The Two-Vīṇā Experiment

Bharata’s Nāṭyaśāstra (chapter XXVIII, śloka 24) describes an experiment: two vīṇās tuned the same way, one of which is lowered step by step to establish the size of the intervals. The application lets you redo it in the browser, after Bernard Bel’s reconstruction. Its main limit: it settles choices the treatise leaves open, and it flags them.

Play the experiment, with nothing to install; headphones or speakers are needed.

How to think of it

Two instruments, side by side. One stays fixed as the reference. On the other, you move the pegs yourself along an axis marked in cents. When two notes are almost in unison you hear beats; they vanish when the notes merge. The ear does the measuring, as in the treatise.

What it does

• Tune the Sa-grāma: a first stage has you tune the scale by ear, fifth by fifth and fourth by fourth.
• Follow the four lowerings: the second stage lowers the movable vīṇā four times in a row. They establish that the pramāṇa śruti exists, and that the intervals of two śrutis, of a tone and of a minor third are identical to one another.
• Show the consonances: when two notes of the same vīṇā form a fifth, a fourth or a third within half a śruti, a line joins them on the dial.
• Place the 22 śrutis: the dial marks the positions of the octave’s 22 śrutis.

The interpretive choices

Bernard Bel shows that the experiment yields 7 equations and 3 inequalities between the 22 śruti sizes: the pramāṇa śruti remains free between about 0 and 56.8 cents (The two-vina experiment). So that something can be heard, the application decides:

• the notes have Pythagorean ratios (Ri = 9/8, Ga = 32/27, Ma = 4/3, Pa = 3/2…), with Sa at 220 Hz;
• the pramāṇa śruti is 81/80, about 21.5 cents, one convention among others;
• the intermediate śrutis, which the literature does not fix, are spread evenly between two notes, for display only;
• the first tuning stage is a teaching reconstruction: the treatise assumes the vīṇā is already tuned.

Common issues

No sound. The browser only opens audio after a gesture: click in the application before playing.

The interface is in French, including on the English version of the site.

Where it stands

Experimental. It runs entirely in the browser, with no server and no audience tracking. It goes with the work on the Indian treatises (icm); its code is not published.

Play · Research · icm · sangitaratnakara · Source: Nāṭyaśāstra XXVIII.24; Bernard Bel, A Mathematical Discussion of the Ancient Theory of Scales according to Natyashastra, CNRS, 1988. Thanks to Bernard Bel, whose demonstration the application rests on.