The dimensions of the pipes in a rank are determined in concert with the wind pressure which will be supplied to them. A physically larger set of pipes is usually paired with a higher pressure wind supply. Conversely, a physically smaller set of pipes is usually paired with lower pressure wind (There can be exceptions to this rule, however, based on the dimensions of the mouths of the pipes). Both a large and a smaller set of pipes can produce approximately the same sound. Wurlitzer, for example produced sets of Tibia pipes in 4 progressively larger scales powered by 8”,10”,15” and 25” wind. This is why regulators to keep the wind pressure steady are so important in organs. It is not uncommon to find different regulators providing different wind pressures to various ranks in the same instrument.
SCALING is defined as the relationship of the width of a pipe to its length. It is one of the primary determinants of power and tonal quality for pipe ranks. Organ builders use esoteric mathematical formulas developed through the ages to determine the diameter of each pipe. One system in common use results in halving the diameter every 17 pipes as you move from note to note up the rank. In principle, the narrower the scaling of a pipe, the less power and foundational tone it produces and the more higher harmonics are present. Conversely, the wider the scaling the more foundational tone is produced and fewer or weaker harmonics are present.
As described in the article on Tonal Finishing, the mouth characteristics of flue pipes can also make marked changes to the final tonal results contributing to the effects of scaling. The width of the opening at the foot of the pipe can also be quite critical.
In reeds similar principles apply relating to pipe scalings. Pipe shapes as well as other relevant factors such as shallot design and reed tongue thickness are important in achieving the desired tones.
The main thing to remember is that for any particular stop, different sets of pipes size wise can be used to produce the same set of musical notes.