Originally posted on the Bad Astronomy blog:

Remember “Close Encounters of the Third Kind“? The aliens “sang” to
the humans…ths “song” being “re mi do (down octave) do sol”. A
common question is, what characteristics would an alien likely share
with humans? e.g. they probably would not be mammals–but perhaps
would take care of their young (a trait that helped mammals evolve to
intelligent humans). So, how about “alien music”? The question
interests me as I am an amateur musician.

One of those times when a science fiction movie didn’t completely miss
the mark is this Close Encounters motif. First–in an atmosphere of
density not far from Earth’s atmosphere, sound would be too good a way
to communicate for some form of “speaking” and “hearing” to not
develop. Music is not all that far from speech (or even bird songs,
for that matter). I conclude that some form of music is likely among
alien intelligences.

Now–no doubt Spielberg or someone working with him chose a major
scale motif (or a pentatonic, or many other modes actually share these
notes) was that it would “sound like music” to audience members, but
would an alien likely recognize the major scale, or would it be
completely different?

Well, it turns out, Pythagoras discovered that the intervals in a
major scale (using the so-called “just” intonation that the human ear
seems to find pleasing) are small-integer ratios of frequencies. An
octave is a factor of 2 (2/1) in frequency. do to sol is a “perfect
fifth” interval, and is a factor of 3/2 in frequency. All notes of
the major scale arise from small-integer ratios of frequencies.

I claim, therefore, that the system is simple enough to be a natural
way for an alien ear to develop as well–I believe many alien
intelligences will have major-scale-based music. (Some might find our
minor scale, or 12-tone pieces, to be weird…of course many humans
find 12-tone pieces to be weird too….)

Now, speaking of 12-tone–how about the “chromatic scale” c c# d d# e
f f# g g# a a# b c (12 notes, 13 if you count the repeated first
note). Well, if a society has music, they will want an effective way
to “play” it–hence the development of instruments. The
small-integer-ratio “just” intonation I mentioned above is fine for
things like violins or trombones, where you can match any pitch fairly
easily, but a piano would require something like 70 keys per octave to
be able to represent the just scale in the key of c, d, f, g, etc., or
only 7 (8 counting repeated first note) keys per octave if you never
change key, which really limits your music.

Thus, the “well-tempered clavier” was invented, using an
equal-tempered scale that is a compromise between the perfectly
ear-pleasing “just” scale, and something that wouldn’t require too
many keys on a keyboard to make playing in a lot of keys possible.
The way the equal-tempered scale works is the frequency of c# is
exactly the 12-th root of 2 times the frequency of c, and the
frequency of d is the 12-th root of 2 times the frequency of c#, and
so on. The “g” you get is then not exactly a perfect fifth with ratio
3/2 of the “c” frequency, but is “close enough” (a difference of 1/10
of a percent in frequency, to be precise). Most ears cannot tell the
difference. Well-trained musician’s ears don’t find the difference
enough to destroy the music. And you can transpose to any of 12 keys.

So, will the aliens invent a well-tempered clavier or something
similar? I believe the answer is “something similar”. They will also
wish to be able to “play” the music, and with more than with trombone
or violin-type instruments. They will come up with some kind of
compromise. It might not be a 12-note compromise, though.

There are other values besides the 12-th root of 2 that can serve as
the fundamental interval. 12 is the smallest that includes the
perfect fifth and perfect fourth, both of which are particularly-good
ratios (3/2 and 4/3) that are unlikely to be left out–so it might be
the most common. But to an alien species with finer
frequency-resolution ears, more notes in the scale would be better–the
41-tone scale and the 53-tone scale are slightly more accurate.

Of course, 53 is getting close to that 70 keys per octave needed to
use just intonation on a keyboard. It probably won’t be more than
this.

My conclusion is, if we hear alien music, it might not be all that
alien! At least in terms of harmonies. Now, for other elements of
music–motifs, counterpoint, etc., I don’t know.