We are going to present a few “unforgettable duets” on this page. First we start with Ud. Ali Akbar Khan and his duets with Ud. Vilayat Khan, Pt. Nikhil Banerjee, and Pt. Ravishankar. The recordings are already available to many of the passionate music lovers/collectors. I have retouched the audio quality a little, and uploaded here. Enjoy!

Ustad Ali Akbar Khan and Ustad Vilayat Khan, Marwa.

Ustad Ali Akbar Khan and Pandit Nikhil Banerjee, YamanKalyaN, Bihag.

Ustad Ali Akbar Khan and Pandit RaviShankar, Bihag.

And finally, a very unusual duet between a vocalist and a Shehnai player:

Ustad Latafat Hussein Khan and Ustad Bismillah Khan, Kamod.

Here is a couple more:
Ustad Vilayat Khan and Ustad Bismillah Khan, Gurjari.

Pandit V G Jog and Ustad Bismillah Khan, Jaijaiwanti.

After so many of them, there arises a couple of natural questions, which one you like most and why? Are there many successful duets in the domain of Indian Classical music? If yes, then which are the ones; if no, then why? Or, it all boils down to a question that what is a duet, and at the end of the day is the idea of duet at all compatible with Indian Classical music especially its Hindustani variant? While I am still busy finding whether there is a definition of duet in the old texts of theory, or even a vague reference to the existence of such a thing, I continue scribbling here in the hope of forming a contemporary notion of ‘duet’ music and placing it in the context of history.

Most successful musical duets have an inherent dramatic element in their form. The drama is usually achieved through the appropriation and re-appropriation of the same musical form through two essentially different/opposing tonal qualities. Before proceeding further with the verbal jugglery, let’s try to understand the objective reality of our music, graphically if possible.

While normally our music rests on a linear structure of tones and time, the third dimension is usually introduced by the volume/amplitude/gain in course of the attack-sustain-release of the phrases and their sequential appearances. The zero-amplitude music becomes the breathing space in the entire structure. In vocal music, ideally, the lyric further enhances the third dimension and thus presents a contour in the audio space that we reckon as a rendition of some music. Accompaniment is used to bring in more variations, or to reinstate and reinforce the form often shadowing or echoing the main form. The time line though theoretically is infinite, yet periodicity becomes important in an accompanied full-fledged rendition. The cycle that the percussion instrument generates, often taken 2 or 3 clubbed together in a linear fashion becomes the boundary of the canvas. In a single rendition, we often use 2 or more different periods, and thus varying the density of the phrase system. For obvious reasons, smaller periods cannot afford as much empty space as the longer,
vilambit, period can.

Having said this, we have now an acceptable way to discover the geometry and the architectonics of a given rendition. That might be interesting otherwise but not really very useful to enjoy the music. Yet, in order to understand graphically, I’ll try to present the following image.

(Please click on the image to get a full view)

In this hypothetical three-dimensional space, the scale is defined on the OX line where only the main frequency of the given tone is counted and not the multiples that are only defining the ‘timbre’ of the sound, the raga with all its legal phrases and extraordinary usages are defined on the OXY plane with an implicit reference to the Z-axis that marks the beginning and ending of any given phrase in real time. Thus in a 56-matra Jhoomra Vilambit cycle (Khada Theka normally playing for 52-64 seconds), we usually get 2 or 3 curves in the space complying with the guide curves on the OXY plane, and then a terminal curve, which is the Mukhda, to mark the end of the cycle. If the artist chooses to continue his sequence to another periodic cycle, he might omit the terminal curve and replace it by any other legal one. And hence, there comes the concept of Badhat, the fourth dimension, where the cycles become numbered. Therefore, in case of a solo performance, with no accompaniment apart from the percussion, the full rendition becomes a three-dimensional fabricated column, where the length of the column is directly proportional to the duration of the rendition. That is true even for an apparently unaccompanied Dhrupadang exposition, for there the performers usually love to mark the end the ‘paragraphs’ with some conventional small phrases, like R-N-S, or N-S-D-N_GR as in the V G Jog – Bismillah Khan recording above. Obviously, nothing is infinite here; the cross-section of the column is limited by the human perception restricted by physiological factors, so also is the duration. A phrase being any longer than a given limit is imperceptible, and smaller than a pre-defined lower bound is unpleasant if not inaudible, however great is the resolution of the sound production system (proponents of infinitely fast taankari, are you listening?).

However, accompanists (Sarangi or Harmonium in case of solo vocal) follow the phrase/curves presented by the vocalists by echoing or shadowing it, often with a small time-lag, and then they invariably manages to join with the main form at the Mukhda, certainly by means of omitting some fraction of the phrases.

So, how does a DUET work?

The trivial answer is, certainly not the same way the accompaniment does. Shadowing or overshadowing the other cannot be the purpose and method in a duet performance, then what is? The drama is often half-achieved by varying the tonal qualities, for instance male-female vocal, Sarod-Flute duo in Satyajit Ray’s music in his films; also, Sitar-Sarod duets are aplenty, etc. But that is not all, and that is why two similar voices or instruments can also make a good duet performance. There are quite a few such duets in the domain of DagarVaNi Dhrupad, and some of them demonstrate the other qualities so strongly that the similarities of voice do not really matter, rather enriches the form.

If we are allowed to go back to the proposed graphical representation, duet can be thought of in terms of adding some mass to the otherwise dimensionless linear movements in the space. While echoing the same phrases, more often than not an octave apart, can be thought of making the fabric look like little bas relief and nothing less; using complementary phrases can actually define a three-dimensional, dense mass — and possibly that is what identifies the duet. Ironically, very few if not none of the duets we come to hear from the maestros of the last century comply with this definition, though we have seen some moments of glory.

