To know the scale of an aulos it is necessary to have a complete instrument. None of the surviving auloi are complete. It is the purpose of this article to attempt to reconstruct the missing parts of several auloi and thus to determine their scales.

All musical sounds consist of regular vibrations. The interval between two notes may be expressed as the rate of vibration of the higher note divided by the rate of vibration of the lower note. This ratio is very roughly the same as the length of the air column for the lower note (i.e. the distance from the reed to the first open hole) divided by the length of the air column for the higher note. This gross over-simplification has been used for all calculations in this article. The width of the air column, the size of the holes, and the reed itself affect the pitch considerably. The player also has a large control over the precise note played. And so the notes obtained by the ancients might have been very different from the notes obtained by ignoring these factors; although the player's control over pitch might have been used to lessen the effects of the other factors.