Yahoo Tuning Groups Ultimate Backup tuning Representing Meantone Tunings with "NNN"

Hey!

A new web page, inspired by Tuning List members Dave Hill, Rick Tagawa, and
Margo Schulter:

"Representing Meantone Tunings with Nowitzkian Note Names"

http://nowitzky.hypermart.net/justint/nnnmt.htm

Comments are welcome. Thanks!

--Mark Nowitzky
nowitzky@alum.mit.edu, AKA tuning-owner@egroups.com

+-------------------------------------------------------
| Mark Nowitzky
| email: nowitzky@alum.mit.edu
| www: http://nowitzky.hypermart.net
| "If you haven't visited Mark Nowitzky's home
| page recently, you haven't missed much..."
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>
> Message: 1
> Date: Wed, 17 May 2000 09:06:36 -0700
> From: Mark Nowitzky <mnowitzky@yahoo.com>
> Subject: Representing Meantone Tunings with "NNN"
>
> "Representing Meantone Tunings with Nowitzkian Note Names"
>
> http://nowitzky.hypermart.net/justint/nnnmt.htm
>
> Comments are welcome. Thanks!
>
> --Mark Nowitzky
> nowitzky@alum.mit.edu, AKA tuning-owner@egroups.com

Hello, there, and I must say that I enjoy your system as one approach to
representing both JI tunings (e.g. 3-limit or Pythagorean, 5-limit) and
meantone temperaments in terms of syntonic comma adjustments. The
explanation of your solution for easily representing both the "comma
number" and octave number (if desired) in ASCII is especially attractive.

Incidentally -- and this may just be my personal quirk -- on first reading
your notation, I noticed a curious coincidence. If the default comma
number is taken as "5", then a pure major third like 5C5 4E5 (with the E a
comma number lower than the C, or in other words a syntonic comma smaller
than Pythagorean) will suggest by the comma numbers the ratio 5:4. Another
way of stating this is that the 5th partial of 5C5 will coincide with the
4th partial of 4E5. Of course, this is just a fortuitous consequence of
choosing a default comma number of "5", but nevertheless could have
mnenomic value. (Here I'm counting the fundamental as the "first
partial.")

Likewise with a pure minor third such as 5E5 6G5 -- suggesting the ratio
of 5:6, although here it's the _fifth_ partial of G which will coincide
with the _sixth_ partial of E.

Of course, one might say that with 5C5 4E5, the "5:4" represents the
string-ratio (or organ-pipe ratio, etc.), while with 5E5 6G5 the
"5:6" represents the frequency-ratio.

Anyway, I found the notation readable, and noticed for example that in
your example of a 5-limit scale, the interval 5D5 4A5 or the like would be
a narrow "Wolf" fifth at 40:27, as is common in such examples.

Incidentally, the part about 72-tet on six keyboards was very interesting.
At first blush, I wondered if an adjustment of 16-2/3 cent might be a bit
small, given that the syntonic comma of 81:80 is about 21.51 cents (closer
to a step in 60-tet) -- but then I remembered that given the "geometry" of
12-tet, subtracting 16-2/3 cents (or 1/72 octave) from a 12-tet major
third gives something very close to a just 5:4. Since a precise adjustment
would be about 13.69 cents, the result is actually a major third about 3
cents _narrower_ than pure, quite close to a Pythagorean schisma major
third (or diminished fourth) about 1.95 cents narrower than pure.

An aside: I've experimented with Pythagorean on two 12-note keyboards, a
"Xeno-Gothic" tuning providing the usual 3-limit intervals plus various
5-limit and 7-limit approximations for intervals generally treated as
unstable in a Gothic or "neo-Gothic" stylistic setting. I wonder if a
notation based on Pythagorean rather than syntonic comma numbers might fit
this system. For example, using your "5" as a default comma number,

5D4 6F#4

would be a major third a Pythagorean comma wider than the usual 81:64,
possibly the kind of wide cadential interval Marchettus of Padua
(1318) may have intended for a progression such as

6F#4 5G4
5D4 5C4

Here we have a new "isotope" of the standard M3-5 resolution by stepwise
contrary motion, with the major third a comma wider than usual, and the
melodic semitone in the upper part a comma narrower than the usual limma
of 256:243 (or ~90.22 cents) -- or about 66.76 cents, a kind of
"third-tone" interval.

Also, I wonder if such a notation could be made "three-dimensional" for
7-limit JI, etc.

Most appreciatively,

Margo Schulter
mschulter@value.net

Representing Meantone Tunings with "NNN"

🔗Mark Nowitzky <mnowitzky@yahoo.com>

🔗M. Schulter <MSCHULTER@VALUE.NET>

🔗graham@microtonal.co.uk