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Indian Tuning Systems (4) – 12 Note Tuning for Fretted Veena

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.

Reference Pitch, Basic Intervals and Ratios

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.

Common Parameters

Key
Offset

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.

Venkatamakhin-Ramamatya Scale

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's procedure for setting Veena frets

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:

1. Set the second fret at a position so that the ma" string produces Pa". As a consequence, you get Re on the Sa string, Dha on the Pa string and Re" on the Sa" string.
2. Set the fourth fret at a position so that the ma" string produces Dha" (which is the octave of Dha we obtained earlier, on the second fret on the Pa string). As a consequence, you get Ga on the Sa string, Ni on the Pa string and Ga" on the Sa" string.
3. Set the sixth fret at a position so that the ma" string produces Ni" (which is the octave of Ni we obtained earlier, on the fourth fret on the Pa string). As a consequence, you get Ma on the Sa string, re" on the Pa string and Ma" on the Sa" string.
4. Set the fifth fret at a position so that the Pa string produces Sa". As a consequence, you get ma on the Sa string, ma" on the Sa" string and ni" on the ma" string.
5. Set the third fret at a position so that the Pa string produces ni (which is an octave lower than ni" we obtained earlier, on the fifth fret on the ma" string). As a consequence, you get ga on the Sa string, ga" on the Sa" string and dha" on the ma" string.
6. Finally, set the first fret at a position so that the Pa string produces dha (which is an octave lower than Dha" we obtained earlier, on the third fret on the ma" string). As a consequence, you get re on the Sa string, re" on the Sa" string and Ma" on the ma" string.

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.

Venkatamakhin's documentation of the 12 note tuning system

Starting with the fact that Pancham is $\frac{3}{2}$ and Madhyam is $\frac{4}{3}$, 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.

1. At the second fret, Re is $\frac{3/2}{4/3}=\frac{9}{8}$ and Dha is $\frac{9}{8}\times\frac{3}{2}=\frac{27}{16}$.
2. At the fourth fret, Ga is $\frac{9}{8}\times\frac{9}{8}=\frac{81}{64}$ and Ni is $\frac{243}{128}$.
3. At the sixth fret, Ma is $\frac{729}{512}$ and re is $\frac{2187}{2048}$.
4. At the fifth fret, ni is $\frac{16}{9}$.
5. At the third fret, ga is $\frac{32}{27}$ and dha is $\frac{128}{81}$.
6. At the first fret, re is $\frac{256}{243}$ and Ma is $\frac{1024}{729}$.

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 $\frac{729}{512}$ (defined by the sixth fret) but that re is taken as $\frac{256}{243}$ (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.

Demo 1. Venkatamakhin-Ramamatya Tuning
• Sa
re
• Re
ga
• Ga
• ma
Ma
• Pa
dha
• Dha
ni
• Ni
• SA
Table 1. Illustration of Venkatamakhin-Ramamatya Tuning
NoteDecimal RatioSymbolic RatioRemarks
Sa11
re1.053497942256/243ma-Pa Gap below ga
Re1.1259/8ma-Pa Gap above Sa
ga1.18518518532/27ma-Pa Gap below ma
Ga1.26562581/64ma-Pa Gap above Re
ma1.3333333334/3Fourth
Ma1.423828125729/512ma-Pa Gap above Ga
Pa1.53/2Fifth
dha1.580246914128/81ma-Pa Gap below ni
Dha1.687527/16ma-Pa Gap above Pa
ni1.77777777816/9ma-Pa Gap below SA
Ni1.8984375243/128ma-Pa Gap above Dha
SA22Octave

Summary

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.

References

1. Śārṅgadeva, Premlata Sharma, and R. K. Shringy. Saṅgīta-ratnākara of Śārṅgadeva: Sanskrit Text And English Translation With Comments And Notes. Delhi: Motilal Banarsidass, 1978.
2. Mukund Lath (Author), Kapila Vatsyayan (Editor). Dattilam of Dattil. Indira Gandhi National Centre for Arts in association with Motilal Banarsidass, 1988.
3. R. Satyanarayana. Chaturdanda Prakasika of Venkatmakhin. Indira Gandhi National Centre for Arts in association with Motilal Banarsidass, 2002.
4. M.S. Ramaswami Aiyer. Svaramelakalanidhi of Ramamatya. Annamalai University, 1932.
5. P. Sambamoorthy. South Indian Music. Indian Music Publishing House, 1963.
6. S. Bhagyalekshmy. Lakshanagrandhas in Music. CBH Publications, 1991
7. Private communications on the theory and practice of Indian Classical music between Ustad Zia Fariduddin Dagar and S. Balachander.