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(iii) Scale-types in modern theory.
Just as the grāma system of the Nātyaśāstra was the basis of the mūrcchanās, so the modern tonal systems generate a number of derived scale-types. Each scale-type is a selection of seven svara from the general scale of 12 pitch positions (svarasthāna). A given scale-type may be common to several rāgas, so scale-types are an aspect of the general tonal system.
The south Indian system of 72 scale-types (melakarta or mela) is produced by a systematic permutation of the variable svara positions shown in Table 3c. The invariable sa and pa are common to all 72. The octave is divided into two tetrachords, sa –ma and pa –sa. Within each tetrachord the variable svara – ri and ga or dha and ni – are systematically rotated through all possible combinations, as shown in Table 7. Scale-types 1–36 are formed by combining each of the six lower tetrachords, having śuddha ma (F) as the fourth degree, with each of the upper tetrachords in turn. By substituting prati ma (F ) for the natural fourth degree, a second, otherwise identical set of 36 scale-types is formed, nos.37–72. This system includes scale-types with augmented seconds and scale-types with consecutive semitones.
When Venkatamakhin outlined the scheme of 72 melakarta in the Caturdandī-prakāśikā he gave names only to those 19 scale-types that were needed for rāgas in use in 17th-century Thanjavur. He named each of these scale-types after the most prominent rāga belonging to it. Subsequently, the remaining scale-types have also been named, and there are now rāgas and compositions in every scale-type. Some have acquired important constituent rāgas as composers and performers have found musically effective ways of exploiting the scale. Nevertheless, there are still no more than a couple of dozen scale-types of real musical significance, having either a large number of constituent rāgas (such as scale-type 28) or one important rāga (such as Nāta rāga from scale-type 36).
The melakarta system has become endowed with a complex nomenclature intended to render it memorable. Each of the 12 lower tetrachords defines a set or ‘circle’ (cakra) of six scales, each consisting of combinations of the lower tetrachord with six different upper tetrachords. Each set has a name denoting its serial number in the system (thus ‘Moon’ is one, ‘Eye’ is two, ‘Veda’ is four etc.). Each individual scale-type also has a name, sometimes derived from that of a prominent rāga belonging to it. The name also bears a two-syllable prefix that encodes in reverse the serial number of the scale-type (thus scale-type 28 is Hari-kāmbhojī, where ‘ri’ is two and ‘ha’ is eight).
An alternative term for scale-type, thāta, first appears in the southern Rāga-vibodha of Somanātha (1609), but it has subsequently been adopted in place of melakarta in the Hindustani tradition. It was used in the 19th century by sitār players to denote the ‘setting’ or positioning of the movable frets on the neck of a sitār necessary to produce the intervals required by particular rāgas. Six thāt are listed by Day (1891), who states that they ‘have no names, but are usually known from the rāgas that are commonly played upon them’. Because the sitār has more than seven frets to the octave, each of these settings can be used to produce more than one heptatonic scale-type, or rāgas that require more than seven pitch positions. Subsequently the term thāt was adopted by V.N. Bhatkhande for his system of ten heptatonic scale-types, which he named after prominent Hindustani rāgas (Table 8). This system lacks the logical rigour of the Karnatak melakarta system, but it does not include any scale-types that are not in common use. As shown in Table 8, it is an interrupted sequence of six diatonic scales with progressively more ‘flats’ (nos.1–3 and 7–9), plus four scale-types with augmented seconds (nos.4–6 and 10). The ordering is based on what Bhatkhande deemed significant degree relationships: the natural second, third and sixth in 1–3, the flattened second with natural third and seventh in 4–6, the flattened third and seventh in 7–9, and Todī thāt in a class by itself.
Despite their pragmatic convenience for classifying rāgas, the melakarta and thāt systems suffer from a number of limitations, as Hindustani musicians in particular are wont to point out. Pentatonic or hexatonic rāgas can only be allocated to heptatonic scale-types on the sometimes arbitrary assumption that particular pitches are omitted. The scale-types make no allowances for variations in intonation of the svara, they separate into different categories rāgas that are closely related by melodic movement (see §2(iii) below), and they bring together rāgas that have no melodic features in common beyond their basic pitches.
India, Subcontinent of, §III, 1: Theory and practice of classical music., Tonal systems.
(iv) The 22 śruti in modern theory.
The ‘microtonal scale’ of Indian classical music has attracted much attention both in South Asia and internationally, particularly since the discovery and publication of chapter 28 of the Nātyaśāstra. It has been claimed that the śruti are evidence for the existence of complex mathematical acoustics in ancient India, or that they are evidence of nearly superhuman pitch discrimination and control on the part of performers. What can and cannot be inferred about the 22 śruti in the ancient period was made plain by Bhandarkar in 1912. The proposition of an unusually consistent microtonal control, advanced by Daniélou (1954) and others, has been experimentally refuted by Jairazbhoy (1963) and others. It is true that the numerous inflections of svara in musical contexts cannot be described fully in terms of a system of 12 pitch positions. But to say that particular shadings of pitch are essential in a particular musical context is not to say that those shadings are best described in terms of a microtonal scale.
Modern South Asian uses of the 22 śruti have usually built from the existing 12-position general scale and the system tonic. The fixed svara sa and pa provide two pitch positions and the five variable svara, each in two positions (komal and tīvra), provide ten more. Then the five komal svara are given five lower variants called ati-komal, the five tīvra svara five higher (ati-tīvra) variants. This generation of a scheme of 22 has nothing to do with either the Nātyaśāstra or Sangīta-ratnākara, but it is neat and suggestive.
Sometimes precise frequencies are proposed, based on a Pythagorean and a just intonation for each pitch position other than sa and pa. However, this supposed precision not only disregards the flexible realities of intonations but in seeking to explain ancient schemes in modern terms fails to account for them.
India, Subcontinent of, §III: Theory and practice of classical music.
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