29 August, 2015

Sampoorna Bhashanga Mela Concept

The concept I have postulated is more an intellectual exercise with theoretical validity, aimed to give a codified structure to what is often attempted in contemporary orchestral/operatic/fusion/film forays with "a Carnatic base".  This is also of interest to scholars of Hindustani music, especially those familiar with the basic 10 That’s as well as Western Music Theorists and ethnomusicologists. My postulate also offers a mathematical extension to such forays since many new combinations can be tried more systematically by futuristic composers interested in venturing into this territory.

Carnatic Indian Classical music, renowned as much for its exciting aesthetics as for its scientific and precise approach, made tremendous strides both theoretically and practically after the 72 parent-raga (melakarta) system was postulated and developed several hundred years ago by Govinda Dikshitar, Venkatamakhin and others.  Prominent classical composers including the Tyagaraja, Muttuswami Dikshitar, Oottukkadu Venkata Kavi and others embraced the system and created attractive pieces which bestowed musical immortality upon this already brilliant concept, which is one of the greatest musical strides ever taken by man.  

Recent developments 

Though a couple of extensions have been proposed in recent times to the grand 72 mela system, only the 36 dvi-madhyama melas (using both varieties of Ma instead of Pa) by Tanjore S Kalyanaraman briefly made it to the stage since the proponent was a noted performer and composer who created pieces in each of the 36 scales.

Of the 5184 mela system of Prof Sambamurthy (which is really ascent of every mela with descent of every mela 72x72), 5183 are only in theory books.  The only one seen in concerts is Manji (S R2 G2 M1 P D2 N2 S - S N2 D1 P M1 G2 R2 S) which existed in folk and classical centuries before the mathematical formula was postulated by the professor. However, both retained only 7 notes in a straight sequence. (Bhairavi is of course more popular in this category though it is technically supposed to use a zig-zag SGRGM. In practice, it also uses straight phrases like NSRGM, RGM etc.)

188 sampoorna bhashanga ragas 

A bhashanga raga is one that uses notes not native to the scale. Since foreign notes is an automatic disqualification for a raga to be considered a parent raga (mela) like the 72, I have not used the term mela for what I proposed on 3 Sept, 2013 (as per my notes).  I merely called them sampoorna bhashanga ragas.

This is a system of 188 ragas which use one or a maximum of two foreign notes in ascent or descent (Arohana/Avarohana) or in both. In some ways, this merely extends the vivadi concept already seen in 40 ragas out of the 72 mela system.  In a manner of speaking, these 40 are also bhashanga since they use 2 varieties of R/G/D/N but vocalise it as a sharp 2nd/6th (Ri/Da) or as a double flat of the 3rd/7th (Ga and Ni).   Again the 72 have only 7 notes.

The sampoorna bhashanga raga system introduces foreign notes to these 72 which means that it will have 8 or 9 notes.


  1. To understand and codify it easily, let us divide the notes into two tetra chords SRGM and PDNS. 
  2. A maximum of one foreign note is introduced in each tetra chord.  
  3. This means that a raga can have one foreign note in either SRGM or PDNS or in both SRGM and PDNS, allowing it a maximum of two foreign notes in all.
  4. Anything more than one foreign note per tetra chord will make it even more boring and weird!
  5. The foreign note can occur in either ascent (arohanam) or descent (avarohanam) or both. 
  6. The 188 ragas I have proposed do not have any zig-zag (vakra) phrases like say, Bhairavi - which uses SGRGM. 
  7. This is not intended so much to extend Carnatic frontiers, which I firmly believe has tremendous beauty and scope as is.  
The calculation:  I have only given below the broad classification here.  Please see image file for details. 

(a) One foreign note in SRGM with PDNS having usual 6 varieties = 14x6 = 84. 
(b) One foreign note in PDNS with SRGM having 6 varieties each with M1 and M2 = 12x4 = 48
(c) One foreign note in both SRGM and PDNS is obviously 14x4 = 56

Grand Total = 84+48+56 = 188

To reiterate, most of these are no more than melodic formulas. They will not fit in with core Carnatic aesthetics. Of these, probably a handful could be interesting in Carnatic-Hindustani jugalbandhis since the latter system is much more liberal about foreign notes (perhaps not surprising since it was deeply impacted by foreign (Persian) concepts for several centuries since the 1300s). 

It would also be appropriate to clarify that the 188 sampoorna bhashanga raga system is in no way related to my concept of melharmony whose primary spirit is to project melodic-harmonic systems' existing and established values and aesthetics rather than extending them.  


PS: I thank Mr Ram Athreya for pointing out a calculation redundancy in my original list. 

14 July, 2015

One more formula for Squares of Integers

Even though I have left formal math behind several years ago (though somewhat later than it had left me behind!), I have always had a fascination for numbers, some of which has been applied in original musical concepts I have popularised over the years including Seamless Korvais.

This topic is completely off the music charts as it attempts to chart a different course in pure math in a fairly populated area - Squaring numbers. Doubtless there are several time-tested and elegant approaches to this including the most well known algebraic formula of (a+b)^2 and others based on pattern recognition.  I found another approach staring me in the face this afternoon, literally in my half-sleep state.

I roused myself to action and tested the concept. It seems to hold good from negative infinity to positive infinity and I decided to not get too greedy and ask for more but share it with heads wiser than mine in the field.  So here goes (in fairly simplistic, rather than formal terms)...

Explanations and examples: (I have uploaded an image file as the Blog formatting didn't seem to have options for exponents):

It can be tried out for any number.

