source file: m1405.txt
Date: Mon, 4 May 1998 16:56:34 -0500 (CDT)

Subject: Re: Reply to Paul Hahn

From: Paul Hahn <Paul-Hahn@library.wustl.edu>

On Mon, 4 May 1998, Paul H. Erlich wrote:
>             I almost wanted to include you, but your concept of
> higher-level consistency seems to support the other side. For example,
> insisting that the approximations to 3-limit intervals be level-2
> consistent means that you care about approximating certain 9-limit
> intervals.

The implications of higher levels of consistency are varied, and I don't
want to get into another flamewar about it at this point, but just let
me say this:

(a) I wish to go beyond basic (level 1) consistency because it is
possible for an ET to be level 1 consistent and still err from a given
just ratio by nearly half the stepsize of the ET.  An extreme example:
18TET is consistent to the 7-limit, but its 11-step "fifth" is only
barely better as an approximation to the 3/2 than its 10-step interval.
One is over 31 cents high, the other more than 35 cents low; the
difference between the two errors is less than four cents! 

(b) There is no inconsistency ( 8-)> ) in supporting both higher-level
consistency and the use of odd limits over primes.  In fact, it would be
rather difficult to adapt the idea of higher-level consistency to a
prime-limit paradigm.

(c) (semi-serious) I said I was on your side; isn't that good enough for
you?  Don't look a gift horse in the mouth.  8-)>

--pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
    O
   /\        "Churchill? Can he run a hundred balls?"
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