Tigun that arrives early: the arithmetic behind Teentaal layakari
The tala station of the practical carries 10 marks. The candidate must recite Teentaal - 16 matras, tali on 1, 5 and 13, khali on 9 - with theka in barabar at 60 bpm, then dugun, tigun, chaugun and aad, marking tali and khali with the right hand. Her barabar and dugun are steady. In tigun the 'dha' starts arriving about one matra early by the third avartan, and when asked to explain, she says she is 'fitting three into one'. In aad she stops after eight matras and says the tala 'does not fit'. Her written homework shows tigun computed as 16 × 3 = 48 matras and aad as 16 ÷ 1.5 = 24 matras, both ticked by a tutor. The examiner has told her the fault is conceptual rather than rhythmic, and that she must be able to say where each layakari's sam falls before she sings it.
1. Compute where the sam of tigun falls in the 16-matra grid at 60 bpm, and explain why the candidate's '48 matras' answer is a category error.
Read the worked answer
In tigun each matra is divided into three equal parts, so the tala still has 16 matras but each matra lasts one-third as long. A complete 16-matra avartan of tigun therefore occupies 16 ÷ 3 = 5⅓ matras of barabar laya. Her sams fall on base matra 1, then 6⅓, then 11⅔, and then at 17, which is sam of the next cycle. At 60 bpm one base matra is one second, so the second tigun sam arrives 5.33 seconds after the first. The '48' answer counts aksharas, not matras: she multiplied 16 by 3 but kept the matra length fixed, which is precisely why she feels she must compress to get back to sam in one avartan. The conceptual correction is that layakari changes the duration of the matra, not the number of matras in the tala.
2. Do the same for aad: show why 'it does not fit' is false, and state where the second sam falls and how often aad realigns with the base sam.
Read the worked answer
Aad laya is three matras in the time of two, so each aad matra lasts two-thirds of a base matra. Sixteen aad matras therefore take 16 × ⅔ = 10⅔ base matras, and the second sam falls between base matras 11 and 12 - inside the third vibhag, shortly before tali 3 at matra 13. So aad does fit; it simply does not fit into 16 matras, and she must carry it across the khali instead of stopping at eight. Realignment is worth stating because it explains her discomfort: three aad avartans occupy 32 base matras, i.e. exactly two base avartans, so aad sam coincides with base sam once every three aad cycles. For tigun the same logic gives realignment every three tigun avartans, since 3 × 5⅓ = 16. Once she can say this, the drift stops being mysterious.
3. Design a 20-minute daily practice plan that removes the drift, using counts rather than adjectives.
Read the worked answer
Set the metronome to 60 bpm with a click on sam only, so she cannot lean on a click at every matra. Mark the three tigun sams physically at 1, 6⅓ and 11⅔; for the fractional sams use a spoken syllable rather than a clap, because there is no tali there. Practise in four-avartan blocks: barabar, dugun, then three tigun avartans, then back to barabar to check that she has not shifted the base. Count in aksharas within each matra, and after each block record 30 seconds and verify that the third tigun avartan still lands at 11⅔. For aad, practise six-avartan loops, since three aad avartans equal two base avartans, so the loop closes cleanly. Ten minutes on tigun, five on aad, five on chaugun with correct khali syllables - 'tin tin ta', 'ta' in the khali vibhag, 'dha dhin dhin dha' in the tali vibhags.