Post created 26 Feb 2015, last updated 24 January 2017. On my academia.edu page there is a pdf of this post, but it is not updated as often as this web page.
Possibly the most famous of all shrutis of Hindustani classical music is the komal gandhara (ga, minor third ) of Darbari. It is often said to be ati-komal (extra flat), which would supposedly mean it is lower than an also supposedly ‘normal’ komal ga (Levy 1982: 109 cites Vilayat Khan, see also Parrikar 2000; my teacher Dilip Chandra Vedi considered this to be common knowledge, although there are some authors who seem unfamiliar with this notion). There are not a great number of such widely recognised ‘shrutis‘ – we have the ga and dha of Darbari kanada, the re of Bhairav, the ni of Bhimpalasi and Miyan ki Malhar, the ga of Todi and perhaps a few more. Most musicians will agree that there is something the matter with these notes, that they are not found in the harmonium, and will say ‘this is the shruti of gandhara in Darbari’. When it is performed ‘correctly’ it will elicit great approval from the audience, marked by interjections such as ‘wah wah‘ (wah wah), ‘kya bat’ (you [don’t] say) and even the very explicit ‘yeh to Darbari ka gandhara [shruti] hai‘ (this really is [the shruti of] Darbari’s gandhara). [for a brief explanation of the names of the notes and their abbreviations in Hindustani music see the “note” at the bottom of this page].
There are probably no two artists who perform this ga in Darbari in exactly the same way, and I proffer that the individual touch in rendering it adds to the wealth, beauty and meaning of the musical repository that we refer to as raga Darbari Kanada. In a very early article by Arnold, Bor and myself it was suggested there are two main ways of producing it, a soft undulating way that creeps from Re to ga, and a more jagged style that descends from ma (Arnold, Bor, van der Meer 1985).
Fig. 1: The soft undulation style that meanders upward from re to komal ga as played by Asad Ali Khan on the bin.
Fig. 2: The jagged style, descending from ma and then twice from shuddh ga, finishing with the movement ma-re as sung by Amir Khan.
Fig. 3: A near straight rendering of ga by Faiyaz Khan and Bhimsen Joshi.
A third way of rendering ga (fig 3) is really rarely heard, most musicians prefer to use the various ways of undulating or shaking the ga. This is called andol (andolit, andolan), literally meaning swing. Still, I have it on the authority of my teacher Dilip Chandra Vedi (who was a disciple of Faiyaz Khan, Bhaskar Rao Bakhle, Alladiya Khan and Uttam Singh) that the near-straight, and extra flat (ati komal), rendering of the ga in Darbari was the hallmark of great masters. There is something to be said for this, if at all we accept the idea that the shruti of ga in Darbari has anything to do with pitch it is rather confusing if that pitch is not steady at all. Jairazbhoy states that “certain musicians use the term shruti to indicate the subtle intervals produced as a result of this oscillation in pitch. They do however, maintain that these microtonal deviations from the ‘standard’ intonation may only be used in oscillation and may not be sustained as a steady note” (Jairazbhoy 1971: 35). In this light it is interesting to recall an anecdote relating to the Dutch composer Ton de Leeuw (1926-1996). In a conference about the meeting of East and West in music Ton de Leeuw explained how he had used shrutis (microtones) in one of his compositions. He told us that one of the difficulties of performing the piece was that the musicians had to produce very steady straight sounds on their instruments to bring the shrutis to life. They were not used to this, as they add vibrato to steady notes. I brought up the point that in reality, shrutis in Hindustani music were never produced as straight notes, they were always ornamented by undulations or glides. De Leeuw vehemently rejected this idea as totally impossible. At that time the famous sitar player Imrat Khan entered the auditorium and joined the discussion. To the surprise and dismay of Ton de Leeuw Khansaheb confirmed my interpretation. I will come back to this in a moment.
