Why Musical Aliens Probably Use the Same Scale We Do

by Brian Dunning
April 5, 2016

Today we're going to take on one aspect of the popular belief that aliens from another world must necessarily be radically different from humans, not only in appearance, but also in art, literature, culture, and behavior. Today I'm going to present a case that for aliens who have a form of music, the fundamental unit of their music — the musical scale — is almost certainly surprisingly similar to our own, and even uses the same twelve notes found on an Earthly piano.

The basic argument is that our chromatic scale of twelve notes is based on the most fundamental fractions. By fundamental fractions, I mean the most obvious ones: fractions that every primitive culture would understand. Two early hunter-gatherers would understand the concept of dividing food in half, even if they didn't have language syntax for it. Three hunter-gatherers would understand dividing food into thirds. Larger social groups, in any environment, on any planet, would be exposed to the concept of fair division of food or other goods. Even when a society develops that divides nothing equally, they would have still been exposed to the concept: You're trying to grow three plant crops, you put an equal amount of water on each. The understanding of basic, fundamental fractional portions is one of the mathematical concepts that would be known to every culture everywhere.

Every tuned musical instrument depends on fractions. The sizes of the keys of a xylophone are based on fractions. The lengths of plucked strings are based on fractions. The resonating space inside a flute, and the parameters that can tune a drum, are all based on these same fractions (though in different ways). So although any individual primitive musician who builds his own instrument might create a scale of notes unlike that of any other musicians, it would be those musicians using the common fractions whose work would be recognizable and repeatable by others.

Thus, the music most likely to gain widespread acceptance across diverse segments of a population is probably going to be based on fundamental fractions. By extension, it is equally probable that music from different planets will also be based on the same fraction-based chromatic musical scale.

How does dividing the day's gathering of berries among three primitive foragers translate to a universal chromatic scale? On Earth, we trace this tradition back to Pythagoras, the Greek polymath who absolutely did not invent the system, but was the first to devise the mathematics that describe it — or, at least the first whose work survived and was popular enough to be known for it. It was understood in China at least two thousand years earlier.

So how exactly does one turn fractions into music? Well, much of this may be very familiar to many listeners, but there is a twist that many of us may not be aware of. We begin with a string of a given length, that we can pluck and produce a tone:

The most basic fraction we can apply to this string is 1/2. Imagine a guitar and you put your finger down on the fretboard 1/2 of the way down the length of the string, and you pluck it again, producing a higher note:

That's an octave. If our original note was an A at 440 Hertz, this higher note with the string half as long would also be an A with exactly twice the frequency: an A at 880 Hertz. Similarly we could go on all day cutting the string in half, or making it twice as long, and play all the A notes there are, and all would have a frequency that is some multiple of 110, 220, 440, 880, 1760, and so on:

Pythagoras noticed that the most common musical interval also happened to match the next most common fraction, 1/3. When you place your finger one-third of the way down the guitar string and pluck, the remaining 2/3 produces a tone at 660 Hz, which is 2/3 the wavelength of 440, and today we call this note an E:

Like the As, Es also come in multiples of two times that 660, such as 165, 330, 660, 1320, and so on:

This interval between one note and another formed by shortening the string by 1/3 is called a perfect fifth, which is defined as two tones having a frequency ratio of 3:2. Pythagoras repeated this again, taking 2/3 the length of his E string to go up another perfect fifth and produce a B at 990 Hz:

And a fourth time to produce an F^# at 1485 Hz:

And a fifth time to produce a C^# at 2,227.5 Hz:

Once he had these five perfectly calculated tones in hand, Pythagoras discovered that he could play almost any popular song:

A scale consisting of these five notes is called a pentatonic scale. You're already familiar with the pentatonic scale; they're the black keys on a piano. Go to any piano and play anything you want using just the black keys, and you're playing Pythagoras' pentatonic scale, all based on that super-simple fraction, 1/3.

