Editing Organ flue pipe scaling (section)

==Dom Bédos de Celles and the problem of scaling across a rank of pipes==

The lowest pipes in a rank are long, and the highest are short. The progression of the length of pipes is dictated by physics alone, and the length must halve for each octave. Since there are twelve semitones in an octave, each pipe differs from its neighbours by a factor of <math> \sqrt[12]{2} </math>. If the diameters of the pipes are scaled in the same way, so each pipe has exactly the same proportions, it is found that the perceived timbre and volume vary greatly between the low notes and the high, and the result is not musically satisfactory. This effect has been known since antiquity, and part of the organ builder's art is to scale pipes such that the timbre and volume of a rank vary little, or only according to the wishes of the builder. One of the first authors to publish data on the scaling of organ pipes was [[Dom Bédos de Celles]]. The basis of his scale was unknown until Mahrenholz discovered that the scale was based on one in which the width halved for each octave, but with addition of a constant.<ref>{{cite book |last1=Adelung |first1=Wolfgang |title=Einführung in der Orgelbau |date=1971 |publisher=Breitkopf & Härtel |isbn=3-7651-0279-2 |pages=91 |edition=2nd}}</ref> This constant compensates for the inappropriate narrowing of the highest pipes, and if chosen with care, can match modern scalings to within the difference of diameter that one would expect from pipes sounding notes about two semi-tones apart.