RE: Canright Revisited: Every Interval is Just

Carl's strict belief that "Consonance is a factor
of the size the number in an intervals ratio" leads to absurdities.
According to Carl, the following sequence of ratios represents intervals
of increasing dissonance:

31/21
301/201
3001/2001
30001/20001
300001/200001
3000001/2000001
30000001/20000001
300000001/200000001
3000000001/2000000001
30000000001/20000000001
300000000001/200000000001
3000000000001/2000000000001
30000000000001/20000000000001
300000000000001/200000000000001

Now these intervals are getting closer and closer to 3/2, and after just
a few of them even the best ear can't tell the difference between them
and 3/2. Yet according to Carl, 3/2 is more consonant than any of these
ratios. Thus we must conclude that Carl's definition of consonance has
little to do with anything you can actually hear.


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From: John Chalmers
Subject: Questions
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On Thu, 23 Oct 1997, John Chalmers wrote:
> are there
> any commercially available recordings of music in the 13th root of
> 3/1 scales?

I don't know how commercially available this is, but the Bohlen-Pierce
scale is discussed in chapter 13 of the following book:

TITLE Current directions in computer music research / edited by Max V.
Mathews and John R. Pierce.
PUBLISHED Cambridge, Mass. : MIT Press, c1989.
DESCRIPTION vi, 432 p. : ill., music ; 24 cm.+ 1 disc (digital ; 4 3/4 in.)
SERIES System Development Foundation benchmark series ; 2.
NOTE Includes index.
NOTE Music,CD copy of examples shelved at circulation desk.
SUBJECTS Computer music -- History and criticism.
OTHER AUTHOR Mathews, Max V.
Pierce, John Robinson, 1910-
ISBN 0262132419.

The accompanying CD mentioned in the cataloging above contains four
samples for that chapter; three of them are short compositions.

--pH http://library.wustl.edu/~manynote <*>
O
/\ "Hey--do you think I need to lose some weight?"
-\-\-- o


SMTPOriginator: tuning@eartha.mills.edu
From: Carl Lumma
Subject: The limits of the ear
PostedDate: 23-10-97 19:20:01
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