The article in which we published the above graphs was part of an ongoing debate between Nazir Ali Jairazbhoy and his disciples on the one hand and the ISTAR team of Bel, Arnold and myself on the other. Jairazbhoy had published an article with Stone in 1963 in which he challenged the very core of the idea of shruti. In 1982 Jairazbhoy’s disciple Mark Levy published a study in which he revisited the research of Jairazbhoy and Stone. He too concluded that the shruti story was nothing but myth and mysticism. It is worth while to cite Levy on the ati komal ga of Darbari:
A number of performers have difficulty in reconciling the two practices [high and low interpretation of ga]. One of today’s most well-known and respected sitar players for example, states that the Ga♭ and the Gha♭ [sic; he obviously means Dha♭] of Darbari are atikomal or very flat (taped interview […]). As seen in Appendix D, nos. 10-12, however this prominent sitarist intones the Ga♭ extremely sharp rather than flat. The artist is thus paying verbal homage to a more traditional style, while actually performing the more contemporary one. (109)
A daring conclusion indeed, and a typical example of ethnomusicological arrogance and conceit. Ethnomusicologists had often proclaimed that ‘indigenous’ (read ignorant) musicians would pay lip-service to ancient and obsolete theories while practicing completely different musical realities, a heritage of ethnological thought. The real problem here is that Levy takes for granted that the intonation of ga by the respected sitarist (Vilayat Khan) is the average of his measurements. Levy produces a table with low, high and average positions of the andol. The low measurements of three different instances are 294, 269 and 284 cents, the high 344, 344 and 414. The averages are 319, 307 and 349. The question is what led Levy to believe that the average is the ‘real’ performed intonation? Did he ask the sitar player? Clearly not. Moreover, it is very doubtful that the measurements of an andol with the technical means at his disposal were at all reliable. For measuring pitch with the strobotuner it needs to be steady for at least half a second. But andols are by nature never steady. We argued in the 1985 article mentioned above (Arnold, Bor, van der Meer) that andols are made on top of the base pitch, which would mean we should take Levy’s low measurements. But even that I would reject completely now, because there never is a steady pitch, and the low positions vary quite a lot. So if there is no measurable pitch there cannot be a contradiction between theory and practice as the citation of Levy suggests. To suggest that Vilayat Khan is saying one thing but practicing another is therefore also not warranted. The sharp ear and equally sharp and analytical mind of Vilayat Khan (whom I have personally known reasonably well) would not easily slip into such contradictions. I frankly believe that Vilayat Khan truly thought of komal ga in Darbari as being extra low. If ever there was a musician with an extraordinary command of tunefulness and intonation on the sitar it was Vilayat Khan. And a discrepancy between thought and measurement is in no way a confirmation of contradiction between theory and practice.
Levy further concluded there was no consistency in intonation among artists and even in the performances of a single artist. Arnold, Bel and myself were furious as we strongly believed that Hindustani music essentially followed the system of intonation as laid down two thousand years ago by Bharata and as reinterpreted by Paterson, Deval, Clements and Fox-Strangways (see Rao and van der Meer 2010 for a discussion of these theories). Briefly summarised this theory holds that Hindustani music used just intonation in which every semitone except sa and pa can have a high (pythagorean) position or a low (harmonic) position. In this theory, the minor whole tone (182 cents) is supposed to be a three shruti interval, while the major whole tone (204 cents) would be a four shruti interval. The difference between these two (a comma of 22 cents) would then be the so-called pramana shruti (the basic shruti). Jairazbhoy & Stone and later Levy demonstrated with a number of examples that this theory was not tenable. Jairazbhoy concluded that intonation in Hindustani music was really closer to equal temperament (ET) than to the supposed interpretation of just intonation. The ISTAR team, to which I belonged, dismissed the findings of Jairazbhoy and Stone and of Levy. We considered the measurements inaccurate as they were done with methods that were – at least in our opinion – outdated. We also challenged the interpretations by Jairazbhoy’s disciple Levy. In particular, he had taken the pitch of the ga in Darbari to be the average of the oscillating movement, looking in particular at the jagged type of andol that undulates between ma and ga (as in Fig. 2). We argued that the oscillation is supposed to have its lowest point as the ‘intended’ pitch, not the average. Levy’s argument for using the average was that this had been shown to be the case of perceived pitch in vibrato. However, it can be demonstrated that this is only true for vibratoes with at least 5 oscillations per second, whereas the andol of Darbari has approximately 2 undulations per second or less. In such a case we actually perceive a rising and falling pitch, not an average.
