Date: Thu, 07 Apr 2011 15:39:40

Author: Thomas J. Bauer

Subject: Re: Tuning forks

Post:

This is a multi-part message in MIME format.

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Attached is a frequency scale given to me by our Physics of Music emeritus
expert Dr. Judy Brown.
Tom Bauer
Physics Dept.
Welelesley College

tap-l@lists.ncsu.edu writes:
>Machele -
>
>I passed your question along to Dr. Bryan Suits - our resident physics of
>music expert - here's his response:
>
>"Using middle C = C4 = 256 Hz is known as the "Scientific Scale." It
>makes
>all of the C's be exactly 2^N Hz, N an integer, and happens to be close
>to
>the A4 = 440 Hz scale, for which C4 is 261.3 Hz for the equal tempered
>scale.
>Back when scientists used tuning forks to make measurements, this might
>have made some sense, though the origins are unclear to me (there are
>several different stories, I don't know which is correct) it seemed to
>arise in
>the early 20th century.
>
>Note also that this scale (usually) does not use equal tempering
>(i.e. intervals determined by powers of the 12th root of two), but
>uses the rational numbers of just tuning for a key of C. Hence, for
>example, the G above middle C, G4, is 3/2 * 256 = 384 Hz and
>A4 would be 5/3 * 256 = 426.667 Hz. It is much easier to tune
>notes to each other by ear with the Just scale since the frequencies
>are related by the ratio of (usually small) integers. I have seen
>tuning forks use C4 = 256 Hz and then other notes determined using
>equal tempering on top of that. That is some sort of mixed system.
>
>You can find a table for the Scientific Just Scale in the Handbook
>of Chemistry and Physics. The rational numbers for the Just intervals
>are at http://www.phy.mtu.edu/~suits/scales.html , among other places.
>
>I have never known any scientists who used this scale for music
>(or anything else, for that matter). I do not know why people still
>make tuning forks with this tuning, but they do. I guess because
>people buy them.
>
>- BHS"
>
>
>--
>Michael R. Meyer
>Lecturer/Lab Coordinator
>Mich Tech Physics Dept.
>mrmeyer@mtu.edu
>906-487-2273
>
>----- Original Message -----
>From: "Machele Kindle"
>To: "TAp-L"
>Sent: Thursday, April 7, 2011 12:52:13 PM GMT -05:00 US/Canada Eastern
>Subject: [tap-l] Tuning forks
>
>
>This is something I've never figured out. As a musician, A4 is 440Hz.
>But, it is common to get sets of tuning forks where A4 is declared to be
>426.6Hz (making C4 256Hz and C5 512Hz = entire series is flat). This
>annoys me to no end. I'm sure there's some logical explanation... anyone
>know?
>
>
>
>
>



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<=21--
body=7Bmargin-left:10px;margin-right:10px;margin-top:10px;margin-bottom:10p=
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Attached is a frequency scale given to me=
by our Physics of Music emeritus expert Dr. Judy Brown.
Tom Bauer
Physics Dept.
Welelesley College

tap-l=40lists.ncsu.edu writes:
Machele -

I passed your question along to Dr. Bryan Suits - our resident phy=
sics of music expert - here's his response:

"Using middle C =3D C4 =3D 256 Hz is known as the "Scien=
tific Scale." It makes
all of the C's be exactly 2=5EN Hz, N an integer, and happens to b=
e close to
the A4 =3D 440 Hz scale, for which C4 is 261.3 Hz for the equal te=
mpered scale.
Back when scientists used tuning forks to make measurements, this =
might have made some sense, though the origins are unclear to me (there are=
several different stories, I don't know which is correct) it seemed to ari=
se in
the early 20th century.

Note also that this scale (usually) does not use equal tempering <=
/font>
(i.e. intervals determined by powers of the 12th root of two), but=

uses the rational numbers of just tuning for a key of C. Hen=
ce, for
example, the G above middle C, G4, is 3/2 * 256 =3D 384 Hz and
A4 would be 5/3 * 256 =3D 426.667 Hz. It is much easier to t=
une
notes to each other by ear with the Just scale since the frequenci=
es
are related by the ratio of (usually small) integers. I have=
seen
tuning forks use C4 =3D 256 Hz and then other notes determined usi=
ng
equal tempering on top of that. That is some sort of mixed s=
ystem.

You can find a table for the Scientific Just Scale in the Handbook=

of Chemistry and Physics. The rational numbers for the Just =
intervals
are at http://www.phy.mtu.edu/=7Esuits/scales.html , among other p=
laces.

I have never known any scientists who used this scale for music
(or anything else, for that matter). I do not know why peopl=
e still
make tuning forks with this tuning, but they do. I guess bec=
ause
people buy them.

- BHS"


--
Michael R. Meyer
Lecturer/Lab Coordinator
Mich Tech Physics Dept.
mrmeyer=40mtu.edu
906-487-2273

----- Original Message -----
From: "Machele Kindle"
To: "TAp-L"
Sent: Thursday, April 7, 2011 12:52:13 PM GMT -05:00 US/Canada Eas=
tern
Subject: =5Btap-l=5D Tuning forks


This is something I've never figured out. As a musician, A4 is 440=
Hz. But, it is common to get sets of tuning forks where A4 is declared to b=
e 426.6Hz (making C4 256Hz and C5 512Hz =3D entire series is flat). This an=
noys me to no end. I'm sure there's some logical explanation... anyone know=
?
=C2=A0

=C2=A0







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