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

The best sounding tuning curve for the piano, is one that is the correct width for the piano and also produces a balanced pair of prime 5ths (A3/E4 & D4/A4).  When those prime 5ths are the same width, they are ‘balanced’.   The prime 5ths are an excellent way to determine the best width for the A3/A4 prime octave as well.

The middle note of the A3/A4 prime octave is D#4.  It’s during the mapping process where we learn where the best settings for 3, D4, E4 and A4 should be for tuning the prime octave.

I made 3 videos on Mapping A3.   Mapping is where I ‘find’ the target notes settings I want to use for the tuning.  Target notes for me are: A0, A1, A2, D3, E3, A3, D4, E4, A4, 5, A6, and A7.  Once I have all the target notes I need for the tuning, I open up the LC spreadsheet, enter in the target note settings, and create the tuning.

Accurately tuning and measuring 5ths, takes some practice.  But with practice it can be done reasonably efficiently and quickly.   Mapping A3 is just like setting the temperament in Aural Only Tuning.  But here we use both aural and technical means to get the best result.   Finding the best width for the octave is first, and then finding the best fitting curve within that octave comes next.  You’ll see when watching the Mapping A3 videos how both of those tasks can be combined for a most harmonious outcome.

Here’s a link to the Mapping A3 video that probably has the most to do with balancing the prime 5ths.

Mapping A3, Part 2.

If there wasn’t a way to actually incorporate all this mapping into my tuning, it would be a waste of time.   But our LC spreadsheet allows us to do all sorts of custom fitting tuning to piano things, based on our own mapping.  And being able to raise or lower the setting for D#4 in order to balance the prime 5ths is just one of them.

More often than not, the best ‘curve’ for the piano, is not created by the software we use to tune.  This is true with all ETDs.   The best way to know if the software curve is a good fit for the prime octave is to measure the prime 5ths.   Ideally, they (the prime 5ths) should be the same width.

If the lower (A3/E4) prime 5th is -2 c. (narrow) and the upper (D4/A4) prime 5th is -1 c. (narrow), the 5ths will beat differently.  The 2.c narrow 5th will beat faster than the 1 c. narrow 5th.

Balancing the prime 5ths is simply a matter of adjusting the midpoint of the octave (D#4).   Our LC spreadsheet allows us to tweak the setting for D#4 and slightly change the curve of the prime octave so that the prime 5ths are exactly the same width.  But don’t think it just changes the location of the D#4, raising or lowering the midpoint in the octave affects the locations of D4, and E4 and the other notes within the octave – recreating a slightly different curve within the A3/A4 octave.

This is exactly what a really good Aural Only tuner does.  Now, with this system and with the LC spreadsheet, we can duplicate – and actually improve on that aural skill – incorporating it into our tuning.   None of the other systems can do this.  They can’t but YOU can.

In the example above, since the lower 5th is -2.0 c. (narrow) and the upper prime 5th is -1.0 c. (narrow), raising the midpoint (D#4) by .5 will make the lower 5th less narrow by .5 c. and the upper 5th .5 c. more narrow, thereby fixing the problem and balancing the 5ths @ -1.5 c. each.  The 5ths will beat the same and the M3rds will progress more smoothly as well.   As will the 4ths, and 6ths, and so on.

*** This -1.5 c. width for the prime 5ths is a good place to start, but it may not be the best width for every piano or every piano technician.  But regardless of the width, a pair of balanced prime 5ths will sound the best, and the routine for balancing them is exactly the same with our LC spreadsheet. ***

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.

Balancing the prime 5ths is a part of Mapping A3.   If you’d like to see and hear this done in real time this little video may answer some of your questions.

Mapping A3, Part 2.