Dear Associates and other interested: In the previous 2 series, I discussed how to practice a small portion of the Baldassin-Sanderson Temperament on each tuning job you do, using the SAT. In this article we will consider how to absolutely nail the middle note, namely B3. In the last article I neglected to mention tuning the C#3 as an octave below C#4 and also as contiguous 3rds between A2 and F3. It's rather simple, just do it. Make the A2 M3rd balance with the C#3 M3rd Now we have the following notes all within .3 cents of where the SAT says they should be: A2 C#3 F3 A3 C#4 F4 A4 If we can accurately locate B3 and then tune down a 3rd and up a 3rd, we will have a whole tone scale of 3rds that can be perfectly even. | | D#4 / B3 / G3 The standard method of locating the B3 is to tune two contiguous 4ths up from F3 and two contiguous 4ths down from F4. If these are carefully done so that each beats exactly at 1 bps, then one can balance the B3 between the G3 and D#4 so that they, as contiguous 3rds will be in a 4 to 5 ratio, just as the F3 and A3 3rds are in a 4 to 5 ratio. The speeds may not be the same in relation to the previously tuned 3rds, but in respect to each other they must be in a 4 to 5 ratio. For beginners, this may be a little diffi- cult. And besides, it will be necessary to redo each of the 4 4ths. A simpler method is to do as Michael Kimbel and Fred Tremper have suggested to me. Tune 2 perfect 5ths, one down from C#4 to F#3 and the other up from A3 to E4, then tune B3 as balanced between F#3 and E4. One of the object- ions to this has been that the 2nd and 3rd partials of notes in this area are often a little irregular and may give unpredictable results because these are the partials which are used in 5ths. Never-the-less, it is possible to tune these intervals with more precision and you have half as many possibilities to go wrong as with tuning 4 4ths, and then trying to estimate the 4 to 5 ratio with decimal point accuracy. So, Tune F#3 from C#4 and check with the m3rd-M3rd test: F#3-A3 = A3-C#4. You may also use the other test: A2-F#3 = A2-C#4. Do the same for the A3- E4 fifth. A3-C4 = C4-E4 or C3-A3 = C3-E4. Both F#3 and E4 will need to be adjusted to tempered 5th later. Now tune B3 as a 4th above F#3 and as a 4th below D4, such that the two 4ths are equal. If anything let the upper 4th be only slightly faster than the lower 4th. This will positively nail down the B3 location. Check with the SAT to see that you are within .3 cents accuracy. Repeat this portion on each piano you tune for the next few days until you can come out within .3 cents of what the SAT calls for. After you tune G3 to B3 to balance equally between the F3 3rd and the A3 3rd and you tune the D#4 to balance the B3 3rd between the A3 3rd and the C#4 3rd, the A#3 can be balanced between the F3 and the D#4 as contiguous 4ths. The C4 can be balanced between the G3 and the F4 as contiguous 4ths. Now it is possible to retune the F#3 as a tempered 5th to C#4, as a tempered 4th to B3 and as a M3rd balanced between the F3 3rd and the G3 3rd. Next, we can retune the E4 as a tempered 5th to A3, as a tempered 4th to A4, as a M3rd to C4 to fit between the B3 3rd and the C#4 3rd. From here on to the finish of the temperament, it is just impossible to make a misteak (Oops). My suggestion is to use your SAT to tune everything up to the two trial 5ths, then practice tuning the trial 5ths and balancing the two 4ths contiguous to B3 until you can always come within .3 cents. >From thereon, you will have no problems. Guaranteed. But still, use the SAT to check on the remaining notes: G3, D#4, A#3, C4, F#3, and D4 to complete this series. When you can do all of these within .3 cents, you will have gained great confidence in your aural tuning abilities. BTW, I used this temperament in my preparation work for the Tuneoff in Chicago, but in the final tuning, I just used the machines SAT and RCT. For those of you who have the Reyburn CyberTuner, you can program in this USER TEMPERAMENT so that the machine will follow this order. Tune in tomorrow for part IV of this series: How to tune the last two notes of the F-F octave, and then the next day on how to complete the two octave temperament. It is amazing how much this is a self-adjusting temperament. You really don't have to remember any beats, just make everything fit as the piano talks back to you. Jim Coleman, Sr.
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