Scaling rules for organ flue pipe ranks and for the string choirs of harpsichords

The criteria for design of an organ flue pipe rank, properly balanced and coherent in power and harmonic development, are discussed in terms of present understanding of the sound production process. A scaling with pipe diameter D proportional to ν1−x, where ν1 is pipe fundamental frequency and x = 0.83, is found to give approximately constant harmonic development across the rank but too much loudness in the bass. The traditional scaling rule with x = 0.75 nearly equalizes the loudness and increases harmonic development towards the bass of the rank. Similar criteria applied to the string choirs of harpsichords, in which decay time must be considered as well, lead to scaling rules which increase wire diameter and move the plucking point progressively towards the end of the string in the bass. The relations between the two types of scaling rule are discussed.