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 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.
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.
Once the location for A2 is known, mapping A1 is very straightforward. A good location for A1 is as a 6:3 octave (from A1), 3.0 cents wide.
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.
Template: A gauge, pattern, or mold (such as a thin plate or board) used as a guide to the form of a piece being made; an overlay; something that establishes or serves as a pattern. Templates are used for mapping the different sections of the piano.
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.
Mapping (and tuning) notes during the mapping process is the equivalent of setting the temperament in aural-only tuning.