Ed, Quite right RE the evaluation of the sine waves. But whether or not they are harmonic or inharmonic isn't the rallying point. Fourier curves and resultants can be plotted with any emanation of sound be it a piano tone or a kettle drum or a dropped piano. Resultant waves relative to two or more sounds can always be plotted and don't have to line up neatly at all, nor do they have to be periodic. Same is true for all physical forces of push and pull. You are correct in pointing out the complicating inharmonicity issue. In fact, inharmonicity in small pianos is what originally hooked me on honing my partials-listening skills. The compromises between integral tuning and it derivatives are great and many. But more than a few of my tunings were saved as I was able to focus on the partials as they presented the least of many evils. Not only the coincident partials, but all the non-coincident partials all forge a sense of singularity, and all play major and minor roles in the outcome of interval tuning, like a symphony of frequencies. But as I said in other posts, I am neither for nor against anyone's methods or listening protocols. Isn't it useful to dissect it right down to the marrow (if that turns you on), and then completely flesh it out again? Some of us will come done harder in one camp than the other. I don't know if there are implications for piano tuning, but there are definite implications for piano tuners. There are lots of different and yummy looking choices at the salad bar. Which do you like? Ciao for now. Nick Gravagne, RPT Piano Technicians Guild Member Society Manufacturing Engineers Voice Mail 928-476-4143 _____ From: pianotech-bounces at ptg.org [mailto:pianotech-bounces at ptg.org] On Behalf Of Ed Sutton Sent: Friday, March 13, 2009 6:58 PM To: pianotech at ptg.org Subject: Re: [pianotech] Aurally pure octaves Nick- There is a problem with this image: it is a demonstration of a harmonic series of sine waves, such as would be found on a Hammond organ. Piano partials are inharmonic. They are not going to line up to produce a nice resultant wave that co-ordinates perfectly with the fundamental. The resultant wave is chaotic and not periodic. I don't know exactly what the implications are for piano tuning, but I suspect it means the co-incident partials play a somewhat larger role in the physical picture. Ed Sutton (back to planing wood) ----- Original Message ----- From: Nick Gravagne To: pianotech at ptg.org Sent: Friday, March 13, 2009 9:01 PM Subject: Re: [pianotech] Aurally pure octaves 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 _____ From: pianotech-bounces at ptg.org [mailto:pianotech-bounces at ptg.org] On Behalf Of William Monroe Sent: Thursday, March 12, 2009 7:13 PM To: pianotech at ptg.org Subject: Re: [pianotech] Aurally pure octaves SNIP I was drawn to the idea that tuners need not listen to beats at their specific pitch levels, since I am one the tuners who has never heard coincident partials at a their actual pitches. Whole sound tuning is where it's at. It is not secret knowledge. I'll be attempting to demonstrate next week at the Central-West Regional Seminar in Wichita. Kent Kent, Can you explain this more clearly? I know it's been (re)hashed many times and, recently, but, where DO you hear the coincident partials if not at their specific pitches? I'm more than open to learning/experiencing this technique, and I've no doubt standing behind you (Virgil, DA, etc.) would be far more instructive, and I intend to do that at GR if DA gets it going; but for now, are you just listening to "everything presented" at once? Or is it something different, specific to partials, but with a slightly different focus? William R. Monroe -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://ptg.org/pipermail/pianotech_ptg.org/attachments/20090313/a80386ca/attachment.html>
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