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(c) The development of the Karnatak general scale.
Whether intentionally or not, Śārngadeva provided the first step towards theoretical recognition and definition of the 12-step general scale that is now the basis of Karnatak music. The process was completed in south India by Rāmāmātya, whose stated purpose in writing his treatise Svaramelakalānidhi (c1550) was to reconcile outdated theory with current practice. He did so by a radical reinterpretation of the grāma system as previously modified by Śārngadeva. The illusion of continuity was maintained by the retention of much of the traditional terminology. His system, which forms the basis of the modern Karnatak rāga classification, is represented in Table 3b. Four changes to Śārngadeva's tonal system were made. (1) The pitches sa and pa were fixed at śruti numbers 4 and 17 respectively, with no modifications allowed; these pitches were by this time provided with drone strings on the vīnā, as they are on many string instruments today. (2) Śārngadeva's ‘fallen’ sa and ma are now treated as raised variants of ni and ga respectively, which consequently now have four pitch values each. Śārngadeva's names for all these pitch values are preserved. Similarly, the lowered pa of the madhyama-grāma is now considered a raised ma. (3) Rāmāmātya eliminates those four of Śārngadeva's modified svara that are at the same śruti positions as primary svara. (4) Ri and dha are each given two additional higher positions, called ‘five-śruti ’ (pañcaśruti) and ‘six-śruti ’ (satśruti). These coincide, however, with the two lowest positions of ga and ni respectively. They do not introduce any new pitch positions into the system but merely provide alternative names.
Thus far Rāmāmātya's changes appear relatively superficial. The scale still comprises 14 pitch positions, located at the same śruti as in Śārngadeva's system. However, he then proceeds to locate these pitch positions on the vīnā, which was by this time no longer an arched harp as in the Nātyaśāstra, but a long-necked, fretted zither resembling the modern Hindustani bīn (see §6 below). This had four melody strings tuned to sa –pa –sa –ma (C–G–c–f). In doing so he reduces the 14 theoretical pitch positions to 12 by allocating a single fret to two of the positions of ni (kākalī and cyuta-sadja), and a single fret to two of the positions of ga (antara and cyuta-madhyama), on the grounds that the pitch differences thereby eliminated are negligible. Rāmāmātya's fretting yields a 12-semitone division of the octave as shown in Table 3c. With small changes of terminology this remains the general scale used in Karnatak music today (Table 3d).
Table 4a shows Rāmāmātya's placement of the frets on the vīnā. Rāmāmātya states emphatically that their positions are predetermined (svayambhū, ‘self-existent’), not open to choice. He demonstrates how the frets are fixed by two sets of octave or unison equivalence, as shown in Table 4b. Fret 2 must be positioned so that the pa (g) on string IV at that fret is an octave above the open string II. Assuming that the frets are at right-angles to the strings, this also determines the pitches at the same fret on strings I to III. Of these, śuddha ni (A  ) on string II fret 2 provides the pitch for fixing the octave higher on string IV fret 4. This in turn fixes kākalī ni (B ) (string II fret 4) from which the octave (string IV fret 6) can be positioned. A similar but descending sequence, beginning with open string III equals string II fret 5 (or IV open equals III fret 5), fixes the positions of the remaining frets (5, 3 and 1). The resulting pitches on fret 1 are out of tune with their namesakes at fret 6, but two of the latter were not used, being available on the next higher strings. Cyuta-pañcama (f ) on fret 1 is also out of tune with kākalī ni (B/b ) on frets 4 and 6. These discrepancies may not have been significant in practice.
As this system is presented by Rāmāmātya the original grāma system of the Nātyaśāstra appears to be intact: all the svara s of that system are still present and allocated to the same śruti positions. But in practice Rāmāmātya's system exhibits three fundamental differences: (1) the actual intervals of the scale now bear little relation to the theoretical śruti positions (compare Table 3b andc); (2) all scales and modes are now transposed to a common tonic, sa, which requires all other svara (apart from pa) to become movable; (3) Rāmāmātya's system makes it possible, for the first time in the Indian tradition, to express the interval of an augmented 2nd (e.g. between śuddha ri (d ) and antara ga (e )). Scales featuring this interval are prominent in his classification of rāgas, and it is possible that the influence of West or Central Asian musical systems played a part in this development.
India, Subcontinent of, §III, 1(ii): Theory and practice of classical music., Tonal systems., i) History of tonal systems.
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