In my last blog post, we explored how certain melodic behaviors rooted in chants informed a modus operandi to move between certain pitches. In trying to understand how Raaga scales are constructed from simple pitch groups, we must understand another important concept – the tetrachord. Tetrachord simply means four strings in Greek and is derived from the word tetrachordum in Latin. In Indian classical music, the most emphasized and implied pitch (voice and tambura) is the tonic, the Sa or Shadja. It is called the adhara shadja as it implies it is the tonic and that every successive pitch is described as an interval between the pitch and the tonic, just like in western music theory. For example, R1 (shudha rishabha) is minor second from tonic. R2 (chatusruti rishabha) is a major second from the tonic. In essence, a unit of three intervals and four notes became grouped as a tetrachord. One can see how the idea of tonality and tetrachord could have evolved together as they are inter-linked in thought. The tetrachord concept also became the basis for pitch hierarchies (dominant, sub-dominant notes) and the concepts of early harmonic relationships within a Raaga scale (the Sa-Ma bhava etc).
In Indian music, an octave is comprised of two tetrachords – poorvanga and uttaranga. Sa-to-Ma and Pa-to-Sa, seperated by a wholetone between Ma and Pa in Shuddhamadhyama raagas and seperated by a semitone in pratimadhyama raagas of the Melakartha scheme. This is a significant point of departure from the classical definition of a tetrachord in western music – which defines a tetrachord as a series of three smaller intervals that span the interval of a perfect fourth (between Sa and Ma). Understanding the tetrachord idea is crucial to understanding the otherwise daunting scheme of classifying Raaga scales under the modern Melakartha Scheme. The notes Sa, Ri, Ga, Ma always form the first ascending tetrachord followed by Pa-Da-Ni-Sa. No tetrachord is constructed on the Ma, so no conjunct tetrachords. Carnatic tetrachords as ordained by the Melakartha scheme are chromatic and always disjunct. More on this later in a dedicated blogpost. It is important to note that the tetrachord is a musical construct that emerged in many cultures – codified from existing music ideas and performance practices. Check out the wikipedia page for a detailed treatment of tetrachord ideas across musical traditions.
Let us examine our first scale Mayamalavagaula, it is made up of two identical but disjunct tetrachords, one constructed on Sa and the other on Pa. Listen to the simple sample of how replacing the D1 to D2 and N3 to N2 in the uttaranga of Mayamalavagowla converts the scale to Chakravaka. The first tetrachord of C, C#, E and F are the identical in both scales.
LISTEN TO BLOG TUTORIAL 2: Tetrachordam Idam Sarvam!
Here is a schematic of the placement of notes of Mayamalavagowla on a piano: NOTE: The tuning of a piano is different from the tuning of a tambura, which follows a just intonation-like schema, but for the purposes of this post, this graphic visualizes the changes effectively.
MAYAMALAVAGOWLA: C C# E F – G G# B C CHAKRAVAKA: C C# E F – G A A# C
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