  • Algebraic formula vs RK formula: While the algebraic formula is very elegant, my approach - which could be viewed as its (distant) cousin - may prove easier in the case of certain numbers.  
  • Other short-cuts vs the RK formula: Most of these are based on simple though multi-layered operations on number patterns. But they need different approaches for different numbers which means one needs to remember different short-cuts based on the final digit and/or the number of digits of the original number.  
RK method advantage

  • Uses one consistent approach across the board 
  • Eliminates one whole level of multiplication
  • Introduces the underscore _ symbol which can find use across the math world. 

I look forward to critical feedback from experts and enthusiasts!

27 February, 2015

A new option to make cricket ODIs more balanced

“ICC has ruined cricket, there is no real contest between bat and ball. Win the toss, bat first and there you go!” screams a cricket lover.  “ODIs now are no less stereo-typical than T20s! Please ICC, change the nature of the wickets,” berates another.

Several thousand feel the same way, whether they voice it or not.  Teams scoring about 200 runs in the last 20 overs have become as unexciting as it used to be when they scored about half the runs in the same space. SA scored about 222 in just 15 overs in the latest against WI with De Villiers raking up 60 plus in the last 14 balls he faced, almost obliterating memories of Chris Gayle’s 215 just a match before.  Ironically, this was 8 shy of their booty a few weeks before against the same team in Jo'berg in the last 15 overs, where AB's strike rate was 333 plus as opposed to a mere 245 in this match. 

With cyber-debris of such numbers hurtling at one literally at the speed of light, even (chrono-) logical awareness is consigned to the black hole of mental fatigue. Rohit Sharma’s 264 seems like a distant galaxy while Kapil’s 175* in 1983 seems as radiant as the Sun. 


This is not nostalgia in full bloom - objectively, AB's phenomenal ability is as timeless as the games' greats. It is a commentary on how predictable batting has become, especially when making first use of the wicket.  Even when a team is no more than 125-2 (or 130-4) after 30 overs, there is a sense of jaded inevitability one feels that they are on par for about 330 or more, based on some great karma in their previous matches (where they may have generously donated much more)!  Even chases of 300 plus have become so clinically risk-free because there is absolutely nothing for bowlers though batsmen like Kohli and Rahane have become mentally tougher and technically versatile to control the game from first to 10th gear in  form of the game.  

Tournament sixes roll is as deadening as spectator turnstile.  In fact the first thing I looked for in the Sri Lanka vs Bangladesh match was how many 6s Dilshan and Sangakara had not scored. I was thrilled that they had hit just one six between them and immediately watched the highlights! 
RIP, 50-over ODI?

Sensible people want keen contests, not mindless marauding.  Between T20 and ICC’s new rules, the ODI is in grave danger of losing its identity or even existence, what with ECB contemplating proposing what could be named an OD-40 format.  Were ICC to accept it, a more apt name could not be found.  

Fans will sure overdose on more 6s off hapless attacks, “boring” new inventive strokes, more brain-drained field restrictions, more concessions to batsmen at the cost of the game on the field.  TV viewers can “extra” OD on cricket between ads, new types of manufactured hypes by commentators long dried out of clich├ęs, sleep-inviting “Extra-hour” analysis by tried and tired ex-players ranging from great to ugly, extra-cricket snippets on camels to crocodiles, desperately trying to maintain eyeball rating for the match and so forth. 

ICC’s synthetic stats

The ICC could well turn around and say that even as such arm-chair analysts are showering it with bouncers, it’s laughing all the way to the bank.  Viewership and sponsorship have surely increased but the questions persist – ‘At what cost?’ and ‘For how long’? As a wag quipped, “Nothing succeeds like success – and nothing exceeds like excess”.

While desperate suggestions have been made even by pundits like Martin Crowe who called for a “Restriction on bat-sizes” and others who have suggested to revisit the two new balls from both ends and field restriction rules, all of them may not be implemented in one stroke nor may they make viewing more exciting. 

Bowler-dominated mismatches

The fact is lopsided contests are inevitable in any game, once in a while and there have been hundreds of such matches dominated by bowlers in the first innings, making chases a foregone conclusion.  A case in point is the latest Eng vs NZ mis-match after Southee’s Seven launched McCullum’s massacre. The 1983 Final threatened to be in this list when India was bowled out for 183 until Kapil Dev’s brilliant catch of Richards and Mohinder Amarnath’s cool-headed dibbly-dobblers thwarted a late recovery attempt by Dujon & Co.

A solution

Thus, changing pitches in favour of bowlers, reducing bat sizes etc may be only partial solutions.  A far simpler and elegant one is staring at us in the face.  Just as Batting Power Play has been introduced, why not a Bowling Clever Play phase of 8-10 overs, preferably over 2 segments? This will not only give bowlers a fair chance but also test batsmen’s skills, something that both T20 and ODIs have omitted to do almost 100%. 

Ideally, the first phase must be compulsory within the first 10-12 overs and the next one can be chosen by the fielding captain any time before the 42nd over, so that the last three overs are back to “general” mode. 
BCP 1 could be with no field restrictions and no free-hits for no-ball.  No sensible captain is anyway going to have 9 fielders guarding boundary ropes at anytime, least of all within the first 15 overs.  BCP 2 can stipulate 4 fielders inside the 30-yard circle but impose the non-free hit rule. 

Ideally the Free-hit rule needs to be banished altogether but that is another story…

Selective Moral Discomforts and Outrages of Convenience against Tyagaraja

As someone who has been passionate from early teens about making Carnatic Music socially broad based and initiated pioneering steps for the ...