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(a) Ancient Indian terms: grāma, śruti, mūrcchanā.
In chapter 28 of the Nātyaśāstra the svara are arranged in two scales, or rather pitch-collections (grāma), named sadja-grāma and madhyama-grāma after their starting pitches. The grāmas are defined in terms of 22 equal microtonal intervals (śruti) and in terms of consonant intervals (samvāda) between specified svara. Each svara is considered to comprise both the pitch of the note itself and the interval of two, three or four śrutis separating the note from its lower neighbour (see Table 2). Representation in Western notation can only be approximate, because the grāmas included three sizes of scale-step, measuring two, three and four śruti. In practice the three śruti steps (ri and dha in sadja-grāma, pa and ri in madhyama-grāma) may have been rendered as undulating rather than as steady pitches, at least by singers and flute-players.
The consonant intervals are defined as measuring nine śruti (perfect 4th) and 13 śruti (perfect 5th); 4ths of ten or 5ths of twelve śruti were not considered consonant. Thus in the sadja-grāma, pa is consonant with sa but not with ri, but vice versa in the madhyama-grāma. Each grāma may be conceived of as chains of consonant 4ths or 5ths. In the sadja-grāma, these are pa –sa –ma –ni –ga plus ri –dha; in the madhyama-grāma, sa –ma –ni –ga and pa –ri –dha. However, the interval ma –ni, though measuring nine śruti in both grāma, is not listed as a consonance in the Nātyaśāstra, perhaps because these two svara are of unequal size (four and two śruti respectively) and therefore occur in different melodic contexts.
In the grāma system only three svara (ga, ni and pa) were of variable pitch relative to the others. In all other instances the śruti between the svara were not recognized as scale degrees. Ga and ni could each be raised by two śruti to serve as sharpened leading-notes to ma and sa. The raised pitches are called antara ga and kākalī ni. The process of pitch alteration is called svara-sādhārana (‘overlapping of pitches’).
Pa is consonant with sa in the sadja-grāma and ri in the madhyama-grāma. Consequently it is one śruti lower, relative to its neighbours, in the madhyama-grāma than it is in the sadja-grāma. This difference, as demonstrated in the Nātyaśāstra by a hypothetical experiment with the tuning of two vīnās (here referring to harps), is the pramāna-śruti (the ‘measuring’ śruti), the unit of measurement by which all other intervals were theoretically defined.
A seven-string bow harp (vipañcī-vīnā) could be tuned in either grāma with any of the seven scale degrees as its lowest pitch. Each of the resulting scales, seven in each grāma, was called a mūrcchanā and was a specific scale-type. However, the ancient mūrcchanā, with their different ground-notes, have been replaced in modern theory by scales with a common ground-note (melā and thāt: see §(iv) below). A hexa- or pentatonic mūrcchanā was called a tāna; this term has survived in modern usage, but with different meanings. In Hindustani music tān means a phrase of a rāga, or rapid passage-work in khayāl (see §5(iii)(b) below). Tānam in Karnatak music refers to a pulsed but unmeasured improvisatory style (see §5(iv) below).
India, Subcontinent of, §III, 1(ii): Theory and practice of classical music., Tonal systems., i) History of tonal systems.
(b) The tonal system of the Sangīta-ratnākara.
By the 13th century the grāma-śruti system of the Nātyaśāstra was almost certainly defunct in practice, though still of fundamental importance to theory. One result was the re-interpretation of the system in metaphysical terms, another was the recognition of ‘modified’ (vikrta) pitches in addition to the primary or ‘pure’ (śuddha) pitches of the sadja-grāma. The process begins in the Brhad-deśī of Matanga (perhaps 8th or 9th century), which restates the grāma-śruti system and discusses the nature and number of śruti and their ontological relationship to svara. It also presents theories of sound (nāda) based on Tantric metaphysics and physiology. In the Sangīta-ratnākara of Śārngadeva these two strands are combined, so that an existential reality is ascribed to the 22 śruti. When Desire brings the nā of Breath and the da of Fire together to form nāda (sound), that primordial nāda passes upwards through the body until it reaches the lowest cakra at which sound becomes material enough actually to be heard: the heart; this corresponds to the chest register of music. Here there are 22 channels from which the 22 śruti are produced. The 22 śruti in the two higher registers are produced in the throat and head. The reality of the 22 śruti is then supposedly demonstrated through the hypothetical tuning of two vīnā, each with 22 strings.
Table 3a shows how Śārngadeva expanded the grāma system of the Nātyaśāstra by introducing 12 ‘modified’ (vikrta) pitches. The impetus for this development may have been a trend in practice towards a 12-semitone scale. However, Śārngadeva's system provides additional pitch positions only in the regions ga –ma and ni –sa, where there were already the alternative notes antara ga and kākalī ni in the Nātyaśāstra system (Table 3c). In Śārngadeva's system, furthermore, wherever one svara is transformed by being on other than its own proper śruti, the svara immediately above it is also transformed, even if it has not moved, since it now no longer has the proper number of śruti below it. Table 3a, line (i), for instance, shows the reduction of pa by one śruti that produces the madhyama-grāma. Pa is now a vikrta svara because it has been lowered, but dha is also vikrta since it now has four śruti (‘catuś-śruti ’) instead of its proper three śruti. The sa and ma in line (ii) are also vikrta because they now have only two śruti, even though they are ‘not fallen’ (acyuta) from their proper positions.
Another curious feature of Śārngadeva's system (Table 3a, line (iii)) is the introduction of a ‘fallen’ (cyuta) sa, perhaps by analogy with the lowered pa of the madhyama-grāma, and similarly a ‘fallen’ ma. Unfortunately Śārngadeva does not explain the practical application of any of these new modified pitches. He gives only the musica ficta-like rules for using antara ga and kākalī ni, in direct or indirect returns to ma and sa respectively, and only these two vikrta are mentioned in rāga definitions.
India, Subcontinent of, §III, 1(ii): Theory and practice of classical music., Tonal systems., i) History of tonal systems.
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