default displaymode would be limited to ~28Khz and so the sample would sound waaaaay downpitched, usually by around an octave.

So we're sure you're ahead of us on this: trackers don't care about anything that exceeds the ~28Khz limit, because trackers are for composing modules which need to be replayable alongside games, demos, cracktros and the like without forcing those programs to change screenmodes or blank/freeze their screens; they also need to use all 4 channels independently, so can't double up for crazy 14bit playback tricks or whatever. If you sample an instrument in MegaloSound at the highest possible mono samplerate (let's say ~55Khz) and load that sample in ProTracker, even playing B-3 on the keyboard will sound about an octave lower than you expect. To get it to sound right you'll have to upsample it by an octave...which discards every other sample so you can play back at a higher frequency...and now you've lost half the sample information, the sample is around 28Khz, and you might as well have sampled at 28Khz in ProTracker in the first place :D

So...that was a long and rambling but hopefully edifying explanation for why - although it's possible to sample at rates way in excess of CD quality - the safe, everyday, practical upper limit of any Amiga sampler cart if you're a tracker musician is pretty much A-3.

Here's a table of ProTracker's notes, note period values, and corresponding PAL and NTSC sample rates (rounded to nearest). You can also finetune up or down by 8 increments between semitones (aka half-steps), so for a comprehensive table of all the intermediate periods check out the Protracker page on exotica.org.uk. It's just a quick reference to give you an idea of which PT note will give you which sample rate - don't rely on it for any serious maths!

Octave 1

PAL 3546895 NTSC 3579545

PT Note	C-1	C#1	D-1	D#1	E-1	F-1	F#1	G-1	G#1	A-1	A#1	B-1
PT Period	856	808	762	720	678	640	604	570	538	508	480	453
PAL sample rate	4144	4390	4655	4926	5231	5542	5872	6223	6593	6982	7389	7830
NTSC sample rate	4182	4430	4698	4972	5280	5593	5926	6280	6653	7046	7457	7902

Octave 2

PT Note	C-2	C#2	D-2	D#2	E-2	F-2	F#2	G-2	G#2	A-2	A#2	B-2
PT Period	428	404	381	360	339	320	302	285	269	254	240	226
PAL sample rate	8287	8779	9309	9852	10463	11084	11745	12445	13185	13964	14779	15694
NTSC sample rate	8363	8860	9395	9943	10559	11186	11853	12560	13307	14093	14915	15839

Octave 3

PT Note	C-3	C#3	D-3	D#3	E-3	F-3	F#3	G-3	G#3	A-3	A#3	B-3
PT Period	214	202	190	180	170	160	151	143	135	127	120	113
PAL sample rate	16574	17559	18668	19705	20864	22168	23489	24803	26273	27928	29557	31388
NTSC sample rate	16727	17721	18840	19886	21056	22372	23706	25032	26515	28185	29830	31677