The Mathematics in our music

By  Narjis Zehra – Electrical Engineering 2020

(Student, School of  Science & Engineering , Habib University)

Reflections on “The Mathematics in our music by Mr. Yousuf Kerai”


Yousuf Kerai’s talk “The Mathematics in Our Music” was organized by Habib University’s School of Science and Engineering (SSE) as part of SSE Public Lecture Series. Held on Friday, November 25th 2016, at Habib University, this talk revolved around the relationship between music and mathematics in South Asian frame of reference.

Yousuf Kerai, a mathematics faculty member of Integrated Science and Mathematics (iSciM) department and an accomplished tabla player, was accompanied by Shehroz, an eighteen years old sitar player. Both were later joined by Mr. Kerai’s ustaad, Khursheed Hussain, for the final performance.

The 12 notes shared in our musical tradition are S r R g G m M P D n N, which when played together sound like a suspense scene from a PTV drama. That is the reason why they are not played together but are broken up into certain divisions, the major notes (represented in upper case alphabets) and minor notes (represented in lower case alphabets).

Western music started with finding a perfect multiplier to generate new frequencies. From the first frequency S to the next one r, the frequencies are multiplied by an irrational number. Multiplying any one frequency by gives the next frequency. This is represented by a general formula Fo ()n = Fn.

With the reference of Western music, Mr. Kerai explained the trajectory of South Asian music i.e. the relationship between the musical notes and the journey of landing on one from the other. It is unlike Western music which revolves around simultaneous occupancies of these notes. Melodically, our music invokes the use of these in-between frequencies called the Shruties which give it its Ras. These are the same characteristics which our vocal chords provide. And so, in the auditorium, not only did the skin of Mr. Kerai’s tabla and Shehroz’s sitar string vibrate, but so did Shehroz’s vocal chords. It started the chain of applause by the audience that night. Different clusters of notes were sung and played which when written would only be aaaaaaaa but hearing them was enough to create a mahol.

When a string is plucked once, a frequency t is produced. When the same string is plucked half way, it produces twice as much frequency with the same tone.  Thus, modulating the frequencies of the string give us new notes.

Mr. Kerai gave his audience an experience of clapping on the 4 beat cycle (which was basically 16 beat cycle in disguise). With the representation of the Awartan of 16 beats and 10 beats and the syllables associated with them, he taught his audience the tehai used in the music which we daily listen to. The world of tehai is incorporated with the world of poetry in tabla that is the art of saying sentences in the language of tabla.

Mr. Kerai concluded this talk by introducing his ustaad, Khursheed Hussain, for the final performance of the night which left the audience jaw dropped.