Mapping the Treble with Templates and a SAT 980
Mapping the treble uses information found when the A4 numbers were measured, and a completed mapping of the prime octave: A3, D4, E4, & A4.
Once the prime octave has been mapped and A3 and A4 have been tuned using the mapping settings, A3 and A4 can easily be used to find a beginning mapping location number for A5. Simply set the SAT to A5 and alternately play A3 and A4 and observe the rotation of the lights.
When A4 is played, the light rotation gives us a ‘view’ of the A4/A5 2:1, and when A3 is played the light’s rotation gives us a view of the A3/A5 4:1 double octave.
Since both of those single and double octaves should be wide, the lights should rotate counter clockwise when each of the reference notes (A3 & A4) are played. Just how fast that rotation should be, is not known yet.
But looking at the cents setting in the SAT will let us know about how wide the A4/A5 2:1 octave will be if we were to tune it to the setting that would put both 2:1 and 4:1 slightly wide.
Since A4 was tuned to A440 which means to it’s fundamental or A4, A4 starts @ 0.0 c.. If the SAT is set to A5, and the cents reading is 2.3 when both A3 and A4 are played alternately with the lights rotating slightly counter clockwise on each, tuning A5 to that setting would result in a 2.3 c. wide 2:1.
Since A3 has already been tuned, and since when tuning A3, the SAT will be using A3’s 4th partial, if the tuning setting for A3 is known to be 1.5, tuning A5 to 2.3, would result in a .8 c. wide 4:1.
By looking at these numbers, if A5 is tuned to 2.3, we would end up with a .8 c. wide 4:1 and a 2.3 c. wide 2:1.
So tuning A5 to that 2.3 setting will be a good place to start for A5. It may get changed slightly a little later on in the mapping but for now, that 2.3 setting will be a good place to start.
Using A5’s setting to find a good starting point for A5:
Now that we have a starting point for A5, a good guess can be made for the starting point location of A6.
For this we will use more information found in the A4 numbers and again, the completed mapping information and tuning of the prime octave (A3, D4, E4, & A4).
The Double Octaves: A3/A5 and A3/A6
We know that both of these double octaves should be tuned wide. But we don’t yet know how much. At this point all we’re looking for is a good guess, a starting point that will be used to select a template we can use to do some tuning and some aural checking.
Using the above mapping for A5, revealed a A3/A5 double octave width of .8 cents. The A4/A6 double octave should be wider than the A3/A5 double. Again, how much is not known yet, but a guess can be made that will get us in the ballpark close enough to select a template that can be used to do some tuning and check the locations of both A5 and A6.
If the A3/A5 octave is .8 c. wide, a good starting point for the A4/A6 octave might be 1.5 c. wide.
So how do we come up with a cents setting for A6 that will give us a 1.5 c. wide A4/A6 double octave?
Using the A4 number info makes it an easy calculation.
When the A4 numbers were measured, the 4th Partial location of A4 was learned. Since the 4th partial is used for tuning A4, that 4th partial location of A4 is the tuning setting for A4. So if the 4th Partial of A4 was measured to be 9.2, the tuning setting for A4 is 9.2 – which puts A4 @ A440.
If A6 were to be tuned to 9,2 the A4/A6 double octave would be pure. But we don’t want that, we want the A4/A6 to be 1.5 c. wide. So, instead of tuning A6 to 9.2, 1.5 c. is added to 9.2 to give us a starting point setting for A6 of 10.7.
Now we have a setting for A5 (2.3) and A6 (10.7).
Using those two settings, a template can be selected for doing some tuning and some aural checking to see how close we came.
The Treble Templates are organized by A6 numbers, so the A6 number will be the 1st priority for selecting a template, and then the A5 number will be used to further refine the template selection.
Once the Template has been selected and the SAT 980 is now on the page in memory that contains that template, we’re ready to do some tuning and some aural checking to see if we have the best locations for both A5 and A6.
Once the template has been selected that has A6 @ 10.7 and A5 @ 2.3, it is time to tune A5 and check it’s location. For this I tune A5 and then D5 and E5 to the selected template.
Now not only have the prime octave notes been tuned (A3, D4, E4, and A4), but now D5 and E5 have also been tuned and can be used to check the location of A5.
The checks most useful are the A4/E5 and the D5/A5 5ths. They will tell us very quickly if A5 is stretched correctly. If either of those 5ths are too noisy, A5 probably needs to be a little bit higher.
The D4/D5 and E4/E5 single octaves and the A3/A5 double octave are good checks too, as is the D4/A5 12th. But the main ones that art eht most helpful are the A4/E5 and the D5/A5 5ths.
If those 5ths tell us A5 is not sharp enough, a different template can easily be selected. But since we need A5 to be a little higher, A6 will also need to be a little sharper as well.
If this first template had A5 @ 2.3 and we want A5 to be sharper, we may want to raise A5 by .5 c. That means we want to use a template that has A5 @ 2.8. Since we’ve raised the A5 target by .5 c. it would probably be good to raise the A6 target by at least that much – maybe .8 or 1.0 cents higher than the 10.7 number.
So now we can select another template, this time with an A5 of 11.5 and an A5 number of 2.8 c.
Now re-tune A5, D5 and E5 to that template and give the 5ths a listen. I don’t do any 5th width measuring here. I just listen to those 5ths. Once I think I like them I check the single octaves, the double octaves and the 12th, and when everything is right, it all should sound pretty good.
Now I know I have a really good setting for A5.
Using that same template, I tune A6, D6, and E6, and listen to the D6/A6 and the A5/E6 5ths. If I want to raise A6 higher, I look for a template with a higher A6 number but with the same A5 number I just mapped. I then go to the page in the SAT 980 that has the template with the higher A6 number and the same A5 number, and re-tune A6, D6, & E6.
Working with the templates like this provides enough aural checks to really zero in on really good locations for both A5 and A6.
I always tune A7 as a pure triple octave (8:1) from A4. And since I measured the 8th partial location of A4 when measuring the A4 numbers, the mapping location for A7 was learned at the very beginning of the mapping routines.
However, if someone wants to use a different location for A7, LC can of course, accommodate that as well. So if someone wanted to tune A7 as a triple plus 5 c., or a double octave 5th, or a double octave, as far as LC is concerned, it doesn’t matter. Whatever number is used for the target setting of A7 will be used by LC to create the tuning.
I suggest that for starters, to stick with the triple octave width and position for A7. Use that easy location while learning this system. The pure triple octave will work and sound pretty nice up there. It will be one less measurement and procedure needing to be done. If you want you can do something different later.