Apropos of Pythagorean and related tunings, I saved this article from
rec.music.early a while ago. Margo is r.m.e's resident exotic-early-
tunings wonk (she plays this way herself on a pitch-configurable
electronic keyboard). I *dare* any of you to ask her to expand on this...
From "M. Schulter" [EMAIL PROTECTED] Sun Feb 18 23:00:09 2001
Status:
Subject: Re: temperament term???
From: "M. Schulter" [EMAIL PROTECTED]
Date: 18 Feb 2001 23:00:09 GMT
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Article 9424
Jonathan Addleman [EMAIL PROTECTED] wrote:
: But it WAS done now and then, if only to accomodate the range of
: various singers. Vicentino talks about this use of the archicembalo,
: since you can play in meantone in any key. Frescobaldi at some point
: mentioned that an organ tuned in equal temperament would be good for
: this reason as well, though I don't know where that reference is..
: (I got it 2nd or third hand...)
Hello, there, and I must admit to being a bit confused by parts of this
thread, which is one reason that I've preferred simply to read rather than
to post up until now -- but maybe I can comment usefully on certain
points, at least.
First of all, I haven't really previously heard the terms "base" or
"focus" in describing a tuning, although I might speak of range, for
example "a 12-note meantone tuning of Eb-G#," or "a 19-note tuning, likely
1/4-comma, of Gb-B#," or "a 17-note Pythagorean tuning of Gb-A#, evidently
of the type described by Prosdocimus de Beldemandis and Ugolino of Orvieto
in the earlier 15th century."
In this thread, there seems to be a focus on two types of temperament: the
regular meantone tunings of the late 15th to late 17th centuries, still in
use in the 18th century, which might feature anything from 12 to 31 notes
per octave; and the 12-note "well-temperaments" of the late 17th to 19th
centuries, where the circle of fifths closes -- as it does, either
precisely or "virtually" for musical purposes, also in a 19-note meantone
tuning of around 1/3-comma, or in a 31-note meantone of around 1/4-comma.
Indeed Vicentino promoted his _archicembalo_ and _arciorgano_ -- his
superharpsichord and superorgan (the latter a kind of positive organ which
could be disassembled, carried on a mule's back, and then reassembled at
the next performance location -- as permitting free transposition. If we
speak in "keys" in an Elizabethan sense as referring to the pitch level of
a modal final, rather than to later major/minor concepts, then it is
indeed correct that Vicentino's 31-note meantone tuning makes available
all intervals on all 31 steps of the cycle.
Basically Vicentino's tuning scheme of 1555 seems to combine two features
which by the late 17th century were recognized to result in _very
slightly_ different tunings. He describes a division of the whole-tone
into five "minor dieses" of equal size, which would call for 31-tone equal
temperament (31-tET), with major thirds very slightly larger than pure; he
also suggests that major thirds are pure (1/4-comma meantone). In
practice, the variations in a tuning by ear could be greater than the
theoretical difference between these two models.
Quite apart from accommodating singers, Vicentino's tuning makes available
"enharmonic" steps inspired by those of Ancient Greek theory, about
1/5-tone in size, which this composer and theorist espouses for their
subtlety and "gentleness." Indeed, these fifthtone steps have a remarkable
effect, and add an expressive dimension to some more typical 16th-century
chromatic progressions also.
More conventional theorists also address the matter of transpositions to
accommodate singers, but within an apparent framework of 12-note meantone,
where transpositions by fifths or fourths, or by a major second up or down
(two fifths on the tuning chain), are most typical.
In 1570, Guillaume Costeley describes a 19-note keyboard arranged in
thirdtones dividing the octave into equal parts -- this, like Vicentino's
31-note tuning in or around 1/4-comma, is a circular scheme, which would
permit free transposition.
In 1618, Fabio Colonna describes his 31-note meantone keyboard, with a
tuning scheme similar to Vicentino's (likely 1/4-comma), but a keyboard
arranged in five groups of seven notes, with each rank tuned 1/5-tone
apart (resulting in some replications of notes). To demonstrate the closed
nature of this system, he provides a composition giving an "Example of
Circulation" which moves through a circle of cadences on all 31 steps of
the instrument, each featuring motion of the bass by a fifth down or a
fourth up.
He also shows how various modes can be transposed to
