Fwd: [tuning-math] Re: ET tuning and rhythm

The FRETS on guitars and such were built for
12toneET, which is not so say that the strings
were more likely to be tuned to frets than to
harmonics. In most tonal music, a succussion
of guitar chords (tuned in harmonics) will contain
SOME arithmetic intervals both within each chord
and between successive chords. The guitar mediates
tuning systems.

---- Original message ----
>Date: Mon, 09 Sep 2002 19:18:52 -0000
>From: "wallyesterpaulrus" <perlich@aya.yale.edu>
>Subject: [tuning-math] Re: ET tuning and rhythm
>To: tuning-math@yahoogroups.com
>
>--- In tuning-math@y..., "Hans Straub" <straub@d...> wrote:
>> > --- In tuning-math@y..., "Hans Straub" <straub@d...>
wrote:
>
>> The formula, of course, applies only for music in 12-TET,
hence
>indeed not
>> for pre-Beethoven.
>
>viols and lutes and guitars were tuned in 12-equal
centuries before
>beethoven.
>
>meanwhile, though 12-equal was fully worked out
mathematically in
>1585 by Simon Stevin and in 1636 by Marin Mersenne, it
would have to
>wait until 1802-1817 (1850s in england and spain) to become
a de
>facto standard. post-beethoven, essentially.
>
>
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--- In tuning-math@y..., <Josh@o...> wrote:
> The FRETS on guitars and such were built for
> 12toneET, which is not so say that the strings
> were more likely to be tuned to frets than to
> harmonics. In most tonal music, a succussion
> of guitar chords (tuned in harmonics) will contain
> SOME arithmetic intervals both within each chord
> and between successive chords. The guitar mediates
> tuning systems.

still, any reasonable guitar tuning using harmonics would lead to an
overall pitch set constrained to be far closer to 12-equal than those
used on keyboard instruments in the 16th through 18th centuries. if
you disagree, please propose a sample guitar tuning by harmonics.