In the following years I left the question of Darbari’s ga aside and dug into hundreds of performances to measure intonation in different ragas, in different performances and by different artists. The ISTAR team had criticised Jairazbhoy, Stone and Levy’s methods of measuring pitches, but our approach was also dubious. In the course of those years I studied theories of pitch perception and their implementation in pitch extraction software. I first started by developing PitchXtractor, based on algorithms used in Leiden and Amsterdam and implemented in the LVS software. I also used the LVS software itself to compare results. Later I started using PRAAT, which currently may be one of the best systems for pitch extraction.
My findings were at best inconclusive. In an article published in the Ratio Book (2000) I showed that the just intonation model could not possibly be maintained, as Jairazbhoy had argued earlier. Intonation showed a tremendous amount of variability. At the same time, it was clear that Jairazbhoy’s theory of an approximation of ET ± 50 cents was too crude. My extensive measurements showed that in performances where the tanpuras were tuned in pa-tuning musicians produced some pitches that were very precise and very close to just intonation. Pa (the fifth) would have 702 cents with a standard deviation of the mean of half a cent. Re similarly had 204 cents with a few cents standard deviation of the mean. Ga turned out to average on 390 cents, not the expected 386 cents, but certainly not the 400 cents of ET. All that is not very surprising, because a tanpura in pa-tuning gives very powerful partials of the perfect fifth (702), the (pythagorean) major second (204) and the (harmonic) major third (386). But all other notes showed much less consistency. In ma-tuning the major sixth was certainly harmonic, but in pa-tuning it turned out to be almost 900 cents (ET). Komal ga, ma and komal ni were all over the place. Interestingly komal re, shuddh ni, tivra ma and komal dha were quite stable at positions that were best described as ‘close to ET’. Generally they are between 90 and 100 cents below or above the tonic and the dominant. But all these intonations were never the object of much interest of musicians. These were ‘common notes’, there was nothing very special about them. What they were interested in, and where the applied the term ‘shruti‘ were those ragas (and a few more) I mentioned in the beginning. And as I recounted in relation to the anecdote about Ton de Leeuw, none of those pitches were steady. It dawned on me that what musicians refer to as shrutis simply isn’t about pitch ratios, about fixed or fixable pitches. In our ISTAR article we had drawn attention to the consistency of tonal shapes, the way pitches are moving between the notes, in tonal space, but we didn’t go the next step, which was to realise that the whole debate with Jairazbhoy was totally moot. It is moot because of the confusion between shruti as a measure of pitch (as in frequency ratios) and shruti as a exploration of tonal space.
Now whether shruti really ever was a measurement of pitch is not clear. Probably it was in Bharata’s time, as he discusses it in relation to tunings of the harp (vina). But he gives no ratios, no string lengths, it is all done by ear. So if it was a measurement it probably was not a measurable measurement :). But the very exploration of tonal space (and please let us not call this ornamentation, and let us not discuss it as deviation from a presumed ‘correct’ or ‘standard’ pitch) is one of the most remarkable inventions of Hindustani music. In the following I will show how Uday Bhawalkar explores the space of ga in Darbari in a short alap and dhrupad he recorded for the AUTRIM project at NCPA. The full piece can be heard (with an introduction and commentary) at http://autrimncpa.wordpress.com/darbari-kanada/.
