Raphi Giangiulio's Homemade Pipe Organ

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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:

The diameters are calculated using the following equation:

DIA(n) = 155.5 / [2^((n-1)/16)]

The equation also works for wood pipes by simply replacing the diameter with the internal width or internal depth.

Click here for a generic Excel spreadsheet for generating a rank of pipes.