There can be several cases; for instance when both the performers belong to the same Gharana, same schooling, and have had a habit of practising together, it becomes easier for each of them to anticipate the other’s movements and design the intricate fabric accordingly. This might work for certain raga where the scope is narrow, that is too say there are not too many legal phrases one can choose from. Such is the case with the pair RS-AAK above. The narrower is the raga, the more successful the duets are. Let’s take “Palash Kafi” for example. The exposition part here is a perfect example of how the complementary phrases are chosen. Even the Gat is introduced by both the artists together, one reciting the ascending part and the other picking up the descending move. In most other places they distribute the phrases among themselves in a manner that complies with the KhandaMeru principle, and thus throughout the rendition they sculpted with the scale and the available phrases.

I think there lays the primary feature of a duet; it differs from the solo in the same fashion a sculpture differs from the painting. Somehow, that didn’t work in the Bihag recording cited above. One is soon past the awe about the aura of their individual skill and depth of understanding the raga, but while together, the sculpture just didn’t happen. Same goes with the other duet, apparently marvelous Marwa between AAK and VK. The chromatic span of D N r G m D, D m D m G r S r N D, the difficult trek for many is explored by both the maestros with awesome ease and dazzling lightness of movements, but in most cases they kept on re-inventing the wheels, one after another. Instead of having conjured up into one single sculpture, the music always remained two different paintings, however skilful, facing each other. The union never happened, while both remained busy imposing their own stylistics! Understandably, this was the second case, while the artists belong to different schools of thought and training. But then, it’s surprising to see the similar thing happening in AAK-NB Yaman KalyaN. But then, it was a private concert, and lot of distractions was there. Later on, when this duo switched to Bihag Gat and drut, it was a different story altogether. In my humble opinion, here they started to get along with each other perfectly because of their commonness in the understanding of Bihag. Both of them approached Bihag from the Khamaj-end, while RS got stuck to the Bilawal-end Bihag in the other example, that of course being his forte.

The other duet between BK and LHK, the recording is interesting because of its historical significance. Many would have never imagined that such a thing might even exist. Having said this, musically the piece of rendition is nothing more than an instance of unusual accompaniment. Latafat Khan Sahab being the lead singer here, dominated the entire scenario, and Bismillah Khan sahab was rather too subdued even for an accompanist. In modern days, even the percussionists are less humble than this, and that might be a lesson for most of our contemporary Pandits and Ustads on Tabla.

However, at any rate, great duets are very few indeed, and I think we still need to learn the ancient technique of compositing, intertwining the multiple layers of audible signals. Apart from some moments of bits and pieces here and there, I am yet to be awestruck listening to a perfect duet of the maestros.

Ustad Amir Khan

On his 37th death anniversary, I am presenting here three land mark renditions from the Ustad himself.

At this moment, I don’t feel competent enough to introduce these recordings to the audience; just a quick note here that the Shuddh Sarang presented here is a really rare one, and as far as I know no book or no discography ever mentions that recording. I was looking for the lyrics of the composition, but couldn’t find any reference whatsoever that Khan Sahab ever sang such a bandish. The Jog tarana was the late Ustad’s own composition, an intrinsically beautiful one. The Shree bandish is a traditional one, also Pt. D V Paluskar recorded the same, but of course with Amir Khan Sahab it has got a different dimension altogether.

Listen for yourself. Click on the links below and a MP3 player should pop up.

Jog Tarana, by Ustad Amir Khan.

Shree, Bandish in Jhaptal, by Ustad Amir Khan.

Shuddh Sarang, Vilambit set to Jhoomra, by Ustad Amir Khan.

Okay ! then lets start with some of the queries .
I would be grateful to you if someone can tell me the meaning of the following Bandish (composition)
ari -eri aali- piyabina
sakhi -kalana-parat -mohe- ghadi -pal-chhina-dina
Jaba – te- piya – pardesh – gamana – kino
ratiya – katata – mohe tar- gina -gina
I request to give the meaning for each and every word and also correct if any word is found to be wrong .

Sakhi/Ari Eri Ali Piya bina
(Sakhi) Kalanapa rata mohe Gharipala ChhinaDina
Jabase (Piya) Paradesa Gawana (Gamana?) Kee no
RatiyaaN kataTa mori Taare Geena Geena
First we listen to a crystal clear rendering of the bandish. Not really my “most favourite”, but her clarity is admirable. Yaman, Ashwini Bhide.
“Eri” here is just a call — “Lo!”. Confusion about “Ali” is legitimate, which Ali? However I will present two explanations that I have heard. First, Ali is not just a name, it means “fine/handsome”: the way we use Shri before a name. Second, I have heard someone to say that it’s not Eri Ali, rather is Yeh Rehali/Rahali! The word “rehali” in Purva-dialect (some regional version) means an absconder. However, both these are befitting, the second one sounds more plausible when majority of the singers use “Yeri”. As you wrote: “Kalna (=kal na) parata mohe” is insisted by some as kal being the double negative of bikal/bekal (restless). However this version is dubious for the word bekal is of Urdu origin and doesn’t go with the rest of the lyric’s language. “Kalanapa” is a broken colloquilaism for Kalpana, which is also thinking hard. However, there is another logically correct alternative. The wordings should be, possibly, “Pala na padata mohe” — Pal being Sanskrit Pakshma, eyelid in English, as in Piu Pal na Laagi more Ankhiyaan — the famous Goud Sanrang composition. How did Pal change to Kal, whose mistake, when, let’s not get into that dispute. “Ghari(ghadi)pala chhinadina” is an expression to literally mean “every moment and fragments thereof”, broadly — always. There is a definite Maithili flavour in the language, so the Sanskrit word “Gamana” is catachretical here — “gawanaa” is probably more appropriate — meaning is same. Rest is simple. So the whole lyric would mean “(Sakhi — no meaningful English translation is possible) In absence of my handsome (absconding) lover (Piya) I am always lost in thinking (can’t close my eyes for a moment), since when he has gone abroad (to a place afar) I am spending all my nights counting the stars”. Hardly any Bhakti here, it’s a typical Shringaar composition. Some people believe that Yaman comes from the word Aiman (Peace, KalyaN) sharing the same Arabic origin with Amen! Possible, how would you translate KalyaN to a courtesan having mixed/Persian origin back in the 15th century? But this bandish represents a restless state-of-mind. I have no clue how after spending sleepless nights and having the Piya absconded one can be in unperturbed peace of mind!

