Beats in 1634, A. Schlick 1511: "wohltemperirt"?

Dear members,

In my booklet (I'm now not trying here to "sell carrotts!")
"Wie stimme ich selbst mein Cembalo?", 3rd edition; English version
out of print, (called "The Tuning of my Harpsichord"),
I wrote, p. 19, Cap. 2.3:

my own free translation - not very satisfactory for me:

The beats are that important; thus, a nice experiment should be
mentioned. To this aim, all you you need is two different combs.
If you put them side aside or one atop the other, will produce
graphic beat-patterns. These arise from the regular, but different
periodicity of the comb's teeth. This phenonomenon is called, after
Moir�, Moir� pattern.

It appears that Arnold Schlick in 1511 had already fully understood
in his "Spiegel der Orgelmacher und Organisten" the character of
beats. In fact, in Cap. VIII, fol. XV he brilliantly formulates:
"da� sich dabei ETWAS SPERRT UND MEHR ODER WENIGER INEINANDER BEGEHRT"
something is blocking itself thereby and strives to greater and
lesser extent together.

Could Schlick's statement convey anything different in this context
of the beats than his profounf understanding? Supposing he has
understood the beat's mechanism, WHY should he refrained from
taking advantage of these beats and to utilize them
for tuning his organ.

By the way: His tuning instructions are difficult to interpret
and even more difficult to convert into clearcut, non-ambiguous
tuning instructions.

advocatus diaboli:
Who is capable of identifying an intrinsic
discrepancy between Schlick's prescription for tuning and
the result of "Werckmeister/Bach/wohltemperirt????

In this regard I'm having difficulties!

Kind regards,

Herbert-Anton

Paul Erlich schrieb:
> --- 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?
>
>
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