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 →

Our system uses the 4th partials from A0 - A4, and the first partials (fundamentals) from A#4 - C8. This partial arrangement makes mapping the treble very straightforward and easy. As in aural tuning, we use previously tuned reference notes from the lower half of the piano. A5 is the first 'treble' note to map. Using information from the A4 Numbers and some quick measuring and tuning of A5 using A3 and A4, a guess can be made at the location for both A5 and A6. A template is then selected as a starting point for mapping the treble. As the locations for both A5 and A6 are refined and notated, templates with the new settings are used to check the tunings for A5 and A6 as well as the Ds and Es in the 5th and 6th octaves. Continue reading →