The following bandish is very popular ( Vilamvit khayal on raga yaman)
kahe sakhi kaise ke kariye,bhariye dina,
eso lalana ke sanga
sunari sukhi mai ka kahu tose
unhi ke janata dhanga
Which is this language ? I can understand the meaning as a whole but find difficult to translate it separately . hope my queries will be solved here .

Some version of Maithili, of course. I guess the correct wordings are:
Kahen sakhi Kaise Kee kariye
Bhariye Dina aiso lalana ke sanga
Suna Ri Sakhi Mai Ka Kahun Tose
Una hee Kya Janata Dhanga
This is most likely to be a description of KrshNa, the speaker being Radha and the listener Brinda. “Tell me Sakhi what do I do? The whole day he is spending with other girls. Listen Sakhi what can I tell you, (you don’t know) how deceptive he is”. A beautiful picturesque description — but again Shringaar.
One thing is common in both the compositions, that Yaman becomes a girl’s voice who is madly in love but is in forced seperation for no fault of hers. I don’t know, is that the appropriate Raga-Dhyan of Yaman?

I think we should be very cleared about the language and its meaning . Why are we still using those ancient bandishes ? Dont you think it is high time to compose new poetry?

I disagree. Yes, if Sahitya is there, you have to know the meaning, better if you know the entire history of it and connotations of all the words and expressions, that would enrich your music. But at the same time, don’t you sing Tarana? Admitted that Amir Khan Sahab believed that Tarana wordings are not meaningless, and he proposed that most of these words are broken Farsi and he also gave meaning of certain words. But even if you don’t know the meaning of the words, even if there are no words at all, say in instrumental music, it will be no less a Yaman. Take this Tarana by Moghubai Kurdikar.
However, it is always high time to produce something new. Compositions are popping out every now and then, but they have to be tested with time. The compositions cited above are clearly against the popular belief about Yaman’s mood, still they have passed the acid-test of time. Let us wait and see if our compositions pass that test. Even if they do, there is no reason to dispose the oldies.

Following is the another example
Pag lagan de maharajkunwar
Sada rangeele peet mune pavan/pawan de
Can you translate the following (sic) [above].

Whatever the dictionary says (Pag=turban, feet, keeping rhythm with feet etc.) here pag is Payal, Nupur, Ghungroo. This is a fantastic compostion in Malkauns, and also is very popular. But where are the other two lines? Don’t try to translate Sadarangile, that’s a signature word of the composer Sadarang. Well, it does have a double-meaning too. “Sadarangile Preet manne pawan de” — Let me have/experience the love that is always colourful. Sadarang assumes here the viewpoint of Meera Bai, and writes.

Can you please give me some ideas on raga Jait Kalyan, and Audav Devgiri.?

This answer will come later on, when we actually start the Raga Analysis section with Pandit Aloke Chattopadhyay. I am not sure if there is any audio sample available for Audav Devgiri.

Is there any objective musical criteria.to classify raga bhupali under Kalyan thaat but Deshkar (which has the same scale) under Bilwal that ?

Same as above, this one demands an elaborate page dedicated to the Bhup’s kingdom.

In which raga Sa and Pa is exceptionally weak ?

To my mind, the best example is Marwa.

The Bhairav scale of Hindustani music in the purvanga (lower tetrachord), with the Kafi scale in the uttaranga (upper tetrachord) is known as Ahir bhairav but what it will be if bhairavi is in the purvanga? Raga Ahir Bhiarav, Ahiri Todi and Ahir Lalit are combination of two .We know a lot about the compounds but where is the pure form of the orginal raga? If it is Ahir+ bhairav,Ahir+todi, Ahir+Lalit where is the original ahir ?

Firstly, this is not the way to understand Raganga. Replacing one note with another, or deforming one tetrachord to sound similar with another scale, you don’t really get another Raga. You have to understand the soul and/or architecture of a Raga. It is such a group, where known arithmatic functions such as ‘+’ or ‘-’ never work. However, Ahiri is almost extinct a scale. No vocal recital is recorded (to the best of my knowledge) on this Raga. Pt. Nikhil Banerjee has played Ahiri, but alas, our self-styled Gurus list that beautiful recording among Todi’s, while Ahiri has nothing Todi about it –it was and still is a Bhairavi variant. Listen to a clip here.

As I told already, I’ll come back to your other queries as soon as possible — yani asap!!

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New article and a new tuning software, an indispensible tool for analysis are in the offing. Also coming up, Dattila’s text.

After discussing the fundamental concept of generating new scales through chromatic shifts or whole scale transposes, let us turn towards the possibility of having a large number of melodies by various other methods among which chromatic shift is just one. Another common method of obtaining a new scale and therefore a new melody is omitting or displacing a note or a phrase in a known melody and then renaming it. Cheaper examples of this latter method are observed far too often in the recent years. Validating the new scales and hence melodies thus obtained in the traditional system is difficult and therefore the orthodox musicologists practically reject the method altogether. In our study we will neither accept nor reject any method practised by real people upfront. Instead, we would try to find the limit of the praxis. In other words, we will try to find the answer to the question that how many scales and melodies can possibly co-exist in the given Shruti based system of ours. We will have to play a little number game therefore.

Studying the modern octave closely we have already seen that each note there apart from S and P effectively enjoy a span of 4 Shrutis each, and still follow Sarangadeva’s observation about the uneven distribution of the Shuddha (standard) notes, and that they are holding the Swaswadya position of their respective groups. The Pancham being fixed is a little problematic though. The location of the Pure Perfect Fifth is a lot dependent on individual perception. By the just intonation system, and our own traditional system, the ratio of the frequencies of P and the keynote S is 1.5, whereas the Western equal-tempered logarithmic scale places it on 1.4983, and our 22-Shruti logarithmic scale proposed here places it at 1.5041. In both the latter cases, the approximate value is 1.5; still there arises an interval of 3-4 Hz in which the P belongs rather fuzzily. While tuning a Tanpura or any other string instrument, even though we are easily guided by the clearly audible harmonic, there often arises confusion about the exact tuning and always the artiste exercises veto to converge on one of the possibilities. If heard separately, the difference is not at all perceptible, but if two different instruments play together, then the beat frequency is clearly audible. However, in our present study we leave it on individual perception (Pa-rception) and ensue assuming P being fixed on a particular somewhere inside that 3-4 Hz interval. For the other notes using up more than their allotted ration of Shrutis, we must also keep in mind that though not so much in the realm of HCM, but the concept of Panchashruti (penta-microtonal) Ri, Shatshruti (hexa-microtonal) Ma etc. was introduced in the realm of CCM as early as 17^th century CE by Ramamatya in his treatise Svaramelakalanidhi. To save ourselves from such a temporal and cultural bias of Shuddha and Vikruta swara that leads nowhere, we would stick to the standard nomenclature.

So in effect, any basic Sampurna-Arohi scale can be designed in 4⁵ = 2¹⁰ =1024 ways. Same is true for the Avrohi (descending) sequence. So there are 2²⁰ = 1048576 different ways to form a melody of Sampurna-Sampurna Jati. The number is huge but still finite. Now this one assumes that only S and P are fixed notes. If we introduce the Vadi-Samvadi pair in it, and if we place them on S and P, no contradiction arises. Now, if we have two different Vadi and Samvadi notes none of which are S or P, then both on Arohi and Avrohi sequences we lose two more notes to fiddle with, and thus the number becomes 2¹² = 4096 only. Now these two notes can be selected in 6 different ways maintaining an S-G, S-M, or S-P relationship between them and that makes the total of possible scales 6×4096= 24576. However, this doesn’t add to the original set of melodies, for these 24576 elements form only a subset of the big set, which is the total event space for the time being. That big set {M} comprising of 1048576 scales (not thaat) may not be the ultimate superset. However, before proceeding further we need to introduce a few more definitions.

Prayoga: The tones and their applications in a melody.

Given any tone and its corresponding note in any given scale, it can appear in 4 or 5 different ways in the melodic structure. Let’s list them now.

1. Flat and unit-duration (Ekmatrik swara)

2. Flat and multiple unit duration (Vahumatrik swara) or that ends a phrase as a dynamically defined rule of pattern

   Interrupting Notes

   1. It is commonly understood that the ‘matra’ mentioned here is not dimension, but rather is a unit of time.  This unit can’t really be empirically measured to mean something of a fixed value as it is relatively defined in the context of stylistics, melodic characteristics, particular phase of the rendering / exposition etc. Stylistics can in turn depend on various non-musical factors like some specific physical attributes of the singer, econo-cultural and indeed eco-cultural ambience at the time of his/her training, certain religious/humanist doctrines about certain melody or the associated lyric, and of course the state-of-emotions of the artiste and audience at the given time of rendering etc. From the very beginning of a performance, the ‘matra’ is amicably settled between the artiste and the audience, implicitly.

   2. Minimum 2 fixed notes or notes of longer duration are required to give a melody some kind of stability in architectural sense that will be discussed later. Usually, these notes are around half an octave apart from each other. Maximum 4 such notes of longer duration are permissible that are among the Vadi, Samvadi, Graha, Nyas, and the keynote Sa itself.
3. Ornamented usage that involves other neighbouring tones, notes. Here we will be dealing in two main types of ornamentation.
   1. Undulated or Andolit swara. It’s an undulation with the next note, tone, or microtone. It happens more often than not, that for the sake of undulation a Shruti apparently extraneous to the given scale is put in use. When the swara to be undulated with is two or three Shrutis apart from the original note, the actual undulation may span only 1 or 2 shrutis intervals respectively. The converse of this observation is applied in practice. Khamaj’s Shuddha N, Poorvi’s Komal d, Gurjari’s Komal r often come with such undulations, since all those are only one Shruti apart from the fixed notes S’, P, and S respectively. It is easy to believe that, Shuddha M in Kalyan (Yaman) and also Shuddha Kalyan appears by the same principle while undulating on the Shuddha G as a longer duration note.

