The Tihai That Does Not Land on Sam: Recomputing Teentaal Matras at Two Layas
Ritu, a Class 12 candidate at a Patna school, submits her practical file ten days before the BSEB practical examination. Her tihai in Teentaal (16 matras, vibhag 4+4+4+4) is built from three repetitions of the four-matra phrase 'dha dha tin na', with one silent matra inserted after repetition 1 and another after repetition 2: 4+1+4+1+4 = 14 matras. In the file she writes 'tihai begins on sam, matra 1' and tells her teacher that it therefore 'lands on sam'. Her teacher has fixed the class tempo at madhya laya 72 BPM, requires the last stroke of the tihai to fall on sam (matra 1), insists that the tihai be bedam (no silent matras anywhere), and wants it to fit inside one avartan. Ritu must also show a dugun version of the same tihai. A classmate's tihai uses three five-matra phrases with no gaps, and Ritu asks whether she can simply copy that structure instead.
1. Using matra arithmetic, show where Ritu's 14-matra tihai actually ends when it starts on sam, and state the one change of starting matra that would make it end on sam.
Read the worked answer
Count positions, not feelings.
- A tihai of L matras whose first matra is placed on matra p has its last matra on position p + (L − 1).
- Here L = 14 and p = 1, so the last stroke falls on matra 1 + 13 = matra 14.
- Mapping: 1–4 (repetition 1), 5 (silent), 6–9 (repetition 2), 10 (silent), 11–14 (repetition 3). The third 'na' lands on 14, three matras before the next sam. Nothing is resolved; the theka simply continues.
- To end on sam we need p + (L − 1) ≡ 1 (mod 16), i.e. p ≡ 1 − 13 = −12 ≡ 4 (mod 16).
- Check from matra 4: 4–7 (rep 1), 8 gap, 9–12 (rep 2), 13 gap, 14–16 and then 1 (rep 3). The final 'na' falls on sam.
So the single change is: start the tihai on matra 4, not on sam. The phrase and the gaps stay as they are.
2. At 72 BPM, calculate the tihai's duration in seconds and the fraction of an avartan it occupies; then do the same for the dugun at 144 BPM.
Read the worked answer
One matra = 60 ÷ tempo seconds.
Madhya laya, 72 BPM
- 1 matra = 60/72 = 0.833 s.
- 14 matras = 14 × 0.833 = 11.67 s (about 11.7 s).
- One avartan = 16 × 0.833 = 13.33 s, so the tihai fills 14/16 = 87.5% of an avartan and spills into the next cycle only if it starts late (as in the wrong version above, where it ends on matra 14 of the same cycle).
Dugun, 144 BPM
- 1 matra = 60/144 = 0.417 s.
- 14 matras = 14 × 0.417 = 5.83 s; one avartan = 6.67 s.
Interpretation: dugun does not change the number of matras or where the tihai sits in the cycle - it halves the clock time. Ritu must therefore rehearse the same 4-1-4-1-4 placement at both speeds, and be able to say the matra numbers (4,5,6,7 / 8 / 9,10,11,12 / 13 / 14,15,16,1) aloud while clapping.
3. The rubric demands a bedam tihai that ends on sam within one avartan. Decide which repair Ritu should make and justify it against the alternative of keeping her 14-matra structure.
Read the worked answer
The two repairs are not equal, because the rubric has three separate conditions.
| Repair | Ends on sam? | Bedam? | Within one avartan? |
|---|---|---|---|
| Keep 14 matras, start on matra 4 | Yes (ends on 1) | No - two silent matras remain | Yes |
| Delete both gaps, 12 matras, start on matra 6 | Yes (ends on 1) | Yes | Yes |
For the gap-free version, L = 12, so p ≡ 1 − 11 = −10 ≡ 6 (mod 16): 6–9, 10–13, 14,15,16,1 - the last stroke is on sam.
Decision: she should delete the two silent matras and start on matra 6. Keeping the 14-matra structure and merely shifting the start to matra 4 fixes the arithmetic but fails the explicit bedam requirement, so it would still lose marks in a practical examination where the examiner is counting aloud.
On copying the classmate: three five-matra phrases give L = 15, which needs p ≡ 1 − 14 = −13 ≡ 3, not matra 1 or 2. Copying the phrase without recomputing the entry is exactly the error that produced the original problem, so she should copy nothing until she has done the count herself.