  Gerbert of Aurillac wrote to Constantine of Fleury in 978 a letter to
describe in detail the procedure to point the star nearest to the North
celestial pole. This was made to align a sphere equipped with tubes to observe
the celestial pole, the polar circles, the solstices and equinoxes. The use of
tubes in astronomical observation is later reported by Alhazen in his treatise
on optics (1011-1021). The description of pointing to the celestial pole
indicates that the instrument must be accurately aligned with the true pole,
materialized at that epoch by a star of fifth magnitude, at the limit of naked
eye visibility, and then the instrument must remain fixed. Solstices and
Equinoxes are points of the orbit of the Sun, so the sphere could be used as a
tool for observing the Sun and probably determine the duration of the tropical
year. This sphere was much more than a didactic tool, given the long procedure
for the accurate alignement. Moreover "Rogatus a pluribus" (asked by his many
students), Gerbert wrote a treatise on acoustic tubes (fistulae) in 980:
Mensura Fistularum. He knew the difference in behavior of the fistulae compared
with the acoustic strings, already studied by the Pythagoreans, and the treaty
is intended to present the law that governs the length of the organ pipes in
two octaves, compared to the corresponding acoustic strings. In terms of modern
physics we know that acoustic tubes require an "end correction" to be tuned,
which is proportional to the diameter of the tube. This proportionality is the
same for every note. The mathematical law is simple, but Gerbert preferred to
create a law in which the proportions of pipes and strings should be calculated
through a series of fractions linked to the number 12 and its multiples.
