The Music and Musical Instruments of Southern India and the Deccan c13: Appendix

The Music and Musical Instruments of Southern India and the Deccan c13

Language: English

c13.s1 Description of Râjah Sir S. M. Tagore's S'ruti Vina — 21 parts

Appendix

Description of Râjah Sir S. M. Tagore's S'ruti Vina

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[The following minute account of the Râjah Sir S. M. Tagore's S'ruti Vina—intended to demonstrate the ancient system of 22—was kindly supplied by the late Mr. A. J. ELLIS, F.R.S.]

A S regards the construction of the instrument, I shall first quote the Râjah Sir S. M. Tagore's own words.¹ “We have hit upon another method to ascertain the nature and position of the s'rutis. The method is as follows:—Take a sitar or vina, measure the distance between Shaja (C) of the Madhya (middle) octave, and Shaja (D) of the next higher octave, in the C of the Tara octave. Divide the space between these two C's by putting a dot or line in the middle ; put a dot or line on either extremity ; place the note F over the dot or line in the middle, the note C on the other extremity of the first half portion of the divided space, and the note higher C on that of the second half portion ; sub-divide the first half portion into *nine* equal and the second half portion into *thirteen* equal parts, and put a dot or line to mark off each sub-division. . . Excluding the line marking higher C, there will be in all twenty-two lines. Each of these will represent a s'ruti.”

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¹ “The Twenty-two Musical S'rutis of the Hindus.” S. M. Tagore. Calcutta, 1886.

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This S'ruti Vina was, in fact, a long-necked sitar rather smaller than usual. It had two strings, one of brass and one of steel; the diameter of the brass wire was ·3 mm. (millimetres), and that of the steel wire was ·24 mm. The brass string proved useless, as the frets made the octave quite wrong with it. Hence it will be disregarded henceforth.

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The string was nearly horizontal. At starting at the nut it was 12 mm. above the finger-board, and at the bridge 13 mm. above the belly, which had curved upwards. But the first fret was 11½ mm. and the last fret only 2 mm. above the finger-board. The string was therefore pressed down only 1½ mm. for the first, but 12½ mm. for the last; consequently, the tension greatly increased as we ascended the scale, so that if we had taken the octave at half the length of the string it would have been much too sharp.

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There were twenty-three frets to give the s'rutis for one octave, numbered one to twenty-three on one side of the finger-board, with letters on the other, thus:--

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The frets for C D E F G A B c were of white metal, the others were yellow. The frets were flatly elliptical with hooked ends, round which a piece of gut was tied, and then brought about three times under the finger-board, catching the hooked ends each time and being firmly fixed. Each fret was therefore tightly fastened in its place, and could not be moved up and down the board without much force. But the fret itself could be deflected to the right or left, leaving the hooked ends fixed. This was not easy, but was possible.

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Then again the distance by which the string had to be deflected to press it on to the fret varied, but not uniformly. The diameter of the frets was different, but I was unable to measure it, as I could not get my gauge in. However, I estimate the white frets at fully 2 mm. in diameter; the others were narrower. The tops were rounded and it was difficult to appreciate the middle point, but I have endeavoured to measure the distance from the middle of one fret to the middle of the next.

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The whole length of the string from nut to bridge was 906 mm. The bridge was thus shaped, [Figure:] B being a ledge cut through for the strings, which lay on the flat part, A B, and the sounding length of the whole string was from the nut to A, but still the part A B was not firmly fixed and possibly influenced the pitch. The part of the string beyond B seemed to be damped by a perforated bead which ran on it.

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The note from the first fret was marked C, but taking the pitch of the string as it was (for we did not venture to screw it up), it made 241·2 vib., which is not far from 244·23, the French pitch of B in the 4-ft. octave, [Figure:] but I adopt the names of the notes as marked on the instrument. In this case the whole string gave F in the 4-ft. octave, a fifth below the first C and an octave below No. 10 fret, marked F, at any rate precisely enough. But the whole length of the string was 906 mm., and to the first fret 298 mm., so that the sounding length of C, or 608 mm., was only a little more than ⅔ of 906 = 604 mm., the increased tension being here slight. The sounding length for F was 463 mm., considerably more than 453 = ½ of 906 mm., because the string was 7 mm. above the F fret, which caused an increase of tension that had to be allowed for. It is impossible to calculate the effect of these increments of tension which, however, served to alter the effect of the lengths considerably.

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The principle followed seemed to be to find the position of the frets 1 and 23, giving the fifth of the open string and the octave of that fifth, by ear only, the shape and heights of the frets being assumed. The height of the first fret was, of course, as great as possible, and the last as low as possible to avoid jars. In this case the fifth is good, but the octave of it, or higher C, is too sharp by a trifle of 20 cents (one cent = the hundredth of an equal semitone, so that an octave has 1,200 cents and a comma 22 cents). The length of string for lower C was 608 mm., and that for higher c, 316·5 mm., which is much more than half the former or 304 mm., and yet the note is too sharp, so great is the distance of this string, 12½ mm., from the last fret.

