Hi Kent: In my opinion you have made a large mistake in your analysis of what should be done to tweak a SAT tuning. Below, you mentioned that you had to set the B2 of the GH1 5.5 cents sharp. That's the wrong way to go to try to fit in a note with extremely high inharmonicity. You seem to forget that the high partials are still going to be there no matter where you tune the 3rd partial or the 4th or the 6ths partial. As you know I have used the RCT quite extensively just as you have. If one looks only narrowly at a few partials, he misses the best balance. It is my experience using the RCT that better control can be had using the 4th partial in the range under consideration. I long ago quit using the 3rd partials for tuning even though it would make 6-3 tuning easier in the Bass. From my experience using the SAT and FAC calculations, I offered an approach for tuning pianos similar to this one. This was posted on the Ctuner list and the example I used was from tuning an Acrosonic spinet. Yes, it is true that one will have some 5ths which are on the wide side instead of the narrow, but this gives better octave and double octave, Octave-5ths, etc. You made a point of showing that the RCT has something to teach the SAT. Actually the reverse is true. The FAC tunings on the new SAT III are the same as on the SAT II or the SAT I. However, the Double Octave Beat control enables one to tweak notes individually and still maintain a semblance of the exponential curves. As I have explained before, when you see the hockeystick type curve at the bottom of the treble bridge, you know that some tweaking is going to be in order. I'm afraid you have left the impression that with the RCT there is no tweaking required. You know quite well that this is not true. Outside of the Unison, the most consonant intervals are the Octaves, Double Octaves and the Triple Octaves when the overall intuneness is considered. When we get hung up on only the 5ths or the 4ths or the 3rds, any one of these, we miss the boat. Piano tuning is a compromise from the beginning to the end.The best compromise considers many relationships. If you were to tune the A#2 and the B2 using the RCT with no tweaking, the B2 M3rd would be very slow and the A#2 M3rd would be very fast. Here is a little advice from the SAT experience to the RCT needs. If you gradually begin adding negative resets as you go down the scale from the point where the hockey stick shape of the treble bridge begins, you can smooth out the scale a little better. Since the foreshortened strings in the hockey stick area have greater inharmonicity, the lower partials need to be lowered in order for their higher partials to fit the rest of the piano better (note that we are no longer using the myopic view of just the lower intervals). This may come as a shock to some who worry about the 5ths going on the wide side, or the 4ths being slightly faster, But when music is listened to, it is the overall intuneness which matters the most. Musicians do not listen to the piano the same way we tuners do. This is why musicians listening to the Historical tuneoff last summer chose Bill Bremmer's MMT tuning over equal temperament. He wisely made his wider relationships more in tune. It gave his piano a greater sonority. The Gh1 is a good piano. It has the same inharmonicity mismatch which we have all seen in such pianos as the Acrosonic spinet, the Wurlitzer spinet, Kimball spinets, Winter spinets, but, in this case the problem is lower in the stringing scale. Spinets deal with this problem usually around F3, F#3, G3, G#3 etc. On the GH1 it climaxes at A#2 to B2. In my opinion, the best compromise in all of these cases is to lower the notes which have extreme relative inharmonicity with a slight raising of the upper wound strings at the stringing break whether it occurs between the Bass bridge and the Tenor bridge or if the break occurs only on the treble bridge. Usually it is not necessary to raise the highest wound strings if they lie on the Bass bridge because here there is a good opportunity to foreshorten the upper Bass strings which results in a little higher inharmonicity and therefore matches the lowest plain strings a little better. However, in this case of the GH1 we can see from your data that even though the A#2 has high inharmonicity for that section of a piano, it still does not match the amount of the B2. We also note that the inharmonicity of the B2 is more uneven in the lower partials (very little difference between the 1st and 2nd partials, and then a big jump to the 3rd partial. Now on the otherhand, there is a smooth rise of inharmonicity of the first several partials of the A#2, but then the 5th, 6th and 7th partials are much more alike. This kind of irregularity is quite common in Bass strings. For the irregularity