The bells and double logs

On 10 Mar 2005, at 09:27, tuning-math@yahoogroups.com

Yahya Abdal-Aziz wrote:
> Speaking as a mathematician, our modes of expression have
> become ever more a telegraphic shorthand, as new concepts
> have taken root and flourished. Consequently, reading an
> author like Harrison can seem strangely elliptical, as it takes
> him forever to state a relationship that we would now describe
> in a word or a short formula.
>
> The reverse of this coin is that certain mathematical
> procedures, once standard fare, have been relegated to the
> dustbin. Few of my students have ever performed a long
> division, or extracted a square or cube root, by hand, and
> none since the late seventies would recognise log tables, let
> alone know how to use them. This makes me wonder what
> methods and techniques Harrison knew that I never learnt,
> because my teachers or theirs deemed them unprofitable?
>
> To me, much of the pleasure in reading the history of science
> is the journey of discovery of ideas. (How DID they ever think
> of that?) So, in teaching, it has been my pleasure to share
> that journey with whoever is willing.
>
>
> If we are right in thinking that understanding Harrison and
> his times is key to understanding his writings, the question
> surely becomes - What is the best way to gain that insight?
>
> Who, on this list, has done much reading of scientific and
> mathematical literature of Harrison's era?

> [YA] I would expect he was looking for some kind of exponential
> or power law relationship, that can only be uncovered by taking
> double logs.
>
> The pi may be unnecessary in the calculations in this case, because it
> could be implied by the circular shape of the bells, and "cancelled
> out".
> I assume that he was working with round plan view (conventional church
> bell-shaped) bells.
> [YA] Seems reasonable.
>

> [YA] If he was thinking of an exponential relationship, perhaps it
> involved a rational exponent eg 3/2 or -2/3, such as occurs in some
> physical formulae.
> _______________________________________________________________________> _
> ... and them for the Thicknesses Double, so they are in each respect > as in
> the two following Tables.
> Log., viz. as deduc'd from the former part of this Book 1/4 Log. for > the
> Diameters.
> Octave ----------- ,0752575
> 5th --------------- ,0436175
> 4th --------------- ,03164
> Sharp 3rd. -------- ,023955
> Larger Note ------- ,0119775
> Lesser Note ------- ,007685
> LogsLog.'s, or as according to the former part of this Book double > Logs. for
> the Thicknesses.
> Octave ----------- ,60206
> 5th ------------- ,34894
> 4th -------------- ,35312
> Sharp 3rd -------- ,19164
> larger Note ------ ,09582
> Lesser Note ------ ,06148
> Things being now as farther prepar'd, I come to their use as with > regard to
> the right, or due proportioning of Peals of bells; viz. so far as > touching
> the Diameters at their Skirts, and Thickness at their Sound-Bows.

The letter was not published in today's New Scientist, on the London newsstands, so I expect it will appear next week.

The set of log numbers above are the same, derived from pi, as used to calculate the intervals for LucyTuning.

Yahya Abdal-Aziz may have spotted the crux of the matter.

So J.H. was taking the log principle to the next stage, and may then have been considering integer ratios.

So it becomes whole number ratios (like JI); yet two geometric steps removed.

JI seekers were/are looking for zero beating in frequency whole numbers;

Harrison was looking for matching harmonic intervals, (which beat) and going via pi to get to integer ratios of double logs, of the dimensions of the metal in circular bells
which could be found in the bells physical properties ?

It does sound convoluted, yet is certainly a novel way of conceptualising tunings, and judging by the success of his previous inventions may actually be practical.

Now we need to try out his formula and see how well works in the real world.

My older brother is at present "playing tourist", in Australia, so I'll ask him to go see the bells people that you pointed me to in an earlier posting, and find out if they are interested in experimenting with his formulas.
The other option seems to be to get some prototypes designed and built to J.H.'s specs here in London, as I did with the guitars 20 years ago, to discover what happens and how well his theory works in the physical world.

Now to explore the maths implications a little further.

Charles Lucy - lucy@harmonics.com
------------ Promoting global harmony through LucyTuning -------
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-----Original Message-----
________________________________________________________________________
Date: Thu, 10 Mar 2005 16:43:32 +0000
From: Charles Lucy
Subject: The bells and double logs

...

> [YA] I would expect he was looking for some kind of exponential
> or power law relationship, that can only be uncovered by taking
> double logs.

[Charles]
The letter was not published in today's New Scientist, on the London
newsstands, so I expect it will appear next week.

The set of log numbers above are the same, derived from pi, as used to
calculate the intervals for LucyTuning.

Yahya Abdal-Aziz may have spotted the crux of the matter.

So J.H. was taking the log principle to the next stage, and may then
have been considering integer ratios.

So it becomes whole number ratios (like JI); yet two geometric steps
removed.

JI seekers were/are looking for zero beating in frequency whole numbers;

Harrison was looking for matching harmonic intervals, (which beat) and
going via pi to get to integer ratios of double logs, of the dimensions
of the metal in circular bells
which could be found in the bells physical properties ?

It does sound convoluted, yet is certainly a novel way of
conceptualising tunings, and judging by the success of his previous
inventions may actually be practical.

Now we need to try out his formula and see how well works in the real
world.

My older brother is at present "playing tourist", in Australia, so I'll
ask him to go see the bells people that you pointed me to in an earlier
posting, and find out if they are interested in experimenting with his
formulas.
The other option seems to be to get some prototypes designed and built
to J.H.'s specs here in London, as I did with the guitars 20 years ago,
to discover what happens and how well his theory works in the physical
world.

Now to explore the maths implications a little further.

[Yahya] Well, it seems like you feel you are on to something, tho I'm
still mystified by _why_ Harrison thought that pi would be involved in
tuning. Good luck with your further researches!

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