My problem with the session was that I didn’t know several of the tunes. My schoolmate Dhanashree Pandit-Rai, a wonderful singer, was using Hindi film songs to introduce her audience to the idea of a raag. But what if the songs were unfamiliar?
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Turned out it didn’t matter. She’d play a tune, then play around with its notes, and we soon understood. A raag is no more than a set of musical notes. Not any old set, but one that forms an unspoken agreement between performer and listener: that if a tune is based on a particular raag, it will use only those notes. Because those notes “go together” in some way.
Much like a Portuguese word would stick out if used in a Tamil conversation, a note that’s not in raag Yaman, for example, will stick out in a composition based on Yaman. That’s why an audience shifts in its seats and mutters uncomfortably at a note that’s besura, or discordant, if a performer happens inadvertently to use one. That’s the meaning of the unspoken agreement.
But what’s this about “going together”? How do we know when a note is besura? Why is it out of place in one raag, but at home in another?
To answer those questions, amazingly enough, you need to hold on to just one basic idea: sounds are produced by vibrations. If you stretch a rubber band between your fingers and pluck it, you hear a sound. Why? Because the rubber band vibrates, which makes the air vibrate, then your eardrum vibrates, and you hear something. What note you hear depends on how fast the band vibrates, called the “frequency” of the vibration. The higher the frequency, the higher the sound it produces. So if your Raja Mama has a “deeper” singing voice than Kamala Mami, that means his notes vibrate at lower frequencies than hers.
Musicians realized long ago that musical notes relate to each other according to their frequencies. In particular, they found that if they played a note of one frequency, then another of double that frequency, listeners heard both as the same note. Except, the second is higher than the first. Two such notes frame the octave, the basis of all music.
So let’s say you produce a “sa” by vibrating a sitar string—I promise you it sounds better than a rubber band—100 times a second (called 100 hertz, or Hz). Then for the next higher “sa”, at the upper end of the sa-re-ga-ma-pa-dha-ni-sa octave, the string vibrates at 200Hz. If you could somehow remove every second vibration of this 200Hz string, you’d be back at the first “sa”. This nice symmetry is exactly why we hear them as the same note.
But what about “re” and “dha” and “ni”, those other musical pals? For convenience, composers divided the octave into a number of notes, each of whose frequencies bears a precise mathematical relationship to the ones on either side. The ratio of the frequencies of “re” and “sa” is the same as of “ga” and “re”, and so on up the scale. (It’s actually a little more intricate, but never mind). The notes are arranged so that the frequency of “pa” is exactly halfway between one “sa” and the next: that is, between “sa”s at 100Hz and 200Hz, you’ll find a “pa” strumming along at 150Hz.
Notes “go together” or not because, again, of the ratios of their frequencies. The 100Hz “sa” and the 150Hz “pa” sound good together because of the simple ratio (1.5) of their frequencies. Similarly, if slightly less pleasing, for 100Hz “sa” and 125Hz “ga”. But that same “sa” and its “re”, at 112Hz, don’t make good music together because their ratio (1.12) is not quite as simple.
But can they still appear in the same raag? Well, hold on tight to that dream.
Every raag uses its notes to paint a picture in our minds, to give voice to a mood. Our ears quickly sense the relationships between such notes and we file them away, perhaps associating them forever with that mood. This is why we know when a performer sings besura. She has hit a note that has an odd relationship to the others in her raag.
Popular music tends to use notes with simple relationships. This is why it has broad appeal—why, in fact, it is popular. Still, it is a good base from which to approach classical music, which is why Dhanashree used Hindi film tunes in that session. Classical music tends to exploit the more uncomfortable relationships between notes—the less simple frequency ratios—creating tension and expressing emotion that way.
Discomfort, tension, emotion, creativity—all from interplay between the ratios, simple or otherwise, between frequencies of notes. Mathematics, even in music. Damn I love this stuff.
Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners. A Matter of Numbers will explore the joy of mathematics, with occasional forays into other sciences. Comments are welcome at email@example.com