   2. Parenthesised or Clustered note(s). In the Bhatkhandenian notation system it is indeed denoted with a bracket (-). (M) would mean either GMPM or PMGM in a single ‘matra’. It can also take a form of PDPMP, or PMDPMP in Bahar, or PDPmP and PmDPmP in Yaman expressed by the same symbol (P).
4. Doubled (or tripled, quadrupled) as in a Gamak. This one shouldn’t, but often does take extraneous Shruti. A singer with a proper Dhrupadiya training would never take a Vivadi (extraneous) Shruti in such Gamak actions and would rather slow down the entire action in order to reach the proper Shruti, and one without that kind of rigorous training would hardly mind. Recorded samples of such careless Gamaks are plenty, even from the maestros, but underlining them would be uncourteous. 

Transitions can be defined as the technique to move from one note to another. A minimal musical phrase would contain two tones S_m and S_n and a transition t_i, and the atom of a phrase can be written as P(m,i,n), where S_m = f.10^md. The known transitions can be listed as follow:

1. Flat: Plain note to note transition whether ascending or descending.

2. Meend: A roll over the all or some intermediate Shrutis, naturally the ascending and the descending Meend will produce different results.

3. KaN: Taking either of the pair of the notes as the touch note or Sparsha or KaN of the other, and again ascending and descending KaNs are different.

4. Krintan or Aash: Same as flat transition, only fast, and there is a significant increase in the levels of volume and harmonics on the second or target note. Again, order becomes important.

5. Silence: One can just insert a bit of silence between two notes. Vocalists use it differently, but in instrumental music it is almost inevitable. As of the vocalists’ technique, rather the notes of longer duration or the fixed notes precede a bit of silence. Once the fixed notes are established, singers stop at that note just as a passing reference, and it is implicitly understood that the note is relatively long and loud. For example, in Kedar, a vocalist can just stop at Shuddha M, and is NOT allowed to stop at Teevra m, for the latter usage would indicate another melody, Chandni Kedar rather than the intended one.

So we have 8 different transitions, and the basic musical event or the atom of a phrase P(m,i,n) = S_mt_iS_n can be formed in various different ways. Common musical sense would tell us that not all applied notes can support all transitions and vice versa. For instance, taking a long note as the touch note for the next one would yield nothing. Avoiding such impossible situations, on a 7-note scale, we actually have 28 applied notes that are commonly used in all phrases. Therefore the total event space for the minimal phrases can contain 28X8X27 = 6048 different events in time. Please note that we have not listed Vakra (twisted) application separately, for such a twist is actually a phrase with a third touch note, or just half of an undulation cycle. Secondly, a roll does not actually roll on all of the intermediate frequencies on the imaginary continuum, but touches only the applicable Shrutis. Sometimes a long roll can appear to be shorter, like P-R roll in Chhayanat, in which case actually it is a combination of notes and phrases like P[silence]G-R, and thus should be treated not as a single event but as a series of events.

Now we come to the series of events that actually comes to us as a melodic movement. The entire rendering of a given raga is actually a series of events relevant to that raga. Yet, quite contrary to the popular belief, we won’t call the music linear. Concept of linearity as against spatiality will be discussed a little later. However, we can combine the basic events as longer phrases to contain 1, 2, 3, 4, … atoms at a time. For each different length, not considering the order of the things, we can have ⁶⁰⁴⁸C_r ways to design a longer phrase where r is the number of events applied. It is to be noted that naturally, singers depending on smaller phrases rather than long, never-ending taan and behlawa, are able to present a wider spectrum of variations. So we finally have 2⁶⁰⁴⁸ (sum of the binomial series S⁶⁰⁴⁸C_r where r = 0, 1, 2, 3, 4, …) different combined musical events on a 7-note scale. This is the ultimate of mirkhand (Khanda Meru). The number is huge, impossible for any human being to learn or remember all the phrases, and that too for only one scale among 2²⁰ possible ones. True that not all of these will be musically ‘pleasing’, but then ‘pleasing’ someone is not the only job of music. Most parts of this space are simply beyond the limits of our perception.

Going back to our original problem of generating melodies, we can and really do add some of the smaller phrases to the monotonic ascending scale to get a new melody. For example, Kamod, Hamir, share the same scale with Yaman Kalyan, as Kedar, Chhayanat are the same scales with Khamaj, but selection of phrases and combinations make them all different. If adding phrases does not necessitate replacing some parts of the monotonic ascendance of one note over another, the number of possible raga on a 22 Shruti scale is even more than 2²⁰. So when one is trying to get a new melody by tweaking and twisting an already known scale, it is most likely that he is actually discovering a series of phrases, i.e. a variant, of another known melody. In terms of probability, his chances of ‘creating’ a new raga are only 1/2⁶⁰²⁸. The orthodox pundits might not be all wrong.

Again, we were so far considering only one octave, the Madhya Saptak. But in practice, that P-R descending event in Chhayanat is often followed by an ascending mirror image of it across the octaves. Mirroring the phrases is one of the major tools to reveal the structure and create balance in the melody. Determining what is pleasing or aesthetic, is a different issue altogether. Since any real musical structure found in any given rendering is finite in time and in number of phrases/events, there is always a tendency towards anchoring it all on the keynote, or the long note where it all begins, and preferably ends. Thus all movements, series of events are designed to go up on the scale and to come down by equal steps. Thus mirror images and patterns are generated. It is not difficult to empirically or statistically show that the aesthetic preference is there towards the phrases that are combined along the diagonals of a Pascal triangle. If a opening phrase is considered as a open parenthesis that must be closed by some other phrase, and in the mean time there would be a series of sub-patterns to fill the space, it gives rise to another known problem (and solution) in Combinatorics defined by Narayana numbers N(n, k) =(1/n)ⁿC_kⁿC_k-1 where n, k are natural numbers. After all, aesthetics is all about the sense of limit, and sense of selection. And that can’t be guided by mathematics alone.

