Years ago, I built a marimba for my daughter, which was quite enlightening in terms of my understanding of overtones. partials and the harmonic series. As piano tech's and/or musicians, we are trained to think of the harmonic series as having a specific relationship to our modern 12-tone musical scale. Actually this is only true of columns of air, as generated by pipe organs or wind instruments. Once you enter the realm of sound generators with significant mass, the partials begin to distort, on the sharp side of what we are trained to expect. In string instruments, we call this inharmonicity, and we all know what that means in terms of tuning applications. With string instruments, where the mass is largely extended along one dimension, this phenomenon is nothing more that what we recognize as inharmonicity. In the case of tuning forks, marimba and xylophone bars, bells, and other instruments, the additional mass in the other two dimensions has a profound effect on the harmonic series, radically higher in frequency than we would expect from the afore mentioned instruments. You may have noticed that marimba and xylophone bars have an arch cut on the bottom side, and a secondary arch at each end of the primary arch. The purpose of these arches is not only to tune the fundamental frequency, but to bring the second and third partials into something close to being consistent with non-dissonant (consonant) frequencies of the modern 12-tone scale. When you remove material from the overall length, you primarily alter the fundamental frequency, but it effects the other partials as well. When you remove material from the primary arch, you primarily effect the second partial, .but it effects the other partials as well. When you remove material from the secondary arches, you primarily effect the third partial, .but it effects the other partials as well. The target ratios for the upper partials is different for marimbas than for xylophones. Any materials removed effects all three partial, but where you remove the material effect one over the other partials. It is quite a trick to remove just the right amount of material at just the right location to get all three partials right where you want them! Since the second and third partials are so much higher than wind or string instruments. anything beyond the third partial is insignificant, beyond the humanly audible range. Frank Emerson ----- Original Message ----- From: pnotnr at aol.com To: pianotech at ptg.org Sent: Wednesday, July 14, 2010 5:01 PM Subject: Re: [pianotech] Tuning fork puzzle I wondered that too, and at the risk of showing how much I don't know about this stuff, I ask the following: (and I understand that we are talking about a fork and not a string) But supposing the fork has a fundamental frequency of 100 bps, the octave (second partial) would be 200 bps. An octave above that (4th partial) would be 400 bps, and an octave above that (8th partial) would be 800 bps. I don't have a frequency chart in front of me, but figuring 6 1/4 times the fundamental (or 625 bps) would that correspond to the 6th partial? Gordon Large, RPT Maine -----Original Message----- From: Susan Kline <skline at peak.org> To: pianotech at ptg.org Sent: Wed, Jul 14, 2010 3:40 pm Subject: Re: [pianotech] Tuning fork puzzle >Now I am told that the first overtone of a tuning fork has about 6 >1/4 times the frequency of the fundamental, so where is this octave >coming from? Beg pardon? Do you mean 6 1/4 times the volume of the fundamental? -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://ptg.org/pipermail/pianotech.php/attachments/20100715/e2344e66/attachment.htm>
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