The late 16th century bearing plan for 2/7 comma meantone?

Hey All,

Monz, I thought you might be able to answer this, as you have done some
research into Zarlino, and had some translation done. But anyone else who
knows, feel free to jump in!

What would be the technique (bearing plan) used by Zarlino's contemporaries to
tune 2/7 comma meantone as accurately as possible? It seems that the addition
of 3 more mean-tone fifths from the normal 1/4 comma tuning would make it
more of a headache. Certainly 14/ and 1/3 comma are a snap in comparison, no?

I know that the starting point for a C-based tuning would be two 5/4's from F
(F-A-C#), but how did they 'calculate' the size of 7 equal fifths by ear? Was
it trial, error, and retrial? Or did they use some kind of monochord-like
reference instead after figuring out the geometry of string lengths or some
similar technique?

The answer I'm interested in here is how they did it way back-I know how to do
the modern approach with beat rates, etc......

Thanks in advance,
Aaron.

--
OCEAN, n. A body of water occupying about two-thirds of a world made
for man -- who has no gills. -Ambrose Bierce 'The Devils Dictionary'

--- In tuning@yahoogroups.com, "Aaron K. Johnson" <akjmicro@c...>
wrote:

>
> Hey All,
>
> Monz, I thought you might be able to answer this,
> as you have done some research into Zarlino, and had
> some translation done. But anyone else who knows,
> feel free to jump in!

OK, i'm here! :)

Aaron is referring to my two webpages:

http://sonic-arts.org/dict/2-7cmt.htm
http://sonic-arts.org/monzo/zarlino/1558/zarlino1558-2.htm

> What would be the technique (bearing plan) used by
> Zarlino's contemporaries to tune 2/7 comma meantone as
> accurately as possible? It seems that the addition
> of 3 more mean-tone fifths from the normal 1/4 comma
> tuning would make it more of a headache. Certainly 14/
> [_sic_: 1/4] and 1/3 comma are a snap in comparison, no?
>
> I know that the starting point for a C-based tuning would
> be two 5/4's from F (F-A-C#), but how did they 'calculate'
> the size of 7 equal fifths by ear? Was it trial, error,
> and retrial? Or did they use some kind of monochord-like
> reference instead after figuring out the geometry of string
> lengths or some similar technique?
>
> The answer I'm interested in here is how they did it
> way back-I know how to do the modern approach with
> beat rates, etc......

i only know the sections from Zarlino's work that have
been translated into English, by Marco/Palisca 1968
(Yale University Press), by Strunk 1950 (revised version
out now by W. W. Norton), and by Perretti 2003 (my webpage
link above).

none of those parts say anything about actually tuning up
a harpsichord. there is, however, an extremely detailed
description of how to set up the monochord to acheive the
tuning. i imagine that comparison with the monochord was
used to tune regular instruments by ear.

-monz

--- In tuning@yahoogroups.com, "Aaron K. Johnson" <akjmicro@c...>
wrote:
>
> Hey All,
>
> Monz, I thought you might be able to answer this, as you have done
some
> research into Zarlino, and had some translation done. But anyone
else who
> knows, feel free to jump in!
>
> What would be the technique (bearing plan) used by Zarlino's
contemporaries to
> tune 2/7 comma meantone as accurately as possible?

calculation of, and tuning by, beat rates was completely unknown in
the 16th century, according to the known history of tuning
technology. as i recall, a monochord was constructed for the purpose.

also, i see no evidence that any meantones were tuned back then with
what we would consider good accuracy today. the fifths would have
probably varied; they could have been made approximately equal by
judging their size *melodically* (in fact that's what was usually
done, according to the historical documents), but there are limits to
how well that can work.

hope that answers your various questions!