Physics and Mathematics of Music


In almost all popular systems of music, there are 12 notes out of which 7 are called pure notes and remaining 5 are flat or sharp notes. In Indian Music system, the pure notes are called “shuddha swara” and flat/ sharp notes are called “komal” and “teevra” swara”. The seven “shuddha swara” are – “Sa”, Re”, “Ga”, “Ma”, “Pa”, “Dha” and “Nee”. The remaining five “swara” are – “Komal Re”, “Komal Ga”, “Teevra Ma”, “Komal Dha” and “Komal Nee”. The twelve notes together form one “Octave” or “Saptak”. There are normally three “Saptaks” – “Mandra”(lower), “Madhya”(middle) and “Taar” (High). Each “Saptak” theoretically has all the 12 notes but in most of the compositions apart from the entire “Madhya Saptak” only 3-4 notes of the “Mandra Saptak” and the “Tar Saptak” are used. This is mainly because of the limitation of the human voice which can not cover more than this span. Instruments of course can span over a much wider range but normally instrumentalists compose tunes in the same range as it sounds much better that way.

Pythagoras, the man in the center with the boo...

Pythagoras teaching music in "The School of Athens"

All the twelve notes of an Octave sound different because they have different frequencies. There are three versions of each note – one in each Octave. For example we have one “Mandra Saptak Sa”, one “Madhya Saptak Sa” and one “Tar Saptak Sa”. If we play these three notes they sound similar yet different. Why? Obviously the three “Sa” have different frequencies so why should they sound similar? It is because all the three frequencies are resonating frequencies. Which means that if the frequency of Mandra Saptak Sa is “f” then the frequencies of “Madhya Saptak” and “Tar Saptak” Sa are “2f” and “4f” respectively.

One “Saptak” comprises of 12 notes having frequencies between “f” and “2f”. The method of assigning the frequencies to the 12 notes is called “Tuning Method”. Various tuning methods have evolved over thousands of years both in Indian as well as in the Western Music System. Interestingly, most of these methods have very interesting mathematical backgrounds and the famous mathematician Pythagoras was the first to propound a mathematical tuning method. I wouldn’t like to load this blog with the technical details but those who are interested can search the web to find out more about this subject.

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