Re: Seeking a Topic ... (for Steven Kallstrom)

Hello, there, Steven Kallstrom and everyone.

In exploring medieval and Renaissance intonations, my own special
fascination in theory and practice, you might focus on a range of
themes. Here I might just mention a few topics, including the extended
Renaissance/Manneristic meantone tunings in which you have expressed
an interest.

For the Gothic era of around 1200-1420, Pythagorean intonation and its
possible variations could provide one theme. A general Pythagorean
tuning FAQ focusing on this era is available at:

http://www.medieval.org/emfaq/harmony/pyth.html

An especially intriguing medieval topic might be the intonational
system of Marchettus of Padua as expounded in his _Lucidarium_ of
1318. Joe Monzo and I have had some discussions about Marchettus on
this List, and Jan Herlinger's modern edition of the treatise provides
one starting point for lots of uncertain but captivating conjecture.

Among other things, Marchettus describes and gives examples of direct
chromaticism (e.g. G-G#-A), proposes what might be considered the
first "microtonal" notation for polyphony distinguishing between more
than two sizes of semitones, and describes the use of extra-wide
cadential major thirds and sixths expanding to fifths and octaves
respectively which _might_ represent new interval types roughly
intermediate between usual Pythagorean major thirds and fourths, or
major sixths and minor sevenths.

Since Marchettus is addressing vocal intonation rather than the tuning
of fixed-pitch instruments, some ambiguity may not be so surprising,
but his apparently accentuated variations on Pythagorean tuning leave
room for lots of experimentation regarding the intonation of music
from his 14th-century milieu, and also for new "neo-Gothic" music
based on a range of extended Pythagorean or "super-Pythagorean"
tunings.

Turning now to the 16th and early 17th centuries, theorists of special
interest from a viewpoint of 31-note meantone tunings and instruments
include Nicola Vicentino (1555) and Fabio Colonna (1618). For some
background and references, you might try among other sources a series
I did here in October of 1999, and also an excellent article of Bill
Alves originally published in _1/1_:

/tuning/topicId_5609.html#5609 (Pt. 1)
/tuning/topicId_5621.html#5621 (Pt. 2)
/tuning/topicId_5646.html#5646 (Pt. 3)
/tuning/topicId_5670.html#5670 (Pt. 4 -- notes)

http://www2.hmc.edu/~alves/vicentino.html (Alves article)

Theorists of this Renaissance/Manneristic era may not have made any
rigorous distinction between a meantone tuning with pure major thirds
(1/4-comma temperament) and one dividing the whole-tone into five
precisely equal parts (31-tET).

By 1666, the theorist Lemme Rossi does make this fine distinction,
with Christian Huygens offering a more rigorous mathematical basis in
his famous advocacy of an equal 31-tone division near the end of the
century.

However, the circulating 31-note tunings of Vicentino and Colonna very
closely approach this model if we assume pure major thirds, and both
Vicentino and Colonna speak at once of a tuning after "common
practice" (i.e. usual meantone of some variety) and of a division of
the tone into five equal dieses.

Therefore, I might prefer the neutral or open category "31-note
meantone systems," including either 1/4-comma or 31-tET or the likely
variations tuned in practice on the archicembalo of Vicentino or the
_Sambuca Lincea_ of Colonna.

These are just a few starting points, and I would be glad to help if I
can either through this list or via e-mail.

Most appreciatively,

Margo Schulter
mschulter@value.net