of the B2, I have always thought of it as having something to do with the lower tension of foreshortened strings and bridge end-effect. I think Dean refers to this as para-inharmonicity. The above problem has nothing to do with RCT or SAT, but will always require a little tweaking during the tuning procedure.It is my contention that it's more easily dealt with using the SAT III Double Octave Beat control. This feature is given this name because the basis of FAC tunings is in the control of the double octave. Of course this affects individual single octaves. The D.O.B. can be invoked anywhere on a note to note basis "on the fly." Most pianos except the ones mentioned above should have tighter octaves than the FAC gives (FAC tuning spread was based originally upon the tuning required for a Steinway D). Since most pianos are smaller, it is wise to reset the Bass perhaps as much as 1 cent higher beginning at B2, then gradually erase that correction as you tune lower and lower into the Bass. The piano under consideration in this post however needs to be gradually lowered all the way down to B2 and then not lowered at all beginning at A# and on down. By using the DOB with a plus .1 beat widening beginning somewhere around E3 and increasing DOB .1 cent for each note or 2, the beat of the M3rd can be kept up fairly well, the octave will be stretched a little more than usual, the 4ths will become a little wider, the 5ths will go to zero and eventually wide, the single octaves will be widened, the double octave will be widened, the octave 5ths will sound good and the triple octaves will be more tolerable. This I believe gives a better balance for this particular piano, but the principles would work on most any piano. Kent, since your approach to tweaking was in the opposite direction, perhaps a tuneoff would be required to determine which way sounds better. However, having used the RCT and the SAT, I believe the SAT handles it much more easily. Jim Coleman, Sr. On Wed, 7 Oct 1998, Kent Swafford wrote: > >...What differences there may be would be so > >small that it would not be discernable. I predicted the same before Virgil > >and I went after it. Then, there would always be the arguments that, it > >wasn't the machine, it was the operator. Well, it would at least make for > >a lot of conversation. There wouldn't be a dime's worth of difference. > >Kinda' like the difference between Republicans and Democrats who spend a > >lot of agitation over whose ox is being gored; they both equally want > >your money and power. > > > >Jim Coleman, sr. > > The fact is that the particular VTD being used may make a substantial > difference in the quality of the tuning of a given piano. It would be > interesting to see if that difference would be substantial _enough_ to > make a difference in the outcome of a tune-off. VTD's vary greatly in > their tuning calculator functions; when one speaks of comparing the > tuning capabilities of SAT and RCT, for example, one is, for the most > part, speaking of the differences between the SAT's FAC and RCT's > Chameleon 2. > > RCT's Chameleon, as good as it has been now for some time, is still in a > constant state of development and can be incrementally improved as new > discoveries are made that can improve its performance. The FAC of the SAT > III is apparently mostly unchanged from the SAT II, adding only the > ability to widen/narrow the 88 note tuning as a whole. (RCT's Chameleon > allows any octave within the 88 note tuning to be widened/narrowed > individually.) > > An example of a specific SAT/FAC tuning problem follows: > > A goodly portion of my career during the past few years has been the > servicing of a single piano, a Yamaha G1R, in a jazz club. The G1R is a > 5' 3" grand with plain-wire all the way down to B2. The tenor break is > horrendous. How do I know this? Here are the RCT Pianalyzer numbers which > document the inharmonicity of the highest wound string and the lowest > plain-wire string, the two notes on either side of the break: > > A#2 B2 > 12th ptl = 20.7 cents 12th ptl = 46.6 cents > 10th ptl = 15.9 cents 10th ptl = 33.0 cents > 8th ptl = 10.8 cents 8th ptl = 22.4 cents > 7th ptl = 8.6 cents 7th ptl = 17.4 cents > 6th ptl = 7.2 cents 6th ptl = 13.5 cents > 5th ptl = 6.2 cents 5th ptl = 9.9 cents > 4th ptl = 6.1 cents 4th ptl = 8.4 cents > 3rd ptl = 4.1 cents 3rd ptl = 5.5 cents > 2nd ptl = 1.8 cents 2nd ptl = 0.2 cents > 1st ptl = 0 cents 1st ptl = 0 cents > > Wildly high inharmonicity on B2, and relatively low inharmonicity on the > A#2 right next to it! I am not picking on Yamaha; as a matter of fact, I > strongly recommend Yamahas to my customers. (Two of my customers bought a > C1 and a C2 respectively during this past summer on my recommendation. > OK?) But there are some