Gerberto e la misura delle canne d'organo

TL;DR

Gerbert of Aurillac's 10th-century method for calculating organ pipe lengths is analyzed, showing a mathematical order underlying acoustical phenomena, supported by modern experimental data and corrections.

Contribution

The paper demonstrates that Gerbert's ancient method aligns with modern acoustics, integrating practical corrections and providing a historical perspective on scientific understanding.

Findings

Gerbert's method matches modern acoustical corrections.

Experimental data support the mathematical order.

The approach links historical theory with contemporary acoustics.

Abstract

Gerbert of Aurillac in the Mensura Fistularum explained how to compute the length of organ pipes. The method is shown on two octaves, starting from a fistula of length L=16 units and radius 1 which is equivalent at a monochord of length {\lambda}=18. The adopted acoustic correction for the first octave to the Pythagorean lengths is L={\lambda}-{\alpha}r with {\alpha}=2. The lower octave starts from L=36-2=34 units. The proportion 16:34=34:x is used for obtaining the next diapason. All lengths of the notes of this second octave follow this proportion and no more the additional acoustic correction. Gerbert finds the same multiplicative law for computing pipes and monochord's lengths, opportune constants allow to switch from monochord (12) to lower organ octave (14+1/3+1/144+1/288) to the higher one (13 + 1/2). The purpose of this treatise is to show the same mathematical order, given by God, below different acoustical phenomena. This is a modern perspective in history of science, because experimental data (practical acoustical corrections) are also taken into account. The treatment is limited to pipes of same diameter, and it is no conceived for organ builders. An Italian translation of the core text of the Mensura Fistularum is offered. The experimental measurement of end and mouth corrections for two pipes of different forms and for the flute is presented to support with modern acoustics approach that discussion.