Mapping the Treble with Templates

I map the treble last.   Our system uses the 4th partials from A0 – A4, and the first partials or fundamentals from A#4 – C8.

Here is a complete graph of our partial arrangement:

The Green line indicates use of the 4th partials and the Blue line is for the 1st partials.

This partial arrangement makes mapping the treble very straightforward and easy.

For instance,  A5 is tuned using it’s fundamental.   So when mapping our location for A5, it is easy to use both A3 and A4 to find a good location for A5, since when using the A4/A5 2:1, the A3/A5 4:1 or the A3/A4 4:2, use the fundamental location or 1st partial location for A5.   Most systems use the 2nd partials for tuning A5.   An FAC tuning uses the 2nd partials for tuning A5.

The only advantage for using the 2nd partials above A4 is a slightly faster light rotation.   But if A4 can be tuned to A440, and when doing so, A4 is using it’s 1st partial or fundamental, it stands to reason A#4 can be tuned accurately when using it’s fundamental as well.   Same way with B4, C4, and so on.

Another advantage of using the fundamentals from A#4 on up, is there are no partials changes in the treble.

Our partial arrangement makes mapping the treble easy and straightforward.

As in aural tuning, we use previously tuned reference notes from the lower half of the piano.   A5 is the first ‘treble’ note to map.

The treble templates are organized by their A6 numbers.  So at first, the locations of both A5 and A6 are estimated using the A4 numbers and a good estimate of where A5 will be tuned using A3 and A4 as reference notes.  (SAT set to A5, while alternately playing A3 and A4 and observing the light rotation).   Once A5 can be estimated, that estimate is used to estimate a location for A6.

Once a good estimate is had for both A5 and A6, a treble template can be selected.   Using that treble template and a treble sequence, A5, D5, and E5 are tuned.   Now A5, as well as D5 and E5 can be checked and used to adjust the location of A5 if needed.  Once the best location for A5 is known, a new treble template is selected using that A5 location.   Once we know where A5 will be, that gives me the width of both the A3/A5 4:1 and the A4/A5 2:1.   Both of those widths guide me to the next more refined location for A6.

A new treble template can then be selected that contains both A5 and A6.  Using that new template A5, D5, E5, A6, D6, and E6 can all be tuned and checked.

At this point, any combination of intervals resulted from playing any combination of A’s D’s and Es all over the piano can be played to get an idea as to how the completed tuning will sound.

A7 is tuned as a triple octave (from A4) so that location is known from the time the A4 Numbers were first measured.

Mapping the treble uses:
1. information found when the A4 numbers were measured and
2. the completed mapping of the prime octave: A3, D4, E4, & A4.

For this post the A4 numbers are:
4th P = 9.4 c.
8th P = 39.0 c.
2nd P = 2.0 c.
The mapped setting for A3 = 1.9

Mapping A5:

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.   In the TUNE mode, 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 reference note (A3 & A4) is played.    Use the buttons on the SAT to adjust the cents so that the light rotation is slightly counter clockwise when each reference note is played.

For example here, lets say an A5 cents setting of  3.2 c. looks good in that the lights rotate slowly counterclockwise when each reference note is played.

If A5 were to be tuned to that 3.2 setting, when compared that setting to the 2nd P number of A4 and the mapped setting for A3, is will be easy to see the widths of both the A4/A5 2:1 and the A3/A5 4:1.

If the 2nd P A4 number is 2.0, and A5 is tuned @ 3.2, the A4/A5 2:1 will be 1.2 c. wide.

If the mapped setting for A3 is 1.9, and A5 is tuned @ 3.2, the A3/A5 4:1 will be 1.3 c. wide.

Tuning A5 to this 3.2 setting will be a good place to start.   It may get tweaked later on during the mapping process, but for now, a 3.2 A5 setting will be a good place to start.

Using A5’s setting to find a good starting point for A6:

Treble templates will be used to map the treble.   The treble is defined here as A4 – C8.

Since the treble templates are ‘organized’ by their A6 numbers, in order to find a good starting template for mapping, a good idea as to the location of A6 will be needed.

Using the previously mapped settings and the A4 numbers,  a good guess can be made for the location of A6:

As above, for this post the A4 numbers are:
4th P = 9.4 c.
8th P = 39.0 c.
2nd P = 2.0 c.
The mapped setting for A3 = 1.9
Preliminary mapped setting for A5 = 3.2
We will also use the width of the A3/A5 4:1.  (A3/A5 4:1 width = 1.3 c.)