Before this a brief note on the artist, Uday Bhawalkar. Uday is by now one of the best representatives of the Dagar style of dhrupad singing. He learned his art during long years of training with the brothers Zia Fariduddin Dagar (1932-2013) and Zia Moiuddin Dagar (1929-1990). Both were known for their excellent command of the art of dhrupad and their profound knowledge of tone, tonality and intonation. The latter especially, as a vina player (binkar), knew the infinite space of tone like no one else in India. My own teacher, Pandit Dilip Chandra Vedi, who upheld very high standards in the art of Hindustani music, had the highest respect for Zia Moiuddin Dagar , which was quite exceptional as he generally considered the younger generations badly trained and incompetent. In passing I might add that apart from Zia Moiuddin Dagar he was content with very few musicians of that generation, the main exception being Kishori Amonkar, whom we know indeed as an inimitable titan of music. The vina, with its long strings is almost like a microscope of microtonality, and it is no coincidence that shruti is discussed in the two thousand years old Natya Shastra by Bharata in the section on instrumental music. Uday fully assimilated this understanding of tonal space from his teachers.
Before entering into a detailed discussion of gandhara in Uday’s Darbari we will take a brief look at a tonagram from his full recording.
Fig. 4.: Tonagram of Uday Bhawalkar’s Darbari Kanada, recorded at NCPA, Mumbai, 2010.
What strikes immediately is that the peaks, which represent the notes S (0), R (2), g (3), m (5), P (7), d (8), n (10) [for a brief note on the note names in India see the bottom of this page] are mostly discrete with exception of the space between R and g, two notes that are much more glued together. The tonagram is a representation of the frequency with which each measurement of pitch occurs [for more information on tonagrams and how they are created see my Praat manual for musicologists. As we can see S (0) is the most used pitch, followed by R (2), P (7) en M (5) in that order and then g (3), d (8) and n (10). It is also evident that S, R, m and P are more distinct peaks, i.e. these notes are used more as steady straight pitches. In a close-up we can also see that these pitches are probably just intonation, conforming the ideas I stated above in relation to tanpura tuning.
Fig. 5: The section from n to m stretched horizontally.
Here we can see that the interval S-R is quite precisely 204 cents, distinctly more than the tempered 200 cents. What is more striking however is that gaussian distribution of g has an average of 275 cents, with a special peak, that we can consider the mode at 260 cents. Now we may start fantasising about ati komal ga, but as I will demonstrate in the following talking about the mean or mode makes no sense whatsoever.
Movie 1: Uday Bhawalkar Darbari kanada fragment 1
In this first fragment there is no ga as such, we hear twice a small twirl that suggests R-gSR- (at 196 and 198 sec) and then at the end of the phrase R-gRSnd- (203). As is evident from the graph what I have written as ga here is really and ever so slight rising from R, it is as if the voice wants to take off from R but is kept down by gravity. Or perhaps these are pains of labour of a ga that is about to be born.
Movie 2: Uday Bhawalkar Darbari kanada fragment 2
The second fragment is the andol shruti of gandhar in Darbari in its first stage of unfolding. At 229 the melody starts creeping up from R very slowly to a point some 35 cents below ga and then meanders very slowly in five consecutive undulations that shift slightly upward every time ending with the obligatory oblique mSR- movement. In this particular phrase it becomes clear at once that there simply is no single pitch whatsoever that we could pinpoint as the measurement of ga. Both the low point and the high point of the five undulations are going slightly upward, and so of course is the average or whatever pitch you might want to select. And yet, much as musicians do, I would say this is the true shruti of gandhar in Darbari. Etymologically shruti means that which is heard, and in musicology it is generally considered that this refers to the smallest interval that we can meaningfully distinguish. However, shruti has another and more important meaning, which is the revelation (of the Vedas), also in the sense of being heard. And it is in this sense that I suggest we should understand the shruti of ga in Darbari. This second fragment is indeed the revelation of this wonderful phenomenon of ga in which not only the tonal space between R and g is revealed as a universe of which the boundaries are ever expanding, but also a revelling of the voice that is exploring the sheer infinity of the liminal dissonant interval.
Movie 3: Uday Bhawalkar Darbari kanada fragment 3
In the third section the opening is again the slow and meticulous meandering of the voice between R and g, but now the melody recedes back into the netherworlds of mandra saptak. Reculer pour mieux sauter!
