Pipe Scaling
Pipe scaling refers to the relationship of the pipe diameters throughout a rank
of pipes. When a rank of pipes is said to halve on the 17th note, this means
that the 17th pipe is half the diameter of the first pipe. The equation for
calculating the diameter of each pipe in a rank is as follows:
DIA(n) = SD / [2^((n - 1)/(HN - 1))]
DIA(n) is the diameter of pipe number n
SD is the starting diameter or the diameter of pipe number one
HN is the halving number
For example, here are the first seventeen diameters of the normal scale which
halves on the 17th note: