the ocular harpsichord of louis-bertrand castel - Gewina

Castel's ocular harpsichord 45
they could see a slight purple before the red. Next he introduced, out of the
blue, a comparison between these colours and the musical scale in C major,
"because the colours can be equally well expressed in numbers as the tones are".
As the fundamental tone, however, he took purple and not red (which was a
second above the root) since
by raising the violet enough, one arives at a new purple, just like in rising along with the tones
one gets from B to C which is an octave higher than the original C. And since in music this
note is given the same name because of their ressemblance, it is the same with the colours,
which, after having risen by the interval of an octave, recover the same names; or rather, two
colours, just like two tones, one of which has exactly twice the number of vibrations as the
other, are taken to be the same colour and carry the same name.*'
Although no-one had succeeded in actually measuring the rates of vibrations of
the various spectral colours, Euler thus not only supposed the rate for violet to
be nearly twice as great as the rate for red, but believed as well, and in this he
was wholly original, that there existed higher and lower octaves of the same
colours.**
It was on this principle, Euler said, that Castel had imagined a kind of music
of colours and had deviced his ocular harpsichord, which he presumed the
princess "had heard talked about on several occasions". It seems Euler in a way
"rationally reconstructed" Castel's ideas within his own theory, discarding
completely Castel's own chromatic scale. This did not, however, affect his
appreciation of the performance of the harpsichord itself, since he doubted
whether "showing various pieces of cloth dyed in different colours would be very
agreeable". According to Euler it was painting "that to the eyes is the same thing
as music is to the ears".^ Nevertheless, later German authors on natural
philosophy who accepted Euler's theory rather than Newton's tended to bring in
Cited in Euler, Lettres, vol. 11, p. 74 (Letter 31): "puisque les couleurs aussi bien que les sons
se peuvent exprimer en nombres"; "haussant davantage le violet, on revient a un nouveau pourpre,
tout comme en monlant dans les sons, on parvient au dcla de B au son c, qui est un octave audessus
de C. Et comme dans la musique on donne a ce ton le meme nom a cause de leur
ressemblance, il en est de meme dans les couleurs, qui apres avoir monte par I'intervalle d'une
octave, recouvrent les memes noms: ou bien deux couleurs, comme deux tons dont le nombre de
vibrations de I'une est precisement le double de I'autre, passent pour la meme couleur, et ont le
meme nom."
See Hakfoort, Optica, pp. 90-113, on Euler's theory. Of course the frequency of blue light is
in fact roughly twice as great as the frequency of red light, but this is purely coincidental.
Idem: "Pour moi je pense que c'est plutot la peinture, qui est par rapport aux yeux la meme
chose que la Musique aux oreilles; et je doute fort qu'une representation de plusieurs morceaux de
draps teints de diverses couleurs, puisse etre fort agreable." If he had not already learned about
Castel's harpsichord, he would have from a letter by Krafft, discussing the St Petersburg Academy
session of 1742. See A.P. Juskevii^ & E. Winter, ed.. Die Berliner und die Peiersburger Akademie der
Wissenschafien im Briefwechsel Leonhard Eulers (Berlin [Ost], 1959-1976), vol. 3, pp. 137-138.