Music translated into Mathematics:

Leonhard Euler (1707-1783) was 24 years old when he wrote "Tentamen novae theoriae musicae ex certissimis harmoniae principiis dilucide expositae" a work of 263 pages, written in Latin, published in 1739.

Euler wrote:

"Duobus autem modis ordinem percipere possumus; altero, quo lex vel regula nobis iam est cognita, et ad eam rem propositam examinamus; altero, quo legem ante nescimus atque ex ipsa partium rei dispositione inquirimus, quaenam ea sit lex, quae istam structuram produxerit. Exemplum horologii supra allatum ad modum priorem pertinet; iam enim est cognitus scopus seu lex partium dispositionis, quae est temporis indicatio; ideoque horologium examinantes dispicere debemus, an structura talis sit, qualem scopus requirit. Sed si numerorum seriem aliquam ut hanc 1, 2, 3, 5, 8, 13, 21 etc. ascipio nescius, quae eorum progressionis sit lex, tum paullatim eos numeros inter se conferens deprehendo quemlibet esse duorum antecedentium summam hancque esse legem eorum ordinis affirmo." "Posterior modus percipiendi ordinis ad musicam praecipue spectat"

which means ...

Nous pouvons reconnaître l'ordre de deux manières. Lorsque la loi qui en est la raison nous est connue, il suffit d'examiner si l'objet à considérer y satisfait. Mais si cette donnée nous manque, il faut chercher à découvrir, dans la disposition même des parties de l'objet, la loi qui a présidé à leur arrangement; la loi reconnue, l'ordre en sera la conséquence. L'horloge citée précédemment offre un exemple du premier cas: le but ou la loi de la disposition des parties y est connue, c'est l'indication du temps. Ainsi, quand nous examinons une horloge, nous n'avons qu'à vérifier si sa construction répond à ce but. Mais si nous avons à considérer, par exemple, la série des nombres 1, 2, 3, 5, 8, 13, 21, etc., sans savoir quelle est la loi de leur accroissement, la comparaison de ces nombres nous fait bientôt découvrir que chacun est la somme des deux qui le précèdent; nous connaissons dès lors la loi de formation de la série, c'est-à-dire, nous connaissons l'ordre qui y règne.

[translated from French]:

"There are two ways in which we are able to perceive order; the one, in which the law or rule is already known to us, and to that matter being proposed, we simply examine; the other, in which the law before we were ignorant and out of the regular arrangement of parts we inquire, so that we may construct laws. The example of the clock given above belongs to the first sort; one already knows the goal or law of the regular arrangement of the parts and we only need to discern its structure to meet our need. But if the number series somehow were 1, 2, 3, 5, 8, 13, 21 etc. and we had to consider unaware, what is the law of their progression, then gradually the comparison of those numbers among themselves will allow anyone to discover that each is the sum of the two previous and consequently thus is the law of their order confirmed. The second manner of recognizing order is present especially in music."

The classification of the fundamental chords according to Euler

Euler's Exponential Series....

Euler created many tables... this one was a breakthrough that helped to decode Gann's Wheel.

The Fibonacci number series is present, but it is not linearly found. As an example find the numbers 13 and 21 or compare the location of 3, 5, and 8. Also compare this table with the one above it. The ratio 1:1 is now 1. The ratio 1:2 is now 2 in a second row. You will understand this notation in more detail as we progress. For now just recognize the patterns.