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The distance C c was divided into half at F, and the distance C to F into nine equal parts, and F to c into thirteen equal parts by frets; at least, that was the intention. Actually C to F contained 145 mm., of which 1/9th = 16 1/9, while the distances between frets really varied from 15½ to 16½. The distance F to C was 146½ mm., of which 1/13th is 11·27 mm., while the distances between the frets varied from 9½ to 13½ mm. as well as I could measure. This gave very varying values to the s'ruti intervals. From C to F they varied from 45 to 73 cents, from F to c they varied from 37 to 84 cents. The intention, I presume, was to make them as nearly equal as possible or 54 6/11 cents each.

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The pitches of the notes produced were determined on May 21, 1886, by Mr. A. J. Hipkins, who tried to touch the frets as evenly as possible, while I furnished the forks from my tuning fork tonometer, the exact pitches of which had been accurately determined. By this means Mr. Hipkins was able to count the beats between the forks and the notes due to the frets for two or three seconds, and then to continue counting at the same rate to complete ten seconds. Each pitch was thus determined by two of my forks, one sharper and one flatter, and there was never so much as half a vibration difference in the determinations. When any difference existed a mean was taken. A scale was thus determined which satisfies modern Indian ears. As the s'rutis in it vary from all the circumstances named, and apparently on no conceivable plan, it is evident that if the mean of all were taken—that is, if a cycle of twenty-two were instituted, as I have effected by a series of forks—Indian ears would still be satisfied. I have endeavoured in the following table to bring out all these facts.

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The width of the finger-board was 80 mm., and the steel wire was 40 mm. from each edge.

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A set of forks was sent by the Râjah to the Inventions Exhibition at the same time as the S'ruti Vina, but as they had been tuned by means of sliding weights, without any appliance to fix them in position, these forks were quite useless, for the weights had shifted on the journey from India, and, in fact, shifted whenever the forks were struck.

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1.) Tuning pegs. 2.) 3.) Nut. 4.)
5. Carved ivory decoration.
6. Tail-pin.

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Table of the Pitches of the Notes furnished by Râjah Sir S. M. Tagore's S'ruti Vina, as determined in 1886 by Messrs. Ellis and Hipkins.

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| Note, name, and number. | Observed number of vibrations. | Cents from note to note. | Cents from lowest note. | Cents from lowest in cycle of 22. | Vibrations in cycle of 22, with same C. | Sounding lengths of strings in millimetres. | Depression or height of string above fret in millimetres. |
| C 1 | 241·2 | — | 0 | 0 | 241·2 | 608 | 1½ |
| 2 | 247·6 | 45 | 45 | 55 | 248·9 | 592 | 3 |
| 3 | 257·2 | 66 | 111 | 109 | 256·9 | 576 | 4 |
| 4 | 266·0 | 58 | 169 | 163 | 265·1 | 559½ | 5 |
| D 5 | 274·3 | 53 | 222 | 218 | 273·6 | 543½ | 5 |
| 6 | 281·5 | 45 | 267 | 273 | 282·4 | 527½ | 5 |
| 7 | 289·5 | 49 | 316 | 328 | 291·4 | 512 | 6 |
| E 8 | 302·0 | 73 | 389 | 382 | 300·7 | 495½ | 6 |
| 9 | 310·3 | 47 | 436 | 436 | 310·3 | 479 | 7 |
| F 10 | 323·0 | 69 | 505 | 491 | 320·3 | 463 | 7 |
| 11 | 330·3 | 39 | 544 | 545 | 330·5 | 451½ | 8 |
| 12 | 337·8 | 39 | 583 | 600 | 341·1 | 441 | 8 |
| 13 | 349·2 | 57 | 640 | 655 | 352·0 | 430 | 9 |
| G 14 | 364·0 | 72 | 712 | 709 | 363·3 | 417½ | 10 |
| 15 | 371·8 | 37 | 749 | 764 | 374·9 | 408 | 10½ |
| 16 | 384·4 | 58 | 807 | 818 | 386·9 | 395½ | 10½ |
| 17 | 395·3 | 48 | 855 | 873 | 399·3 | 384½ | 10½ |
| A 18 | 409·6 | 62 | 917 | 928 | 412·1 | 373 | 10½ |
| 19 | 418·5 | 37 | 954 | 982 | 425·3 | 363½ | 10½ |
| 20 | 432·9 | 59 | 1013 | 1036 | 438·9 | 351 | 10½ |
| B 21 | 449·3 | 64 | 1077 | 1091 | 452·9 | 340 | 11 |
| 22 | 465·0 | 59 | 1136 | 1146 | 467·4 | 330 | 11½ |
| C 23 | 488·0 | 84 | 1220 | 1200 | 482·4 | 316½ | 12½ |