Balancing the prime 5ths, involves raising or lowering the midpoint (D#4) of the prime octave.

The best sounding and best fitting tuning curve for the piano, is one that produces a balanced pair of prime 5ths (A3/E4 & D4/A4).  When the prime 5ths are the same width, D#4 is in a good place for the tuning.

However, more often than not, because of the piano, the ‘software created’ curve will not be a good fit for the piano’s prime octave.  If the lower (A3/E4) prime 5ths is -2 c. (narrow) and the upper (D4/A4) prime 5th is -1.c. (narrow), these 5ths will beat differently and not be balanced.

Raising/lowering the midpoint of the octave will balance the prime 5ths.  In the example above, since the lower 5th is -2 (narrow) and the upper -1.0 (narrow), raising the midpoint by .5 would make the lower 5th .5 c. less narrow and the upper 5th .5 more narrow, giving us a pair of -1.5 c. (narrow) prime 5ths.

Al Sanderson said that to hear the difference in a Major 3rds beating, the width of the interval needed to be changed by .3 c.  Clearly, a .5 c. ‘fix’ in the middle of the prime octave can be heard in the prime octave’s intervals.

Balanced prime 5ths improve the sound and the evenness of beating of all the intervals in the octave.

Lowering the midpoint of the octave increases the width of the upper 5th while reducing the width of the lower 5th.
And vice versa:
Raising the midpoint of the octave decreases the width of the upper 5th, while reducing the width of the lower 5th.

Being able to adjust the prime octave’s midpoint is an adjustment available with our LC Spreadsheet.   The correction is learned thru the mapping process, but it is incorporated into the tuning thru the LC Spreadsheet.