Khamaj is the smallest departure the ten frames allow. One swara moves — Ni drops to komal Ni — and the other six stay exactly where Bilawal leaves them, which makes it the frame to reach for when the question is what a single altered position does to everything built on top of it.
The seven swaras, from Sa
Declared as semitone offsets from Sa, then read through the same fixed chromatic-to-sargam table every thaat on this site uses — the frame’s seven available positions, not a raga’s actual phrasing. Against the Bilawal reference this frame moves one swara.
| Degree | Offset (semitones from Sa) | Swara |
|---|---|---|
| 1 | 0 | Sa |
| 2 | 2 | Re |
| 3 | 4 | Ga |
| 4 | 5 | Ma |
| 5 | 7 | Pa |
| 6 | 9 | Dha |
| 7 | 10 | Komal Ni |
Where it falls on the sitar
With Sa placed on C, every fret across all five strings whose pitch class is one of Khamaj’s seven swaras — computed from the registry’s true open pitches and the instrument’s fifteen-fret board:
| String | Frets | Swaras |
|---|---|---|
| 5th string (C3) | 0, 2, 4, 5, 7, 9, 10, 12, 14 | Sa, Re, Ga, Ma, Pa, Dha, Komal Ni, Sa, Re |
| 4th string (G3) | 0, 2, 3, 5, 7, 9, 10, 12, 14, 15 | Pa, Dha, Komal Ni, Sa, Re, Ga, Ma, Pa, Dha, Komal Ni |
| 3rd string (C4) | 0, 2, 4, 5, 7, 9, 10, 12, 14 | Sa, Re, Ga, Ma, Pa, Dha, Komal Ni, Sa, Re |
| 2nd string (G4) | 0, 2, 3, 5, 7, 9, 10, 12, 14, 15 | Pa, Dha, Komal Ni, Sa, Re, Ga, Ma, Pa, Dha, Komal Ni |
| 1st string (C5) | 0, 2, 4, 5, 7, 9, 10, 12, 14 | Sa, Re, Ga, Ma, Pa, Dha, Komal Ni, Sa, Re |
The whole difference from Bilawal is one fret, and it appears in two different places depending on what the string opens on. On the three C strings, fret 11 goes dark and fret 10 lights in its place. On the two G strings — which open on Pa rather than Sa — the same swara lands at fret 3 instead of fret 4, and because komal Ni recurs within a fifteen-fret span where Ni did not, each of those strings carries one extra position: forty-seven in total against Bilawal’s forty-five.
A frame, not a raga
Ragas conventionally classified under Khamaj include Khamaj itself, Des, Tilak Kamod and Jhinjhoti, and classification is a convention rather than a law — authorities differ on where individual ragas belong, and several of these ragas use shuddha Ni in ascent and komal Ni in descent, which no single set of seven positions can express. The thaat fixes what is available; it does not describe what a performance does with it.
Where to start
Play Bilawal and Khamaj back to back on one string: the only thing that changes is the seventh position, and hearing it in isolation is the point of a one-swara frame. In 12-TET terms this same set of seven pitch classes is what the scale library calls Mixolydian — a reference approximation, not an equivalence, since it says nothing about meend or which swaras a raga leans on. Then run the position table through the fretboard explorer.