To be continued …

Gangubai Hangal at a concert, 1973

For a detailed biography, please click here.

My most favourite recording by Gangubai Hangal, Shudh Kalyan with a difference.

Doyen of Hindustani classical music Gangubai Hanagal died in Hubli, Karnataka, on Tuesday after a brief illness.

Gangubai, 97, was put on life support system on Monday night after her condition turned critical and she breathed her last this morning, Dr Asho Kalamadani, her physician, told PTI.

She passed away at 7.10 am, Gangubai’s grandson Manoj Hanagal said. The singer is survived by two sons and a daughter.

Gangubai was admitted to the hospital on June 3 but had returned home on July 12. Two days later, she was again admitted to the hospital after she developed respiratory problems.

Gangubai, one of the most acclaimed exponents of Khayal gayki of the Kirana gharana, was born in a family of professional musicians in Dharwad in Karnataka.

Winner of the Padma Bhushan, Padma Vibhushan and Sangeet Natak Akademi awards, she mesmerised fans for over six decades with her melodious voice.

Umrao Bundu Khan
Son and disciple of Sarangi-Nawaz Ustad Bundu Khan; adept at both vocal music and Sarangi; migrated to Pakistan during the partition. Probably the last dynamic representative of Delhi Gharana. These are not commercial recordings that we have compiled here, in fact Umrao Khan hardly had any commerciallly released album attributed to his name. In vocal music he was not known to be a perfect singer in the sense the professional vocalists are, but watch the Josh in his music. He had his moments when his was Music at its very best.
We have also uploaded a longer piece here, a duet with his cousin Zahoor Khan on Violin, where he is rather playing the second fiddle most of the times. Along with music, please also note the Tehzeeb associated with the entire Culture of HCM.
[You need Real Player for the longer piece, please get it from www.real.com]

A dictionary or a book of grammar is not meant for justifying a misuse, and when it appears to do the same it is not a fault of the user, but of the grammar instead that is just a bit too lenient to accommodate everything that is right and wrong. Imperfection that slashes between the artiste’s quest for the perfect and his individuality is so palpably inevitable and material that one tends to define individuality as a given set of imperfections. From the perspective of the perfect, his individuality is seen through, or rather obscured by, the set of imperfections going by the name of style statements, and the real individual hides behind the illusion of styles. To save theory from being idealistically dissociated from the real praxis, it must take into account the ideal of perfect along with the commonly observed styles, and at the same time must be careful not to confuse style and imperfections with the Ideal, with or without a big ‘I’ in it. This is, however not to say that the ‘Ideal’ would exist irrespective of the praxis; rather my contention is that the ideal is always synthetic, being result of a synthesis between the constant antagonism of desire and ability. Indian philosophers knew about this dialectics by the name of the antagonism (‘dvanda’) between ‘Purusha’ (consciousness) and ‘Prakriti’ (phenomenal realm of matter). Theory must take all of those into its account, the thesis, the anti-thesis and the probable synthesis.

Having this said, let us turn towards one of the fundamental problems of Indian music and its theories. One of the key concept of Indian music is that the keynote can be defined randomly anywhere on the continuous scale of audible frequencies. Since music is produced by the human beings and for the human beings, the keynote has to lie in the range of audible sounds, 20-20K Hz. However, in reality the range for musical sounds is much smaller than this, only 100-5k Hz. Anything below 100 Hz is recognized as a humming noise only, and anything above 5k is primarily meant for adding to the tonal quality; for a main note any more shriek than the 6th octave, that is higher than 3520 Hz simply painful to the human ears. For vocal music, the maximum range for the base chord keynote, that is the most dominant frequency among all the harmonics in it, is around 230 – 800 Hz. ‘Sa’ can be anywhere in this range. For most male vocalists the range is between 300 – 550 Hz, while for the female vocalists the ‘Sa’ spans between 410 – 550 Hz. Once the keynote is fixed at X Hz, only a handful of singers are there who can produce sound for than 3 octaves; one octave lower down to X/2 Hz, and two higher up to 4X Hz, of course with the help of falsetto. For instrumental music the range is easily expanded, but higher than 3000Hz is not pleasing to the ears at any rate, while below 125 Hz, it becomes very difficult to recognize the actual musical phrases and patterns.

As we have mentioned in another page, the Indian situation is not quite similar to its Western counterpart where the musicians play on a rather level field. On a standard Piano or any other instrument the pivot rests on the 4th octave first note A, i.e. on 440 Hz, often mentioned as A4 or A440. The lower octaves run down to 55 Hz, A1, and the higher go up to 3520 Hz, A7. This is more or less uniform for everybody, vocalist or not. However baritone or soprano one gets, that has to be within this range having the implicit reference point at A440. However, in Indian classical music the reference point changes with every artist, with his/her schooling, style, or the age of the artist and etc. Some of the professional (non-classical though) artistes even shuffle the reference point(s) in view of the specific item he/she is going to present! However, even after all these shuffling and fiddling the audience’s perception is not hindered by any means to register and recognize a melody, or a scale. Let us re-invent the wheel then; the entire musical structure is built on the keynote and all the other tones and semitones and microtones are obtainable from some function of the keynote itself. We have already modelled that ‘some function’ in a previous article.