If A6 were to be tuned to 9.4, the A4/A6 would be a pure 4:1.

Our starting tuning setting for A5 is 3.2, which results in a 1.3 c. wide A3/A5 4:1.   (A3 = 1.9, A5 = 3.2)

So, we want to tune the A4/A6 at least 1.3 c. wide or 10.7 c..   (9.4 + 1.3 = 10.7)

Tuning A6 to 10.7 would mean the A3/A5 and the A4/A6 doubles would be the same width.

But the A4/A6 4:1 should be wider than the A3/A5 4:1.   So instead of tuning A6 @ 10.7,  start by adding 1 c. to the width of the A3/A5 and start with a setting of 11.7 for A6.

Now a template can be selected for tuning the treble:  A template with an A6 @ 11.7, and an A5 @ 3.2

An A6 setting of 11.7 would result in an A4/A6 double being 2.3 c. wide.  (11.7 – 9.4 (A4) = 2.3 c.)

The A3 (1.9)/A5 (3.2) double is 1.3 c. wide (3.2 – 1.9 = 1.3).

The Treble Templates are organized by A6 numbers, so the A6 number will be the 1st priority for selecting a template.  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.

The selected template is used for tuning not only A5 and A6, but also D5, E5, D6, and E6.  In addition to all the previously mapped notes, the D’s and Es will be used for aural checks in the treble.

Refining the position of A5:

Once the template has been selected, it’s time to tune A5 and check it’s location.   For this, tune A5,  D5 and E5 to the selected template.

Now, in addition to the mapped and tuned prime octave (A3, D4, E4, and A4),  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, the A3/A5 double octave, and the D4/A5 12th should be listened to as well.   But the most helpful checks seem to be the A4/E5 and the D5/A5 5ths.

If the 5ths indicate A5 is not high enough, a different template can easily be selected.  But since we need A5 to be a little higher, A6 will probably need to be a little higher as well.

If this first template had A5 @ 3.2 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 @ 3.7.   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.

So now we can select another template, this time with an A6 around 12.4 and an A5 number of 3.7 c.

Now using the newly selected template, re-tune A5,  D5 and E5 and give everything a listen.   I don’t do any 5th width measuring here.   I just listen to them.   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.

A6:

Using that same template, tune A6, D6, and E6, repeat the checks used when finding A5.

If A6 needs to be adjusted either up or down, look for another template with a higher or lower A6 number but with the same A5 number as before!

For instance, A5 is good @ 3.7, but A6 needs to be even sharper than 12.4.  Look for a template with 13.0 for A6 and a 3.7 setting for A5.

Select the template with the hopefully better A5 and A6 settings, re-tune A6, D6 and E6, and run the checks.   Do this as many times as necessary to get good sounding results.

Working with the templates like this should provide enough aural checks to really zero in on really good locations for both A5 and A6.

{Generally speaking, when everything is right, the single octaves in this 5th and 6th octave area, will be stretched nicely, without any ‘fast’ beating in them.   I’ve heard some systems leaving beats in the single octave almost faster than 1 beat per sec. in the treble.  

Of course this system will allow you to put those fast beats in there if you like, but, since my approach and goal is minimal beating, not only do I just not like 1 beat per sec beating in there,  I think that kind of octave beating in the treble is unnecessary.  Trying to ‘bring out’ the treble by adding beats – especially in the 5th and 6th octaves- is to me,  a poor tuning practice.   Maybe that’s what a little lacquer is for – ie. voicing, rather than tuning?}

Last but not least:  A7

Since I always tune A7 as a pure triple octave (8:1) from A4, I knew the mapped setting for A7 as soon as I measured the A4 numbers!

AS above, for this post the A4 numbers are:
4th P = 9.4 c.
8th P = 39.0 c.
2nd P = 2.0 c.
The mapped setting for A3 = 1.9
Final mapped setting for A5 = 3.7
Final mapped setting for A6 = 12.4
Final mapped setting for A7 = 39.0

However, if someone wants to use a different location for A7, LC can 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.

For starters, I suggest sticking with the triple octave position for A7.   It’s easy and the pure triple octave will sound nice up there and be one less measurement and procedure needing to be done.