The A4 Numbers
WHEN we have practiced good actions awhile, they become easy; when they become easy, we take pleasure in them; when they please us, we do them frequently; and then, by frequency of act, they grow into a habit. –Tillotson
The A4 numbers give us a lot of information that will be used for the mapping.
Once A4 has been tuned to A440, the locations of it’s 2nd, 4th, and 8th partials are measured.
To measure A4’s 2nd Partial:
Set the AccuTuner to A5, play A4, and stop the lights (with the cents buttons). The cents setting is the location of A4’s 2nd P.
To measure A4’s 4th Partial:
Set the AccuTuner to A6, play A4, and stop the lights(with the cents buttons). The cents setting is the location of A4’s 4th P.
To measure A4’s 8th Partial:
Set the AccuTuner to A7, play A4, and stop the lights(with the cents buttons). The cents setting is the location of A4’s 8th P.
Here is how those three A4 numbers are used:
- A4’s 2nd partial is used to tune A3 as a pure 4:2 octave.
- A4’s 4th partial is the tuning setting for A4.
- A4’s 8th partial number will be the final tuning setting for A7.
- The location of A4’s 2nd partial will be used to find A3, A5, and A6
How A4’s 2nd Partial is used in mapping:
Once the A4 numbers are known (and written down), the 2nd partial number of A4 is used to tune A3 as a pure 4:2 octave from A4.
To do this, simply set the AccuTuner to the 2nd P setting of A4 and tune A3 to stop the light rotation. The result is an A3/A4 pure 4:2 octave. Even though the A3/A4 octave will probably end up being either a wide or narrow 4:2, now the pure 4:2 location is known.
When Mapping A3, once the A3/A4 pure 4:2 octave has been tuned, it gets measured as a 2:1. To measure the A3/A4 octave as a 2:1, set the SAT to A4, play A3 and stop the lights (with the cents buttons). The cents setting is the width of the pure A3/A4 4:2, when measured as a 2:1.
Knowing the width of this 2:1 will come in handy for mapping A3. When A3 is finally mapped, and it’s correct setting known, it will be easy to know the widths of both the A3/A4’s 4:2 and 2:1.
That information will also come in handy when mapping A5. Knowing the 2:1 width of the A3/A4 2:1, when mapping A5 it will be a good bet the A4/A5 2:1 will need to be at least as wide as the A3/A4 2:1. In most cases it will need to be wider. Knowing the width of the A3/A4 2:1 can help find A5.
Of course A5 is not found solely by the width of it’s A4/A5 2:1, but it is useful information when mapping.
The 2nd P of A4 is also used when mapping A6. Once both A3 and A5 are mapped, it is easy to see the width of that A3/A5 4:1 octave. When mapping A6, there is another double octave: A4/A6. Knowing the width of the A3/A5 4:1, gives us helpful information for mapping A6 because the A4/A6 4:1 will need to be at least as wide as the A3/A5 4:1 – and probably wider.
All of this is really handy information, and can help to speed up the treble mapping process by combining some good technical information with some aural checks when using the templates and listening to the 4ths and 5ths within those octaves.
And, all of this is made so much easier because of the partial arrangement used by this system and the LC Spreadsheet. I know when this system was created, it was the only one to use this partial arrangement. Our system uses the fundamentals from A#4 – C8. That means that when A5 is tuned, it is using it’s 1st partial.
Every other system, uses the 2nd partial for tuning A5. That means that when A5 is being tuned the SAT or whatever the other device is, is ‘listening’ to A6 rather than A5.
Using the fundamentals above A4 make all of this so much easier and faster, and more accurate. Getting rid of a partial change in the treble is a really good thing, since partial changes are an error waiting to happen.
How A4’s 4th Partial is used in mapping:
Once the 4th partial of A4 is measured and known, the tuning setting for A4 is also known. When A4 is tuned during the tuning, the SAT is listening to the 4th partial. A4 is done, no mapping required. Just measuring where the 4th P of A4 is located give us the mapping tuning setting for A4.
During the mapping process, when selecting a template for mapping A3, the A4 setting on the template is known. It is the 4th P of A4. The setting for A3 is not yet known, but the setting for A4 is.
Once A3 has been tuned as a pure A3/A4 4:2, and the 2:1 width of that octave is measured, a good starting template may be one that results in a pure A3/A4 4:2, i.e. the template selected should be the one with the A4’s 4th P number for A4, and A4’s 2nd P number as the A3 setting.
Most of the time, the A4/A6 4:1 octave needs to be wide. How much depends on the piano of course. But knowing where the 4th P of A4 is, knowing A4’s 4th P number, it is easy to see how wide to the A4/A6 4:1 is when either selecting a template to try, or to see how wide it is when A6 is mapped in a nice spot.
For instance if we know the 4th P of A4 is 10, and we end up tuning A6 @ 11.5, we know the A4/A6 is about 1.5 c. wide. Again, that little bit of math is easy to see and do after mapping A5 and wanting to find a good location for A6.
How A4’s 8th Partial is used in mapping:
The 8th P location of A4 is the tuning setting for A7, if an A4/A7 triple octave is desired. Some Tuner/Technicians may prefer a wider or less wide location for A7, and the LC spreadsheet can accommodate.
If the Tuner/Technician prefers a slightly higher A7, 3 or 4 cents or whatever can be added to the 8th P setting of A4, and that number can be used as the location for A7 with the LC Spreadsheet.
Of if the triple octave is too sharp, a lower number can be used. For instance, if the the Tuner/Technician wants to tune a double octave up there instead of a triple, once A5 has been tuned and mapped, he can set the SAT to A7, play A5, and stop the lights with the cents buttons. The number displayed will be the 4th P setting of A5, which will result in an A5/A7 4:1 or double octave.
Again, the LC spreadsheet will accommodate these type of tuning preferences.