For a quick recapitulation, let’s remember the basic concept. For a given frequency f, the middle/working octave spans between f and 2f= 10^log2f. 22 Shrutis are placed within this span. With the classical assumption that the Shrutis are equal, or equally weighted, we assume that each consecutive Shruti is d= (log₁₀2)/22 apart from the previous one, and thus the nth Shruti S_n = 10^nd, n is an integer between 0 and 21. With a chart of frequencies thus generated we have already seen that the basic scale follows the hypothetical distribution of notes that is 4 Shrutis for S M P each, 2 each for G N, and 3 each for R and D. However at the same time, since S and P consume only one Shruti each being fixed notes in any octave, effective span for every other tone is 4 Shrutis. Further observations can be made on the chart; that

1. The position of Shuddha Madhyam (M) is not really the middle of the scale, and people are always experimenting with that position. Earlier it was on the 13th Shruti, where now it is on the 10th, but never on the 11th! But at the same time, certain melodies are there like Kedar, Hamir that consistently use the 11th Shruti Madhyam as the Shuddha Madhyam. However, M doesn’t belong to the set of audible harmonics (possibly comes as third of fifth of fifth harmonic).
2. It can be easily concluded that although the Shruti distribution has changed during the 18th century CE from Swaswantya to Swaswadya, in practice both these systems are very much in vogue till date. A typical Indian response to new outlook/theories, the newer one is accepted all the same, but still there will be people sticking to the old one, and a queer mixture of the two would be seen in praxis.

The equation S_n = 10^nd n being an integer reminds one of another equation that is used for determining the tones in the Western scale having reference point at A4, which is as follows:

F(n) = 440 X 2^(n-49)/12 where n is integer, and F(n) is the n-th note of the Chromatic (12 tone) scale.

The equations above are similar to some extent, and the tones thus produced by changing values of n are close. However, not quite. The following table would show the difference.

The third row represents the Western scale of 7 notes (Major), and the fifth row represents the Indian Shuddha scale according to the Shruti values. Listen to the difference in audio. In the Western scale the R, D, and N are particularly off-key by the Indian standards. Moreover, it can’t really place the special uses of Komal r, Komal d, Shuddha N etc. which is central to the application of notes in Indian Classical music.

Why do we abandon the already tested equation and opt for a new one requires some more explanation, and the explanation requires introduction of another concept from the past. It was believed that a chromatic shift would give rise to a new scale, and the phenomenon was known as Gram Parivarttan. In other words, given one chromatic scale C₁ and a keynote K₁, there is always another scale C₂ played on K₂ that would use the same tones as in C₁, and vice versa. Consider the following example.

On the top row with key note K₁, all Shuddha notes are played / highlighted, while at the bottom row, the keynote is shifted to K₂, which is N of K₁, and the resulting scale is something like Kaushi Bhairavi. Listen to the audio sample using the Bilawal scale already used. How to handle that extra Teevra m is a different issue altogether. It can be omitted right away, can be used with special reference to Sindhu Bhairavi, or can be modified to become a P. Similarly if the keynote is shifted to G of K₁, Khat is available.

There are three fundamental observations that can be made from the table above.

1. It is absolutely necessary that the transpose still produces elements from the same set of the tones, otherwise locating them back to the original octave would be impossible. [Rule 1]
2. On an uneven chromatic scale like ours such shift or transpose may result into fractional notes that can be defined only by microtones, or Shruti. Therefore we can’t really dispose the Shrutis off. [Rule 2]
3. The transpose can not affect the system of phrases (phraseology) of the original scale, but then the phrases are translated to the new scale, and thus the architectonic quality of the new melody is defined and guided by the original melody. [Rule 3]

Now let’s get back to the Piano tuning formula. If the reference point is shifted to a random frequency F Hz from A440, then by Rule 1 & 2 there would be two integers m and n so that 440 x 2^(n-49)/12 = F x 2^(m-49)/12 without which the transpose would not work at all. Taking log(base 2) of both sides we get m-n=log₂(440/F)¹². Finding such an F where m-n will still be an integer is a little too tough an ask. Again, if F is already a tone in the known octaves, that is if F=440 x 2^(i-49)/12 for some i, then the relation becomes 440 x 2^(n-49)/12 = 440 x 2^(i-49)/12 x 2^(j-49)/12 and therefore n=i+j-49, which means a transpose is meaningful more than 4 octaves apart that might be well outside the normal range of musical tones. If the same is tried on the equation we proposed here, it becomes pretty simple. If K₂= K₁x10^ndalready, then the m-th microtone of K₂ is simply the (m+n)-th one of K₁. In practice the keynote is taken from the Western scale and then the internal relationship between the notes are applied by the Indian perception. The resulting sound table is completely haywire. Let us see the following table A3 onwards.

There is no real chance of getting a transpose, new scale, anywhere on this table as all the tones are just unique.

From the above we conclude that actually the form of the equation is important, not the number of microtones. Therefore when there is already a known set of 22 Shrutis, there is no reason to deviate from that.

The function d=(log2)/22 is, however, an ad hoc one. I think that the relation is really not that simple, though the simple one produces pretty good result.

To be continued

This Shloka is quoted from Sangit Ratnakar, and nobody ever challenged the distribution of notes in an octave that is proposed in this formula.
Let me explain a little. The octave in our music is imagined to be split into 22 microtones, called Shruti. These Shrutis have names like TeevrA, Kumudvati, etc. All female names, but they are not deities. The reason why such names are assigned can be a different issue to discuss later on. However, out sakes and for the sake of convenience these microtones are imagined to be uniformly distributed and equal, though there are recent empirical observations that apparently would make one believe that they are not. However, I have a different explanation for that. But before we pass on to that, let us look at the almost universal formula that tells about the position of the notes in the octave.
The problem is where is the note? It can’t take up all the shrutis at once. If Sa and all subsequent notes takes the last Shruti of the allotted group (Swaswantya) then the all-Shuddha scale becomes something close to our Kafi. But if they are placed on the first Shruti of the group (Swaswadya), only then the all-Shuddha scale becomes our Bilawal. One can be sure that we are following the modern Swaswadya system. Now this ancient Swaswantya positioning system has been last recorded in Srinivasa (RagatatvaVivodh: beginning of 18th century) which is clearer in formulation in comparison to the other older texts such as Sangeet Parijat, and therefore it can be assumed with certainty that all raga mentioned before this period have undergone a massive isomorphic change after the first half of the 18th century. It is a matter of different research that how to back-calculate these isomorphic changes and place the modern Ragas at par with the older Ragas.
The following table would make an interesting lesson for those who are interested in the history of the Indian musical traditions. Here I am trying to describe the Bhatkhandenian thaat system on a Shruti table.

