The Algebra of Indian Music


Though there are hundreds of articles on the various types of music in India available to musicians, few discuss how to apply their conceptual aspects to practical scale studies. This is unfortunate, as merely running up and down a melodic pattern (raga) in different keys does not provide the student with the most valuable lesson: how to fully grasp and utilize the intellectual and/or structural power of Indian rhythm in one’s studies. And a key ingredient often missing in such study is the mathematical underpinnings of Indian music, and how they can be applied to practical scale practice. Thankfully, one does not have to be good at math to understand the system and begin exploring it, but if you get still get a little confused by the terminology, try out the exercises further along in the lost and you will be able to hear/feel what I am talking about. First though, we must know a little about the principles of rhythm in the various Hindustani (Northern) and Carnatic (Southern) styles of music.

(Note: Having studied both North and South Indian styles of classical music, I often intermingle the Tamil and Hindi names for various rhythms and concepts, so if you see such a mix it is habitual. Also, many Tamil and Hindi words are both singular and plural, so for the sake of ease of understanding in English I will use words like talam/talams or jati/jatis separately as singular and plural.).

These principles (in Carnatic music) are called the Dasa Prana, the 10 vital elements of rhythm. Among the ideas discussed are the various modes of indicating rhythm, subdivision, tempo, classification, and the idea of “time” in general. The beat cycles in South Indian music (talams) are considered to have developed over time from Sanskrit poetry, and out of this system five basic lengths of time (jati) developed: chatusra (4), tisra (3), misra (7), khanda (5), and sankirna (9). Groupings of beats and notes can be arranged quite creatively using the Dasa Prana, and thus I will discuss them in terms of how you can begin to use such groupings to your advantage in jazz improvisation.

Basic jatis, and how you group them within a talam, are a major part of the incredible creative science of Indian musics. And the key to understanding the power of jatis lies in understanding structure. For example, Chatusra Jati is a grouping of four notes or beats, and so a talam based on it will contain various groupings of four. This is extremely important to know, as talams are algebraic: they can be expressed as symbols which when memorized give an improvising musician an advanced level of control in both melodic and rhythmic improvisation. For example, the talam known as Dhruva contains the form X+Y+X+X, or XYXX. Thus if we assign both X and Y numbers, the form stays the same but the length changes. So Dhruva Talam, when based on Chatusra Jati, is 4 + 2 + 4 + 4, a 14 beat cycle. But if Dhruva is based on groupings of three (Tisra Jati) it becomes an 11 beat talam (3 + 2 + 3 + 3). In fact, one of my favourite talams is Dhruva when it is based on Misra Jati (7), which produces a flowing 23 beat cycle (7 + 2 + 7 + 7).

Taking this into consideration we can then analyze the various talams as algebra, and memorize/utilize this information for improvisational or compositional purposes. For example, Matthya Talam can be expressed as XYX, so Matthya is a 10 beat cycle using Chatusra (4 + 2 + 4), an 8 beat cycle using Trisra (3 + 2 + 3), a 16 beat cycle in Misra (7 + 2 + 7) and so on. Another talam (Triputa) can be expressed as XYY, and thus can become an 8 beat Chatusra cycle (4 + 2 + 2), a 7 beat Tisra cycle (3 + 2 + 2), a 9 beat Khanda cycle (5 + 2 + 2), and so on. This means we can also adapt the alphabetical symbols in such a way as to make memorization easier for our particular style of learning. Some people are better visual learners, so memorizing XYXX as images might make the process easier, imagining pieces of fruit (apple/banana/apple/apple), colorful shapes, emojis, or even the faces of Star Wars characters, whichever way makes learning the patterns fun and personal.

The next step is applying these algebraic patterns to our practice regimen. There are many ways to do this, but the most effective way to start is using the C major scale as our primary set of notes. So if we want to study Dhruva Talam using Chatusra Jati, we can practice scales in straight eighth notes: CDEF – ED – CDED – CDEF, then DEFG – FE – DEFE – DEFG, and so on (giving us the scale step pattern: 1234 – 32 – 1232 – 1234, 2345 – 43 – 2343 – 2345, etc.). Once you have moved from the bottom to the top of your horn and back down again, then you can move on to do the same in the remaining eleven keys. This approach is an extremely effective way of practicing scales in different keys while getting used to the flow of Carnatic rhythm, developing two different skills two at once. If we want to then move on to another talam using Chatusra Jati (Aja Talam for example: XXYY or 4 + 4 + 2 + 2) we can utilize the same concept: CDEF – CDEF – GG – GG, DEFG – DEFG – AA – AA, and so on (1234 – 1234 – 55 – 55, 2345 – 2345 – 66 – 66, etc.).

A really powerful use of this approach is in the study of the chromatic “scale”, all twelve the notes of the Western pitch system. Playing every single note from the bottom to the top of your horn is called “the” chromatic scale, and since there is technically only “one”, few people study it as intensively. But breaking up the chromatic scale into segments using talams and jati reveals the power of chromatic patterns, and provides for you very advanced technical control and flexibility on your instrument. For example, if you can run through Dhruva Talam using chromatic Chatusra Jati (CC#DE♭ – DC# – CC#DE♭ – CC#DE♭, C#DE♭E – E♭E – C#DE♭E – C#DE♭E, etc.), all the way up and down your horn in eighth notes evenly with a metronome (e.g. ♩ = 200 bpm), all other scales will seem like child’s play, at any tempo. But remember, it is not speed that makes this skill powerful, it is creative flexibility and control over your horn that is vital, so practice slowly and carefully, focusing on making music and expanding your mind.

The algebra of classical East Indian music is a true treasure and gift to the world, so I encourage you to explore it deeply and thoughtfully. Good Luck!



12 thoughts on “The Algebra of Indian Music

  1. This is really helpful. Even for an iffy guitar player like me. i don’t know if it is lazy, but i open tune in variations of C & this allows for some nice use of miind with the strings being looser & the scales are there to be discovered organically, because it is already in C, which seems to allow for greater emotional complexity & improvisation, plus the high notes give off a drone. i tried to play in standard, but the emotion suffers for the tautness. Open tunings are much better for raga improvisation.
    i am definitely going to try & play with some of these jati patterns.

    1. Ahhh… open tunings are so great, so much opportunity for creative exploration. And there is nothing “lazy” about being different! Joni Mitchell used to retune her guitar(s) in order to create more interesting chords since she had no guitar training when she began. Look where that got her!

      The fun is in the exploring, so go for it! 🙂

          1. You can just play & play & never stop, it is infectious, i broke my slide, but i could happily pick a single string & slide away just making up daft lyrics off the cuff for fun. Need a new slide now i’m thinking blues. i am glad i learned to improvise rather than bemoan my memory or learn to read music, i’m never short of just ideas to just play, it just happens, it is very fortunate.

            1. My next post is actually about EXACTLY what you are talking about.

              I told Okaji Sensei the central story of the next post, but since you have brought all this up, I think it would make a useful (???) or at least fun post about something hilarious that happened when I was in Grade 7.

              Stay tuned…

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