Hey, Vsauce. Michael here. And 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. So, let's begin there, with digital
downloads, MP3's, CD's, and a calculation made by Covered in Bees.
Digital music is made out of "bits." Lots and lots of bits. But 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. And 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? Well, 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?
I mean, 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, as
was famously shown by The Axis of Awesome's "4 Chords." I've linked it in the description,
it's worth a watch if you haven't seen it already. These guys sing more than 40 different
songs using the same four chords...
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. Kirby Ferguson has a fantastic series looking into this called "Everything
is a Remix." I've also linked that down in the description. 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.
There's a great video on YouTube that I've linked below in the description that uses
captions to let you see just how these all fit together.
Oh, and don't forget one of the greatest compositions taking advantage of common meter's commonness:
Stairway to Gilligan's Island.
And you know what? 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.
And as always,
thanks for watching.
Fantastic, you're still here. If you want to hear music from people like you, from Vsaucers,
go check out WeSauce. You can submit music, animation, short films, anything that you're
making and putting on YouTube to us and we'll feature it on WeSauce. It's like a trailer
for what Vsaucers are doing.
Speaking of which, Jake Chudnow, who does all of the music in these videos, has a brand
new song out over on his channel, which I highly suggest you go give a listen.