Could we run out of combinations of musical notes to create new melodies?

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Will composers run out of new combinations of musical notes to create original melodies? Or are there endless combinations?

Sandeep Bhagwati (composer)

Concordia University, Montreal, Canada

A melody is more than a simple sequence of notes. The rhythm, the variations in volume and the length of the musical phrases enhance the sequence of notes to make an “original” melody. Each of them adds a huge layer of possible combinations. Further, the notes used by Western composers are meager abstractions that represent culturally selected frequencies from across the continuous human auditory range.

Most of the music in the world uses frequencies between western notes. With these “microtons”, the range of possible notes extends considerably, as does their combinatorial potential. If you are ready to accept or even invent new musical and aesthetic styles, the potential for composing and savoring new melodies is endless.

“There must be several googols (10100) of different possible melodies that can be composed without repeating themselves ”

Richard ellam

Bristol, United Kingdom

We won’t run out of new melodies anytime soon. Although the number of possible melodies is finite, it is so large that for all practical purposes the offer of new melodies is endless.

I play the bagpipe (small bagpipe, not Highland) and my chalumeau only plays nine notes, whereas most orchestral instruments can cover about three chromatic octaves, for a total of about 36 notes. So if anyone runs out of new songs, it will be the pipers.

We pipers play a lot of marches, and one of the simpler marching rhythms is only four quarter note beats in each bar. If you only have nine notes to play and four places in a measure to fill, you can have a total of 94 or 6561 clearly different bars. If you put them together in 16 bars of music, there are 656116 possible arrangements – a very large number. Many of these tunes would be horrible or boring, or lack harmonious intervals. But even if there is only one piece in a billion billion (1018) follows all the other rules for composing pipe treads, you always have something like 1.2 × 1043 possible melodies. And these are just pipe marches – we also play waltzes, jigs, reels, hornpipes, slow tunes and the rest.

If you do a similar exercise for instruments with a wider range of notes, and for longer and more complex melodies, you realize that there must be several googols (10100) of possible melodies that can be composed without repeating themselves.

Bryn glover

Ripon, North Yorkshire, UK

It depends on what is meant by “notes”. A piano has a finite range of predetermined notes, depending on the fixed tuning of the open strings, but a violin has a theoretically endless range of possibilities, depending on the varying placement of the fingers.

But given the range of notes represented on a piano, and assuming the questioner is referring to the standard Western notion of seven-note octaves (A to G), then there is a finite number of notes and therefore a finite number of combinations, however large the number. Even if we add in scales and scales, for example, music from China, India, Bali and elsewhere, the answer will always be the same.

Richard Bridge

London, United Kingdom

The composer Sergei Prokofiev, famous for his melodies, gave an answer to this question, which was asked by a reader of Pioneer revised in 1939.

He started with the chess analogy, calculating that on the white player’s fourth move there are 60 million possible variations. There are also 25seven variations to choose from in a short eight-note melody, he said, which offers about 6 billion possibilities. Among these, a composer might be able to find something melodious. Add different lengths of notes, rhythms and harmonies, and the 6 billion are multiplied again.

He added that some melodies that were once considered attractive are no longer attractive today, and vice versa. He concluded that “we need not fear that there will come a time when all melody will be exhausted and we will be forced to repeat old tunes”.

Prokofiev is a good source on this subject: his work is full of melodies in a great Russian tradition. I think Peter’s theme in Pierre and the Wolf is one of the most touching melodies I have ever heard. He was also a chess master, so he knew the options.

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