In part 3, we reconstructed one of the most significant tuning systems used in Indian Classical music, namely, the Shadaj Gram scale. The Shadaj Gram and (the related) Madhyam Gram scales gave rise to musical structures called Jatis from which many modern day Indian Ragas have evolved.
Another equally significant tuning system used in Indian Classical music was due to the music scholars Ramamatya and Venkatamakhin. We look at it in this part.
Before we begin reconstructing any tuning system, let us start with the concept of the fundamental note Sa. In Indian Classical music, all musical notes are defined based on their relationship with Sa. You can use the settings below to set the Sa to any pitch you prefer. All the demos on this page would play according to this setting.
Note: This article features high quality audio demonstrations which are an integral part of the narrative. For ease of understanding, these demos have been presented in the form of a musical keyboard which many would recognize. Simply click on Start to activate and tap a key to play. Please try and use a pair of headphones or good quality speakers to listen to the samples with maximum clarity.
Ramamatya laid down a practical procedure for setting the frets on a Veena, and in the process dividing an octave into 12 notes. Venkatamakhin documented the 12 note divisions of the octave and calculated numerical ratios for each of the 12 notes. Taken together Ramamatya and Venkatamakhin created a tuning system for Indian Classical music which was both practically and theoretically well defined. The tuning system defined by Venkatamakhin and Ramamatya is equivalent to the Pythagorean Tuning system.
Ramamatya in his Swaramelakalanidhi has described 3 types of Veenas: Sudha Mela, Madhya Mela and Achyutharajendra Mela. For the purposes of our discussion here, we will consider the Sudha Mela Veena (for details, see Swaramelakalanidhi of Ramamatya by M.S. Ramaswami Aiyar).
Ramamatya's procedure starts with using a four string Veena with its notes tuned as Sa, Pa, Sa" and ma" from the lowest to the highest. Here, Sa denotes the fundamental, Pa the fifth and ma the fourth, as before. But, we denote notes in the upper octave with a ". Thus, Sa" denotes the octave and ma" the octave of the fourth. The tuning of the four strings is prescribed to be done by ear, and it is expected that a veena tuner can accurately set the octave, Pancham (fifth) and Madhyam (fourth) intervals.
Then the following procedure is prescribed:
Ramamatya's procedure is so clearly defined that it is used even today by veena makers to set the frets on the instruments they produce.
Starting with the fact that Pancham is and Madhyam is , it is possible to derive the ratios for each note of the 12 notes which would result from Ramamatya's procedure. This documentation is credited to Venkatamakhin.
You may have noticed that ratios for Ma and re at the first and sixth fret are different. Venkatamakhin prescribes that Ma is taken as (defined by the sixth fret) but that re is taken as (defined by the first fret).
You can hear the Venkatamakhin-Ramamatya scale in Demo 1 below. The calculations for deriving the ratios for each note are summarized in Table 1.
|Note||Decimal Ratio||Symbolic Ratio||Remarks|
|re||1.053497942||256/243||ma-Pa Gap below ga|
|Re||1.125||9/8||ma-Pa Gap above Sa|
|ga||1.185185185||32/27||ma-Pa Gap below ma|
|Ga||1.265625||81/64||ma-Pa Gap above Re|
|Ma||1.423828125||729/512||ma-Pa Gap above Ga|
|dha||1.580246914||128/81||ma-Pa Gap below ni|
|Dha||1.6875||27/16||ma-Pa Gap above Pa|
|ni||1.777777778||16/9||ma-Pa Gap below SA|
|Ni||1.8984375||243/128||ma-Pa Gap above Dha|
We have reconstructed the two significant tuning systems used in Indian Classical music. The Shadaj Gram and Madhyam Gram scales gave rise to musical structures called Jatis from which many modern day Indian Ragas have evolved. Similarly, the Venkatamakhin-Ramamatya scale gave rise to a classification system for Indian Ragas called Melakarta system which has again given rise to many modern day Indian Ragas. It is necessary to understand and define these tuning systems, to understand the role of harmonics, microtones and consonance in Indian Classical music and musical scales.
In a following article, we try and examine how these tuning systems have influenced the music of today.
Tuning SystemsTuning SystemsFretted VeenaFretted VeenaPancham (Fifth)Pancham (Fifth)Madhyam (Fourth)Madhyam (Fourth)MelamMelamThaatThaatPythagorean TuningPythagorean TuningRamamatyaRamamatyaVenkatamakhinVenkatamakhin