The Music and Musical Instruments of Southern India and the Deccan c6.80

c6.80

| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Frets. | Millimetres from nut. | Sounding lengths of string. | Pitch or numbers of double vibrations. Nov. 18, 1887. | Cents in the interval from the lowest note. | Intervals in cents from note to note. | Intervals in cents calculated from column 3. | Cents in the interval from the lowest note from column 3. |
| Nut | 0 | 555 | 210·7 | 0 | 0 | 0 | 0 |
| 1 | 31 | 524 | 222·8 | 97 | 97 | 99 | 99 |
| 2 | 59 | 496 | 236·6 | 201 | 104 | 96 | 195 |
| 3 | 85 | 470 | 246·2 | 270 | 69 | 93 | 288 |
| 4 | 110 | 445 | 260·9 | 370 | 100 | 94 | 382 |
| 5 | 134 | 421 | 275·0 | 461 | 91 | 96 | 478 |
| 6 | 156 | 399 | 289·2 | 548 | 87 | 93 | 571 |
| 7 | 179 | 376 | 310·5 | 671 | 123 | 104 | 675 |
| 8 | 200 | 355 | 325·3 | 752 | 81 | 99 | 774 |
| 9 | 219 | 336 | 346·3 | 860 | 108 | 95 | 869 |
| 10 | 236 | 319 | 365·6 | 954 | 94 | 90 | 959 |
| 11 | 253 | 302 | 385·8 | 1047 | 93 | 95 | 1054 |
| 12 | 269 | 286 | 421·5 | 1200 | 153 | 94 | 1148 |
| 13 | 286 | 269 | 447·2 | 1303 | 103 | 106 | 1254 |
| 14 | 301 | 254 | 472·5 | 1398 | 95 | 99 | 1353 |
| 15 | 314 | 241 | 494·1 | 1476 | 77 | 91 | 1444 |
| 16 | 327 | 228 | 523·6 | 1576 | 100 | 99 | 1548 |
| 17 | 341 | 214 | 553·3 | 1672 | 96 | 107 | 1650 |
| 18 | 352 | 203 | 583·4 | 1763 | 91 | 91 | 1741 |
| 19 | 363 | 192 | | | | 97 | 1838 |
| 20 | 373 | 182 | The rest of the notes were too high for my forks. | Auxiliary Table. | The great uncertainty in these intervals renders any hypothesis as to the intended nature of the scale impossible. But col.7, in conjunction with the auxiliary table in col. 5, shows that the mechanical rule of making the successive lengths as 18:19, or 17:18, or 16:17 hence that the maker intended the frets to be arranged for equal temperament. | 102 | 1990 |
| 21 | 383 | 172 | | | | 98 | 3028 |
| 22 | 392 | 163 | | Cents. | Intervals. | 93 | 2121 |
| 23 | 401 | 154 | | 92 | 128:135 | 99 | 2220 |
| 24 | 410 | 145 | The height of the string above the frets varied from 1 to 5 millimetres. | or larger limma | | 104 | 2324 |
| bridge | 553 | 0 | | 94 | 18:19 | | |
| | | | | 99 | 17:18 | | |
| | | | | 100 | 84:89 | | |
| | | | | 105 | 16:17 | | |
| | | | | 112 | 15:16 | | |
| | | | | 151 | 11:12 | | |
| | | | | 155 | 32:35 | | |
| | | | | | Applied in column 7. | | |
| 100 times these numbers give the cents in equal temperament. | to the beginning of the bridge, but the real sounding length is as 555 millimetres. | From these lengths are calculated columns 7 and 8 on the hypothesis that pitch varies inversely as the sounding lengths | A cent is the hundredth part of an equal semitone. | | | | Compared with column 5, this shows the erroneous nature of the hypothesis that pitch varies as the sounding length on fretted instruments. |