Understanding Low 4th A4 Numbers in Piano Tuning
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.
Piano Midrange Mapping: Tuning Templates and Procedures
This procedure is for pianos whose 4th A4 Number is generally less than 2.0 c. When the 4th A4 number is less than 2.0 c., the prime octave’s 2:1 can be either expanded or contracted – based on what the prime 5ths dictate – and still remain less than 3.0 c. wide. Most of the time on these pianos, the prime 4:2 octave will be either wide or pure.
The Prime 5ths: A3/E4 & D4/A4
My approach to midrange tuning is minimal beating. I don’t want to stretch any more than necessary to get a pair of good sounding prime 5ths contained within the prime octave.
Understanding Unusually High “4th” A4 Numbers
Though not absolute by any means, there is a useful ‘relationship’ between the prime octave width and the widths of the prime 5ths.