Hi richard: The F, A, and C were chosen for very important reasons. If you know what the inharmonicity of F3 is and can locate that note, you know how you want to tune Bb0 (it is the 6th partial of Bb0). If you know the inharmonicity of A4, you can accurately locate A4, A3, A5, A6 and A7. If you know the inharmonicity of C6, you can locate C6, C7, and C8. If you can locate all of these, then you can do a mathematical smooth curving of the plotted points and have a complete tuning for the piano. Sure, you could measure all of the notes and make a more precise tuning (maybe), but it is not practical except in Lab work. It takes a very lengthy computer program to do this. There is another wise choice Dr. Sanderson made in choosing these notes and the partials by which all notes are to be tuned. The Bass is tuned from A0 thru B2 using the 6th partials. The section from C3 thru B4 is tuned using the 4th partial. The section from C5 thru B5 is tuned using the 2nd partial. In each of these section these are the most important and usually the strongest partials to be heard. The reason for measuring the difference between the 4th and 8th partials of F3 is because you get more consistent answers as to the the general inharmonicity of that note. The same goes for the A4 (using 2nd and 4th partials) and for C6 (using 1st and 2nd partials). There is no attempt to try to tune the 5ths. If the scale of the piano is rather decent, they will come out pretty good. If the scale is not good, you cant do much better anyway. Oh sure, you could give more attention to the 5ths, but this would be at the expense of consistency in 3rds, double octaves, 10ths etc. You can't have it all on a poor scale even as "you can't make a silk purse out of a sow's ear". Once an inharmonicity curve is plotted, you can tune any note by any partial you wish. Just think how many intervals are controlled by the 4th partial which is used in the most critical part of the tuning. Octaves (4-2 relationship), M3rds (4-5 relationships), 5ths (6-4 relationships), P4ths (3-4 relationships), m7ths (4-7 relationships). I just can't think of any other partial which affects so many intervals. Oh, I forgot Double Octaves (4-1 relationships). Tuning Octave 5 by the 2nd partials gives more accuracy than tuning by the fundamental. Above that, the fundamental is strongest and best to tune by. On Sat, 22 Aug 1998, Richard Moody wrote: > Hi Jim > Hmm across the board they were off one cent give or take .2 or .3 cents. > It looks like A4 dropped a little. But not enough to call for a pitch > raise.... > > You wrote... > > > For those who are not familiar with FAC numbers used with the SATs, the > > first number represents the difference between the 4th and 8th partials > of > > the note F3. The second number represents the difference between the 2nd > > > and 4th partials of A4. The third number represents the difference > > between the 1st and 2nd partials of C6. > > > Jim could you explain for us "donkey cart tuners", (I hope you appreciate > that ; ) (OK so it seems I put my foot in it ) why F3, A4, and C6 were > chosen for the FAC, and why the difference between such a wide range of > partials beginning with the 4th and 8th partials of F3? > From theory F to C is a fifth which is sounds 3 partial to 2 partial. How > come a third partial isn't measured? > > Actually you don't have to explain as from what I have heard of the FAC > formulation, these machines seems as accurate as the ear, and I am sure > there are demonstrations that prove that either is superior, or both are > better. > As an aural tuner, I am wondering how you feel about the choice for > partials that are measured in the FAC. > > Richard Moody > > ps You wrote > > > When I came back today to do the fine tuning, they were: 14.5, 8.0, > 5.7. > > The change is not due to the strings getting longer, but shorter if > > anything. The diameters did not change. The bends at the terminations > > may have changed slightly. I still think that it has something to do > with > > the soundboard loading. > > My guess is, if the soundboard presses up on the strings a little more > they go sharp. If the crown dips a miniscule, the pitch drop it seems can > be detected by machine... If the cabinet door sticks in wet weather, I > wonder what the sb does. > Actually in this case the strings pressed down upon the soundboard harder. This puts the soundboard under greater compression. This changes the impedance match or mismatch. I believe as this changes, more energy is absorbed by some partials, and less energy goes into other partials. The lower numbered partials seem to wobble more than the higher partials do. If you view a bar graph of the partial strengths of the various partials, you can see that more energy goes into some partial than in others. I could go on and on, but I might only be guessing at this point. Jim Coleman, Sr. > Richard Moody > > > > ---------- > > From: Jim Coleman, Sr. <pianotoo@imap2.asu.edu> > > To: Richard Moody <remoody@easnet.net> > > Cc: pianotech@ptg.org > > Subject: Re: Inharmonicity > > Date: Friday, August 21, 1998 5:03 PM > > > > Hi Richard: > > > > When a partial is flatter than its theoretical harmonic, we know that > > something unusual is going on. Dean Reyburn invented the word > > para-inharmonicity to cover a multitude of these kind of sins. I suspect > > > that it has something to do with soundboard movement. > > > > Perhaps related to that is something I documented today on a > pitch-raising > > job. The FAC numbers I measured before pitch raising were: 15.3, 9.0, > 7.0. > > When I came back today to do the fine tuning, they were: 14.5, 8.0, > 5.7. > > The change is not due to the strings getting longer, but shorter if > > anything. The diameters did not change. The bends at the terminations > > may have changed slightly. I still think that it has something to do > with > > the soundboard loading. > > > > For those who are not familiar with FAC numbers used with the SATs, the > > first number represents the difference between the 4th and 8th partials > of > > the note F3. The second number represents the difference between the 2nd > > > and 4th partials of A4. The third number represents the difference > > between the 1st and 2nd partials of C6. > > > > Jim Coleman, Sr. > > > > PS the amount of flatness observed for the second partial on some pianos > > has usually been on the order of .5 cents. For pianos with the 1 inch > over- > > wrap at the bridge ends, it has been more extensive and it has affected > > more than just the second partials. I have also seen a few cases where > the > > 3rd partial was flatter than the 2nd partial. Usually everything smooths > out > > by the time you get the 4th and 5th partials. This is my primary reason > for > > not tuning by 3rd partials in the tenor area. JWC > > > > On Fri, 21 Aug 1998, Richard Moody wrote: > > > > > Hi Jim > > > > > > >>There are two > > > 7' pianos in which the second partial of C5 is flatter than the > > > fundamental.<< > > > > > > The second partial of C5 is FLATTER that the fundamental? You mean > it is > > > flatter from 2x the fundmental.?? > > > What pray tell could cause that? It seems that in piano wire with > > > stiffness being a factor of ih, all partials MUST be sharp. > > > How much flatter? > > > > > > Richard Moody > > > > > > ---------- > > > > From: Jim Coleman, Sr. <pianotoo@imap2.asu.edu> > > > > To: Richard Moody <remoody@easnet.net> > > > > Cc: pianotech@ptg.org > > > > Subject: Re: Inharmonicity > > > > Date: Thursday, August 20, 1998 12:52 AM > > > > > > > > Hi Richard: > > > > > > > > The variations of inharmonicity especially in the lower numbered > > > partials > > > > is something which can be seen even in plain wire strings. There are > two > > > > 7' pianos in which the second partial of C5 is flatter than the > > > fundamental. > > > > This is most unusual. > > > > > > > > More variation is observed in wound strings in general. The most > weird > > > thing > > > > is found when the copper wrap is over wrapped for about one inch at > the > > > > bridge end of the strings. This often causes more than just the > second > > > > partial to be flatter than the fundamental and makes tuning by any > means > > > > utterly impossible. This phenomenon was witnessed on one of the most > > > > prestigious 6' piano in the world. > > > > > > > > Jim Coleman, Sr. > > > >
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