Re: Diesis in 29-tET -- thank you, Marc

Dear Orphon Soul (or Marc),

Please let me say how moving I found your reply: this kind of response
is one of the things that keep us going both with music and with
sharing ideas about it.

We evidently share a love of 29-tET, and I'm excited to meet someone
else fascinated by the "Diesis Thesis" of this tuning. As Paul Erlich
might have me add, it's noteworthy that both Marchettus of Padua in
1318 and Nicola Vicentino in 1555 were champions of the direct
fifthtone or diesis in radically different musical contexts.

Vicentino's _archicembalo_ dividing the octave into 31 near-equal
parts (1/4-comma meantone with pure 5:4 major thirds would be very
close to 31-tET) fits a Renaissance style, just as Marchettus's
fivefold division of the tone (whether we take it as a vocal tuning
system roughly modelled by 29-tET, or something different) and once
fits and amplifies a Gothic setting in ways still open to exploration
in the 21st century.

What I want to say above all, though, is that I love 29 in ways not
always so easy to put into words. I hope to make available some
improvisations in this beautiful tuning soon, maybe the best
commentary of all.

Thank you for your philosophical and artistically engaging articles,
which add to this enthusiasm. Maybe I could add a bit of philosophy,
following your very readable example, which might suggest another
angle of what neo-Gothic style is about.

From one view, neo-Gothic is simply a 3-limit system: the basic ratios
are 2:1, 3:2, 4:3, and 9:8, plus octave complements (e.g. 16:9) or
extensions (e.g. 3:1, 9:4).

At the same time however, it is a "continuum-oriented system," because
all of the other intervals are free to follow just about any pattern
which art or fancy may suggest. Generally Pythagorean diatonicism and
modality (often taken quite flexibly) do favor certain patterns, but
Bob Valentine's 9-note or "nonatonic" scale as I call it shows how it
is possible to do quite radically new things on what I might consider
a "neo-Pythagorean" basis.

While "n-limits" are the basis for much discussion on this List,
neo-Gothic intervals are often described in terms of "flavors," with a
"major third" -- or maybe "submajor-major-supramajor third" taking on
any size from a bit smaller than 21:17 to around 13:10, say somewhere
from 363 to 455 cents or so. This isn't to discriminate against more
neutralish thirds or small fourths either.

There are 13th-14th century roots for a continuum of concord/discord,
and an intonational continuum seems to give this richness a new
musical dimension.

Of course, if you're curious about neo-Gothic, I'd be delighted to
answer questions on or off the list, and it's mainly questions which
teach me how to explain things more clearly, and sometimes to how
understand them more clearly myself also.

You bring an enthusiasm which is precious, a gift which deserves a
response as generous as yours to my article.

29 29 29 29 29 29 29 29 29 29 29 29
29 29 29 29 29
29 29 29 29 29 29 29 29 29 29 29 29

Most appreciatively,

Margo Schulter
mschulter@value.net