Re: Just intonation definition -- Aaron (1523)

Hello, there, and in response to queries about early uses of the term
"just" in an intonational context, I might cite the keyboard tuning
instructions of Pietro Aaron (or Aron) in his _Toscanello in musica_
(1523), where this term seems at once to suggest the idea of a pure
interval, and to illustrate Monz's connection of the "just" concept
with the 5-limit trends of the late 15th and 16th centuries.

In a description of how to tune a harpsichord written in Italian for a
"popular" audience, Aaron suggests beginning by tuning the octave C-C
so as to give it as much "unity" as possible.

Then he directed tuning the major third C-E to make as "sonorous and
just" (using the terms _sonora_, _giusta_) as possible, again to give
the interval as much unity as possible.

Here it seems reasonable indeed to take _giusta_ as referring to a
pure octave or 5:4 major third -- and to note, as Dave Keenan might,
that Aaron describes this "justness" as synonymous with "sonorousness"
or "as much unity as possible" without saying anything about
mathematical ratios.

Interestingly, this use of _giusta_ occurs in a description of
_participatio_, a term generally translated into English as
"temperament." After describing the tuning of the first octave C-C and
major third C-E, Aaron then explains how each fifth in the chain
C-G-D-A-E should be made somewhat narrow, then directing that the
process be continued in the flat or sharp direction for the rest of
the tuning.

Aaron's tuning is often cited as the first known description of
1/4-comma meantone with pure major thirds at 5:4, and Mark Lindley has
argued that the term _giusta_ elsewhere in the tuning directions may
refer to tempered intervals also.

However, the idea of tuning a major third to make it as _giusta_ as
possible would appear to tie in very nicely both with Dave Keenan's
focus on "justness" as an aural quality, and Monz's association of
this concept with emerging 5-limit systems of the Renaissance.

Most respectfully,

Margo Schulter
mschulter@value.net

--- In tuning@egroups.com, "M. Schulter" <MSCHULTER@V...> wrote:

> http://www.egroups.com/message/tuning/16502
>
> Hello, there, and in response to queries about early uses of
> the term "just" in an intonational context, I might cite the
> keyboard tuning instructions of Pietro Aaron (or Aron) in his
> _Toscanello in musica_ (1523), where this term seems at once
> to suggest the idea of a pure interval, and to illustrate
> Monz's connection of the "just" concept with the 5-limit
> trends of the late 15th and 16th centuries.
>
> ...
>
> Then he directed tuning the major third C-E to make as
> "sonorous and just" (using the terms _sonora_, _giusta_)
> as possible, again to give the interval as much unity as
> possible.
>
> Here it seems reasonable indeed to take _giusta_ as referring
> to a pure octave or 5:4 major third -- and to note, as Dave
> Keenan might, that Aaron describes this "justness" as
> synonymous with "sonorousness" or "as much unity as possible"
> without saying anything about mathematical ratios.

Thank you *very much*, Margo, for digging up this reference!

Aron's use of the Italian term _giusta_ is indeed an exact
cognate of the Oxford English Dictionary usage of the term,
appearing here some 288 years earlier than the O.E.D. definition.
I suspected that "just intonation" first occurred in Italian
at around this time; I appreciate your confirmation of it.

> ...
> Aaron's tuning is often cited as the first known description
> of 1/4-comma meantone with pure major thirds at 5:4, and Mark
> Lindley has argued that the term _giusta_ elsewhere in the
> tuning directions may refer to tempered intervals also.
>
> However, the idea of tuning a major third to make it as
> _giusta_ as possible would appear to tie in very nicely
> both with Dave Keenan's focus on "justness" as an aural
> quality, and Monz's association of this concept with emerging
> 5-limit systems of the Renaissance.

I think it's very good that you point out that Aron's use
of the term "just" may not refer to the entire tuning system
(which I would agree is a description of 1/4-comma meantone),
but rather that it seems to refer specifically to the sonorous
quality of the "major 3rd", which whether in JI or in 1/4-c MT
is intended to be composed of pitches forming a 5:4 ratio.

Of course, as I've been stating continuously, there are
certainly other possible definitions of "just intonation"
possible which have evolved over the succeeding centuries.
But it's good to finally pin down both the date and the
meaning of the earliest use of the term.

-monz
http://www.ixpres.com/interval/monzo/homepage.html
'All roads lead to n^0'