I've come across pianos whose '4th A4 Number' is 0.0 c.!   I didn't know that was even possible until I measured one.   Yes, what that means is that when the A3/A4 octave is tuned as a pure 4:2, the A3/A4 2:1 is also pure. Continue reading →

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. Continue reading →

Even though the width of the prime octave's may be perfect, the piano's scaling within that octave often results in a pair of 'unbalanced' prime 5ths: (A3/E4 & D4/A4) Continue reading →

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. Continue reading →

My approach to midrange tuning is minimal beating.   I don't want to stretch any more than necessary to get a pair of good sounding prime 5ths contained within the prime octave.  Continue reading →

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. Continue reading →

Even the smoothest set of software-created numbers for the prime octave's tuning 'curve', will often not be a good fit for the piano in front of us. Being able to adjust the midpoint of this prime octave makes for a better sounding tuning because the tuning is now a better fit for that particular piano. Continue reading →

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'. Continue reading →

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. Continue reading →

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. Continue reading →

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. Continue reading →

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.  Continue reading →