"Self tuning piano" questions

Robert Scott robert.scott@tunelab-world.com
Fri, 26 Dec 2003 00:23:28 -0500


Don A. Gilmore wrote:

> ...Obviously the largest, slowest waves would be from the Big Daddy A0 
> string
> at 27.5 Hz.  Then the counter would read 10,000,000 / 27.5 = 363,636 
> pulses.
>
> The resolution of the counter is, obviously, one count (it can't count
> fractions of a count, only integers).  The frequency at one cent above 
> A0 is
>
> f = 27.5 x 2^(1/1200) = 27.5159 Hz
>
> This results in a count of 10,000,000 / 27.5159 = 363,426.  This differs
> from the other count by
>
> 363,636 - 363,426 = 210 pulses
>
> That's 210 pulses difference in reading to detune the note by just one 
> cent.


I agree.  So one pulse difference (the smallest difference that can be 
read) would be 1/210 of a cent, not 1/6000 of a cent, as you claimed.  And 
even that requires that you be able to trigger your counter to an 
uncertainty of no more than 100 nanoseconds, which is hard to believe for 
a voltage that takes over 36,000,000 nanoseconds to rise through the 
trigger threshold.  No way, man!  In fact, if you derive your measurement 
 from the period of a single cycle of 27.5 Hz and don't average over 
multiple periods, your accuracy is probably no better than 2 full cents at 
A0.  Partials can be picked up by even the crappiest pickup, and these 
partials will distort the sine wave of the fundamental so that the 
one-shot triggering time has an uncertainly of many many clock pulses.

Robert Scott
Real-Time Specialties

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