Perishing Logic

Fret positions on surviving early instruments are weak evidence of tuningpractice for several reasons. First of all, the frets were tied on so that
their position is likely to have shifted. Second, the frets were made of
natural materials (especially gut) so that they tend to decay over time.
Third, as all players of fretted instruments know, the position of the fret
is only one factor in the pitch produced. Most players can adjust the pitch
considerably with their fretting fingers.

Lindley's book on Lutes, Viols, and Temperaments (has someone got the
reference handy?) gives some ideas about how a set of frets can be subtlyset so as not to yield the same ratio on each string. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Mon, 14 Jul 1997 01:46 +0200
Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA03296; Mon, 14 Jul 1997 01:47:27 +0200
Date: Mon, 14 Jul 1997 01:47:27 +0200
Received: from ella.mills.edu by ns (smtpxd); id XA03246
Received: (qmail 17869 invoked from network); 13 Jul 1997 23:30:34 -0000
Received: from localhost (HELO ella.mills.edu) (127.0.0.1)
by localhost with SMTP; 13 Jul 1997 23:30:34 -0000
Message-Id:
Errors-To: madole@mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu

>}>In each series below, each term represents the number of notes in the
>}>simplest equal temperament that improves upon the accuracy of the
>}>previous one. Tunings in parentheses are the second-best for up to that
>}>many notes. I don't go beyond 200TET. Accuracy is defined with respect
>}>to JI in the indicated odd limit; equal temperaments not consistent
>}>within the given limit are excluded.
>
>}This chart ROCKS! Could you tell us more about how you define "limit"?
>
>Limit can refer either to a standard of consonance or the design of a just
>tuning system. In the latter usage, a prime number characterizes the largest
>prime number occuring as a factor in any of the just ratios. When referring
>to a standard of consonance, it usually refers to the largest ODD factor in
>all the ratios considered consonant. Partch usually used it in this way, as
>he subscribed to a fairly strong form of octave equivalence. As it happens,
>Partch's music can be called 11-limit using both definitions. I was using the
>standard of consonance definition in this chart. I have already posted on
>consistency, otonal limit, utonal limit, and saturated chords; unfortunately
>I don't think an archive exists for the last two years of the digest.


SMTPOriginator: tuning@eartha.mills.edu
From: Johnny Reinhard
Subject: Re: My Friends the Aliens
PostedDate: 19-12-97 19:12:31
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: 19-12-97 19:10:23-19-12-97 19:10:23,19-12-97 19:09:59-19-12-97 19:10:00
DeliveredDate: 19-12-97 19:10:00
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 C1256572.0063D22B; Fri, 19 Dec 1997 19:12:15 +0100
Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA19893; Fri, 19 Dec 1997 19:12:31 +0100
Date: Fri, 19 Dec 1997 19:12:31 +0100
Received: from ella.mills.edu by ns (smtpxd); id XA19849
Received: (qmail 12624 invoked from network); 19 Dec 1997 09:54:02 -0800
Received: from localhost (HELO ella.mills.edu) (127.0.0.1)
by localhost with SMTP; 19 Dec 1997 09:54:02 -0800
Message-Id:
Errors-To: madole@mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu