Robert Conrad, Registered Piano Tuner/Technician, Tucson, AZ

Adjusting the Mid-Point of the Prime (and Sub-Prime) Octaves

Balancing the prime 5ths, involves raising or lowering the midpoint of the prime octave.

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.

Using Direct Interval tuning, you can check this for yourself.   Using the software-created tuning, simply tune A3, D4, E4, and A4 and measure the prime 5ths (A3/E4 & D4/A4).   If the two prime 5ths are balanced (the same width), the midpoint of the octave is in a good place for the tuning.   But if they aren’t, raising or lowering the midpoint of the octave will balance the prime 5ths and the rest of the intervals in that octave sound better and progress more evenly.

This first chart is a an octave with an A3 @ 2.5 and an A4 of 10.

This chart is what a tuning ‘curve’ may look like.
(Click chart to enlarge, and then click your browser’s or mouse’s back button to return to this article.)

The next chart contains a blue line which is simply a straight line between those two notes.
(Click chart to enlarge, and then click your browser’s or mouse’s back button to return to this article.)

 

This next chart shows the original curve (red line) with 2 other ‘curves’ each with the D#4  midpoint being .5 c. lower.
(The starting and ending points of 2.5 and 10 are exactly the same in all these charts.)

This is how the charts will look when the midpoint of the original curve is lowered.
(Click chart to enlarge, and then click your browser’s or mouse’s back button to return to this article.)

 

This chart compares the ‘curves’ to the straight line.
(Click chart to enlarge, and then click your browser’s or mouse’s back button to return to this article.)

 

Each one of these curves (including the straight line!!) may result in a balanced, equal beating, equal cents widths, pair of prime 5ths!  It just depends on the piano.

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 makes for a better sounding tuning because the tuning is now a better fit for that particular piano.

This midpoint adjustment is available with our LC Spreadsheet in the Prime and Sub-Prime (A2-A3) octaves

However using this midpoint adjustment in the sub prime is not necessarily for ‘balancing’.    It’s use there is for finding the best sounding midpoint between A2 and A3.  Those subprime 5ths, are rarely balanced.   Due to the scaling and the stretch slightly expanding in the sub-prime octave, most of the time I find the lower sub-prime 5th being a little less narrow than the upper sub-prime 5th.

 

 

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