source file: mills2.txt


Subject: 7Limit--MOre & Thanks

From: HFORTUIN@delphi.com

First of all, let me thank Paul E for suggested references, and his offer
 of exchange. Sorry I did not respond earlier, but I generally check my home
e-mail once per week, to allow me to maintain a healthy balance between
practical and theoretical xenharmony. Paul, I accept--shall you mail first, or
I? To what address? Let me know by e-mail.

Secondly, I appreciate Garys recent posting on the 7/7, 8/7, ...14/7 scale, and
Brians on the Moreno. vs. Blackwood-Rapaport extremes of xenharmonic theory
<Regener should be added to the Blackwood group, by the way--I will call them
BRR>. Let me offer part of my own evolving view in xenharmonic theory, which
will be formalized in a musician-readable manner in my upcoming paper:

I agree with Brian in the July 11 posting:
<<...the great drawback of trying to force all equal
temperaments into the conceptual framework of 12-TET
is that it leads the composer to completely overlook 
many useful <but highly non-twelvular> melodic and
harmonic resources.>>

WE NEED TO START LOOKING AT THOSE <<non-twelvular>> RESOURCES!! 

One important difference between most of the common >12ETs is the presence of
intervals with good matches to the simple 7-limit ratios. While 12-ET theory &
its BRR extensions provide some useful beginnings for analyzing their
functionality, such views fail to consider how the 7-limit intervals can be
UNIQUE TONAL HARMONIC FUNCTIONS, supplementing the 3 & 5-limit intervals
represented in such tunings. In other words, I would like to provide at least a
good beginning for a 3-5-7 tonal harmonic theory, which would be at least
relevant to revisiting late Romantic and tonal jazz harmony. Because there are
several >12ETs in common use, I will describe these functions from a JI basis.

A great example of the error of neglecting 7-limit intervals comes with the
mapping of 4/5/6/7 into >12-ETs. Proceeding from BRR, it should be spelled above
C like this: C-E-G-Bb. However, this mapping is not even correct in 19-ET, let
alone higher ETs. Already in 19-ET, the best match to 7/4 <1.75> would be the
15th pitch above C, Bbb <ratio 1.728>, rather than Bb <ratio 1.793>! As one
would expect, the chord formed with the Bbb is clearly more consonant than that
with Bb.

So far, I find the best start on the voice-leading implications of this to be in
Fokkers New Music in 31 Tones. 

By the way, I think a HTML version of the eventual paper might be a great
way to distribute it, in addition to a printed publication. I'll let you
know when it's all ready.

Harold Fortuin
hfortuin@delphi.com

------------------------------

Topic No. 3

Date: Sun, 14 Jul 1996 21:57:00 -0400 (EDT)
From: John Maxwell Hobbs <jmax@interport.net>
To: tuning
Subject: Mclaren's ravings?
Message-ID: <Pine.SUN.3.91.960714214649.18127A-100000@interport.net>


Let me see,

1.  Lincoln Center is bad because it won't present music in alternate 
tunings at Alice Tully Hall.
2.  Bang On A Can is good because they will present music in alternate 
tunings.

- For your information, Bang On A Can presents its concerts in Alice 
Tully Hall.
3.  Therefore either Lincoln Center or Bang On A Can cannot possibly exist.

1.  The mainstream musical establishment is bad because it "censors" 
music in alternate tunings.
2.  The music of John Cage is bad.  How do we know this is true?  Because 
the mainstream musical establishment says so.
3.  Therefore, either the mainstream musical establishment is correct in 
"censoring" music in alternate tunings, or the musical establishment is 
incorrect in saying that the music of John Cage is bad.

And Mclaren wonders why people say he's raving.

P.S.  On an unrelated matter - Don't fixed tunings only matter on fixed 
pitch instruments?  


-John Maxwell Hobbs
jmax@interport.net

------------------------------

Topic No. 4

Date: Sun, 14 Jul 1996 22:38:15 -0500 (CDT)
From: Paul Kenneth Roser <pkroser@csd.uwm.edu>
To: tuning
Subject: Scale database?
Message-ID: <199607150338.WAA06287@alpha2.csd.uwm.edu>

   I seem to be unable to locate the database of scales, which I believe
Manuel has assembled (apologies if I'm attributing this work to the wrong
person). I think it was an ftp site, but I'm not sure, and can't find it in
my notes. Could someone point me in the right direction?
   Many thanks,

Paul Roser (pkroser@csd.uwm.edu)