question for robert and another meantone coincidence

robert, have you read this book:

http://mmd.foxtail.com/Tech/jorgensen.html

?

btw, the "equal beating" temperaments discussed there are not at all
like the ones coming up here . . . they have large numbers of like
intervals producing *identical beat rates* as one ascends the
interval, in parallel, up the the keyboard.

anwyay,

5/18-comma is on the optimal meantones table (and it's about halfway
between 2/7-comma and 7/26-comma) *and* essentially the same tuning
was advocated by robert smith back in 1749 -- the perfect fifth and
the major sixth above a given note beat at the same rate. i'm not
sure if this came up right before or right after you got in on the
discussions here -- but "the reason everyone's talking about
meantone" is "actually" "poptimality" . . .

the point being that far more (though not everything) was understood
about beating by musicians in 1749 than in 1558 . . .

for one thing, people had gone around for millenia equating musical
interval ratios were string lengths on a monochord, and the equation
of pitch to phenomenally fast rates of vibration had to wait until
galileo and benedetti -- the latter immediately realized the
implications that vibration-ratios had for the periodicity
of "consonant" chords, though suddenly (though this took centuries to
ripple through the literature) the association of 4:5:6 with minor
and 10:12:15 with major were flipped around . . .

for another, the discovery of the phenomenon of beating (as well as
of the harmonic series, and of sympathetic resonance) dates back no
earlier than this (in recorded history), and it took Mersenne,
Galileo, Kepler, Huygens, Descartes, and others to create a
consistent description of the phenomenon (remember, there was no
fourier around in those days) . . .

finally, with all the pages that jorgenson devotes to historical
tunings (and the evident *muddle* surrounding them, with all the
evidence pointing to *cents* of uncertainty) that can be tuned by
synchronizing beats, you would think that if some big fan of 2/7-
comma meantone knew how to get it real good by doing so, it'd be in
there . . . well, maybe *someone* thought of it, but why name names
before you've done some checking? all right, i'll shut up until
someone translates zarlino for us . . . :)

good night.

--- In tuning@yahoogroups.com, "wallyesterpaulrus
<wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:
> robert, have you read this book:
>
> http://mmd.foxtail.com/Tech/jorgensen.html
>

I've been wanting to get ahold of it. I understand it's out of print.
Any idea where I can get it? What I know of what's in it has coem to
me second hand.

Schlaf gut!

Bob

P. S. I'm aware of the difference between "equal beating" and what
I'm doing. That's why I call my temperaments "synchronous". I
personally feel the latter gets at the most compelling reason for
looking at coordination of beats and that's why I have focused on it.

--- In tuning@yahoogroups.com, "Robert Wendell <rwendell@c...>"

/tuning/topicId_42620.html#42646

<rwendell@c...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus
> <wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:
> > robert, have you read this book:
> >
> > http://mmd.foxtail.com/Tech/jorgensen.html
> >
>
> I've been wanting to get ahold of it. I understand it's out of
print.
> Any idea where I can get it? What I know of what's in it has coem
to
> me second hand.
>

***Hi Bob,

I've been having some success over at abebooks:

http://www.abebooks.com/

Out of print (not "out of tune" books):

Both the Murray Barbour _Tuning and Temperament_ and the Easley
Blackwood _The Structure of Recognizable Diatonic Tunings_ came in
over there at good prices. Unfortunately, it took about a *year* for
the Blackwood, at least, but it *did* happen. (I foolishly gave up
and purchased though Barnes & Noble's used services for more...)

You might want to place a search over there and just wait a while.
It will *finally* happen...

best,

Joe Pehrson

>P. S. I'm aware of the difference between "equal beating" and what
>I'm doing. That's why I call my temperaments "synchronous". I
>personally feel the latter gets at the most compelling reason for
>looking at coordination of beats and that's why I have focused on it.

Could you go into a little more detail on the differences between
equal beating and synchronous beating, and your thinking here?

-Carl

--- In tuning@yahoogroups.com, "Joseph Pehrson <jpehrson@r...>"
<jpehrson@r...> wrote:

> Both the Murray Barbour _Tuning and Temperament_ and the Easley
> Blackwood _The Structure of Recognizable Diatonic Tunings_ came in
> over there at good prices. Unfortunately, it took about a *year* for
> the Blackwood, at least, but it *did* happen. (I foolishly gave up
> and purchased though Barnes & Noble's used services for more...)
>
> You might want to place a search over there and just wait a while.
> It will *finally* happen...

If a book is out of print, get a (often, they are free) university
library card from a nearby university, or use interlibrary loan at
a public library. Then, go to Kinkos. For out of print books this may
be a gray area of the law, about which you could ask a lawyer. However,
academics do it all the time.