The iTunes store contains 28 million different songs. Last.fm carries 45 million songs and the Gracenote database of artists, titles, and labels, contains 130 million different songs. That’s a lot. If you were to listen to all of the songs in the Gracenote database one after the other in a giant playlist, it would take you more than 1,200 years to complete. But, since there are a finite number of tones our ears can distinguish and because it only takes a few notes in common for two musical ideas to sound similar, will we ever run out of new music? Will there ever be a day where every possible brief little melody has been written and recorded and we are left with nothing new to make? A good rule of thumb might be to say that if modern recording technology can’t distinguish the difference between two songs, well, neither could we. Digital music is made out of lots of “bits”.

However, each individual bit exists in one of two states: a “0” or a “1”. Now, what this means in that for any given, say, 5-minute-long audio file, the number of possibilities, mathematically speaking, is enormous, but mind-blowingly finite. A compact disk, which samples music at 44.1 kHz, is going to need about 211 million bits to store one 5-minute song. Because a bit can exist in two states, either a “0” or a “1”, the number of possible different ways to arrange those 211,000,000 bits is 2 to the 211th million power. That value represents every single possible different 5-minute-long audio file. But, how big is that number? Let’s put this in perspective. A single drop of water contains 6 sextillion atoms. 6 sextillion is 22 digits long. That’s a long number. But the total number of atoms that make up the entire earth is a number that is about 50 digits long.

And estimations of the total number of hydrogen atoms in our universe is a number that is 80 digits long. But, “2 to the 211 millionth power”, the number of possible, different 5-minute audio files, is a number that is 63 million digits long. It is a number larger than we can even pretend to understand. It contains every possible CD quality 5-minute audio file. Inside that amount, is everything from Beethoven’s “5th” to Beck’s “Loser”, it even contains a 5 minute conversation you had with your parents when you were 3 years old. In fact, every one of them. It even contains every possible conversation you didn’t have with your parents when you were 3 years old. But, it is finite, not infinite. It’s cool to think about, but it doesn’t come very close to answering the question of this video, which is, “how many possible different songs can we create and hear the difference between?”.

So, for that, we’re going to need to narrow down our hunt. On Everything2, Ferrouslepidoptera made a calculation that involved some assumptions, that I think, helped narrow the field down in a really nice way. She took a look at the total number of possible different melodies you could create within one octave, containing any or all of the intervals we divide octaves into. Of course, sound frequencies can be divided much more granularly than that, but giving ourselves more notes might mean we could make more technically different melodies, but they wouldn’t necessarily sound any different to our ears. Now, given a single measure containing any combination of whole, half, quarter, eighth, sixteenth or thirty-second notes, she calculated that there would be this many possible unique measures, which is a smaller number than we had before, but, to put it in perspective, this is how many seconds old the universe is.

Yerricde’s calculation is even more specific. He stayed within one octave, but instead of looking at a complete measure, he only considered the number of unique combinations of 8 notes. He also assumed that typical melodies, as we know them today, only contain about three different types of note length. For instance, quarter, eighth and sixteenth or whole, half and quarter. To be sure, that will most likely not always be true. Musical tastes hundreds, thousands of years from now will most assuredly be different, but given melodies as we know them today, across 8 notes, over 12 intervals, there are about 79 billion possible combinations. We’re getting relatively small here. I mean,

under this definition of melody, 100 songwriters creating a brand new 8-note melody every second would exhaust every possible melody within only 248 years. But it’s still a huge number, way bigger than the total number of songs that have been written that we know about.

So, you can quite safely say that, no, we will never run out of new music. But here’s the rub. If that’s the case, why are there so many commonalities between songs? Even across hundreds of years, how come so many songs kind of sound the same? If we have more possibilities than we could ever exhaust, why is “Twinkle Twinkle Little Star”, the “Alphabet Song”, and “Baa, Baa, Black Sheep”, all the same melody? “My Country Tis of Thee” and “God Save the Queen” interestingly enough, are the same song. “Love Me Tender” is exactly the same as the old American Civil War song “Aura Lea.” And, a seemingly uncountable number of songs merely sound like other songs. The Spongebob Squarepants theme has a very similar cadence to “Blow the Man Down”. Soundsjustlike.com is a great resource for exploring this further.

It’ll show you two songs and how they sort of sound alike. And, when it comes to musical chords, it’s almost as if there’s no variety at all. Even though the number of possible different melodies is gigantic, us humans tend to gravitate towards certain patterns that we like more than others and we are influenced by what came before us. The commonalities he shows are pretty crazy. Well, even when it comes to lyrics, to writing, even though, mathematically, there are more possibilities than we could ever exhaust, we have gravitated towards a few. In fact, there’s a form of poetic meter that is so common it’s called “Common Meter”. I’ve composed a verse using it to explain what it is. Line one contains eight syllables. The next contains just six. For emphasis: iambic stress.

That’s it, no other tricks. Here is a list of songs that are written in common meter, also known as “Balad Meter”. The commonness of common meter is the reason you can sing the Pokemon theme song to the tune of Gilligan’s Island, or House of the Rising Sun, or Amazing Grace. You could also use almost any of Emily Dickinson’s poetry. Sure, they’re different melodies, but their lyrics are written in the same meter. And don’t forget one of the greatest compositions taking advantage of common meter’s commonness: Stairway to Gilligan’s Island. Our brains may also be keeping us from enjoying the entire mathematical space of available songs. For instance, research has shown that the way a song compresses, using software, can help us predict how enjoyable it will be. Too simple, too easy to compress, like, say, a rising scale, and the song doesn’t challenge us, it’s boring.

But too complicated, say, white noise, and the file won’t compress very much at all, and, likewise, we don’t seem to enjoy it. There’s a magic zone where a file is compressible by a computer, and also happens to be enjoyable by us. So, interestingly, even though mathematically speaking, there are so many possible unique melodies that we can safely say, there will always be room for new music, we don’t seem to be wired to care. We enjoy certain patterns

and melodies and calculating how many there could be is a lot less interesting than how connected and similar all the ones that we enjoy are. It’s as if we have more space than we need, more space than we could ever hope to see all of, or visit all of, or know all of, but no matter what new place we go, in a general sense, new, popular music will always remind us a bit of home. As always, thank you for reading and make sure to leave a comment.