From: pianotech-bounces at ptg.org [mailto:pianotech-bounces at ptg.org] On Behalf Of PAULREVENKOJONES at aol.com Sent: Friday, March 13, 2009 6:32 PM To: pianotech at ptg.org Subject: Re: [pianotech] Aurally pure octaves Nick, et alia... Virgil's first impulses in this direction came somewhere about 15 years ago as a resistance (for whatever reason) to the ETD's use of "single" partial reading and coincident set selection. I surmised at that time that what he might be referring to is also reflective in speech recognition physics, the phenomenon of "formants" which are the two, three, or four major frequencies of a given person's "voice", blended as one into a recognizable individual. There is in this also a "dominant" frequency which defines the blend, and this may also be the "resultant" of which you speak. Yes, this is a fine analogy, except that the singer's formant is primarily related to blending vocal harmonics for a desired resonance. Still, the analogy holds well. It is still in the piano a coincident set of partials which establish this most audible (by practice and recognition) of frequencies, whether we recognize it at the pitch at which it is happening or not. Yes, I agree with the second half. Yet I am not so sure that, across the board, the partials establish the most audible of frequencies for all of us; maybe for you and many others. From an energy perspective, the higher partials contain the least energy. The force of the Fourier, however, contains the composite effect of all the energies. Each string contains an entire package of superimposed frequencies. The Fourier blend sounds like a single tone to the uninitiated or lay person, if you will. We tuners should be able to zero in on the coincident partials relative to the interval, yet appreciate the integrated effect of the whole. I personally no longer hear the pitch of the beating, just the beating. Exactly - sounds like whole tone or whole sound listening here. I hope you're OK with that :-) I can easily figure out the pitch which it should be since I know the interval ratios and what they imply. Focusing on the partials as a skill set of useful tools. But it is "recognizable" as the sound I want to hear; it defines, whether it is discrete, formant, or resultant mathematically, the character of the interval that I am trying to create. Exactly - again and quite pragmatic: sounds like whole tone or whole sound listening here. Wherein, in all this, lies the difference between us? Is this a question for me, or does the "us" imply a dichotomy of entrenched camps where never the twain shall meet? I frankly don't see a real difference, but apparently there is a perceived one for some folks. I think it is useful to be aware of both harmonic dissection followed by integration for whole tone listening. NICK In a message dated 3/13/2009 8:04:23 P.M. Central Daylight Time, gravagnegang at att.net writes: William et al, I remember a tuning class held at a large chapter meeting. Intervals were played and the beats were obvious to both newbies and veterans. Adjustments were made and we could all hear the beats speeding up and slowing down. A fine temperament was set by adjusting the beat rates for even thirds and sixths, and "quiet" fourths and fifths. A young man asked about coincident partials: "where exactly do they line up?" The instructor said he used to know but wasn't sure; there was some head-scratching in the room of 35 attendees, but a few had the answers. "You've been reading Braid White's book, haven't you?" Virtually all the veteran tuners adamantly opined that it is best to listen to the "obvious" beats, those we had been listening to during the demonstration. These obvious beats "sounding" at the fundamentals are what this list is now calling "whole tone" or "whole sound" listening or tuning. That chapter meeting was held in New Jersey in 1973 and I was among the newbies. I learned to tune by hearing the whole package, although later on I was pleased to isolate the partials. Tuning then became a balancing act of checking the whole sound with the partials of choice. Virgil Smith is not a mathematician, but he had latched onto the concept of resultant forces. Ten forces of different magnitudes pulling an object in many opposing directions can all be reduced to one significant force --- the resultant force. And the object will move steadily in one direction and at one speed. The energy force in a vibrating string divides itself up among the multitude of partials; many sine waves superimpose themselves. The famous French mathematician J. Fourier (1768 - 1830) analyzed this phenomenon and gave us the famous Fourier curve, the single resultant curve/force that essentially represented the integral (the whole) of the many constituent superimposing partials, including the fundamental. The single curve does not look like a simple sine wave; rather it is bumpy and strange yet periodic. For fun, go to http://id.mind.net/~zona/mstm/physics/waves/standingWaves/standingWaves1/Sta ndingWaves1.html and see a violin string animation of the Fourier curve as the resultant wave (the white wave) of partials. You have to build the Fourier pulse by clicking on the partial selections. These curves do not simply exist for the convenience of study, they point to the reality of our physical universe. The simple act of standing up amounts to the resultant force of a multitude of smaller forces, equilibriums and gravity. Fortunately, we do not need to analyze these to simply stand up. What is true of physical mechanics is true of sound. Now if the temperament note F exists as a single resultant curve, and A above it the same, then the superimposing of these two single waves running along a time plot will indicate an interference of 7 bps, and all this will be experienced by the ear at the fundamental level. Even more fascinating, the F and A will coalesce into its own single resultant curve, also periodic in nature. The relatively small energies that exist at the higher coincident partials could not possibly affect the intensity of the beating effect we have at the pitch frequencies unless the whole tone resultants are interacting. And yet more mind boggling is that a single resultant curve exists for a sustaining chord played in different positions up the keyboard. There comes a whole brilliant swirling and shimmering sound, but shot through with tiny laser beams. Only piano tuners and certain musicians can surgically dissect these. It seems to me there must be a study or lab experiment that demonstrates this reality. RicB: it is not a stretch to borrow from the world of higher mathematics and refer to partials as "derivatives" and to the combining of all these derivatives as the "integral". Math purists might balk due to the implied functions, but relative to our discussion, we would then have Derivative tuning as partial-focused, and Integral tuning as whole tone, Fourier tuning. These sterile terms lack warmth, but they point theoretically in the right direction. Regards, Nick Gravagne, RPT Piano Technicians Guild Member Society Manufacturing Engineers Voice Mail 928-476-4143 _____ -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://ptg.org/pipermail/pianotech_ptg.org/attachments/20090313/e8e97a2e/attachment.html>
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