Re : [tuning] Tuning-related Science Fair Question

Keenan asked:

> Does anyone have any open questions about alternative tunings (especially
> JI) that might be suitable for a middle school science project? All
> suggestions are welcome, even stupid ones.

Perhaps demonstrate ratios in the way Pythagore did: 6 identical strings,
all with the same vibrating length, but with different weights at the end ,
giving a different string tension for each of them. A small design
on 'Pitagoras' from Gafurius, 1492 shows the numbers 4, 6, 8, 9, 12 and16 on
the weights.

A friend of mine's daughter demonstrated a monochord in her class. An
acoustic box with one reference string and one string with a moving bridge.

Sorry, if this is too *easy*. I would like it if I was 13!

--Wim

Wim wrote,

>Perhaps demonstrate ratios in the way Pythagore did: 6 identical strings,
>all with the same vibrating length, but with different weights at the end ,
>giving a different string tension for each of them. A small design
>on 'Pitagoras' from Gafurius, 1492 shows the numbers 4, 6, 8, 9, 12 and16
on
>the weights.

Another myth. Weights wouldn't work. Lengths on a string would, though.
Pythagoras either did the latter, or neither.

Dear Paul H. Erlich;
Would you happen to know what the results of weights on equal strings are?

"Paul H. Erlich" wrote:

> Another myth. Weights wouldn't work. Lengths on a string would, though.
> Pythagoras either did the latter, or neither.

-- Banaphshu
North American Embassy of Anaphoria island
www.anaphoria.com

>Would you happen to know what the results of weights on equal strings
are

It depends on factors like the frictional coefficients at the bridges . . .

Dear Paul H. Erlich;
what if these minimal and equal?

"Paul H. Erlich" wrote:

> >Would you happen to know what the results of weights on equal strings
> are
>
> It depends on factors like the frictional coefficients at the bridges . . .
>
>

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com

>what if these minimal and equal?

If there were zero friction (i.e., pulley wheels), then doubling the weight
would increase the pitch by the square root of two (i.e. the equal-tempered
tritone).

Paul wrote:
>
> Another myth. Weights wouldn't work. Lengths on a string would, though.
> Pythagoras either did the latter, or neither.

I saw a reconstruction of Pythagore's instrument, with the weights and
numbers on them, in the Museum of Art History in Vienna. Standing before it,
the acoustical guide (headphone with infrared system), made me listen to
three metallic strings, sounding as 1/1, 3/2 and 2/1. So I really thought
that came from the instrument I saw. Today, I checked the information on the
CD from the Museum and saw that I was supposed to hear a 'monochord'. Still:
three strings...

Paul, I understand now that there's no linear,
mathematical relation between weight/ string tension and pitch.
So, the Museum gives definitely a false impression! They should at least
explain
why this is a myth.

--Wim