A Tihai That Will Not Add Up: Jhaptal Vibhags, Khali and the Arithmetic of Resolution
A tabla candidate's theory script and his practical announcement contradict each other. In the script he writes: "Rupak - 7 matras, vibhag 3+2+2, sam with tali at matra 1, khali at matra 5" and "Jhaptal - 10 matras, vibhag 2+2+3+3, tali at matras 1 and 5, khali at matra 9". His Jhaptal theka, however, is written correctly as dhi na / dhi dhi na / ti na / dhi dhi na, which does not fit the vibhags he has stated. In the practical he announces a tihai in Jhaptal: three identical phrases of four matras with no gaps between them, beginning two matras before sam, explaining that "twelve matras will fill ten". The examiner stops him and asks him to justify the calculation and the notation together, since the same paper carries marks for tala notation and for the tihai.
1. Correct the two tala entries and explain the principle that links vibhag to tali and khali, using the theka bols he already knows as evidence.
Read the worked answer
Principle. Vibhags are the sections of a tala; a tali mark stands at the first matra of a vibhag, khali marks the vibhag that is deliberately left "empty" (usually the third), and sam is the first matra of the first vibhag. Sam is normally tali, but not always.
Jhaptal. 10 matras, vibhag 2+3+2+3; tali at matras 1, 3 and 8; khali at matra 6. His own theka confirms it: dhi na (1–2) / dhi dhi na (3–5) / ti na (6–7) / dhi dhi na (8–10). The clap pattern 1, 3, 8 with khali at 6 is the only reading consistent with these bols, so his 2+2+3+3 with tali at 5 and khali at 9 is self-contradictory.
Rupak. 7 matras, vibhag 3+2+2, but sam at matra 1 is khali, with tali at matras 4 and 6. Rupak is the standard case a candidate must memorise as an exception: sam and khali coincide. Writing sam as tali at matra 1 destroys the one feature that makes Rupak recognisable.
Correction to write on the script: Jhaptal 2+3+2+3, tali 1, 3, 8, khali 6; Rupak 3+2+2, khali 0 at 1, tali at 4 and 6.
2. Evaluate the announced tihai. Give the general condition a tihai must satisfy and produce at least two workable arithmetic solutions for Jhaptal, with the reasoning shown.
Read the worked answer
Why his tihai fails. Three phrases of 4 with no gaps total 12 matras, not 10. Starting two matras before sam means the twelfth matra falls two matras after sam - the tihai overshoots the resolution point, which is the one thing a tihai may not do.
Condition. For three equal phrases of p matras separated by two equal gaps of g matras, total length = 3p + 2g, and the group must be positioned so that its last matra is sam. Equivalently, the first matra is (total − 1) matras before sam.
Workable solutions in Jhaptal (10).
- p = 2, g = 2: 6 + 4 = 10. Starts on matra 1 and resolves on sam of the next cycle. Simple, audible, and the one to play in an exam.
- Longer-span version: 3p + 2g = 30 (three cycles) gives p = 8, g = 3, or p = 6, g = 6, or p = 4, g = 9. Valid, but the internal repetition is harder to keep even at Matric level.
If he insists on four-matra phrases (total 12): that is legitimate only if the group starts 11 matras before sam, i.e. on matra 10 of the cycle two cycles earlier, so the twelfth matra lands on sam. It works mathematically but is a poor choice for a candidate who cannot yet keep the 10-matra version steady.
Recommendation: play p = 2, g = 2, and count the two gap matras aloud while practising so the resolution is heard, not guessed.