Tuning Templates

From the Merriam-Webster Online Dictionary:

Definition of ‘template’

Templates are not tunings.

First of all, what templates are not:  templates are not ‘tunings’, they are simply a pattern or mold used for finding target notes.

With 3 pairs of shoes, 3 pairs of pants, and 3 shirts, if we can wear one pair of shoes with each of the 3 pairs of pants and then again, each of those combinations can be worn with each of the 3 shirts, we have many more combinations of outfits.  That’s the way it works with bass, midrange, and treble templates.

With 800 ‘tunings’ we only have 800 tunings.  But with 800 bass templates, 800 midrange templates, and 800 treble templates, their combinations are a very large number.

This ‘template’ approach for mapping allows us to try different octave or double octave widths.  Using a template to map the prime octave allows us to also tune some other notes within that octave so we can hear show it would sound if it was used for the tuning.

Just getting the octave the right width, isn’t enough.  The ‘shape of the curve’ within the prime octave can also be analyzed.  Once the octave width has been determined, the upper and lower prime 5ths can be tuned and measured to see if they are ‘balanced’ or not.   Being able to tweak the curve of the prime octave is a unique and wonderful feature of this system of mapping with templates and then using the LC Spreadsheet to create the tuning.

Click on this link to to download and view the complete list of templates in my SAT 980:
Template Header Sheet

The templates are divided into 3 sections: bass, mid-range, and treble.
The page numbers is the column on the left.
The note of the piano is shown at the top of each column.

The vertical blue line separates the Bass template from the Midrange template.
The vertical red line separates the Midrange template from the treble template.

There is also some color coding to make it easier to read.
A4 is the red column and is underlined and in italics.
A2 and A3 are green.
A0 and A1 are in italics and are in a blue color.

The treble, A5, A6, and A7 are purple with A6 being underlined.

Again, each page is NOT a tuning. Each page contains 3 templates: bass, midrange, and treble.

The Midrange Templates

The Midrange templates are organized by the A4 numbers, going from lowest to highest. Scrolling up and down thru the header you will notice the A4 number on Pg. 141 is 4.2, the A4 number on Pg. 300 is 8.2, the A4 number on Pg. 650 is 11.0, and so on.

For each A4 number there are probably more than one template.

For instance, pages 637 – 651 all have the same A4 number of 11.0. The difference between each of those pages is the A3 number.
Page 637 has an A3 number of 1.1, and a A4 number of 11.0
Page 645 has an A3 number of 3.0, and a A4 number of 11.0
Page 650 has an A3 number of 4.1, and a A4 number of 11.0

The 2nd level of organization for the midrange templates is the A3 number.

Mapping begins by tuning A4 to A440 (A4 @ 0.0) and then measuring the location of A4’s 2nd, 4th, and 8th partials.
Since the 4th partial is used tuning A4, the 4th partial location is the tuning setting for A4.

The 2nd step in mapping is to tune A3 as a pure 4:2 octave.   A3 is tuned to the 2nd partial of A4.
Once the 4th and 2nd partial locations of A4 are known, a template can be selected using that A3 and A4 information.

For example, when A4 is tuned to A440, if it’s 4th partial is @ 8.8, and it’s 2nd partial is @ 2.1, select the midrange template on page 359 that has it’s A4 setting @ 8.8 and it’s A3 setting @ 2.1 c..    Tune A3 and A4 using page 359.  Any of the other notes contained within the prime octave (A3-A4) can be tuned as well if needed to check the pure 4:2 width to make sure it is the best width for the prime octave on that piano.

If the 4:2 octave needs to be wider, a different midrange template can be selected with a lower A3 number.
Maybe page 356 which puts A3 @ 1.4 (instead of 2.1) and keeps A4 @ 8.8.
Using page 356 instead of page 359 will expand the A3/A4 4:2 by about .7 c.
Any notes within the octave can be tuned to see if the wider 4:2 is a better fit.

There is another midrange template with an even lower A3 number (same A4 number) that can be tried. Page 353 puts A3 @ .8 while keeping A4 @ 8.8.

A2 is  -1.9 c.  on every template.

