vINa S Balachander on instrumental music

Miscellaneous topics on Carnatic music
shankarank
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#26 Re: vINa S Balachander on instrumental music

Post by shankarank » 26 Jul 2018, 09:19

Yeah, that numbers could be related to geometry - is it a mystery , when we use real numbers as measures in geometry? An imaginary number can be added / multiplied, only by artificially extending algebra of real quantities to complex numbers. Complex numbers are always pairs of reals - two dimensions. So a number significant to two dimensions will play a role in it's algebra. A single dimensional organism would not know of existence of any curvature.

As regards 22 & 7 , the standard model is contrived by putting in lot of parameters by hand to explain elementary particles. 22 and 7 are some arbitrary parameters, we put in to explain the limit of our own musical cognition.

Legend ( as mouthed by many a Northy teen in College) has it that Bimshen Joshi can vocalize the 53 commas!
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uday_shankar
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#27 Re: vINa S Balachander on instrumental music

Post by uday_shankar » 26 Jul 2018, 10:45

Another important and mystical CM connection to the number 22 - the length of a cricket pitch in yards
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shankarank
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#28 Re: vINa S Balachander on instrumental music

Post by shankarank » 27 Jul 2018, 09:21

If you consider ShaTJa as the base and remove it, there are 6 left signifying 6 balls in an over. There could be wide and Nos too. 22 players. Removing ShaTja there are 11 of them each side : 1 + 11 notes. Just in terms of numbers the mystery deepens!
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SrinathK
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#29 Re: vINa S Balachander on instrumental music

Post by SrinathK » 27 Jul 2018, 09:51

Sounds like all of you are onto something equivalent of seeing shapes in flames and clouds :- https://en.wikipedia.org/wiki/Pareidolia
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#30 Re: vINa S Balachander on instrumental music

Post by shankarank » 27 Jul 2018, 10:10

uday_shankar wrote:
25 Jul 2018, 17:56
, I have to confess I have aways been fascinated by Euler's relation
e^(i*pi) = -1
It is a kind of numerical fascination :P ...
The relativistic wave one in physics :

BOX A = 0;

is another beauty.

Good old Al beautified many an equation by collapsing them : https://en.wikipedia.org/wiki/Einstein_notation - he considered this one of his greatest achievements.
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uday_shankar
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#31 Re: vINa S Balachander on instrumental music

Post by uday_shankar » 29 Jul 2018, 10:37

While we're talking about Einstein, I thought it would be appropriate to quote the great Subrahmanyan Chandrasekhar, who as one of the greatest relativists as well as an ardent CM rasika, links Einstein with CM :), on Roy Kerr's exact solution to Einstein Field Equations:

"In my entire scientific life, extending over forty-five years, the most shattering experience has been the realization that an exact solution of Einstein's equations of general relativity, discovered by the New Zealand mathematician, Roy Kerr, provides the absolutely exact representation of untold numbers of massive black holes that populate the universe. This shuddering before the beautiful, this incredible fact that a discovery motivated by a search after the beautiful in mathematics should find its exact replica in Nature, persuades me to say that beauty is that to which the human mind responds at its deepest and most profound."
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shankarank
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#32 Re: vINa S Balachander on instrumental music

Post by shankarank » 13 Aug 2018, 05:02

uday_shankar wrote:
25 Jul 2018, 17:56
In an effort to keep things scrupulously honest, I have to confess I have aways been fascinated by Euler's relation
e^(i*pi) = -1
It is a kind of numerical fascination ...
May be nature will razz back at you!!
Furey mostly demurred on my more philosophical questions about the relationship between physics and math, such as whether, deep down, they are one and the same. But she is taken with the mystery of why the property of division is so key.
https://www.quantamagazine.org/the-octo ... -20180720/
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#33 Re: vINa S Balachander on instrumental music

Post by uday_shankar » 13 Aug 2018, 08:35

Fascinating stuff. Thanks for sharing, although there's no pretending there's any CM connection left :P.
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shankarank
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#34 Re: vINa S Balachander on instrumental music

Post by shankarank » 13 Aug 2018, 08:42

What? CM has suddenly lost all it's charm , beauty and symmetry? ;)
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thenpaanan
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#35 Re: vINa S Balachander on instrumental music

