“Are they related?” asked my li’l one. Apparently, his maths teacher had broached the topic in school and being both musical as well as mathematical, it intrigued him immediately. “Ummm, yes..they are”, I began. Even as we spoke, there were so many things, some scientific, some flip episodes from my childhood, some words of wisdom from my music guru, that started coming up in my mind. And then of course, I went back immediately to find out whatever I could on the net…its maddening! From music courses that Maths tutors deliver in reputed schools to Pythagorian notions of “perfect musical numbers” and from Bach’s “Air on the G string” to how Beethoven composed music whilst going deaf using maths, the evidence is staggering. While browsing through the mathematical evidence, I almost had the same goose-bumpy feeling that only Kishori Amonkar rendering Jogiya in sublime form can create.

How can you ignore it? Musicians and mathematicians would need similar types of skillsets: An ability to create a precise output from the abstract, the skill to implement progressions deftly, to create sets and sequences within them. When Fibonacci, perhaps the greatest mathematician that Europe saw, gave those wonderful sequential numbers to the famous rabbit question (If one pair of rabbits is kept in a room and give birth to a young one, then there are potentially two pairs which can now give birth to two rabbits….so the sequence progresses from 2 to 3 to 5…), I wonder if he himself saw what profound truths would stand revealed in those numbers. When Peter Higgs got the Nobel for Physics for the revelation of the nature of the God particle, I had thought about whether the Fibonacci sequence could be re-named the God algorithm. It looks like this is the way nature progresses. Much has been made out of how flowers seem to mostly have petals that are multiples of 3 or 5 (both are Fibonacci numbers), but there are flowers that would also show exactly 34, 55 or 89 petals. And then, there are those superb Fibonacci rectangles. If you draw squares of the Fibonacci number sizes and arrange them to always create rectangles, you will see how these rectangles form the building blocks of the spiral shells of the sea creatures…if the Lord God made them all, Fibonacci saw them all. He saw the pattern, he saw the construction of the underlying nano-processes in a mathematical form.

Music is intrinsic to nature. You know where I am headed, right? Is it possible that the Fibonacci algorithm would not apply to music? Of course not! I mean, you just have to look around and there it is, staring at you in your face. An octave is C-D-E-F-G-A-B-C with 8 notes in it, a Fibonacci number. In Hindustani music, we do talk about the seven swaras or the saptak, but an octave stands defined only with a root and an end…so Sa to Sa is an octave (For the sceptics and outright disbelievers, I offer one more statement…Just like the Fibonacci sequence, you may also want to look up the Lucas sequence, which starts with 2 and1 and then progresses like Fibonacci…2, 1, 3, 4, 7, 11, 18…Now, here is the saptak, which is a derivative of a Fibonacci-*like* sequence). If you examine the octave from C to C on the keyboard, there are 13 keys, 8 white and 5 black. Pancham or Pa is the 5^{th} note of the major scale and it is incredibly the 8^{th} note of all the 13 notes in the octave. Pancham, that backbone of all Ragas. The check point. Since Pancham is the 8^{th} of the 13 notes, it is actually 8/13 = 0.61538, which is….phi! Phi, the golden number, the golden ratio. If we divide the Fibonacci numbers as in 2/1, 3/2, 5/3…they eventually just move towards….phi. The ultimate truth.

It didn’t sound this mathematical all those years ago when I was learning Hindustani music under Manik Bhide, a very strong exponent of the Jaipur Atrauli gharana. “Please, please teach me Marwa”, I used to ask her, 3 years into learning music. And she would give me the same answer patiently “Marwa is not easy because it doesn’t contain Pancham..you are not ready for it…when the backbone is missing, there is no checkpoint for the swaras. Also, you have to use Shadja i.e. Sa sparingly. Without Sa and Pa, you are in a space where you only have to feel the other swaras and you are not really sure where you are…Only the masters, who can peep into HIS creation can sing it.” His creation, the phi, the Fibonacci. On another occasion, I had asked her to teach me Hansadhwani. It is a Raga containing 5 (Fibonacci number!) swaras- Sa Re Ga Pa Ni..its a very sweet Raga and one of my all time favourites and I was truly excited about learning it. “No Manasi, you are not ready for it” came the answer again. “Why?” I was adamant. “If I can do Bhoop, which is – Sa Re Ga Pa Dha- why can I not do a Hansadhwani- Sa Re Ga Pa Ni?” “Because child, jumping from Pa to Ni is tough, really tough.” Well, I remember thinking that if I could jump from Dha to Sa during Bhoop, why could I possibly not jump the distance from Pa to Ni? “Because musical distances are not uniform”, she had told me. “From Pa, any distance is mighty. Because you are letting go of the anchor. Pancham. The backbone”. Phi.

It all falls into place. As I looked tenderly at my little musician, I wondered how I could even begin to explain this. There was once a mad guy called Fibonacci, I began…

Ma’am, loved reading it. Always thought ( i would say felt/visualized) ‘waves’ like patterns when i hear Pt Ajay Chakrobati. Calm. Slowly bringing in some variations and mixing up different ragas. But never thought of a Fibonacci sequence in Music. Also loved the comment by your music teacher on Raga Marwa.

PS: Bhairavi and Pahadi are my favorites.

Regards Gopal Hariyani Placement Assistance Committee Symbiosis School of Banking and Finance Mobile (+91) 9049405927

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Hi Gopal,

Thank you for the comment..its heady, this combination of Maths and Music, isn’t it? Happy to know that there’s a music lover in the class! Cheers!

Manasi.

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Simply Beautiful

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Thank you so much, Ashwini!

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A nice article.. you’ve always been an inspiring storyteller!! Please keep writing so that you can reach out to a larger audience than the class 🙂

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Hi Sarath!

Wonderful being connected to you again, after all this time! Hope to see you in all the future classes 🙂

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It was an interesting post ma’am. Fractals is another example for relation between music and maths.

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Wow! So you know about fractals…they are impressive, aren’t they?

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wonderful read ma’am! 🙂 I myself for one have been intrigued by the Fibonacci series’ relationship with music. There is a song by the band Tool, which follows the Fibonacci series. I hope you do enjoy rock music, ma’am, but nonetheless you would be amazed to watch this one. 🙂

here’s the link:

The number written along with the lyrics is the number of syllables (which follows the Fibonacci Series)

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Hi Vishwanath!

Thanks for the comment..and for sending me the link..had not seen it before and its truly amazing!

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