Canright Revisited: Every Interval is Just

Don't get me wrong here. I like equal-step tunings as much as the next guy.
I even like 12. I am always amazed at how good it sounds, and at how
powerful it is.

But I do not think of it as imitating any type of Just Intonation. I think
of it as imitating a 12 note scale of 100 cent steps. No interval can
imitate another. Intervals are not actors or comedians. And it is at least
highly un-likely that the ear ever helps out.

>From the time I first got involved with JI, I've been hearing a lot of talk
about equal-step tunings "approximating" Just tunings. I always felt
something was wrong with this argument, and here I attempt to put it into
words. I'll use a recent posting for fresh meat...

>So 22et forces you to abandon much of what you have learned about how
>music works. It has much better 7-limit approximations than 19et, and
>will even get you as close to the 11-limit as Harry Partch's own voice
>could (max. error 20.1 cents). 34et is not consistent beyond the
>5-limit.

There are a coupla problems here. First, the author uses the cents
deviation method to compare 22et to various forms of JI. While this can be
useful to say how far one interval is from another, it cannot be used to
compare the consonance of one interval to another. Consonance is a factor
of the size the number in an intervals ratio.

For example. An interval 16 cents flat of the sublime 6/5 has frequency
ratio 19723/16585. This, of course, is our quite dissonant 12et minor
third. An interval 18 cents flat of the 6/5 bears ratio 19/16. It is a
very consonant minor third found in the duple 16-32 of the harmonic series
(or, to use Denny Genovese's excellent syntax: Mode 16 of the harmonic series).

Second, he is making a statement about the accuracy of Partch's voice.
There are so many ways to measure this (and I doubt any can be any good),
that this data is useless without knowing how it was measured.

Third, he says "max error 20.1 cents". Here, he is probably referring to
22et, in which case the maximum is the kind of error to consider. But, to
make his statement about getting as close as "Partch's own voice could"
work, he must use minimum error when referring to Partch's voice. Partch
wouldn't sing with a minimum error of 20 cents if he was drunk.

Lastly, the author assumes that Partch was trying to imitate 11-limit
intervals when he sang. This is the classic ploy of the
cents-deviation-user: get the intervals within the tuning error of a common
instrument and they might as well be the same. If Partch thought this, he
too should be told that performance is divine; it doesn't imitate anything.

(Incidentally, I don't think Partch thought that. He seems to be stretching
when he uses the fact that the higher identities are more sensitive to
mis-tuning against many ET's in Chapter 17 of Genesis, although this is also
an important consideration.)

To put it another way, and to touch upon the pop in microtones issue
(again!?), we might think music consisted of two parts: Composition and
Performance. This can work even if the two take place simultaneously (as in
improvisation).

Composition is done within a framework, beit 12et, 11-limit JI, or even the
Alvian "free JI" (in this case the framework is Mr. Alves' style of using
ratios, and bravo to his cut on the tape swap).

Performance is done within a sound-making device. Only on the sound-making
devices of keyboards and fretted strings are Composition and Performance
working with the same pitches.

The rest of the time, one of two things happen: Performance exceeds
Composition or Composition exceeds Performance. In the case of Barbershop
singing, or in Reinhard's favorite Pink Floyd, the Performance is correcting
for the deficiencies used in the (12et) Composition. In the case of
Stravinsky, Honeggar, and Shostakovitch, the Performance is mistuning the
Composition (which could sound as well as it controls your mind).

The point is that the finished product, music, is what it is. The ear
doesn't do the watoosee, it hears the intervals played. Intervals don't
imitate anything.

|----------------------------------------|
|Carl Lumma |
|http://users.nni.com/source_of_goodness |
|----------------------------------------|


SMTPOriginator: tuning@eartha.mills.edu
From: Eduardo Sabat
Subject: Dinarra
PostedDate: 20-10-97 20:40:38
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: 20-10-97 20:39:51-20-10-97 20:39:51,20-10-97 19:40:30-20-10-97 19:40:30
DeliveredDate: 20-10-97 19:40:30
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 C1256536.0066847E; Mon, 20 Oct 1997 20:39:46 +0200
Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA21961; Mon, 20 Oct 1997 20:40:38 +0200
Date: Mon, 20 Oct 1997 20:40:38 +0200
Received: from ella.mills.edu by ns (smtpxd); id XA21966
Received: (qmail 1755 invoked from network); 20 Oct 1997 11:40:34 -0700
Received: from localhost (HELO ella.mills.edu) (127.0.0.1)
by localhost with SMTP; 20 Oct 1997 11:40:34 -0700
Message-Id: <199710201843.PAA08962@mail.adinet.com.uy>
Errors-To: madole@mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu