Perspectives on music and other subjects from math through sports to philosophy.
31 August, 2020
Deccan Chronicle: Carnatic Music and Communal Harmony
Background: A few years ago, attempts were made in some quarters to sully the reputation of the legendary singer and philanthropist Dr M S Subbulakshmi, whom millions hold in the highest esteem. This rebuttal of mine in early Dec 2017 in Deccan Chronicle appeared the very next day of another such posthumous attack on her in the same publication.
In 2015-17, I was the only artist who stood up to pen such articles in the mainstream media or speak strongly in public to against attempts to disrupt Indian music and culture by manufacturing caste divisions or tarnish the memories of great artists and composers.
Though most of my colleagues commended me for doing this, they chose to not speak out in public at that time, which was a systemic failure of the entire field, leading to wrong narratives taking roots in the general public consciousness.
Ironically, the very institution - Music Academy Madras - that was radically opposed to such dastardly attempts made a 180 degree turn around Nov 2018 but came out the closet in 2024 by announcing its highest award to the prime mover of the same.
I stood by my principles and returned the same Sangita Kalanidhi Award which I had received in 2017.
29 August, 2015
Sampoorna Bhashanga Mela Concept
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.
Details
- To understand and codify it easily, let us divide the notes into two tetra chords SRGM and PDNS.
- A maximum of one foreign note is introduced in each tetra chord.
- 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.
- Anything more than one foreign note per tetra chord will make it even more boring and weird!
- The foreign note can occur in either ascent (arohanam) or descent (avarohanam) or both.
- The 188 ragas I have proposed do not have any zig-zag (vakra) phrases like say, Bhairavi - which uses SGRGM.
- This is not intended so much to extend Carnatic frontiers, which I firmly believe has tremendous beauty and scope as is.
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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
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.
- 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
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!
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 clichés, 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%.
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.
19 July, 2014
Law of Collective Inertia...
Colloquially, inertia is cited more as a mental - usually negative - phenomenon to explain a person’s recalcitrant, indifferent and non-proactive behaviour.
But closer examination reveals that:
In a collective context, whole groups can tend to have Positive or Negative Inertia, based on influential individual's within that group, the organization's leadership skills and other factors.
Organizational leadership is about:
Individual Inertia (II) of an employee (per day) = Average number of Actual Productive Hours (APH) - Average number of Theoretical Work Hours (TWH) that one is contracted to work per day (calculated using standard man-hours it takes to complete a given job/project for an individual/group).
Example 1: If A, who is contracted to work 8 hours a day for 5 days a week puts in 30 actual hours a week, his Individual Inertia is = (30-40 )/5 = (-10/5), which is a Negative Inertia of -2.
Ex 2: If B works 55 hours per week, his II score = (55-40)/5 = +3, a Positive Inertia.
Ex 1: If an org X with 100 employees, had 60 people with a CPI of 150 hrs and 40 with a CNI of –80 hrs, the STI of the org would be 150+(-80) = 70.
Ex 2: If org Y had 200 employees with 50 with CPI of 200 and 150 with a CNI of 300, its STI would be 200 + (-300) = -100
Ex 3: If org Z had 300 employees , 200 with a CPI of 400 and 100 with a CNI score of 400, STI would be 400 + (-400) = 0
It is obvious that:
Z with an STI = 0, is in a state of Organizational Equilibrium (OE).
X with STI > 0, is enjoying a mild positive performance from its staff while
Y with an STI < 0, is burdened by an under-performing team.
Daily Simple Average Inertia (DSAI): This is an important tool to get a macro picture of how the whole organization or groups within it are performing. DSAI is measured in Hours/Person and can be calculated from the formula:
Again, in the above examples, the Weekly Simple Average Inertia (W=SAI) of X is 0.7 x 5 = 3.5 hrs/person (assuming 5 working days/week). Its Annual-SAI is roughly 182 hrs/person (3.5 per week X 52 weeks). With its average employee working above expectation, the organization has cause for cheer, in normal circumstances.
However, the DSAI of Y = -100/200 = - 0.5, WSAI = (-2.5) and ASAI = - 130 hrs/person means the org should take necessary steps to reverse this under-performance.
In reality, numerous companies may have staff working much higher or lower than the examples given. An organisation's long term results may tend to be best in a state of Organizational Equilibrium (OE) or mild Positive Inertia.
Note: There are Weighted Total Inertia (WTI) and Weighted Average Inertia (WAI) formulas which take into consideration other factors such as the level of each employee but that is a much more involved subject.
Staff Inertia Management (SIM) is an essential part of Corporate Leadership, which has to ensure that STI never gets to the Red Column, which is where my Corporate Melharmony comes in. But I'll reserve it for another post!
08 August, 2012
Pitch Perfection - a psychological perspective
- The reason could be professional - lack of practice, lack of effort on every note, thinking musicianship or commitment to perfection.
- The reasons then get to physiological such as health, which (at least in some cases) are beyond an individual's control. Or it could simply be aging related weaknesses.
- Or it could be scientifically attributable to personal habits. It would be prudent to point out the non-judgmental view of a person closest to God that the planet has seen in sports, Don Bradman. 'Surely certain habits can impact on the reflexes and efficiency of movement,' is all he said but that is profound indeed.
- An over-eager, over confident, aggressive, frenzied, agitated mindset with Attitude, may result in music higher than shruti (over the short or long term).
- A person tends to be below key when tired, deflated, weak or under-motivated, again over short or long term.
- A person tends to be both these when sporting a frivolous, happy-go-lucky or take-it-easy style complacent mindset.
- A person tends to waver, sway or float on plain, sustained notes when the mind is unsteady or afflicted by fear, guilt, lack of confidence or personal esteem.
- A person tends to slip a lot on dynamic phrases when the mind is distracted or cluttered with unwanted baggage and unclear thoughts.
- A person tends to produce dry music that can be all over the pitch-map while in a frustrated frame of mind.
09 July, 2012
Success through Inertia
It dawned upon me this morning that inertia is not responsible for only this pathetic apathetic state of mind. It can as easily be tapped positively so that we end up doing a lot of things beneficial to ourselves or others.
In fact, millions have done it (and continue to do so) under various garbs.
What is inertia? To paraphrase Newton, "An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction - unless acted upon by an external force".
This is as true for human minds and bodies too. In fact, to a lesser degree, it is true for human emotions too.
We see the victims all the time - sedentary people continue to revel in it day in and day out, alcoholics and other addicts continue to be so and so forth.
To a lesser degree, we also see the opposite - fitness fanatics cannot stop exercising, those who follow strict practice-ethics would often be hard pressed to stop practicing and so forth. These are the beneficiaries of positive inertia.
At a slightly macro level, we see teams that have developed a systematic habit of winning over time are unstoppable during their streak and vice-versa. Same goes for countries that have developed or developing. The latter tend to stay in their side of the court for decades or even centuries at times...
How to build positive inertia: The key is to get out of negative inertia first. This will take us to a neutral zone - if not anything more. From here on, one can work towards building a momentum in positive things - be it practice or exercise or academic pursuits or something as simple as getting up early in the morning. After a few days or weeks, positive inertia kicks in and takes over. From here on it is generally smooth sailing. For instance, someone who has got into the habit of getting up at 4 am can more often than not do it even if he or she slept in very late on certain days. Someone who has got used to practicing music for 4 (or 8 or any number of) hours will find ways to do it even if there are other unavoidable engagements on certain days.
All these are results of inertia - which, at the end of the day is only a neutral thing. It is entirely we who make it positive or otherwise...
08 March, 2011
The Dot-Connect Theory & Test
- Every individual picks up bits and pieces of information during the course of life.
- These are on various fields, subjects and topics (be it mathematical formulae, everyday news, musical facts, philosophical thoughts or literary learning).
- Each bit of information is stored in various parts of our brain.
- Each bit of information can be visualized as a discrete dot.
- To continue the visualization, the brain can be seen as a rectangular canvas or even a multi-dimensional space which houses these dots.
- The mind monitors this information gathering process and shapes it in various ways.
- Each person finds some connection between some pieces of information either because of (i) external influence (like reading, learning from or discussing with others), (ii) by introspection and analysis, (iii) personal experiences or (iv) by a mere association of ideas.
- Normal people may often find connections in an orderly, progressive and predictable manner (for instance, 2+2 could be connected with 2+3 or 200+25000).
- Creative or even weirdly imaginative people, geniuses and highly introspective individuals may find connections between two seemingly unrelated topics - it could be as much a leap as a simple 2+2 being connected in their brains with an obscure Greek philosophy or a volcanic eruption somewhere (to give extreme examples).
- Each connection that a person finds represents a connected dot.
- The connection of any dot can be with one or more dots - like a hub and spoke route map of a major airline (but of course the brain is more than just 2 dimensional). To give a simple illustration: a tiger could be connected to a forest and a zoo in some people; it could be related to a national park & other animals in a few others; in some cases, it could include all the above connections plus connections to strong or scary people that one knows or hears about (and numerous other things).
- Thus, the discrete bits of information become analogous within the brain as the person evolves and matures.
- It should however be noted that not every bit of information needs to be connected with one or more bits; many may remain unconnected pieces for lifetimes, depending on the type of individuals and the evolution path of each.
- Thus, the process of individuation can be defined as the metamorphosis of digital information into analogous flow of ideas.
- With millions of bits of information picked up in the course of life, every individual may connect the dots differently.
11 September, 2010
Practice - I
Selective Moral Discomforts and Outrages of Convenience against Tyagaraja
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