Archive for September 23, 2015

Are We Running Out of Melodies?

First warning: This article contains math.

Second warning: I’m not very good at math.

I don’t know why, but tonight I found myself pondering the question “How many melodies are there?” Maybe I was worried that we’re running out of them. (A quick survey of recent pop music might suggest this.)

Human beings have been writing songs for as long as there have been human beings. The oldest written song is the Hurrian Song to Nikkal, written around 1400 BC, but even in prehistoric times there were no doubt songwriters, whose melodies are now lost to us.

There are now more than 7 billion people in the world, so there must be more songwriters living now than at any other time in history. Heck, there are probably more songwriters now than there were people at some point in the past.

And all those songwriters are using up melodies. Not always of course, since imitation and blatant thievery are well-established parts of the creative process. But unless we’re all just endlessly recycling the same melodies, some of us must be inventing new ones and therefore depleting the supply of melodies not heard before.

How long until there are no new melodies?

OK, here’s where the math comes in. For the sake of this discussion, let’s limit ourselves to the Western chromatic scale, i.e. all the keys on a piano. But two melodies that are different only by shifting some of the notes to a different octave aren’t going to be heard as different melodies. For example, consider these two melodies:

melody 1


melody 2



If you tried to claim that the second melody is original, I’m afraid people would laugh at you, and if you took it too far, Mozart might sue you.

So we’re really only dealing with 12 notes, because every other note is just one of those notes shifted to a different octave.

How many melodies can we make with 12 notes? It depends on how long the melody is. If our melody is only one note long, then obviously there are only 12 possible melodies. If our melody is two notes long, then there are 12×12, or 144, possible melodies. Here are the first 36 of them; you can probably figure out the rest:

two-note melodies





Now, what about a melody that’s 3 notes long? There are 12x12x12, or 1728 possibilites. Similarly, there are 12x12x12x12 (­20736) 4-note melodies, 12x12x12x12x12 (248832) 5-note melodies, and so on. The formula to calculate the number of possible melodies using N notes is 12^N, meaning 12 multiplied by itself N times. So if we want to know how many possible 20-note melodies there are, we just multiple 12 by itself 20 times. The result of that calculation is 3,833,759,992,447,500,000,000.

Now we’re getting into some big numbers, and I’m starting to feel a little better about the remaining supply of melodies. In fact, the number of possible 22-note melodies is roughly the same as the number of stars in the universe. Now I’m feeling safe.

But so far we haven’t tried to draw any distinctions between good and bad melodies. Those 144 two-note melodies, for example, are probably not very interesting. And a random collection of 22 notes generated by a computer program might be a melody but is not likely to be a good melody.

So even though on a theoretical level we’ll never run out of melodies, the more important question is “will we ever run out of good melodies?” I don’t know. But here’s a melody, which I think is a pretty good one:

22-note melody



It has 22 notes, so it’s like one out of all the stars in the universe. And if you hum it, there’s a good chance that you and I and other readers of this article are the only human beings who have ever lived who have ever heard this melody.

That’s pretty cool.


On Self-Reflection

Look at yourself in the mirror. What do you see? Now… what do you really see?

When was the last time you held a mirror up to your inner artist and tried to give honest answers to questions like these?

  • What are my strengths?
  • What are my weaknesses?
  • What do I like doing?
  • What do I not like doing?
  • What do other people like about my art?
  • What do other people not like about my art?

You can take this as far as you want to. It can be as simple as “what are my best songs / what are my worst?” or, at the opposite extreme, it can be “what do/don’t you like about me?”

Now comes the even harder part: Find a mirror. By that I mean a couple close friends. Really close friends. I don’t just mean the people you like to have a few drinks with, watch some TV, or go to an occasional sporting event with.

I mean someone you’ve known for at least half your life, someone who has stayed your friend despite the two of you having grown as artists and as human beings, someone with whom you’ve had arguments and disagreements, perhaps even temporary periods of not being on speaking terms. Someone who has stood with you in your darkest hour, and someone for whom you’ve done the same.

For the purposes of this exercise, someone other than your spouse.

Now ask those close friends to answer the same questions about you and be brutally honest. The exercise can be reciprocal (but only if the other person agrees). Make a verbal contract ahead of time that you will not be offended and that this will not hurt your friendship; in fact, if done in the right spirit, it can strengthen your friendship. But you’ll need to be prepared to hear things like “I think your songs are great, but you’re not a very good singer.”

Now on to the next part. All the self-reflection in the world isn’t much good without subsequent action. For example, “you’re not a very good singer” can lead to actions like (1) not singing, (2) teaming up with a good singer, or (3) taking voice lessons. Or “your piano instrumentals are your best work” might prompt you to start working on a new collection of piano instrumentals. But if you’ve chosen to go to a deeper level with this self-reflection exercise, then comments like “sometimes you say things that seem like gossip” might lead to a healthy habit of double-checking what you’re about to say before deciding whether to say it. Or “you have always been a faithful friend” might simply mean “keep doing that; that’s worth more than art.”