Don: You've described an interesting procedure. How precise is the definition of "one cycle" in this system? It would seem that the start and stop timing of one cycle would be the most critical one. Have you compared the frequency data derived in this way to data from other measurement systems? dave __________________________________________ David M. Porritt, RPT Meadows School of the Arts Southern Methodist University Dallas, TX 75275 ----- Original message ----------------------------------------> From: "Don A. Gilmore" <dgilmore@kcmpi.net> To: <robert.scott@tunelab-world.com>, Pianotech <pianotech@ptg.org> Received: Wed, 24 Dec 2003 23:30:05 -0600 Subject: Re: "Self tuning piano" questions >----- Original Message ----- >From: "Robert Scott" <robert.scott@tunelab-world.com> >To: <pianotech@ptg.org> >Sent: Wednesday, December 24, 2003 8:03 PM >Subject: Re: "Self tuning piano" questions >> Don, >> >> When you say "The method I use for pitch measurement is accurate to about >> 1/6000th of a cent at the low end of the piano", was that a misprint? >> That is equal to about one part in 10 million. Even at A-440, that means >> a difference of one beat in 6.3 hours! If you can read such a difference >> in under 10 minutes, then you must be able to detect a phase difference at >> A-440 of 9.5 degrees. But the note won't sound for that long without >> active stimulation. I have done active probing for resonsances similar to >> what you did for an article in the Journal, "Measuring Inharmonicity Using >> Continuous Excitation", June 1993. I found that the resonsant peaks, even >> when measured in this manner, are still too broad to define a resonant >> frequency to any better than about .02 cents. So 1/6000th of a cent is a >> bit beyond belief. >> >> Robert Scott >> Real-Time Specialties >I can indeed get that accuracy and I can do it in a few milliseconds, >believe it or not. You have made the assumption that frequency counting is >the only solution to determining frequency (as many in the past have). To >get 1/6000th of a cent takes a fast processor like we intend to use, but I >can (and did) do it with three simple chips from Radio Shack and still get >an accuracy of 1/200th of a cent and do it in 36 ms! >The signal from the pickups is super-clean (virtually no overtones). I >convert this wave to a square wave using a simple chip called a Schmitt >trigger ($0.16 at Radio Shack). Then, rather than count waves for a long >time to get a frequency, I determine the "period" (the time for one complete >vibration), which is just the reciprocal of the frequency and is just as >useful. >How do I get it so accurate? Well, if I'm willing to splurge another $0.86 >I can get a little 10 MHz crystal oscillator. This puts out 10 million >square-wave pulses each second and is ultra-accurate. Then for another five >bucks (this is getting expensive!) I buy me a programmable counter chip. >The counter chip has several independent counters that can count pulses this >fast. I use two of them. >The first one is a one-shot counter and I feed it the square wave from the >piano string and tell it to count to "one". The way the counter works (I >can get into more detail if you like), this produces an output pulse equal >in duration to exactly one vibration of the string. I feed this signal to >the "gate" of the second counter. All the gate does is tell the second >timer when to start and stop counting. So if I feed it my one-vibration >pulse it will turn the counter "on" for one vibration and then back "off". >What is it counting? The 10 MHz oscillator! Then I read the number out of >it to see what I got. What I get is how many times a 10 MHz oscillator >pulses during one vibration of the string. Do you see where we're going >here? >Let's use A-440 for an example. An oscillator pulsing 10 million times a >second would pulse >10,000,000 / 440 = 22,727 times >during one period of A-440. If I wanted a string to vibrate at exactly 440 >Hz, I would have to tune it until my counter read 22,727. And remember, the >time it takes to do this measurement is just one period, or >1 / 440 = 2.3 milliseconds. >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. >And it took >1 / 27.5 = 36.4 milliseconds >For about $6.00. >Actually I have found that an accuracy of better than a tenth of a cent or >so is futile since the string naturally wavers more than this even when held >at a constant volume. It's also far better than any but the finest ear >could detect. >Don A. Gilmore >Mechanical Engineer >Kansas City >_______________________________________________ >pianotech list info: https://www.moypiano.com/resources/#archives
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