source file: mills3.txt
Date: Sat, 3 Jan 1998 17:38:20 +0100

Subject: Horizontal and vertical

From: gbreed@cix.compulink.co.uk (Graham Breed)

Melodic notes do take part in the harmony, whether you like it or
not.  You may have lead and accompaniment using different pitch
sets, but chords are everything.

I also hold that harmony is as much about connecting chords as
considering their properties in isolation.  I quantify the
"dissonance" of a chord change from the dissonance of the two
chords taken together.  If horizontal dissonance is too high, the
harmony sounds arbitrary.  If too low, it sounds weak.  This is
relevant to atonality, where you deliberately avoid both
horizontal and vertical consonance.

I don't agree that tempering resolves the conflict between melody
and harmony.  Melody works fine in JI, it's horizontal harmony
that's the problem.

The structure of a diatonic key puts a limit on the dissonance of
chord changes within it.  The prohibition against roots
progressing by one scale step avoids the most dissonant changes.
The idea of octave equivalence means you can't just keep playing
inversions of the same chord, giving excessive consonance.

Lots of people say that tonality is based on acoustic principles,
but they never give you a full derivation.  I think this has got
something to do with it.


SMTPOriginator:  tuning@eartha.mills.edu
From:  "kris peck" <kpeck@wavetech.net>
Subject:  Johnston, Schneider, Catler, tape swap
PostedDate:  03-01-98 17:39:11
SendTo:  CN=coul1358/OU=AT/O=EZH
ReplyTo:  tuning@eartha.mills.edu
$MessageStorage:  0
$UpdatedBy:  CN=notesrv2/OU=Server/O=EZH,CN=coul1358/OU=AT/O=EZH,CN=Manuel op de Coul/OU=AT/O=EZH
RouteServers:  CN=notesrv2/OU=Server/O=EZH,CN=notesrv1/OU=Server/O=EZH
RouteTimes:  03-01-98 17:36:40-03-01-98 17:36:41,03-01-98 17:36:00-03-01-98 17:36:00
DeliveredDate:  03-01-98 17:36:00
Categories:  
$Revisions:  

Received: from ns.ezh.nl ([137.174.112.59]) by notesrv2.ezh.nl (Lotus SMTP MTA SMTP v4.6 (462.2 
9-3-1997)) with SMTP id C1256581.005B3EE3; Sat, 3 Jan 1998 17:38:35 +0100
Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA07323; Sat, 3 Jan 1998 17:39:11 +0100
Date: Sat, 3 Jan 1998 17:39:11 +0100
Received: from ella.mills.edu by ns (smtpxd); id XA07365
Received: (qmail 3325 invoked from network); 3 Jan 1998 08:38:14 -0800
Received: from localhost (HELO ella.mills.edu) (127.0.0.1)
  by localhost with SMTP; 3 Jan 1998 08:38:14 -0800
Message-Id: <199801031634.KAA10878@riptide.wavetech.net>
Errors-To: madole@mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu