Music Meets Pseudoscience

You have probably seen several YouTube videos which claim to have converted “the artistic subtle beauty hidden in math” into a musical beauty such as “Making Music by Number Pi”, “Turning Fibonacci Sequence into Music”, “Making Music by Euler’s Number”, so on and so forth.

Before diving into the link between the rules of musical composition and mathematics, let us observe the mathematical structure of transcendental numbers and the methods they use in integrating them into music.

The most common method that is used in those type of popular content is as follows:

-Choose a prominent musical scale (that almost always is a major scale and generally C major)

-Assign each note in that scale to a figure from 0 to 9 (that is going to look like 0 = C (do), 1 = D (re), 2 = E (mi)…)

-Get a list of the figures of a transcendental number (this is [3, 1, 4, 1, 5, 9, …] for π)

-Substitute each number in that list with the note assigned to it

After doing the process for π, we end up with a pattern starting with those notes: F (fa) – D (re) – G (sol) – D (re) – A(la) – E (mi)

The procedure that we have just gone through, of course, is not the only one, but the principles are the same: assignment of a musical parameter to a list of figures.

Some numbers in math are special in specific mathematical operations. Zero is special for addition, One is special for multiplication, both of which are subject of identity laws of their respective operations. Exponential number is special in the solution of most of the differential equations.

In our case, which is simply expressing numbers, Ten is very special, for we use base 10. Since we are excessively used to it, it might not even seem obvious. It is when one tries to compose the algorithm expressing a number, that one sees that the procedure is not as simple.

>>>A = "23452346234"

>>>Alist = list(A)

>>>P = len(A)

>>>number = 0

>>>i = P

>>>while i > 0:

 >>>   number += int(Alist[i-1])*10**(P-i)

 >>>   i -= 1

>>>print(number)   

Above is a python code to demonstrate the algorithm of our perception of numbers in the base of ten, with the assumption that we already are able to perceive figures, which are numbers with one decimal place. How the number 10 takes places in the procedure can be seen in line 7.

Although number ten has a crucial role in expressing & interpreting numbers, this role did not pop out from a mathematical phenomenon implying a special feature only inherent in 10, but rather it is a result of the simple fact that we have ten fingers. Therefore one would not be wrong if one states that the amount of fingers that humans have entirely changes the way they express number.

As a result, all the irrational numbers would have been written in an entirely different way, had the number of fingers been different than ten. Here is first sixteen digits of π in base two:

                                             π = 11.00100100001111 (base 1+1)

*It is more convenient to indicate bases lower than ten as a repeated summation of 1, since number two in base two is expressed as "10" and the figure "2" does not exist in base two, the only thing on which all the bases might agree is explicit summations of 1.

Therefore, one can attribute no special meaning to the numerical representation of a number, for it is entitely dependent upon the arbitrary choice of base. But even if that was not the case, there are even better reasons to not buy the claim of so-called "musical subtle beauty hidden in the number Pi".

In all of the music schools, even for those that are conceived as the most "revolutionary" or "unconventional" such as The Second Viennese School, one always looks for and tries to establish patterns to construct music. Patterns are essential in almost any form of art, and do you know what a transcendental number such as π lacks? Patterns! No matter what base is used, it is well known that transcendental numbers can have no patterns in their decimal representations. You have probably heard romantic descriptions of π such as "You can find any number in it, including your birth date, numerical equivalents of any book that has been and will never be written, answers to all the questions you could possibly ask..." which is related to the randomness and non-repetitiveness that any transcendental has.

*The property of containing all possible number combinations cannot be concluded only from randomness and non-repetitiveness of a sequence, although that is a strong clue for the existence of that property. In fact the number π is not known to have this property, but it is expected to be true.

In theory you could construct a string of finite number of all the words in English, which in some of its parts contains "answers to all the questions you could possibly ask". But this property is useless, since most of that string will be garbage and you will have no a priori knowledge of locating that answer.

For most of the conventional composers, the link between music composition and mathematics is no point of interest, since what we follow to make music that sound good is essentially statistical data, regarding the works of great composers the we think are sounding good, rather than iron rules. But even if it was a point of interest, the randomness in the transcendental numbers, where it is settled that there can be no track of patterns, is the last thing a serious composer - with a care of integrating maths into composition rules - might use.