Thaats

Recently I learned a little about ragas in Carnatic music, which is prevalent in the south of India. I discussed them here:

• Melakarta ragas.

Now let me give an equally superficial introduction to ragas in Hindustani music, which is prevalent in the north.

In Carnatic music we start with 72 different seven-note scales called ‘Melakarta ragas’, and then build many more ragas by leaving out notes and other tricks. Hindustani music is a bit similar: we start with 32 seven-note scales called ‘thaats’, and then build many ragas by leaving out notes and other tricks.

I should admit right away that this is not how ragas arose historically: both Carnatic and Hindustani music have been going on for centuries, and they diverged in the 1100s. But the Melakarta ragas were used to organize Carnatic music only around 1640, and the thaats were introduced to do the same for Hindustani music even later, in the early 20th century. Furthermore, everything in reality is more messy than the mathematician would like it to be. For example, there are Hindustani ragas that don’t fit into the thaat system.

But let’s just do the math of thaats, and see why there are 32 of them. I’ll use western notation and call the 12-tone scale

To be a thaat, a subset of these tones needs to obey some rules:

• It needs to contain C and G. (So, it needs to have the tonic and perfect fifth, a very reasonable constraint by western standards.)

• It also needs to have either D♭ or D—but not both—so that’s 2 options. (In western terminology we’d say it needs to have a second, which can minor or major.)

• It also needs to have either F or F♯, but not both—so that’s 2 options. (So, it needs to have a fourth, which can be perfect or augmented.)

• It also needs to have either A♭ or A, but not both—so that’s 2 options. (So, it needs to have a sixth, which can be minor or major.)

• It also needs to have either B♭ or B, but not both—so that’s 2 options. (So, it needs to have a seventh, which can be minor or major.)

This gives a total of 2⁵ = 32 thaats.

The rules I just listed are more restrictive than the rules for Melakarta ragas, so the 32 thaats can be seen as a subset of the 72 Melakarta ragas. There is some nice combinatorics there, which I will let you ponder.

We can visualize the thaats using a chart I found here:

• George Howlett, Thaat scales: Bhatkhande’s base forms and beyond.

Howlett’s webpage is also a great introduction to thaats. Here is his chart:

As you can see, it shows 5 binary choices leading to a total of 32 thaats. But what do the letters mean?

The notes in any thaat are called

or for short

These are a lot like the western “do re mi fa so la ti”. But for only 5 of these notes, namely R G M D N, do we have a choice: we can use them unmodified, as in the major scale, or we can alter them. That’s what the chart shows.

Now it’s time to admit a bit more reality into the discussion. Of the 32 theoretically possible thaats, Bhatkhande chose to focus on ten. These are more popular than the rest! Let’s see what they’re like.

• Six are modes of the major scale:

(There exists a seventh mode of the major scale, Locrian. But it can’t be a thaat, because it has a flat 5.)

• One is the double harmonic scale, which looks like this in the key of C:

In my article on Melakarta ragas I showed you a rare western pop song in the double harmonic scale.

• One might be called Lydian ♭2, which looks like this:

• One might be called Lydian ♭2 ♭6:

• Another might be called Lydian ♭2 ♭3 ♭6:

But that name is ridiculously long, so it might be better to call it Phrygian ♯4 ♮7.

Of course, all these thaats have Hindustani names. The only reason I’m not giving them is that I don’t want to throw too much information at you all at once. You can find them on George Howlett’s page or here:

• Wikipedia, Thaat.

For example, the thaat I called Lydian ♭2 ♭6 is really called Poorvi. According to Wikipedia the corresponding raga is rarely performed these days, and it’s “deeply serious, quiet and mysterious in character”. All of these seem to make sense, given the quirky combination of Lydian’s bright augmented 4th with the dark minor 6th and—even stranger—the dark and dissonant diminished 2nd.

Different ragas are meant to be played at different times of day, and Poorvi is performed at sunset. Here’s an example:

If you want vocal pyrotechnics, start around 29 minutes in. There you will hear that passages often end by dropping down a half-step from the minor second to the tonic (i.e. D♭ to C if we were in the key of C). By western standards this is a very unusual cadence. But that’s why I like it! This piece doesn’t shy away from the minor 2nd—it really leans into it.