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

The “4th A4 Number”

The “4th A4 Number” is the width of the prime’s 2:1 after it has been tuned as a pure 4:2.

When the 2nd Partial location of A4 is known, its easy to tune the Prime Octave as a Pure 4:2.   Simply tune A3 to the 2nd partial setting of A4.

After A3 has been tuned as a pure 4:2, here’s how to measure the prime as a 2:1 :
1.)  set the SAT to A4
2.) play A3
3.) stop the lights using with the cents buttons.

The width of the 2:1 is the  “4th A4 Number”.

I make this “4th A4 Number” measurement right after I have the A4 numbers.   This “4th A4 Number” reveals a lot about the piano.

The “4th A4 Numbers” vary from piano to piano:

Pianos with “4th A4 Numbers” between 0.0 c. – 1.0 c.:

The prime octave on pianos in this 0.0 c. – 1.0 c. range almost always end up as wide 4:2s.

Some pianos pure 4:2 prime octave yields a pure 2:1.   I didn’t know that was possible until I discovered that relationship on a Yamaha Studio Console.

The A3/A4 width on these pianos will always end up with a wide 4:2.

Pianos with “4th A4 numbers” between 1.1 c. – 2.4 c.:

Most pianos will fall within this 1.1 c. – 2.4 c. range.

The A3/A4 width on pianos that fall within this “4th A4 Number” range, will mostly end up being wide 4:2s.  But on some pianos the prime 4:2 best width can be pure or slightly narrow.

Pianos with “4th A4 Numbers” above 2.8 c.:

Pianos with high “4th A4 Numbers” can be more challenging.   When the prime’s 2:1 is around 3.0 c., the beating in the octave (at the 2:1) can start to get too fast.   Of course this can be subjective, but my flags start to go up when I find a piano with a “4th A4 Number” over this 2.8,  2:1 width.

I’ve measured pianos with 4th A4 numbers as high as 3.7 c..  And since the A3/A4 octave was tuned as a pure 4:2,  the offensive beating is all in the 2:1.

These high “4th A4 Number” pianos, can cause the prime’s 4:2 to end up being tuned narrow.   Reducing the beating in the 2:1 means contracting the 2:1 octave, and that means the 4:2 is also being contracted.    On those pianos, the prime 5ths will often need to be narrower (than -1.5 c.) as well.
(More on dealing with these situations will be discussed in the post on Mapping A3).


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