Full View

The first row of the table tells about the old system, Swaswantya. There are groups of 4, 3, and 2 Shrutis and the notes are placed on the last Shruti of each group. On the second row, we place the notes on the first Shruti of each group respectively, but shift the row to the right, for we can’t afford to lose the Tanpura tuning for such a horizontal shift for whatever reason. And then we notice two more things, that firstly M and P do not change their place, the fifth is the fifth and the middle one is the middle one be the system ancient or modern; and secondly effective range for all five notes R, G, M, D, N are 4 Shrutis each. Actually the invariance of S and P is responsible for that. They are always Shuddha, sacrosanct. However, Shuddha M is not that serene and has been methodically and scrupulously molested by many people. We shall come to that point later. The third row graphically shows the effective range of the notes, and in the fifth row, I have tried to make a gross distinction between the Komal, Shuddha, and Teevra groups, with approximately two Shrutis allotted for each. There is another interesting and very important observation to make. The all-Shuddha scale of the earlier days would sound like our Kafi! S R g M P D n S’.
From the sixth row onwards; there are the 10 known basic scales, the thaat that are mentioned in Bhatkhandenian diction, listed “in order”. Please note that this order is also important for the system, remembering the names somehow would not be enough. There is a concept of overlapping between the basic domains, and actually most of our popular ragas are intermediaries, “Paramelpraveshak” – that which invades the neighbouring domain. If the order is forgotten, then it becomes impossible to identify the locus, and modus operandi of any given raga. The most pathetic example is of Alhaiya Bilawal. Because of the usage of a flatter n in an all-Shuddha scale, it belongs to the adjacent Khamaj Mel (scale). Its characteristic phrase D-G also comes from the Khamaj’s typical GMPDGMG; but many of our friends’ believe that it is a classic example of Bilawal, and all the more problematically, that D-G is the characteristic of Bilawal! Also note that there are definite relationships and similarities between the consecutive scales, more so if we agree to group the first five together, while the others forming another group where a different set of rules apply. However, we shall come back to this point on separate pages while discussing the individual ragas.
Here our focus would be on the Shrutis and their identities. In the above table we have marked the individual Shrutis for each of the scales. Now, how to find that position precisely? Is there at all any means to understand a scale as a numbered Shruti-scale? If there is, then a lot of apparent problems in the theoretical domain would be solved at once. We are made to believe that the microtones can’t be precisely located and therefore that “Shruti [is] Ageya”. One can hear and perceive the ‘difference’ in two Shrutis but cannot sing the Shrutis themselves. There is some, only some truth in this sweeping statement.
Let’s understand the problem from a different angle. We are given that any tone or keynote can be our S, and the double of the frequency of S will mark the beginning of the next octave for that pitch of Sa. That is to say, any given frequency f Hz will find its next octave and the subsequent ones by doubling the frequency to 2f, 4f, etc. It doesn’t tell however, that how exactly the intermediate notes would be placed on the frequency continuum between say f and 2f. We already know that this precise positioning is largely Culture-specific, and therefore there is more history in it than science; and that is an utter lie. Locating A precisely on 220 Hz or C on 261.6 Hz may have its historical connotations in the Western system, as of now, and then semitones, and cents, and other calibration methods can rest on the foundation of those fixed notes. But in Indian music, nothing is fixed that way. The Western A, B, or C here just denotes its respective pitch neighbourhood and nothing else. Once the Tanpura is tuned, people can easily abandon all their harmoniums, black keys and white keys, and go on singing with all their fervour. So there is the catch: ‘once the Tanpura is tuned’, that is once the S is determined, that is to say once the frequency f is fixed, everything else is revealed at once. This means the whole octave, all tones and microtones, are values of some simple function of f. How is that? There is another clue. When Sharngadev formulated that Shruti grouping, he also assumed that all Shrutis are equal.
Now if the series of whole octaves is an exponential series like f, fx10^log2, fx10^log4 etc., then for the intermediate notes we can think of some coefficients that would be in the form of 10^f(log2) where f(log2) is some function of log2 and is a number upper-bound by 0.3 (approx). When f(log2) is 0.3, a new octave starts. At this point, the other clue that ‘Shrutis are assumed to be equal’ becomes all the more important. According to our formulation, the clue translates as; the logarithmic series up there as index of 10 must be in some sort of regular progression. Expectedly, log2/22 would be the regular increment d since there are 22 Shrutis, 22 intervals to be precise, value of which is approximately 0.01363636… and since it is a recurring decimal, exact value will never be determined. This is the share of truth in the mystic existence of Shruti. Rest is child’s play, and all the microtones become terms like fx10^nd when n lies between 0 and 22. Applying this much of mathematics to the octave starting with C (261.6 Hz) as Sa, we get the following table of Shrutis, the coefficients, and the corresponding frequencies.

Base frequency = 261.6 Hz