Pianos with low 4th A4 Numbers haven’t caused me much problem.
A low 4th A4 Number just means that when the prime octave is tuned as a pure 4:2, the resultant 2:1 is also pure or very close to pure.
I’ve come across pianos whose ‘4th A4 Number’ is 0.0 c. I didn’t know that was possible until I measured one. I’ve read this is a sign of a well scaled piano, but I’m not so sure about that. The first piano I found with a pure 4th A4 number was/is a particular Yamaha Studio Console, which is a nice piano. But I’ve never found a 4th A4 number of 0.0 on a long scale Steinway, Yamaha, or Kawai, Mason & Hamlin, etc.
From a stretching viewpoint, a low 4th A4 number gives the technician more leeway for midrange stretch. The 4:2 can be stretched wider before the 2:1 starts to get too wide and start beating objectionably.
However, caution should be taken to not tune the prime octave too wide. Use the prime 5ths as a guide. This may sound counterintuitive, but the 5ths @ -1.5 c. may be too wide for a piano with a pure or really low 4th A4 Number. The -1.5 width may push the 4:2 octave too wide and cause beating in the 4:2. The prime 5ths may need to be closer to -1.8 c. or maybe -2.0?? Remember a 1 c. wide 4:2: is .5 beats per second. So, if the 4:2 is tuned 2 c. wide, the octave will be beating @ 1 bps. which I think for most of us would be too fast for the octave.
As I’s said before, I like to keep the 2:1 less than 2.8 c. wide. But in this situation, if I widen the octave to the -2.8 c. width, the 4:2 is going to be close to 2.8 c. wide as well. Which is a too wide for a 4:2 in that area of the piano. At least it is for me. So, a little less stretch in the prime octave and the prime 5ths sounds better.
Knowing what was going on in the prime octave and the prime 5ths, makes it easy to come up with a nice sounding compromise. On these pianos, the 5ths needed to be a little more narrow than the -1.5 starting point.
Isn’t it t interesting how it seems the end result is the same? Mapping a piano with a low 4th A4 Number results in a slightly more narrow prime 5th; and mapping a piano with a high 4th A4 number can also result in slightly more narrow pair of prime 5ths. After all it’s a piano, each with their own iH.