Movie 4: Uday Bhawalkar Darbari kanada fragment 4
And indeed in the next fragment the same movement between R and g is now followed by a straight m (and subsequently P). Herewith the exploration of the shruti of g has been completed in the ascending progression. It should be noted that the recordings that were made for the AUTRIM project were supposed to be succinct, without sacrificing essential elements of raga delineation. In passing it should be explained that a full exposition of the slow alap (intro) would normally take at least half an hour and could be stretched to a full hour, especially in a ‘big’ raga like Darbari. Teachers and musicologists have attempted to simplify and summarise the information necessary to define the raga. At its most compact this would consist of an ascending and a descending line (in Darbari S R g m P d n S’, S’ d n P g m R S. Most musicians are not satisfied with such a rudimentary definition and prefer a slightly longer summary of important phrases known as chalan (route, way of going around in the raga). For the AUTRIM project we asked musicians to go one step further and demonstrate the raga in a more complete format, while not expanding it fully. As a result, what Uday has revealed here in four phrases would normally require many more, ever varying, ever discoursing statements of the raga.
Movie 5: Uday Bhawalkar Darbari kanada fragment 5
The fifth instance is a reiteration of the fourth, but now with a sweeping onset S/P\SR- and a more solid transfer from m to P at the end (not part of the sound file segment, but visible in the graph). The whole phrase has become slightly more relaxed, as if the first adventurous steps have now been consolidated.
Movie 6: Uday Bhawalkar Darbari kanada fragment 6
The sixth fragment pushes the exploration of the gamut further beyond P (the fifth) and towards the high octave, but before actually consummating high S a return to the space of g postpones the completion of the octave. Since now the g is coming from far above, the whole movement starts from m, or rather from shuddh G (the major third) instead of R. Also, the undulations are slightly broader, more daring, and on the whole a little higher. Again, if we would have to discuss this g in the light of pitch measurements we would be at a loss. Not only is there no steady or fixed pitch that we can pinpoint as the ‘true’ position of g, but moreover the whole constellation g is demonstrably higher than in the earlier fragments. And if it can have two distinct pitch ranges how can we (re)define these in terms of shrutis with a fixed pitch ratio?
Movie 7: Uday Bhawalkar Darbari kanada fragment 7
The underlying concept of the seventh fragment is very similar to the sixth, just giving some different twist to the basic statement.
Movie 8: Uday Bhawalkar Darbari kanada fragment 8
Finally, the eighth fragment initiates the return to the tonic after having completed the full exploration of the octave, including high S. Again g is approached with a broad movement that swoops down from n straight to shuddh G, where a slow mind (glissando) to R starts and then undulates rapidly and with just two waves to end in g.
It might be useful here to listen again to the whole recording (link) up to the point where the composition begins (with accompaniment by the pakhavaj drum).
Movie 9: Uday Bhawalkar Darbari kanada fragment 9; g in the composition (first cycle)
Movie 10: Uday Bhawalkar Darbari kanada fragment 10; g in the composition (second cycle)
I have included the g from the first two cycles of the composition (pada) showing yet another angle of rendering this characteristic note. The composition’s lyrics consist of the names of the notes sung to those notes with some of the inflections and structural elements that typically belong to those notes. Ga in this case takes on a dramatic appearance as it rise up from a full octave below in a very slow glissando movement, followed again by the usual undulations. The similarity between the ‘faces’ of these movement is evident in the image below, where they have been superimposed with a vertical shift.
Fig. 6: The ga’s from the first two cycles of the composition superimposed.
The recording discussed above was a studio recording, with, as stated before, the aim to give the briefest possible overview of Darbari’s main features. In a live, full fledged recording of Darbari the gandhara spacetime will expand more. A small impression of the what could happen and what has is this rendering of Darbari Kanada by the inimitable Faiyaz Khan (1886-1950).
