Generative Theory of Indian Music
The Generative Theory of Indian Music (GTIM) is a theoretical framework that provides computational perspectives on various aspects of Indian Music such as Raga, Tala, Swara, Shruti, Saptaka, Raga Vistara, Bandish etc. The GTIM also provides an axiomatic framework for understanding Indian Music.
Indian music is practiced, performed and understood in a variety of ways. India has two well-established streams of musical traditions, the Hindustani and the Carnatic music. There exists popular music and folk music as well. There are multiple styles of presentation of music from classical, semiclassical to light classical. A plurality of musical practices and expressions is observed. The Generative Theory of Indian Music (GTIM) contends that this plurality of musical practices is a surface-level phenomenon. Beneath this plurality and diversity of musical expressions lies a strong framework of musical logic. The GTIM argues that musical logic is generative by nature. From one base swara or a musical note seven swaras as well as twenty-two (or even more) microtones (shrutis) are generated by a consistent logical process. By application of the rules of musical logic to these swaras, and shrutis, musical phrases are generated. With certain other logical operations musically significant combinations of these phrases are generated that leads to the desired musical expression. Thus, from a single base swara the entire domain of music is generated. The GTIM has been implemented in AI systems and tested through computer simulations.
Evolution of Raga System
A brief historical overview suggests that the evolution and development of Indian music was an organic process. One can see certain evolutionary patterns in this growth that resulted into the doctrine of Raga. The concept of Raga as musical designs of swaras is quite note-worthy. From antiquity to the medieval and modern times, Ragas are considered as the core of Indian musical expressions. The evolutionary path to the present definitions begins with ‘Jati’ music, ‘Grama Ragas’, Raga-Ragini systems, and culminates into the Mela system and later on in the Thaata system. Indian music has a formidable doctrine of the Raga music. The GTIM augments this definition by adding a computational dimension to the definition of the Raga.
Role of Consonance in GTIM
The GTIM views India’s melodic tradition through the lens of induced harmony. Based on research regarding harmony perception by periodicity detection, the GTIM exposits the idea of aural inference. It contends that whenever a note is played during a performance, it must harmonize with the inferred extension of the preceding note, as well as with the drone or the Tanapura that is a staple of musical performance. Chord Progressions in Indian music are therefore considered to be implicit and are inferred by the discerning ear. Thus the fundamental harmonies of Indian Classical Music, the Shadja-Panchama-Bhava and the Shadja-Madhyama-Bhava are analogous to the Rule of Fifths and the Rule of Fourths respectively.
Axiomatic System for Indian Music
Based on identified Harmonies and consonances in Indian music, the GTIM develops an axiomatic system suitable for Indian music based on the principles mentioned in the Natyashastra. Laws of musical intelligence are extracted from the Natyashastra, musical practices, principles of consonances, contemporary musical practices and computational simulations of the same. These laws help generate valid logical results in a consistent manner. The Axioms and Laws proposed in GTIM are listed below.
Axiom 1: Axiom of existence:- A base swara ‘Sa’ exists.
Axiom 2: Axiom of Octave Equivalence:- For any base swara ‘Sa’ there exist higher and lower equivalents hSa and lSa with frequencies double and one-half of the base respectively.
Axiom 3: Axiom of Consonances: For any swara, there exist swaras excluding the swara and its octave equivalents such that these swaras are consonant to the original.
Axiom 4: Axiom of Equal Temperament: There exists a set of frequencies in geometrical progression beginning at ‘Sa’ and ending at hSa.
The commonly used 12-tone scale for Indian Music may be thus described as
ET-12 = {Sa, kRe, Re, kGa, Ga, Ma, tMa, Pa, kDha, Dha, kNi, Ni}
Laws:-
Law 1:- Law of fundamental consonances: The most consonant intervals in Indian Music are Unison, Octave, Perfect Fifth (Shadja Panchama Bhava) and the Perfect Fourth (Shadja Madhyama Bhava).
Law 2:- Whenever there is a necessity of selection of swaras in musical rendering, the swara with higher ‘harmonic strength’ or ‘degree of harmonization with Sa’ is selected.
Law 3:- The favorability of a pair of swaras in musical rendering is governed by their degree of mutual harmonization.
There also exist sub-domain specific laws that are applicable when considering the large scale structure and viability of a composition.
Computational Definition of Raga
The GTIM defines Raga as a 6-Tuple
Raga = {S, A, D, V, VRJL, GL}
It is assumed that S = Sa is a default tonic swara of the Raga.
V stands for a Vadi swara (dominant note).
A is Aroha
D is Avroha.
VRJL is a set of Varjya or omitted swaras.
GL stands for the set of Generative Laws that are either implicit or specific.
For example, we may consider the Raga Malakans.
6-tuple for Malakans
RagaMalakans = {S, A, D, V, VRJL, GL}
S = Sa
A= [‘Sa’, ‘kGa’, ‘Ma’, ‘kDha’, ‘kNi’, ‘hSa’]
D= [‘hSa’, ‘kNi’, ‘kDha’, ‘Ma’, ‘kGa’, ‘Sa’]
V= ‘Ma’
VRJL = [[‘Re’],[‘Pa’]]
GL = All laws of musical inference. No specific laws.
Using the above definition of a Raga, we can generate several musical phrases. Musical phrases are generated by operating additional laws of composition on the above tuple. The four principle categories of musical phrases are, Sequential (Ascending/Descending), Mixed, Ornamental and Legato/Arpeggio.
References
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