Jim, Although I don't own an electronic tuning device yet, I really appreciate your articles. I have borrowed a SAT for a few weeks from a friend, and had the exact questions that you have been answering. My best wishes to you this Christmas season. doug richards Quantum Corp. San Jose, CA PS: Glad to hear you enjoyed your latest birthday! ______________________________ Reply Separator _________________________________ Subject: SAT Part 4 Altering Stretch Author: Jim <pianotoo@IMAP2.ASU.EDU> at SMTP Date: 12/22/96 8:32 PM This is #4 of 6 SAT Part4 Altering the stretch In the first three articles we have discussed the effect of altering the A4 stretch number of the three FAC's. One can take this to an extreme, but I would suggest going no farther than an additional 1 cent stretch, for this will provide a single octave stretch of 1/2 bps or more. This gets close to the limit which one can tolerate in the sound of the center single octave. If more stretch of the high treble is desired, then altering the C6 stretch number is required. For an example of this, let us create a Page 3 tuning using the FAC #'s 8.0, 8.5, 8.5. We then find a comparison between Pages 1, 2, and 3 as follows: C5 C6 C7 C8 Page 1 3.0 4.0 13.8 43.8 Page 2 3.2 4.2 14.7 44.4 Page 3 3.2 4.2 14.7 46.6 Now please remember that in increasing the stretch of A4 by ..5 cents, it was necessary to reset the SAT on the sharp side by .5 cents at the note C5 and another .1 cent at C6 so that the real values of the above should be: C5 C6 C7 C8 Page 1 3.0 4.0 13.8 43.8 Page 2 3.7 4.8 15.3 45.0 Page 3 3.7 4.8 15.3 47.2 Since the stretch is based on an exponential curve (steeper and steeper climb to the right), There is not any difference at note C7 in this example, but if one uses a higher addi- tional stretch like 2 cents for C6, you will see a more dramatic change in the numbers as shown in Page 4 where the stretch numbers are: 8.0, 8.5, 10.0 C5 C6 C7 C8 Page 1 3.0 4.0 13.8 43.8 Page 2 3.7 4.8 15.3 45.0 Page 3 3.7 4.8 15.3 47.2 Page 4 3.7 4.7 15.5 54.0 For pages 2,3, &4 the corrective reset of .5 cents at C5 and ..1 cents at C6 have been included due to the change of the A4 stretch number from 8.0 to 8.5. Now for an extreme example, let us take a 1 cent change at A4 and a 2 cent change at C6. Our FAC numbers will now be 8.0, 9.0, 10.0 and we will program this on page 5. Let us see first of all what the change in the A4 number creates. We will compare Page 1 with Page 5 in respect to the locations where the partial being used changes. B4 C5 diff. B5 C6 diff. Page 1 12.2 3.0 9.2 10.8 4.0 6.8 Page 5 13.0 3.2 9.8 12.4 4.1 8.3 ===== ===== .6 1.5 As a result of this, it is necessary to reset the SAT at plus .6 cents when you get to C5 and an additional 1.5 cents when you get to C6. You can see the exponential increase over the resets for the .5 increase of the stretch number for A4. Now let us apply this change to the readings of Page 5 in the following comparison. FAC's C5 C6 C7 C8 Page 1 8 8 8 3.0 4.0 13.8 43.8 Page 2 8 8.5 8 3.7 4.8 15.3 45.0 Page 3 8 8.5 8.5 3.7 4.8 15.3 47.2 Page 4 8 8.5 10 3.7 4.7 15.5 54.0 Page 5 8 9 10 3.8 6.2 17.0 55.5 >From the above you can see that varying the A4 stretch number makes more difference than varying the C6 stretch number except in the upper top octave. You can apply these above principles on any piano if you desire to change the amount of stretching of the octaves. There is one other type of change for the treble which needs to be addressed and that is where you wish to compress the octaves for some reason. One example that comes to mind is in taking the PTG test. Since one of the requirements for the top octave is that they be tuned in simple 2-1 fashion, that is where the C7 is in tune with the 2nd partial of C6. For this purpose, one could decrease the normal C6 stretch number which in turn would decrease the cents especially in the top octave on an exponential basis. The location of C6 would normally fall within the tolerance range anyway, but by choosing a slightly smaller number for the C6 stretch value, it would in effect tend to flatten out the normal exponen- tial upward curve from C7 to B7. Here is an example of decreasing the C6 stretch number by 1 cent: FAC's C5 C6 C7 C8 Page 1 8 8 8 3.0 4.0 13.8 43.8 Page 6 8 8 7 3.0 4.0 13.8 39.2 A much simpler way to tune the top octave for PTG test purposes would be to tune C7 to the 2nd partial of C6, and continue in like fashion up to B7. It is my opinion that those who do the master tuning, should use this same method since there is the ARBITRARY requirement that the examinees be judged on this basis. Aural tuning IN THIS AREA brings with it more variance than does electronic tuning. In the next article, we will explore the possibilities of varying the F3 stretch number and its effect on the Bass and Tenor areas. Jim Coleman, Sr.
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