YOUR FRIDAY MATH with Mathematician KP Hart

Here’s Mathematician KP Hart’s Math Question and Answer for Friday, March 4th!

Can original music keep being composed until infinity?

It surprises me that for centuries people have composed music, using just one octave and a few sharps and flats, without repetitions

So that we can do a few calculations we restrict ourselves to the terms mentioned in the explanation: octave, sharp, flat. By combining notes with sharps and flats we can mark off twelve positions in one octave that are half a tone apart. Let us consider a very simple kind of music: a sequence of twenty-five notes, all chosen from the twelve in our octave. The number of sequences that we get is 12²⁵ and that is roughly equal to 9,5×10²⁶, a number with 27 digits The presently known compositions make up only a minute fraction of this total.

The number of `compositions’ of 25 notes is very large. To get an idea how large we perform a thought experiment. Assume there are at any time a billion people on earth with musical aspirations and that they start to compose like mad: every second each one of these people makes one composition as described above. To create all our 12²⁵ pieces of music in this way will take 30 billion years. According to current estimates we can expect to live under our sun for about5 billion years still. There is still a lot of music to be composed, although some compositions will probably never be played because they are too monotone or too irregular.

In the above we did not take any other aspects of music into account: tempo, division in beats, …; these will give untold many variations in the compositions.

Can we keep composing into eternity? Theoretically yes, because we did not put a maximum length on our compositions. Even with our one octave and its sharps and flats we can keep going on for ever.

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Read all of KP Harts math questions here!

About Dutch Mathematician KP Hart: In the beginning of this year the Dutch government opened a website, The Dutch Science Agenda, where everyone could post questions that they thought were of scientific interest. This was an attempt to involve the whole country in determining what the Dutch science agenda should be in the coming years.

I looked through the questions and searched for terms like `mathematics’, `infinity’ … to see what mathematical questions there were and I noticed various questions that already have answers (and have had for a long time). On a whim I decided to post answers to those questions, in Dutch. For your edification I will translate these posts into English.