RE: [tuning-math] Digest Number 1226

Charles,

There is a little introductory material on relevant design
considerations at the Australian Bell site I mentioned
recently on the tuning list, particularly at the Evolution
of Modern Bells page
http://www.ausbell.com/Understanding/evolution.html
and the Harmonic Bells page
http://www.ausbell.com/Harmonic/titleharm.html

The maths is such that in designing new bells, they have
resorted to finite element analysis (FEA) using computers.
FEA is essentially an engineering approach to modelling
complex systems that do not admit of direct analytic
solutions, and bells are very much a case in point.

They claim that a difference of 1 micron in thickness can
radically affect the outcomes of bell making; we can only
consider ourselves lucky that making many of our favourite
instruments, such as guitar, woodwinds and piano, is not
quite so sensitive to dimension.

In their discussion of Musical Perception of Pitch and
Harmony,
http://www.ausbell.com/Understanding/pitch.html
and tuning inharmonic instruments, it's nice to see they
explicitly mention Bill Sethares' book Tuning, Timbre,
Spectrum and Scale.

Because of the need for FEA in designing bells, I am not
hopeful that John Harrison actually found a method
of tuning a bell involving only simple surds. I also share
Gene's scepticism about arriving at pi using surds. Any
such connection is likely, I fear, to be mystical or, dare
I say, transcendental ...

I've had a quick look at the transcription, but can no
find mention of pi, nor even a reasonable approximation
to its first few digits. I did notice his use of the term
Radical, and of both logarithms and double logs (Log Log),
which can express some transcendental relations. Tho
I haven't yet followed thru his examples to see his method
of working out, he seems to be discussing primarily a
means of designing a new tenor bell based on the
proportions of an existing one. He's also not too fussed
about the exact relationship of the major dimensions,
making t vary from 1/15 down to 1/16 depending on vague
notions of scale.

I'll have another look later when I can make time, and see
if anything stands out, mathematically.

Regards,
Yahya

-----Original Message-----
________________________________________________________________________

Date: Sun, 6 Mar 2005 11:07:26 +0000
From: Charles Lucy <lucy@harmonics.com>
Subject: Tuning of bells. Does anyone on the list know anything about the
maths of bell tuning?

As you prolly already know I have been researching the writings of John
'Longitude' Harrison for the past twenty odd years..

I have unearthed his "lost" manuscript, and have transcribed it.

I am hoping to get a letter or article published in New Scientist soon,
asking the scientific community to look at what he wrote and attempt to
understand it.

I have puzzled over the meaning and significance of his radical
numbers for about a year now and seem to be getting nowhere with it.

Maybe someone on this list has some insight that I have missed

My letter/article will direct them to this url:

http://www.lucytune.com/radnums.html

where I have put the transcription.

It seems that this recipe using radical numbers is to get the bells to
sound the meantone tuning that he proposed derived from pi.

Charles Lucy
________________________________________________________________________
________________________________________________________________________
Date: Sun, 06 Mar 2005 18:11:52 -0000
From: "Gene Ward Smith" <gwsmith@svpal.org>
Subject: Re: Tuning of bells. Does anyone on the list know anything about
the maths of be

--- In tuning-math@yahoogroups.com, Charles Lucy <lucy@h...> wrote:

> It seems that this recipe using radical numbers is to get the bells to
> sound the meantone tuning that he proposed derived from pi.

I don't see how he would get to pi by taking square roots.

________________________________________________________________________
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--- In tuning-math@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...>
wrote:
>
> Charles,
>
> There is a little introductory material on relevant design
> considerations at the Australian Bell site I mentioned
> recently on the tuning list, particularly at the Evolution
> of Modern Bells page
> http://www.ausbell.com/Understanding/evolution.html
> and the Harmonic Bells page
> http://www.ausbell.com/Harmonic/titleharm.html
>
> The maths is such that in designing new bells, they have
> resorted to finite element analysis (FEA) using computers.
> FEA is essentially an engineering approach to modelling
> complex systems that do not admit of direct analytic
> solutions, and bells are very much a case in point.
>
> They claim that a difference of 1 micron in thickness can
> radically affect the outcomes of bell making; we can only
> consider ourselves lucky that making many of our favourite
> instruments, such as guitar, woodwinds and piano, is not
> quite so sensitive to dimension.
>
> In their discussion of Musical Perception of Pitch and
> Harmony,
> http://www.ausbell.com/Understanding/pitch.html
> and tuning inharmonic instruments, it's nice to see they
> explicitly mention Bill Sethares' book Tuning, Timbre,
> Spectrum and Scale.
>
> Because of the need for FEA in designing bells, I am not
> hopeful that John Harrison actually found a method
> of tuning a bell involving only simple surds. I also share
> Gene's scepticism about arriving at pi using surds. Any
> such connection is likely, I fear, to be mystical or, dare
> I say, transcendental ...
>
> I've had a quick look at the transcription, but can no
> find mention of pi, nor even a reasonable approximation
> to its first few digits. I did notice his use of the term
> Radical, and of both logarithms and double logs (Log Log),

Can you show me where the double logs come up? I looked in the link
but couldn't find it. I'm very interested!

"Yahya Abdal-Aziz" <yahya@melbpc.org.au> writes:

> and tuning inharmonic instruments, it's nice to see they
> explicitly mention Bill Sethares' book Tuning, Timbre,
> Spectrum and Scale.

I think this is the first I've ever heard of this book. So today I
was off making my weekly check of the new books shelf... and there it
was! Not in the main library with most of the music books, halfway
across campus, or in the science library, a couple buildings away, but
in the tiny little physics library, down the hall and down the stairs.

Must be a Sign.

Wonder who requested it?

- Rich Holmes

--- In tuning-math@yahoogroups.com, Rich Holmes<rsholmes@m...> wrote:
> ...in the tiny little physics library, down the hall and down the
stairs.
>
> Must be a Sign.

I'm reminded that when Harry Partch was at the university in Madison,
WI, the place they chose to place him was in the basement of the
physics building.

> Wonder who requested it?

No idea, but I hope it is the recent, 2nd edition.

Cheers,
Jon