[sdiy] 440Hz Reference Oscillator.

[Magnus Danielson]

From: Seb Francis <seb at burnit.co.uk>
Subject: Re: [sdiy] 440Hz Reference Oscillator.
Date: Wed, 07 Jun 2006 00:06:07 +0100
Message-ID: <44860A5F.2070706 at burnit.co.uk>

> Andre Majorel wrote:
> > Yep. If you're willing to depend on the accuracy of a sound card,
> > there are more expedient ways.
> >
> >   
> 
> Is the accuracy of a sound card really so bad?  Even the cheapo sound 
> card I just took out of my PC has a 24.576MHz crystal which divided by 
> 512 is exactly 48kHz, so surely a 440Hz sine wave through a PC sound 
> card will be spot on.  I can't believe there are sound cards that play 
> your music out of tune!

They all do, by definition, but the deviation is so small that you don't
notice it.

It is all nice and dandy that the math goes together on your sound card, but
there is more to it. Your crystal oscillator does not make EXACTLY 24576000
cycles in a SI second, it only nominally does that. Most oscillators is of the
standard variant giving some +/- 100 ppm of accuracy, or +/- 2457,6 Hz in your
case. Now, that is only a 3-sigma value so it is only within that range for
99,7 % of all devices made, and BTW for such precission you don't see any
temperature compensation or stabilisation. Changes in temperature will also
cause the crystal to age and drift away to some new nominal frequency which it
only reaches assymptotically. Long before that the temperature changes again.
Add to that non-gaussian noise sources which contribute to the long term
behaviour.

All oscillators does this, crystal or not.

However, does it matter? Not really. +100 PPM is only +0.32 cent, which we
don't perceive as an absolute pitch change. We could hear it as a relative
pitch-shift however, as a beating relative some sound not comming out of that
sound card but of a different source. A 1 kHz tone would have a 10 second
beating period.

What does matter is really how good approximation the frequency synthesis is.
The best way to create a reference 440 Hz sine would probably be the digital
equalent of a bi-quad sine/cosine generator. Requiring very little processing
it can give a very accurate frequency of sine-waveform. It can be implemented
in both integer and float math. Four multiplications and two additions in
straight-forward implementation. A modern CPU gets bored between the samples.

So, can you "trust" a sound-card based tuning? Well, if you verified the
software, go ahead. It should work well enough.

Cheers,
Magnus