Using Beats to Tune Organ in 1634

Dear Tuners,

Below is a translation of an excerpt from Marin Mersenne's "Harmonie
Universelle" (1634) concerning tuning keyboards by beats. Isn't this earlier
than Owen Jorgensen accepts?

Johnny Reinhard

"It is certain that the pipes tremble when they sound together,
although they are not in tune. For example when they do not make unison, the
octave, or the fifth; and they do not tremble when they are tuned exactly;
thus if one could recognize the number of beats they make when one diminishes
their tuning to render them tempered as required, one would be able to tune
them, because one would diminish their justness until they made the number of
the said beats. For if they ought to beat twenty times in the space of a
measure to be perfectly tempered, it would be necessary simply to observe
this number to put them in tune. But it is necessary to experiment how many
times the pipes, or the parts of air which are pushed or enclosed within,
sound beats in all the distances from unison and the other consonances, if
one wishes to learn the universal method of tuning the organ.

"And if one can recognize these beats or throbbing without the ear, it
will not be necessary in tuning the organ, for if, for example, the pipes
must beat ten times in a second to make the tempered fifth, one will be
assured that the organ will be in tune, when all the fifths beat ten times
and the ear is not necessary for this, if the hands which hold them and touch
the pipes can tell the said number of beats through the sense of touch.

"Now this consideration of beats serves not only for recognizing the
tuning and temperament of the organ, but also as the object of an excellent
speculation which consists in searching for the causes of this throbbing,
which is different according as the pipes are more or less removed from the
consonances, since they beat as much when they are lacking a diesis of making
a unison, as when they are removed by a major second and an equal distance
from the fifth does not make them beat like that of the unison. Thus it is
necessary to consider these distances in as many manners as there are
consonances; for as to the dissonances, they make the pipes beat and throb
even when they are in the exact intervals. Yet one can consider whether they
make them tremble more or less when they are just than when they are
tempered."

Marin Mersenne (1634) Proposition XXX (p. 450)

--- In tuning@y..., Afmmjr@a... wrote:
> Dear Tuners,
>
> Below is a translation of an excerpt from Marin
Mersenne's "Harmonie
> Universelle" (1634) concerning tuning keyboards by beats. Isn't
this earlier
> than Owen Jorgensen accepts?
>
> Johnny Reinhard
>
> ["]But it is necessary to experiment how many
> times the pipes, or the parts of air which are pushed or enclosed
within,
> sound beats in all the distances from unison and the other
consonances, if
> one wishes to learn the universal method of tuning the organ.
>
>
> "Now this consideration of beats serves not only for
recognizing the
> tuning and temperament of the organ, but also as the object of an
excellent
> speculation which consists in searching for the causes of this
throbbing,
> which is different according as the pipes are more or less removed
from the
> consonances, since they beat as much when they are lacking a diesis
of making
> a unison, as when they are removed by a major second and an equal
distance
> from the fifth does not make them beat like that of the unison.
Thus it is
> necessary to consider these distances in as many manners as there
are
> consonances; for as to the dissonances, they make the pipes beat
and throb
> even when they are in the exact intervals. Yet one can consider
whether they
> make them tremble more or less when they are just than when they
are
> tempered."
>
> Marin Mersenne (1634) Proposition XXX (p. 450)

Johnny, does Mersenne go on to provide a means of _calculating_ beat
frequencies? Because it appears that what he is saying here, is that
one has to know how to set the temperament first _by other means_;
then one can observe _empirically_ and count the beating; and then
use these counts to set the temperament in the future -- and that a
mathematical theory of beating is a matter for future "searching".
Jorgenson may have overlooked this, but it's a far cry from actually
_calculating_ the correct beat frequencies a priori.

Nonetheless, I recall reading in Jorgenson that the theory of beat
frequencies was fully understood long before any tuners actually
_used_ this theory to tune. But how could Jorgenson know what _all_
tuners did or did not use?