Music and numbers

If we explore the way the numbers in the sound ratios manifest itself, we may better understand the old saying about numbers and music.  

A historic known example is Plato’s mathematical calculation of the Pythagorean scale. Plato did by inserting the harmonic and arithmetic means respectively between each of the terms in the two geometric progressions, 1,2,4,8 and 1,3,9,27 succeeded in corroborating mathematically everything that Pythagoras had discovered on the strings of his monochord or lyre. More about numbers and the Pythagorean Scale later.

First we have to remember some basic about prime numbers, which first are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29….p. (Usually 1 is not considered a prime). The only even prime number is 2.

Prime numbers are the building factor in the body of Natural numbers because any number can be divided into primes in one and only one way. They are a product of prime numbers.

Any musical sound can be expressed into numbers by its ratio; e.g. 4:3, the Fourth, which is the double of the double (2x2) and is effectively a repletion of the fundamental and in that respect do not contain a new identity.

The fifth harmonic on the other hand, the major third by the ratio of 5:4, is in that respect a “new” interval with the prime number 5.

(The musical terminology can be very confusing. The fifth harmonic is the major Third referring to the third tone in the diatonic scale and so do the Fifth, which is the third harmonic!)

The seventh harmonic got it right since it is called the Seventh and is considered as another “new” identity.

Looking at the 9^th harmonic, the major second, 9:8, we have some more confusion, since it should just be the third double above the fundamental, the first odd composite, but because 9 is not the double of anything, it sounds like something new.

The purpose in saying that numbers and music has something more in common than frequencies ratios, we have to expand the scope into the symbolic representation of numbers.  
It may sound odd for the present man that musical scales reflects  meta physical properties. Nerveless, the ancient Eastern scales and the antique Greek scales was deeply related to symbolic values of numbers. 
Music was considered as a symbolic representation of the relationship between heaven and earth and as such have to reflect the celestial influence. The Pythagoreans believed that it was not necessary to go beyond the third power (Cube) of a number, as one can not go above the three dimensions. 

The Chinese regarded the first 5 primary sounds of the fifths, the Pentatonic scale, as a representation of the perceptible world (the five Elements), and the first 12 fifths (the circle of fifths) as an reflection of the Zodiac signs. 
For the modal Indian music with its 22 intervals with the 7 notes of the scale, a more subtle representation can be found by regarding twenty two relating to seven in the ratio 22/7, which is the approximate expression of the relation between the circle and its diameter, so these two numbers represent the circle, the most perfect shape. 

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