Carolyn Gordon has a paper in the *Mathematical
Intelligencer* (1989, vol 11, no. 3, pp. 39 - 47) entitled "When
You Can't Hear the Shape of a Manifold." Accompanying this article
are a sidebar and floppy vinyl record by Dennis DeTurck. Reproduced
here, with Dr. DeTurck's permission, are the tracks from the record
in .mp3 format; I've included his comments from the sidebar with each
track. Two tech-tips: (1) you might need to turn the volume up (I
forgot to amplify them when I was editing them) and (2) if you play
more than one of these at once, it sounds **really** weird.

However, I'm not going to discuss the mathematics on this page.

Track 1:

The "harmonic sequence" of the circle S^{1 }(e.g., sine
tones whose frequencies are integer multiples of the first one
heard). Then we build a complex S^{1 }-tone (e.g., beginning
with the fundamental tone, more and more additional frequencies are
mixed in, based on the circle's eigenvalues). Then the complex tone
is repeated, with other characteristics added (attack and decay
envelope) to get an "electronic piano" sound. As an example, the
*Dresden Amen* is played on this "circular" piano.

Track 2:

The analog of 1 for the two-sphere S^{2}: the "harmonic
sequence" of S^{2} (just like 1, but with the sphere's
eigenvalues), then we build a complex S^{2 }-tone, repeat it
with the piano's attack-decay envelope, and perform the on the
"spherical piano."

Track 3:

The effect of dimension: A simple piano exercise is repeated,
first on S^{1}, then on S^{2}, then on S^{3}
(which has the same eigenvalues, but not multiplicities, as the
complex projective plane **C** P^{2}), then on
S^{6} (same as the quaternionic projective plane **H**
P^{2 }), and then on S^{12} (same as the Cayley plane
*Ca* P^{2 }).

Track 4:

The "Romanza" movement, from Beethoven's *Sonatina in G* is
performed on various "spherical pianos." The first section is played
on an S^{1}-piano, the second on S^{2}, the next on
S^{3}, the next on S^{6}, and a codetta back on
S^{1}.

Track 5:

A chorus of projective planes: The "Bouree" from Handel's
*Fourth Flute Sonata* is performed with **C** P^{2}
playing the flute part, *Ca* P^{2} doing the bass line,
and **H** P^{2} providing the realization (middle
parts).

Track 6:

The piano exercise is played on S^{1} again, then on
various flat rectangular tori. The first is the square torus
T_{1:1}, then on tori whose side ratios are 3:5, 11:13,
21:23, and finally 31:33. (Hear the effect of the ratio being close
to but not equal to 1?)

Track 7:

Torus music: Robert Schumann's *Wild Rider* is performed on a
piano whose strings are T_{3:5}.

Track 8:

More torus music: J. S. Bach's *Two-part Invention No. 4 in d
minor *is performed on a T_{11:13} piano.

Track 9:

Spheres and tori together: The "Presto" movement from Scarlatti's
*Sonata in C* (Longo S.3) is performed, with the upper voice
played on T_{21:23} and the other parts on *Ca*
P^{2}.

Track 10:

A "one-minute quiz": Chopin's *Valse in D-flat*,Opus 64, No.
1 ("*Minute Waltz*"). The oom-pahs are performed on a standard
S^{1}-piano. Can you identify the seven manifolds that play
different sections of the tune?

In the *Intelligencer*, answers were provided on p. 79.
However, I didn't look at that page, so if you need to know the
answers... for now, you'll have to go to the library.

Tech thanks to Jon Fretheim for the embedded-player code and to Sean Kinlin & UNI Electronic Media for letting me use their sound-editing equipment.