Working with a Low “4th A4 Number” Piano
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.
Mapping A3: 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.
Working with the Prime 5ths
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.
Working with a High “4th A4 Number” Piano
Though not absolute by any means, there is a useful ‘relationship’ between the prime octave width and the widths of the prime 5ths.