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Indian Tuning Systems (1) – Sama Gana Scale

In an earlier article, we looked at the historical evolution of Indian Classical music. Let us turn to the fundamental principles behind Indian Classical music and look at the role of harmonics, microtones and consonance in Indian Classical music.

For that, it is necessary to understand its underlying tuning systems. In this four part article, we reconstruct two significant tuning systems used in Indian Classical music:

1. The first is a 22 note scale whose earliest reference is due to Bharat in Natya Shastra and which was later documented by Sarang Dev in Sangeet Ratnakar. Note that Dattilam by Dattila, a contemporary or possibly earlier work compared to Natya Shastra, also refers to a division of an octave into 22 notes.
2. The second is a 12 note scale first devised by Ramamatya in Svaramelakalanidhi and which was later documented by Venkatamakhin in Chaturdanda Prakasika.

In a couple of related articles, we cover how tuning systems influence musical scales and how this affects the tuning of a Tanpura to play these scales.

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

Next, it is useful to familiarize ourselves with the four basic intervals of Dviguna (octave), Pancham (fifth), Madhyam (fourth) and Gandhar (major third). You can play and check these intervals using the keyboard below (just click on Start to activate and tap a key to play). Here Sa denotes the fundamental and Ga, ma, Pa and SA denote the Gandhar, Madhyam, Pancham and Dviguna respectively. Note that the notes here do not match up with today's standard 12 tone equally tempered scale.

Demo 1. Basic Intervals
• Sa
• Ga
• ma
• Pa
• SA

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.

As you can hear from Demo 1, Pancham, Madhyam and Gandhar are pleasant sounding intervals. For the musically inclined, they may be easy to recognise by ear. It is also possible to determine their frequency ratios in relation to the fundamental.

One way in which this can be done is by comparing lengths. Firstly, we can observe that the pitch of a string is inversely proportional to its vibrating length. Secondly, taking a certain string length to represent the fundamental, we can observe that if we touch the string at a third of its length from one end and pluck the remaining two-thirds, it results in the string sounding the fifth. Similarly, touching it at a fourth of its length from one end results in the remaining three-fourths to sound the fourth, touching it at a fifth of its length results in the major third, and touching it at the midpoint results in either half to sound the octave.

So by inverting these string lengths, we can infer that with Sa = 1, we have SA = 2, Pa = 3/2, ma = 4/3 and Ga = 5/4. Try and remember these frequency ratios, as we will use them repeatedly.

Sama Gana Scale

The first scale we will examine is the Sama Gana scale which was used to sing passages from the Sama Veda. Folk music or informal music was always around in India. But Indian music started to get formalized as the chants of Rig Veda evolved into a more sing-song way of rendering passages from Sama Veda. Rig Vedic chants already used three notes called Svarita (neutral drone), Udaatta (higher note) and Anudaatta (lower note). This evolved further in Sama Gana.

Sama Gana is the act of singing the Sama Veda. According to Ustad Zia Fariduddin Dagar, a typical arrangement employed three groups of singers with one group singing at the pitch Sa, the second at ma and the third at Pa. Each group in turn used three notes, a center note, a low note and a high note, similar to those used in Rig Vedic chants. The center note was whichever pitch they were singing, i.e., Sa, ma or Pa. The high note was higher than the center note by a specific tone and the low note was lower than the center note by the same tone. Refer to Demo 2 below.

A traditional rendition of Sama Gana

Observe how the different groups stop and start chanting at appropriate points during the rendition, so that overall it creates an impression of a musical scale. The rendition is roughly in the scale of G.
Demo 2. A traditional rendition of Sama Gana (courtesy of Sri Bhakti YouTube Channel).

Knowing the Pa and ma intervals, it is possible to derive the ma-Pa interval. For the musically inclined, you may be able to recognise it by ear. The size of the ma-Pa interval can be calculated as 3/2 ÷ 4/3 = 9/8. This ma-Pa interval was used as the tone to derive the high and low notes from the center note. Note that the ma-Pa interval is different from the whole tone used in today's standard 12 tone equally tempered scale. The whole tone is 200 cents wide, while the ma-Pa interval is a bit wider at 203.9 cents.

Using this, the Sama Gana scale as depicted in Table 1 can be derived. The method of derivation is given in the remarks column. The Sama Gana scale is discussed and documented in a number of references (for example, see Lakshanagrandhas in Music by Dr. Bhagyalekshmy).

Table 1. Illustration of Sama Gana Scale
NoteDecimal RatioSymbolic RatioRemarks
Sa11
Re1.1259/8ma-Pa Gap above Sa
ga1.18518518532/27ma-Pa Gap below ma
ma1.3333333334/3Fourth
Pa1.53/2Fifth
Dha1.687527/16ma-Pa Gap above Pa
ni1.77777777816/9ma-Pa Gap below SA
SA22Octave

You can play and check how the Sama Gana scale sounds using Demo 3 below.

Demo 3. Sama Gana Scale
• Sa
• Re
ga
• ma
• Pa
• Dha
ni
• SA

In this scale, the intervals Re-ga and Dha-ni were regarded as Vivadi (dissonant). The concept of Vivadi notes is mentioned in Dattilam and Sangeet Ratnakar (see Chapter Sangita Ratnakara in Lakshanagrandhas in Music or Chapter Nada, Sruti and Svara in Sangeet Ratnakar, Part 1). The size of these intervals can be calculated to be $32/27 ÷ 9/8 = 256/243 = 1.053497942$. This interval $\frac{256}{243}$ was recognized and known as Purna Shruti. Note that the Purna Shruti is roughly comparable to the semi-tone used in today's standard 12 tone equally tempered scale. The standard semi-tone is 100 cents wide, while the Re-ga interval is a bit narrower at 90.2 cents. This scale may have been appropriate for chanting, but as a musical scale, it was not considered appropriate. In order to make it musical, the music scholars of the day felt that the Re-ga and Dha-ni intervals needed to be slightly increased.

In the next part, we will attempt to answer the question of exactly how the tuning of these intervals was manipulated and what came about, as a result.

Summary

To summarize, we have introduced the concepts of basic intervals in Indian Classical music, and we have reconstructed the Sama Gana scale. This scale is really old, probably dating back 3000 years. It can be regarded as the true origin of scripture based or Classical music in India. However, in this scale, the intervals Re-ga and Dha-ni were regarded as vivadi or dissonant. The Shadaj Gram scale was likely devised as a musical solution to this problem of vivadi intervals of Re-ga and Dha-ni. We will look at Shadaj Gram in the next part.

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.