Post by thenpaanan » 21 Aug 2018, 20:54

uday_shankar wrote:
23 Jul 2018, 13:22
As a matter of practice, I tune 34 strings everyday by ear, using simple rules of consonance. Some go out of tune, and may be a couple cents off, a few cents off in some cases, but there's an organic cohesion to the whole thing and the whole idea is to keep it in tune all the time.
Indeed. Even for an extremely simple instrument such as a tambUrA you can tell that on the days when all the strings are tuned well together the overall sound of the instrument is fantastically alluring. But no systematic string-by-string tuning seems guaranteed to make that happen because of the interaction between the strings -- the tuning can be close but that magical complete harmony is mostly by accident. Over the years I have learned to not force the issue -- it almost feels like the instrument is a live animal and if you relax the tambUrA will also relax into tonal harmony. :D
uday_shankar wrote:
23 Jul 2018, 13:22
On the other hand, take the vina frets. Just to take one example, the second fret of the vina is set to 10/9 swarasthana which will work correctly for the panchama string as 5/3 for D2. But that means the vainika is always playing 10/9 for R2 on shadja string, and 9/8 for R2 on the second string (which falls on the panchama fret). So these differ by a pramanashruti (9/8)/(10/9) = 81/80. Does any vainika from Muthuswamy Dikshithar to Jayanthi Kumaresh know or care ? In practice, I prefer 9/8 for R2 instinctively because of the panchama consonance but when everything else is in good tune, it really doesn't matter. Many great violinists had poor intonation (and tuning) but were so good in other matters that it didn't matter. Same with equal temperament. U Shrinivas only played in equal temperament but carried it off so well.
There are two possible ways I can process this. One way is to say that we never stay still on any note. Except for Sa and Pa every other held note is subject to oscillation so the sruthi values don't really matter because we are deliberately smearing them. The other way is to say that what matters is not the absolute sruthi value (within the relative-to-Sa system) but the inter-note values. So when you change the Ma up to pratimadhyamam, we move the chatusruthi Ri down or the kAkali Ni up intuitively because it sounds better that way? And this keeps changing even within the same composition as different note combinations are played in sequence? And when you have to adjust four or five swara positions together for a tODi for instance, where the Ri or the Dha have to land for optimal consonance is a combinatorial nightmare that a musician solves on a daily basis, albeit unknowingly? For vocalists like me it is hard to even know if we are doing this subconsciously. Perhaps the instrumentalists of the genre are more aware of this phenomenon as they play and can tell us what we are doing (as opposed to what we think we are doing).

You have a good point that for the extremely good musicians the theory did not matter one whit. U Shrinivas' tonal quality and sheer musicianship more than made up for all these gaps in the theory.

-T
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shankarank
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#36 Re: vINa S Balachander on instrumental music

Post by shankarank » 22 Aug 2018, 10:28

SrinathK wrote:
27 Jul 2018, 09:51
Sounds like all of you are onto something equivalent of seeing shapes in flames and clouds :- https://en.wikipedia.org/wiki/Pareidolia
Some people see money in it!! https://www.youtube.com/watch?v=keLN89CWZ-A :lol:
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shankarank
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#37 Re: vINa S Balachander on instrumental music

Post by shankarank » 19 Sep 2018, 00:46

Well here is one from NPR based on numbers! Since we went through that above.

From the son of Sri B.K Chandramouli who passed away recently ( based on a local whatsapp post )

https://www.npr.org/2018/08/10/63747069 ... i-sequence
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shankarank
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#38 Re: vINa S Balachander on instrumental music

Post by shankarank » 29 Sep 2018, 21:50

The number π has very less to do with the circle if the circle is infinitely large especially. You will have to see the video till the end to see how that is established.

https://www.youtube.com/watch?v=d-o3eB9sfls

Does that make it less mysterious?

The number π is now liberated from the circle of samsara! :D
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#39 Re: vINa S Balachander on instrumental music

Post by uday_shankar » 30 Sep 2018, 02:57

shankarank wrote:
29 Sep 2018, 21:50
The number π has very less to do with the circle if the circle is infinitely large especially. You will have to see the video till the end to see how that is established.

https://www.youtube.com/watch?v=d-o3eB9sfls

Does that make it less mysterious?

The number π is now liberated from the circle of samsara! :D
Fascinating, thanks for sharing. I would still argue that since it is a "limiting case" argument, you have not really "liberated" pi from its circular origins :).

The same is probably true for the infinite series calculations for pi, from Leibnitz and earlier Indian mathematicians. You end up integrating trigonometric functions, which are also intimately tied to the circle.

So perhaps there's really no purely number theoretical extraction of pi ?
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shankarank
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#40 Re: vINa S Balachander on instrumental music

Post by shankarank » 30 Sep 2018, 20:48

uday_shankar wrote:
30 Sep 2018, 02:57
I would still argue that since it is a "limiting case" argument, you have not really "liberated" pi from its circular origins .
Well the inverse square series as specified is purely in number theory domain. That it converges can also be proved , I suppose without resorting to Geometry. The value can be calculated to some digits depending on the computational power available at any time.

The circular limit is invoked only to show that , the value is indeed same as the "pi" talked about as that ratio of circumference to radius and not some other number.

The inverse square law from which he relates to the inverse Pythagoras theorem, was demonstrated using isosceles triangles containing a light beam or a solid angle in 3D with lines emanating from a center. That the two vertices of the triangle ( or the 4 vertices of solid angle) also have the same symmetry as that of a circle ( or that of a sphere!) is tenuous. In fact a circle can be imagined as a limiting shape of juxtaposition of small isosceles triangles , an infinite of them. So a circle is an emergent shape then?

I think fundamentally, we need the concept of a distance and a concept of a point. Inverse square law can then be proven with a 2 D plane of solid angles that grow geometrically as squares.

Concept of distance is defined using measure theory , [:cough;] a branch of pure mathematics ( as introduced by a Math 201 prof.). So it doesn't need geometry! It rather ties geometry with number theory I suppose.

Well that leaves the concept of a point [:cough;] as a limiting end state of what ? - could that be defined? If truly, the real points of existence are centers of rotation, then yeah - you brought [:cough;] the circle to the center stage! At that point there is no this pure math, it is an observational physical world!

We have made a circular argument ;) :mrgreen: then!

I remember a conversation from Prof. V. Balakrishnan's class. He mocked at the question: what is the physical meaning of golden mean? It is just a number , he continued in a retort, what is the physical meaning of "pi"?
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