Re: [Phys-L] music scales

[Todd Pedlar <pedlto01@luther.edu>]

It's a good question from the point of view of modern tuning fork sets that
one might want to use for physics... it would probably be great to have
standard sets for physics demonstrations that use the currently agreed upon
440Hz for 'concert A'.

However, prior to the 1950's there wasn't a universally agreed upon
standard - tunings were all over the map from the Baroque period onward,
and, even worse, equal temperament wasn't often used until the 20th
centuries, because many thought that equal temperament sounded ugly.  I'm
not sure what would have been typical for a set of tuning forks for piano
tuners.  435 was common in France since the 1860s, 432 in Italy after
Verdi, etc... and, then, again... probably wouldn't have been equal
tempered.

On Mon, Feb 17, 2025 at 2:17 PM Anthony Lapinski via Phys-l <
phys-l@mail.phys-l.org> wrote:

> Thanks! The more I research, the more interesting (and confusing) this
> becomes!
>
> So this equal temperament (ET) scale - used for all pianos. All instruments
> today, too? So why are all "physics" tuning
> fork sets different? I know they were developed in the 1700s. Why aren't
> they ET to match all instruments?
>
> On Mon, Feb 17, 2025 at 3:06 PM Paul Nord via Phys-l <
> phys-l@mail.phys-l.org>
> wrote:
>
> > Also notice that what you've got there is the standard "physics" set of
> > tuning forks.  The 256 Hz is close to the common tuning for a C.
> However,
> > in the usual equal tempered scale the frequency is closer to 262 Hz.  A
> 256
> > Hz tuning fork seems to have been developed for physics classrooms.  It's
> > easy to do the math to show that 512 Hz and 1024 Hz are simple octaves.
> >
> > Each half step on the musical keyboard is separated by a ratio of
> 2^(1/2).
> > Going down 9 half steps from A 440 Hz we get:
> > 2^(-9/12) * 440 = 261.63 Hz
> >
> > Paul
> >
> > On Sat, Feb 15, 2025 at 9:17 PM Anthony Lapinski via Phys-l <
> > phys-l@mail.phys-l.org> wrote:
> >
> > > I'm teaching a sound unit (in my high school class) in a few months. I
> > was
> > > reading/revising some of my class notes and wanted to add a small
> section
> > > about tuning forks when I introduce waves and frequency.
> > >
> > > I have a standard set of tuning forks (C D E F G A B C) with these
> > > frequencies (Hz):
> > >
> > > 256, 288, 320, 341.3, 384, 426.6, 480, 512
> > >
> > > I often wondered why two of them (F, A) were decimals...
> > > They sound like a normal scale.
> > > So (512 - 256)/8 = 32 Hz
> > >
> > > The first three (C, D, E notes) differ by 32, as do the last two (B, C
> > > notes); the others don't.
> > >
> > > I then searched the history of tuning forks and came across the equal
> > > temperament scale (same frequency ratio of adjacent notes):
> > >
> > > 261.3, 293.66, 329.63, 349.23, 392, 440, 493.88, 523.25
> > >
> > > Pianos and guitars are tuned to this scale. Any other instruments?
> > >
> > > I'm NOT a musician. Does anyone know when and why these scales were
> > > developed? And why aren't standard tuning forks equal temperament to
> > match
> > > what some instruments produce? Any information, web references, or
> > > textbooks will be much appreciated. Thanks!
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-- 
Todd K. Pedlar
Professor of Physics and Physics Department Head
Luther College, Decorah, IA
pedlto01@luther.edu
(563) 387-1628
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