scaling, uh, weaknesses in the small Yamaha > grands which I am familiar with because I tune so many of them. The tenor > break in the current production GH1, which also has a plain-wire B2, is > as bad as any piano that is commonly seen by tuners, hence my comment a > few days ago that using GH1's for a tune-off would "tell the tale." > > I have been tuning the jazz club G1R since before RCT and this piano > (with a few others that are similar) is the reason that I "outgrew" FAC. > FAC tunes B2 at its 6th partial. A quick comparison of the two 6th > partial readings above will suggest that there may be a problem if both > of these notes are tuned from the curve drawn through the 6th partials. > The high inharmonicity of B2's 6th partial would leave the 5th, 4th, 3rd, > and 2nd partials too flat. Way back when, I tweaked the tuning of B2 and > saved it, and I still have that tuning in my SAT. I find, looking at the > tuning now, that I had to raise B2 5.5 cents away from the FAC reading, > which means, as far as I am concerned, FAC made a gross tuning error on > this one note. (The scaling may be gross too but that is another matter.) > > RCT's Chameleon 2, on the other hand, tunes B2 from the 3rd partial and, > as calculated for this same G1R, the RCT-calculated reading for B2 is > about the same as in my _aurally corrected_ FAC tuning. In other words, > where FAC makes a gross tuning error, Ch2 makes no error at all. Tuning > and taking measurements of the lowest plain-wire strings on a piano like > this are very difficult. The strings exhibit remarkable instability. > However, FAC's error on B2 on this piano and on current production GH1's > appears to be in the area of 5-8 cents. > > I have been preaching the benefits of tuning the tenor plain-wire strings > from the 3rd partial as RCT can do. Here is a review of those benefits: > > There often is aberrantly high inharmonicity in the lowest plain-wire > strings, often associated with a hockey-stick shape of the tenor end of > the long bridge and the resulting short speaking length of these lowest > plain-wire strings. > Tuning these strings from the non-octave 3rd partial in the tenor > _automatically_ splits any "unanticipated" inharmonicity between the 2:1 > and 4:2 octaves. In other words the octave is automatically compromised > between two important sets of coincident partial pairs. > Tuning the lowest plain-wire strings from the 3rd partial will mean that > the 3:2 fifths formed between these strings and the notes above will be > clean. (If they are tuned from the 4th or 6th partial, the third partial > may be flat and the fifth formed above the note may be expanded instead > of contracted.) > The most common way of tuning octaves in the bass is with the 6:3 > relationship. If the bass notes are tuned at the 6th partial as is common > in RCT, and the plain-wire strings are tuned at the 3rd partial as they > can be with RCT, then the important 6:3 relationship will be preserved by > direct-interval tuning even when the inharmonicity is unexpectedly high > in the lowest plain-wire strings. > > I am not anti-SAT by any means. But FAC makes an error in the specific > situation of the B2 of some current model pianos. The error is the > unfortunate result of FAC's tuning the bass notes up through B2 from the > 6th partial, and some piano's plain-wire high-inharmonicity tenor > extending down to B2. An SAT work-around is in order and I believe that > there is one. This workaround has been suggested by my experiences with > RCT. (Yes, I am suggesting that knowledge gained from RCT can help SAT > tuners.) > Let's assume that one tunes up from A0 chromatically to C8. As mentioned, > FAC tunes the bass notes from the 6th partial. If one suspects that there > may be high inharmonicity in the lowest plain-wire strings as in the B2 > described above, when the tuner has tuned up through the wound strings, > one could first tune B2 to its normal FAC reading, then hit the Octave > Down button. The 6th partial "octave-down" reading will be at the _3rd_ > partial of B2; if the display is spinning "flat" when reading B2 at the > B1 reading, that means that the 6:3 octave is contracted by the amount > indicated by the rate of spin. We usually expect this 6:3 octave to be > stretched. One could raise the plain-wire string until the 6:3 is > slightly stretched, perhaps matching the spin-rate difference between > B1-B2 to the spin difference of the next door A#1-A#2. Such a procedure > (that is, tuning B2 just slightly sharp of the B1 reading) might allow > SAT tuners some of RCT's benefits of using the 3rd partial in the tenor. > > Although it might be preferable just to go ahead and buy RCT. <big > grin!> > > Thanks for reading, > > Kent Swafford >
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