More Margo for those that want it

[Richard Moody]

----- Original Message -----
From: <A440A@AOL.COM>
To: <pianotech@ptg.org>
Sent: Thursday, January 11, 2001 4:41 AM
Subject: More Margo for those that want it


|
|    From: "M. Schulter" <MSCHULTER@VALUE.NET>
| Subject: Re: Canto Sacro -- Welcome to Maurizio Umberto Puxeddu
|
|, I would like to say, speaking only for myself , that I regard just
intonation or "JI" as a very diverse category
| of tunings,  .....................................|
| First of all, I regard "JI" as an approach to tuning based on integer
| ratios, rather than a specific tuning or musical style: a "JI" major
| third might be 81:64 (medieval Pythagorean), 5:4 (Renaissance), 9:7 or
| 14:11 or 21:17 or sometimes 13:10 (neo-Gothic), and so on.
|Margo Schulter


 I prefer the simpler approach, that Just Intonation (JI) be limited to just
that, just, or pure intervals ie beatless.   Thus a 5:4 3rd would be major
and just.  The 81:64 is also (sounds like) a major 3rd but beats because
one of the harmonics makes it slightly wide of the Just 5/4 .  This is
realized because 80/64 reduces to 5/4. While it misleading to ponder this as
"1/64" more than 5/4 nevertheless it does tell you it is sharp to a just
3rd.
    This excess does have a name, in this case the comma of Didymus, or
syntonic comma.   The syntonic comma is based on the fact that 4 pure (just)
5ths create a wide 3rd (not just) and this wideness from just is called one
(syntonic)comma.
    That a series just intervals do not beget just intervals is the reason
why we are all here today, or there would be not much to talk about (or
tune) if every note in the scale formed a just interval with every other
note.   To keep JI to mean just or pure intervals, I think would make for a
clearer and more inclusive discussion between tuners, musicians, music
historians musicologist, and <gasp> perhaps even critics.
    As far as expanding JI to include integer ratios, even the ET semitone
can be expressed for musical purposes as 18/17. (98.95 cents) And this
satisfies the Greek notion of the significance of superparticular ratios, as
a mathematical indication of a "beautiful" proportion.
    From  Greeks came the idea of 2:1, 3:2, 4:3, 5:4 ratios with all the
rest of the intervals comming from combinations of these.   However some
superparticulars (ratios with a difference of one between the numerator and
demoninator) are not formed out of any combination of 5:4:3:2:1. namely, 7:6
or 8:7.   When you get to 9:8 and 10:9 you are back in the fold again.  Why
7:6,  a seemingly simple ratio and should be easily formed on the monochord,
is not used, I leave to the microtonalists.  I suppose it has something to
do with only the primes 1,2,3, and 5 are used to make up our "Western"
intervals.    I wonder what 7:6 sounds like.  Is there really a 9:7?  If
there is a 5:3, I supppose so.   -=-ric