From: Dave Rusin
Date: Fri, 26 Mar 1999 15:09:25 -0600 (CST)
To: ajjmae@globalfrontiers.com
Subject: Re: Why 12 tones per octave?
> Do you have a website with some of your articles??
http://www.math.niu.edu/~rusin/uses-math/music/index.html
>about the shape of the harp?
If the frequency of a string were dependent only on the length (it's not)
then we would need the lengths to double with each octave downward. If the
harpist were at the origin and the harp on the positive x-axis, (the harpist
sits at the high-note end) then the string at position x would have to
have a length varying like y = A * 2^x (with distances along the
x-axis measured in octaves). To make room for the harpist's body, the
bottom of the string is not on the floor; rather, it's attached to the
soundboard -- a straight but tilted plane. Thus the bottom of the string
which is x octaves down from the highest note is elevated to a height
of the form y = a * (1 - x/k) where a is the height of the bottom
of the shortest string (a is about 5 feet) and k is the number of octaves
until you reach the floor (about 6). OK, we know now where the bottom of
each string is, and we know how long it is; where's the top? Must be at
y = a * (1 - x/k) + A * 2^x. We can even determine A here if we assume
that the top of the bass strings is about equal to the height of the top
string: we need y(k) = y(0), which is roughly A*2^k = a. So the shape
of the top of the harp is something like A*( 2^k*(1-x/k) + 2^x ).
(This is a little bogus: to get deeper notes they don't just take longer
strings but also make them thicker and, at the very bottom, change material
(from gut to coiled metal). These affect the necessary lengths -- the
lengths needn't grow so fast but rather grow like A * r^x for some r < 2,
or so it appears by sight.)
dave
From rusin@math.niu.edu Tue Jan 16 01:51:44 2001
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From: Dave Rusin
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Date: Tue, 16 Jan 2001 01:51:43 -0600 (CST)
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To: pirashennah@home.com
Subject: Re: Help, please...
Cc: rusin@math.niu.edu
Status: R
No, I never really thought about it, but a quick search of Google.com
is informative. Just type in harp mathematics and it finds this,
and more!
Harp mathematics
... Harp mathematics. To: harp-l@garply.com; Subject: Harp
mathematics; From:
Snaruhn@aol.com; Date: Thu, 17 Feb 2000 03:28:50 EST; Sender:
owner-harp-l. ...
www.garply.com/harp-l/archives/2000/0002/msg00349.html - 3k -
Magic Soloist
... Prev by Date: Harp mathematics; Next by Date: William Clarke
LP's & CD's; Prev
by thread: Harp mathematics; Next by thread: Re: Magic Soloist;
Index(es): ...
www.garply.com/harp-l/archives/2000/0002/msg00350.html - 4k -
Harp Mailing List 1996 Digest Archive: Harp Digest #130
... I have a centered place from which to venture into my cross-cult
investigations
of music, harp mathematics, and Austrian cuisine. I encourage everyone
on the ...
tns-www.lcs.mit.edu/harp/archives/digests/1996/0316.html - 31k -
Harp Mailing List 1996 Digest Archive: Harp Digest #83
... of Mittelshmerz, Austria is happy to announce is 20th Annual
Fall Mathematics
Retreat for Harp Practitioners and Musicians. Music is simply an
acoustic ...
tns-www.lcs.mit.edu/harp/archives/digests/1996/0263.html - 48k -
MAVIS Mathematics Accessible to Visually Impaired Students ...
... index three" is read verbally. A harp twang at c5 indicates branch
two ... of tabular
structures, the rest of mathematics notation is similarly
hierarchical, and ...
www.dinf.org/csun_99/session0255.html - 8k -
Andrew Lawrence-King
... and College Orchestra, my academic subject was Mathematics, which
I followed up to
MA level ... to a party given by the harp-maker, Tim Hobrough. It must
have been ...
ourworld.compuserve.com/homepages/Harp/bio.htm - 8k -
Good luck
dave