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).