Music from every populated region on Earth has been found to use the pentatonic scale. Other systems also existed here and there, and some musicians also tweaked the notes in the pentatonic scale a bit, but that pure pentatonic scale is the one that became the universal musical language on Earth, all stemming from 1/2 and 1/3. By the same inescapable progression by which the concepts of 1/2 and 1/3 permeated every society on Earth, we can reasonably expect that the pentatonic scale will be found in every musical society anywhere in the universe.

But there are still some gaps between the five-note pentatonic scale and the twelve-note chromatic scale. On the piano, these gaps are the white keys. But notice two things: there are more white keys than black keys; and the black keys come in a group of three and a group of two, the groups being separated by two white keys, whereas the individual black keys are separated by only one white key. This is because that pentatonic scale covers enough of the keyboard to allow you to make great music, but it does not completely cover the entire frequency spectrum with evenly separated intervals. Pythagoras decided to keep going, to continue splitting off 1/3 of the string, to create a new musical note. His sixth note was a G^#. His seventh note was a D^#. He continued this interval and created an A^#, an F, a C, a G, a D, and then... miracle of miracles... cutting off 1/3 of his D string and plucking brought him all the way back around to an A. Pythagoras had found the mathematically perfect solution to a 12-note chromatic musical scale.

Now, I know some of you are screaming at me and tearing your hair. Relax. I said there was a twist. We'll get to it right now.

The twist is that I lied. Pythagoras knew it was not exactly right. Starting at A440, Pythagoras had originally followed twelve perfect fifths to produce an A exactly one octave up, an A880. 880 Hertz was the target frequency to create a perfect chromatic scale. When he went all the way around his twelve divisions of the octave, that last note — his A — was not exactly 880. It was pretty close, but it wasn't exact. It was just a little bit over 892 Hz. It was close enough, though. It was close enough that most music listeners would probably never know the difference. Pythagoras could have gone round the world again — finding new notes each a perfect fifth up from the last, and created a much finer scale with many more than twelve gradations of the octave, and gotten closer to 880; but that wouldn't have been a good solution. Music sounded really good with just those twelve notes. Pythagoras also could have taken a smaller number of notes; for example, the eighth note in his process was an A^# and he could have squeezed them all down a little bit for an eight-note chromatic scale, but that wouldn't have been any good either.

For a long time, Earth musicians tried various ways to deal with this imperfection in the musical scale, by making various adjustments called temperament. Leaving the notes just as Pythagoras calculated them, based on mathematical perfect fifths but with one little off-interval, is called Pythagorean tuning. A temperament called just intonation was developed where all the notes were jostled around just a tiny bit such that they were related by frequency ratios that could be expressed using whole numbers that were as small as possible. An important development was well temperament, popular in the 18th and 19th centuries, which brought everything closer into line and allowed songs to sound good when played in any key, but with enough variation that the same song, played in the same mode, would have a slightly different feel when transposed to a different key. Today nearly everything is based on equal temperament, where the intervals between all adjacent notes are exactly the same, which is 2^1/12.

Might aliens have taken a different option than Pythagoras did to resolve the fault in the scale? Certainly. But twelve notes is a great number. The twelve-tone chromatic scale, and the pentatonic scale as well, are in the same ballpark as the number of digits on human hands, which makes an instrument easy to handle. It's a good ballpark, and the next higher round-the-world of perfect fifths starts to get out of control. My bet is they would have stopped within one round of where Pythagoras did.

I've heard it argued that rhythm is probably also the same in alien music, based on ambulation and a host of influences in nature. It may be that the chromatic scale, perhaps even the chords, match our own. Steven Spielberg's Close Encounters of the Third Kind certainly portrayed such a parity. If the fundamental fractions that informed the music of every culture on the planet Earth also did the same on other worlds, then it may indeed be the case that music is, as bards have long proclaimed, the universal language.

Correction: An earlier version of this said diatonic in a couple places where chromatic was meant. —BD

Clarification: It has been pointed out that wherever Pythagoras is referenced in this episode, it would be more appropriate to reference the Pythagorean school in a larger sense, rather than credit a single man. —BD

By Brian Dunning
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