Pitch Accuracy

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   A few years ago, I started a design for a music keyboard that stored sounds in an array of EEPROMs. I set the restraint that ALL the electronic components should be available from RS and Farnell. This prevented me from buying a specially made crystal oscillator chip, which would have been prohibitively expensive. Instead, I had to use run-of-the-mill oscillator chips then divide the frequencies down with a counter, BUT how accurate should the frequencies be?
By my calculation, the frequency ratio between ANY 2 adjacent notes on a keyboard is 1.0594631. This means that, for example, the F# frequency is 5.94631% higher than the F frequency. With the exception of A (which, for the A below middle C is exactly 220.000Hz), ALL the frequencies are irrational values, AND will be impossible to generate exactly. I did find something on the net (Boulder University???) years ago that said an accuracy of 1500ppm (parts per million), corresponding to 0.15%. Is this right, because to me, it looks a very generous figure, compared to 5.94631. I can understand why it doesn't have to be all that accurate for monophonic sounds, but it will matter when you are churning out chords.
There has to be some Electronic Engineers out there that can help me out.

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John McIntyre Members Profile Send Private Message Find Members Posts Add to Buddy List Reviewer page Forum Groupie Joined: February 03 2009 Location: Edinburgh Status: Offline Points: 91	Topic: Pitch Accuracy Posted: March 08 2011 at 16:05
	A few years ago, I started a design for a music keyboard that stored sounds in an array of EEPROMs. I set the restraint that ALL the electronic components should be available from RS and Farnell. This prevented me from buying a specially made crystal oscillator chip, which would have been prohibitively expensive. Instead, I had to use run-of-the-mill oscillator chips then divide the frequencies down with a counter, BUT how accurate should the frequencies be? By my calculation, the frequency ratio between ANY 2 adjacent notes on a keyboard is 1.0594631. This means that, for example, the F# frequency is 5.94631% higher than the F frequency. With the exception of A (which, for the A below middle C is exactly 220.000Hz), ALL the frequencies are irrational values, AND will be impossible to generate exactly. I did find something on the net (Boulder University???) years ago that said an accuracy of 1500ppm (parts per million), corresponding to 0.15%. Is this right, because to me, it looks a very generous figure, compared to 5.94631. I can understand why it doesn't have to be all that accurate for monophonic sounds, but it will matter when you are churning out chords. There has to be some Electronic Engineers out there that can help me out.
	I am one of only about 1,800 people in the world with an original M400 Mellotron!

mono Members Profile Send Private Message Find Members Posts Add to Buddy List Reviewer page Forum Senior Member Joined: May 12 2005 Location: Paris, France Status: Offline Points: 652	Posted: March 10 2011 at 08:25
	0.15% is clearly excessing. We can easily differenciate frequencies down to 0.03%. I think if you go under 0.01%, you should be safe. Still, you don't need to be this precise on the whole spectrum... Can you easily find hardware this accurate? (accumulated tolerances don't help....)
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