Missing Manuscript - Help Please!

As a result of reading the recent postings on Greek philosophy,
mathematics, music, etc.: it seems to me that we at at a crossroads
in musical tuning, similar to that which mathematics passed,
a couple of hundred years ago.

Many still seem to judge the validity of a tuning system only
by its proximity to integer frequency ratios and the "harmonics"
which are arrived at by this (to my mind) simplistic logic.

>From my readings, experiments, and observations, I am convinced
that John Harrison had managed to break through this barrier
in the mid-eighteenth century.

At the end of a very successful scientific career, during which he
made
three major new inventions, and "won" the prize for Longitude with
his horological designs, he devoted his last years to the study of
musical tuning.

This is a subject very closely akin to his other particular areas
of expertise, i.e. navigation, pendulums, harmonic motion, and
the study of mechanical systems with regard to TIME.

In his book "Concerning Such Mechanism ......"

[A transcription of which is at:

http://www.wonderlandinorbit.com/projects/lullaby]

(after "slagging off" his contemporaries), he very
clearly states his conclusions: The "Natural Notes
of Melody" may be derived mathematically from pi.
He gives no experimental details, except that he used monochords,
and clearly understood and criticises WNR (whole number ratio) logic
and practice.

He seems to have been criticized for this work, in the same way
that his tunings are criticised today.
[Not for their impracticalities, tunelessness, or any musical
reasons - (it works exquisitely for musical harmony, modulation,
and transposition for all types of "ethnic" music which I have
encountered to date); yet for its lack of "scientific proof"].

After "CSM ....." was published he wrote a manuscript

HARRISON, John. "A True and Full Account of the Foundation of
Musick, or, as principally therein, of the Existance of the
Natural Notes of Melody". An unpublished manuscript of 182 pp.,
which is cataloged as item 8961 in Bibliotheca
Chemico-Mathematica issued by Messrs. H. Sotheran of London in
1921, but has since been lost.

I have seen only one page of this manuscript. It arrived at my
London address from a horological researcher, about ten years ago.
I hear that it was by way of a Folkestone antiquarian bookseller.
The page was a diagram of a clockface, with the note names written
around the circumference, and marks where later steps of fourths
and fifths would arrive.
It showed the Large interval at the angle of the radian
i.e. 360/(2*pi) 57.3 degrees.

C was at 6 o'clock and the other naturals were arranged
ascending clockwise.

>From this page and the title, I suspect that the missing
manuscript revealed Harrison's experiments. I heard that the offices
of Sotheran were destroyed during the London blitz by a direct hit.

I wish to attempt to reconstruct Harrison's experiments, for I
believe that they will give us much greater insight into his
thinking,
and possibly provide us with "scientific proof".

Any help, pointers, or comments about this manuscript will be
appreciated.

lucy@hour.com








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Will Grant wrote:
>
> Well, I stand corrected re key or pitch in reference to
> Jonathan Walker's remarks, but I don't see what essential
> difference it makes to what I was saying.
>
> Of course, you can't tune one choir of strings to more
> than one well temperament at a time; but you could tune
> differently on Tuesdays and Thursdays, or you could tune
> one 8' one way, and another 8' another, couldn't you ?

I'm afraid this will get you no further: it can never be the case that
one well-tempered scheme will give you a C# (and not a Db), while
another will give you Db (and not C#). _Any_ well-tempered scheme will
simply give you C#/Db -- neither can be in a favoured position. The only
way I can construe you here is to conclude that you are confusing well
temperaments with other keyboard tunings, like meantone, which don't
close a chain of fifths into a circle. If this isn't the case then I'll
be happy to hear your explanation, but from what you've said so far I
can't come to any other interpretation.

While you haven't said anything to suggest it, how about this: is it
remotely possible that you were thinking of, say, two notional
well-tempered schemes, one of which would give you a very good
approximation of a 5/4 above A, while the second would instead give you
a similarly good 5/4 below F? So the first you would call your good C#
tuning, and the second your good Db tuning? This is as much as I can do
by way of speculating about your intentions. I'll wait to see what you
have to say.

> In fact, for 1/4-tone music, etc., ordinary harpsichords
> are, I think, a lot more convenient than ordinary pianos.

What, if they have two ranks? Vishnegradskij managed well enough with
two pianos: each is in standard 12TET, but in relation to each other,
they are tuned a 2^(1/24) apart. I still find it a little comical,
because I'm tempted to listen to each part separately -- the musical
style was not particularly daring for its times, beyond the tuning
aspects; but perhaps I should try harder.
--
Jonathan Walker
Queen's University Belfast
mailto:kollos@cavehill.dnet.co.uk
http://www.music.qub.ac.uk/~walker/



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