You're right, Rainer - but just in case there's any misunderstanding:
In a meantone temperament you don't expect all the apparent octaves to
be pure, for example the Gb on the first fret (high position) of the 4th
course with the F# on the fourth fret (low position) of the 2nd course -
this is just a consequence of having frets which are straight and cannot
be in different positions on different courses. You still expect the
"proper" octaves to be pure, such as 2nd fret 4th course with open 1st
course. Anyone using meantone fretting has to be aware of the
limitations and test only some octaves and not others (and move frets
according to the notes required by the piece).
Best wishes,
Martin
Spring, aus dem, Rainer wrote:
-----Original Message-----
From: Sam Chapman [mailto:[EMAIL PROTECTED]
Sent: Saturday, October 04, 2008 12:40 AM
To: Andrew Gibbs
Cc: Lute List
Subject: [LUTE] Re: Temperament wondering...
In any tempered fretting system that's been worked out properly you
need to first set the frets, then tune the strings to each other in
perfect octaves or unisons, since these intervals must be pure in all schemes.
If you insist on all unisons and all octaves being pure you have no choice -
you must use equal temperament.
This is a straight forward calculation in linear algebra.
Best wishes,
Rainer aus dem Spring
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