Shruti is a sacred revelation, that which is heard, heard by the sages who passed on this knowledge to their disciples and the people in general. Much later, this manifestation in sound was committed to writing. In the Indian tradition this written form is not really reliable, much is missing from it. Nicholas Cook remarked that “the score conceals as much as it reveals”1and this can be applied to that idea of shruti, the full monty comes only in the oral tradition. Leo Treitler challenges the reliability of oral transmission because of the dynamic nature of memory2. However, he is thinking of the memory of the individual brain, whereas the oral tradition depends on the collective memory. Treitler should have realized this because with early manuscripts we see a similar phenomenon. The hand-written copies (of copies of copies) often have many errors, to the extent of being unintelligible. But the art of the historian is to compare the manuscripts and ‘reconstruct’ a probable or possible original.

In music shruti has a different meaning. In ancient times it seems that it was some measure of tuning the harp (vina). Perhaps the basic meaning of ‘that which is heard’ took on the meaning of ‘what CAN be heard’ in the sense of the smallest difference in pitch. Later musicologists, starting with Ouseley and Paterson3interpreted the ancient shruti’s as a system of just intonation. They equated Bharata’s 4-shruti interval with the major whole-tone (204 cents i.e. frequency ratio of 9/8) and the 3-shruti interval with the minor whole-tone (182 cents i.e. frequency ratio of 10/9). It seems an elegant scheme, the sum of these two intervals would be the harmonic major third. The difference would be the UR-shruti, the smallest audible interval of a comma (22 cents i.e. frequency ratio of 81/80). 2 shruti’s would be the just semitone (112 cents i.e. frequency ratio of 16/15) and therefore the perfect fourth is 4+3+2 = 9 shruti’s while the perfect fifth is 13 shruti’s. A small hitch in the scheme is that the single shruti would have to have several different values, not very practical. This becomes especially awkward with more complex scales with chromatic intervals.

Be that as it may, the application of the ancient concept of shruti in contemporary practice of intonation is simply untenable. Extensive measurements of intonation have shown that

  1. Intonations exceed by far the range of the 22 shruti’s in an octave.
  2. There is no consistency in intonations among artists and among performances by the same artists
  3. There is no consistency in intonations in relation to ragas
  4. When musicians speak of shruti the pitch is never steady, it is a melodic shape with various undulations and slides.

The latter point is of particular importance because such sliding and undulating melodic movements cannot be described in terms of a fixed pitch. Mark Levy took the average of the andol (undulation) of komal gandhara in Darbari and concluded it was quite a bit higher than the expected minor third.4I knew this obviously was not how we hear the undulation, we actually do hear the pitch going up and down. So I thought we should look at the low position of the waves, but it soon became clear that this low position is not consistent.5The fundamental problem here is that musicologists have tried to describe Indian music in terms of fixed, discrete frequencies and ornamentations around those frequencies. In a lecture at the annual ESEM meeting in Lithuania I pointed out that this model is a colonial superimposition of music theory on Indian music. In the end it is about squeezing Indian music into a five line system. I presented the evidence of the musicians’ way of using shruti’s and explained they were not about pitches. One of the stalwarts of ethnomusicology, Simha Arom intervened and suggested that those shruiti’s then were ornamentations. And this is exactly were we go wrong. Fixed frequencies and ornamentations, discrete lines and their in-between. The essence of shruti is that it is an independent musical entity, a melodic shape, a toneme.

This doesn’t mean that there are no pitches. Every svarmandal, sitar or sarangi player who has to tune his instrument knows all about it. The tonal system is very similar to the European system, twelve semitones consisting of seven ‘pure’ (shuddha) notes (similar to the major scale) and five ‘altered’ notes (four flats and one sharp). These pitches are known as svaras. There is a skeleton, but there is also the flesh. In the European tradition the skeleton gradually gravitated to equal temperament. In Bach’s time there were several ways of tuning instruments that were partially just and partially tempered. In Indian music there is no single consistent tuning scheme. It varies from artist to artist, it varies by raga, it varies from performance to performance, but without any consistency. The major fifth tends to be very accurately harmonic, that is a 3/2 frequency (702 cents). Uncannily so, the Standard Deviation of the Mean is extremely consistent. The major third tends to be close to the harmonic, but slightly on the higher side and with a somewhat larger spread than the fifth. Some of the minor notes are all over the place, especially the minor seventh.

The vertical axis on the left is the cycle of fourths upward (low harmonic position) on the right downward is the cycle of fifths. These axes are harmonic tunings. The dotted diagonal represents equal temperament. The selected recordings are all using pa-tuning. In this tuning we hear very clear partials of the perfect fifth, the major second, and the harmonic major third. the distance between the cycle of fourths and the cycle of fifths is 24 cents. Not surprisingly the fifth and the fifth of the fifth (the major second) are spot on the cycle of fifths, although the major second already has a considerable larger standard deviation. The major third is not too far from the harmonic position but it is a bit higher, even though out of reach from a tempered position, and surely never pythagorean. But apart from these the spread of the standard deviation is quite considerable and neither high, low, nor tempered positions are evident. Most important is to note that the deviations from any of the expected positions are not related to raga, artist or school (gharana).

Closely related to svara is the concept of sur. But whereas svara is the theoretical concept sur is the sound. Besur (out of tune) is the worst of musical crimes. Tunefulness is based on partial (overtone) matching between the instrument/voice and the drone. The rich spectrum of the drone makes it easy to match those notes that are present in that spectrum. Reversed matching is far more difficult. By reversed matching we mean that the partials of the instrument or voice have to match the drone. Thus, the drone produced a clear fifth and the voice can match this fifth. However, the fourth is not produced by the drone. When we sing or play the fourth we have to match the fifth of the voice with the octave of the drone. In practice this is much more difficult and hence the fourth is much less stable than the fifth.

  1. Nicolas Cook, Music, A Very Short Introduction, Oxford University Press, 1998.
  2. Leo Treitler, Reference to be found
  3. Rao, Suvarnalata and Wim van der Meer, “Construction, Deconstruction and Reconstruction of Shruti”, in: J. Bor, F. Delvoye and E. te Nijenhuis (eds.), Hindustani Music: Thirteenth to Twentieth Centuries, Manohar Publishers, New Delhi 2010, pp. 673-696.
  4. Levy, M., Intonation in North Indian Music, New Delhi: Biblia Impex, 1982.
  5. Wim van der Meer, Gandhara in Darbari Kanada, the mother of all shrutis?