<!doctype html public "-//w3c//dtd html 4.0 transitional//en"> <html>   First of all let me thank all those who have contributed so far to a posting which seems to be digging up old ground for those of you who have studied these things from a much more advanced viewpoint then my education allows. My original posting was a request for data which showed the measured frequencies of all 88 notes for partials upto and including the 12th (preferably the 16th) partial. As always one thing leads to another and the issue of a beat counter as a tool in itself quickly came into play. These two are related and yet easily seperated as seperate issues and tools. As is their eventual usefullness or lack thereof . I'd like to review some of the disscussion with you all. As to the idea of a beat counter as a tool for direct use in tuning. >From what I understand the most telling argument against this approach is that with present technology such a device would require a wait time of at least 10 seconds for any result to be displayed. Clearly this severely limits such a tools usefullness. Other arguments against seem a bit less convincing to my mind. Given that such a device could be made to function quickly enough in regards to time, it would seem to me to be a valuable aid. One could for example quickly progress through such tests as contiugious intervals, thirds/tenths/seventeenths, and indeed all such tests and make the exact same judgments and decisions as aural tuners do every day. Yet even tho aural tuners have a miriad of checks and cross checks to accomplish this, there are moments of doubt that are encountered. Such a tool would provide an added assurance in such cases, and would probably serve to speed up the whole process, again given that its response time was quick enough. Now of course all that is a moot point if it simply cannot be done. The point that other existing tools accomplish the same thing from a different approach is another discussion which touches on issues such as who's making the decision, the puter or the person. As for the business of the complete frequency data. As I stated in my last response to Dr. Coleman. I ran into such a table in an old copy of the PTG Journal. Tho it was far from complete in the sense I am looking for. It did however provide some measure of understanding to things that have bothered me for years. It also instantly raised some new and more specific questions. According to the "theory" fourths and all coincidental partials they generate should become increasingly faster as one progresses up the piano registers. Further they should be "wide". Yet this is not the case. the 6-8 partials are wide (starting at C3), and decrease in wideness until at C4 they are beatless, afterwhich they become increasingly narrow.  This same applies to the octave taken as a 3-6. Also of note is the radical divergence from the theoretical of the octave taken as a 4-8. This (at c4)  coincidental beats (narrow) at 4.7 bps. One question that comes to my mind immediatly is how to account for this using the math for figuring frequencies based on string tension / stiffness. I ran into a three page discussion on this some years back and have spent the day looking for it. I may have to hunt that one down again on the net. :)  I wonder what a larger set of data would show, and if after looking at several sets what I could find out. Another question is one that relates to when we change over to different tests for different regions of the keyboard. For example just when in the treble do we start viewing an octave as a 2:1 octave type instead of a 4:2. I wonder if there is anything I can find in such data that relates or corresponds in any way.  These are questions that I want answers to. I do not find the answers written anywhere certainly not in enough detail to satisfy my "thirst". So I am out looking for them. My reasons for wanting / needing to know the answers to such things are perhaps hard to explain clearly. But put as simply as I can, it is to satisfy my curiosity, to prod my thinking processes, and to improve my understandings and expectations of the profession I have spent the last 25 years at. With each new influence through those years, I have improved, gotten better at balancing a tuning, learned to better hear and use controll intervals. Yet I am always left feeling I have a long ways to go. And through it all I never have felt like I have developed a satisfactory overall "picture" of what the "well tuned piano" really is.  Recent events in my professional life have pushed me in this direction, and knowing me as I do <smile> I am going to have to follow up until I get where I want to go. So again, if anyone out there DOES have such data assembled, and if it is no trouble to you, send it along to me. I am very interested in looking closer at it. Richard Brekne    </html>