Mapping will determine the best location for A2, but the starting point for every template is -1.9 c.

Before the LC Spreadsheet, these templates were used for tuning. But now that we have the LC spreadsheet, these templates are only used for mapping.

Mapping is not tuning every note in the octave.  The goal with mapping is to map as few notes as possible but enough notes to give us enough information about the piano to allow us to create a really well fitting custom tuning.

A thorough mapping will include settings for A0, A1, A2, D3, E3, A3, D4, E4, A4, A5, A6, and A7.  Other notes will be tuned during the mapping process and used to determine the settings for these main target notes.   But these notes are the notes the LC

The Bass Templates:

Before the LC Spreadsheet, the bass templates were used for tuning. And of course they still can be. Before LC, 3 different pages were used for each tuning.

The transition going from the midrange template to the bass template was the most critical aspect of tuning a piano using templates.

First of all,  often times DOB needed to be used for placing A2 in the best spot.

For a smooth transition midrange to bass transition, an offset was often needed when switching pages between the bass page and the midrange page

That method works much better than anything else I’d done up to that point.  But the LC spreadsheet made that midrange to bass transition  unnecessary.  It also made it more accurate and faster.

In the past the bass templates were used for both mapping and tuning. But when using LC, the bass can be mapped without using the bass templates.

The Treble templates.

The treble templates are used for mapping the treble. Using them allow us to hear how things are going to sound up during the decision making process.   Since each treble template has specific settings for A5, A6 and A7, it is easy to test the target locations, by tuning not only the A’s but also the D’s and E’s, which allow us to hear the A4/E5, and the D5/A5 5ths.

The 5ths are the best indicators as to whether or not A5 is well positioned. And they are easy to hear.

If those 5ths don’t sound like we want them all we need to do is select a template with a slightly higher or lower A5 setting, re-tune A5, D5 and E5 and listen again.

Tuning A5 allows us to hear the A4/A5 octave, the A3/A5 double octave, and the D5/A5 5th.
Tuning E5 allows for listening to the A4/E5 5th.

Once A5 is in a good place, and the 5ths in that A4-A5 octave sound good, the setting for A5 is known.

Now that A5 is mapped, it is helpful to look at the settings (numbers) for A3 and A4. Now it is easy to see what the width of both the A3/A5 double octave and the A4/A5 single octave are.

Because the A4 numbers were measured and recorded earlier, the location of A4’s 2nd partial is known.   Let’s say the 2nd P. of A4 is 1.5 c.   If we tune A5 to 2.5, we can easily see the width of the A4/A5 2:1 is 1.0 c. wide

Also, now that the tuning setting for both A3 and A5 are known, it is easy to see the exact width of that A3/A5 4:1 double octave.    If the setting for A3 is 1.3, and the setting for A5 is 2.5, the width of that A3/A5 4:1 is 1.2 c.

Now we can use that info to make a guess at a location for A6.

The A4/A6 4:1 double should be a bigger number than the A3/A5 double.

If the A3/A5 double is 1.5 c. wide, the A4/A6 double might need to be 2.5 c. wide.   So all we need to do is add 2.5 c. to the A4 setting and that will be a good guess for the starting point for A6.   If the 4th P location of A4 is 8.8, adding 2.5 c. to that would be 11.3 c.

A template can now be selected that has an A5 number of 2.5, and an A6 number of 11.3.   Most of the time there will be a template that will come very close to each of those settings.

Since the location for A5 has already been confirmed, it’s just a matter now of tuning A6 and D6, and E6 to the template, and listening to everything to make sure all is right where we want it.

Of course if the D6 and E6 don’t confirm the placement of A6, then another treble template with a higher or lower A6 can be selected, and D6 and E6 re-tuned and rechecked until the setting for A6 is found (mapped).

Since A7 is tuned to the triple octave (from A4),  the mapped setting for A7 has been known since first measuring the 2nd, 4th and 8th partials of A4.   Of course LC allows for tuning A7 to a different location if desired.

Using the templates in this way are a way of mapping and getting to hear how the targets notes will sound with other notes withing the treble octaves, namely the D’s and E’s.