Movie 11: Alap in Darbari kanada by Faiyaz Khan (click here to view in new window)
I already mentioned that Faiyaz Khan would make the andol on ga very shallow so take a quick look at the tonagram of this section:
Tonagram of the excerpt of Darbari Kanada by Faiyaz Khan. Notice how both Re and ga are low! (if you cannot see the vertical dotted lines please click on the picture and see it full size).
My main aim in discussing gandhara in Darbari with the example of Uday Bhawalkar’s recording for the AUTRIM project has been to clarify the nature of shruti. In the process I may have overstressed the idea that the exploration of tonal space in time is a phenomenon that has immediate and intrinsic meaning. Undoubtedly one of the hallmarks of this kind of music is its slow and deliberate magnification of the very spaciousness of the tonal universe. What would seem to be such a small step as a semitone is expanded to enormous proportions. But this is not to say that that’s all there is to it, such would be a Hanslickian reduction. In the next article I will come back to the ramifications of meaning that are inherent in this piece of music.
- The note names in Hindustani music are Sadja, Rsabha, Gandhara, Madhyama, Pancama, Dhaivata and Nishada. These are abbreviated to Sa, Re, Ga, Ma, Pa, Dha and Ni or further to S, R, G, M, P, D, N. In this article low positions of the semitones are in lowercase, the higher positions in uppercase: S r R g G m M P d D n N, roughly corresponding to C, Db, D, Eb, E, F, F#, G, Ab, A, Bb, B (assuming that Sa would be C, which is not necessarily the case).
- Faiyaz Khan, Classical Songs by Great Masters, Hindusthan Records, EP LH.33, Side one track one, ND.
Arnold, W. J., Bor, J., & van der Meer, W. (1985). On Measuring Notes, A response to N.A.Jairazbhoy. ISTAR Newsletter, 3-4, 46-51. [download at http://members.ziggo.nl/wvandemeer/archives/istar/ISTAR3-4.pdf]
Jairazbhoy, N A, and A. W. Stone. (1963) “Intonation in Present-day North Indian Classical Music.” Bulletin of the School of Oriental and African Studies, University of London 26:119-132.
Jairazbhoy, N.A. (1971) The Rags of North Indian Music. London: Faber and Faber.
Levy, Mark. (1982) Intonation in North Indian Music: A Select Comparison of Theories with Contemporary Practice. Biblia Impex.
Parrikar, Rajan P. (2000) The Kanada Constellation (Part 1/3). http://www.parrikar.org/hindustani/kanada/ accessed 4 Feb 2015.
Rao, S., & Meer, W. (2010). Construction, deconstruction and reconstruction of shruti. In J. Bor, F. Delvoye, & E. Te Nijenhuis (Eds.), Hindustani music: Thirteenth to twentieth centuries (pp. 673-696). New Delhi: Manohar.
Van der Meer, W. (2000) “Theory and Practice of Intonation in Hindusthani Music.” Pp. 50-71 in The Ratio Book, Ed. C. Barlow. Köln: Feedback Papers.
A Great Study here…
with excellent citations…
Thanks for sharing
Very helpful article!
Thanks a lot!
Beautiful update of our old dream!
“the revelation of this wonderful phenomenon of ga in which not only the tonal space between R and g is revealed as a universe of which the boundaries are ever expanding”- very interesting observation. It is as if you are describing a quantum system where the particle can be in a superposition of states (that is until you perform a measurement, at which point it has to collapse into allowable discrete eigenvalues).
You may have hit the nail on the head in describing sruti as not a discrete frequency to be discerned but as an “exploration of tonal space”. After all Hindustani music being a “by the ear” music, what we keenly perceive I guess, is how the voice moves between the notes and not so much the note (or frequency) itself. I feel this is also why discussions of how Marwa, Puriya and Sohini are similar are moot. Their “tonal spaces” are very different.
Thank you for this superlative analytical exposition. The playable fragments and the tonograms bring out the concepts discussed with such clarity.
Thanks for this commentary! I hope I have somewhat clarified the confusions and misunderstandings related to the concept of sruti.