Mapping A3: Procedures

This procedure is for pianos whose 4th A4 Number is generally less than 2.0 c.  When the 4th A4 number is less than 2.0 c.,  the prime octave’s 2:1 can be either expanded or contracted – based on what the prime 5ths dictate – and still remain less than 3.0 c. wide.  Most of the time on these pianos, the prime 4:2 octave will be either wide or pure.

Mapping A3

This system uses the relationships of the prime octave (A3/A4) to the prime 5ths (A3/E4 & D4/A4) to determine the ideal widths for both the prime octave and the prime 5ths.   This relationship will be found using the A4 Numbers the 4th A4 Number, and ‘Templates’.

The “4th A4 Number”

The ‘4th A4 Number’ is the width of the prime’s 2:1 after it has been tuned as a pure 4:2. Knowing this 4th A4 number from the very beginning lets me know immediately what I’m going to be dealing with on that particular piano.

Balancing the Prime 5ths

Balancing the prime 5ths involves tweaking the shape of the prime octave ‘curve’ by slightly raising or lowering the mid point of the prime octave curve, while leaving A3 and A4 unmoved. Since using D#4 is not practical to be used as a mapping note, D4 and E4 are used instead.  D#4 can easily be placed between the settings of D4 and E4. Being able to apply this tweak to the tuning is a unique feature of this system of mapping with templates and then using the LC Spreadsheet to create the tuning.

The Prime 5ths

The prime 5ths are used to determine the best prime octave width for the particular piano being mapped and eventually tuned. When the widths of the prime 5ths are added together, when that total is -3.0, the prime octave width is about right.

Mapping the Treble with Templates

For years and years, I have used the triple octave location for A7.  It’s not a bad spot either.   But since March 2020, I’ve begun tuning A7 higher than that.   I’ve started using the triple octave +5th as a starting point for my A7 location. 

Mapping A0

Mapping A0 can be done any number of ways. It can be mapped however you like, but just like A1, once you have it where you want it, it’s location must be measured using it’s 4th partial, since the LC Spreadsheet uses the 4th partials for A0 – A4.

The Prime Octave

When we were working on all this, we kept needing to talk about the A3/A4 octave. Over time, it just became easier to use the words ‘Prime octave’ instead of saying the A3/A4 octave.