The Point - Extension conundrum

Ideas and innovations in Indian classical music
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shankarank
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#1 The Point - Extension conundrum

Post by shankarank » 19 Feb 2016, 10:40

To celebrate the detection of gravitational waves predicted in general relativity (Einstein is right again!) I draw attention to some ideas outside of mainstream science – but still seems to have some scientific feel to them.

Einstein spent his later part in Princeton as an artist building theories which are symmetrical and elegant but largely ignored by the rest of the scientific community who were busy curve fitting experiments to their standard models – which is often hated by beauty seekers of aesthetics for the number of arbitrary parameters (numbers) put into those models - more of philately than philosophy.

But once in a while there are efforts to resurrect Einsteinism in theorizing. Sometimes those go beyond normal senses into the paranormal sphere.

https://www.academia.edu/12035946/The_E ... rn_physics

Above requires a google or facebook login to download.

The author is researcher in a field called para-physics – making it all spooky.

While understanding the whole paper requires expertise in theoretical physics and quantum gravitational theories – some of the interesting basic geometrical arguments can be cited without a deeper understanding of the whole paper.

1. Mathematical continuity (any finite extension consists of infinite number of points) can only be established from higher dimension by constructing loops into that dimension assuming some curvature as well ( Page 45 thru 50)
2. Any notion of curvature requires an extension and cannot be defined for a dimension less point.
3. Only dimensionless points that emerge naturally are center of rotation or centers of mass. ( Page 21)

The last one is quite analogous to swaras in Indian music where the Adhara Sadjam and pacamam are always fixed points.

But can we go further and assert that they are the only fixed points – rest of the swaras are all extensions no matter what rAga we take up – scalar or otherwise?

The correlates to a vikRti swara ( other than sa-pa-sa) as a fixed pitch position frequently identified by the finger position on the fret board of a vINa – are they really indicative of an actual pitch position in the context of a rAga?

Even when supposedly a note is transited without much gamakam – as a plain note – is it really plain in the transition?

These questions lead us to a potential alternative view that – if a musician were really halting for an extended time on a specific note other than sa-pa – he/she is not conveying the original rAgA’s essence any more – he/she is essentially preparing the ground for a potential graha-bedam where the note being dwelt on is a new “center of rotation” – a new AdhAra Sadjam if you will – where it loses its extension character as it was in the original rAga – and becomes a point around which other notes start to swirl!!

Now more analogies : Just as the mass is defined by curvature in space-time , the weightiness of the music is defined by the curvature of these new things called extensions !!

So nobody need to search for the cent/Sruti values for tOdi gandhara – Eureka!! it is an extension – we need to measure it’s curvature instead. :idea: :!: :ugeek:

A final declaration can be made with a pallavi line :

tOdi gAndhAriyai azhaitOdi vAdi | inda sadasukku :P
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kvchellappa
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#2 Re: The Point - Extension conundrum

Post by kvchellappa » 19 Feb 2016, 12:14

I am like gandhari while reading this (blindfolded).
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shankarank
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#3 Re: The Point - Extension conundrum

Post by shankarank » 19 Feb 2016, 18:26

Lets wait for more people to help untie your blind fold :) We all have an opportunity to become immortal (or invincible should I say?) then if we wished ;) :lol:
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uday_shankar
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#4 Re: The Point - Extension conundrum

Post by uday_shankar » 20 Feb 2016, 08:09

Brilliant shankarank. So given that the distortion/curvature of space time depends on the amount of mass, "weighty ragas" distort more. The traversals follow the geodesics of the distorted space-time. In the absence of "weightiness" we end up in a scalar raga space and the space-time grid is near Euclidian. The geodesics are near straight lines, I.e. zero curvature. Thus "scalar" ragas have no curvature.
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Nick H
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#5 Re: The Point - Extension conundrum

Post by Nick H » 20 Feb 2016, 12:37

Is this anything to do with gravity waves? Was it predicted by Einstein?
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uday_shankar
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#6 Re: The Point - Extension conundrum

Post by uday_shankar » 20 Feb 2016, 13:55

Nick H wrote:Is this anything to do with gravity waves?
Not quite yet. That's one step further. You can think of it crudely as follows:
1) Really large masses distort the space (really space-time since light follows the distorted world lines) around them...the distortion being significant close to the mass and less as you move away.
2) When two really large masses start moving close to one another, such as two neutron stars orbiting each other, the mutual interaction of their respective distortions creates the ripples in spacetime known as gravitational waves. Sort of :).

We are still in step 1 above, distortion, curvature, etc :).

Anything to do with General Relativity starts with Einstein. "Special relativity", the relativity principle of inertial frames of reference in uniform motion postulated by Einstein in 1905, was somewhat anticipated by the work of Lorentz, Poincare and others. But "General Relativity", a generalization of special relativity to all frames of reference and any Gaussian co-ordinate system, is a principle of immense profoundness, almost completely due to Einstein (1915). The great 19th century mathematician Bernhard Reimann anticipated the application non-Euclidian geometry to physics but that's only a small step towards General Relativity. Similarly, the mathematician Hilbert worked out some of the field equations concurrently with Einstein in 1915 and there was a small controversy regarding precedence. That nobody outside the world of mathematics has heard of Hilbert is testimony to the truth that Einstein alone deserves complete credit for the edifice known as General Relativity.
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SrinathK
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#7 Re: The Point - Extension conundrum

Post by SrinathK » 20 Feb 2016, 20:13

What if the point is seen as a zero dimensional entity unto itself? If there is something called a zero dimensional universe, it's hypothesized properties might surprise you.

1) The point will be both the universe and it's creator and it's ultimate sole inhabitant -- the one existence.
2) Space and time are simply constructs in it's consciousness -- ideas in the mind if I could say -- that means it can be as big or as small as it thinks itself to be. In fact to define it by a size kind of becomes meaningless.
3) Everything it "creates" exists in it's field of consciousness (mind) and all creations will be an extension of it's own consciousness in it's own being -- this means the point can be both omnipresent and omniscient and experience oneness with the universe. It is both infinitesimal and infinite -- more than everything and less than nothing.

Does this start sounding familiar to you?

By the way, S and P can have some gamakas on them -- the jaaru and the vibrato are two of them. The usage however does not compromise on their fundamental positions and only a vibrato can be sustained on them for any length of time.
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Rsachi
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#8 Re: The Point - Extension conundrum

Post by Rsachi » 20 Feb 2016, 21:54

Well well well. To all those totally scarified by the abstruseness of our beloved Carnatic music, i used to say you don't have to be an Einstein to understand it. I shall desist from such nonchalant advice in future. The warp and woof of our music is inextricably caught in a time-space logjam and "grahaNa" means understanding but more importantly here it means eclipse! No wonder all our ragas and talas and swaras as grahas are being bhedafied by our brilliant musicians like a piece of meduvada is deconstructed into pasty shapelessness in a particle collider.
Is it true that the first sight of a mushroom cloud was greeted by all living creatures singing Nasamani?
Last edited by Rsachi on 21 Feb 2016, 06:32, edited 1 time in total.
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vasanthakokilam
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#9 Re: The Point - Extension conundrum

Post by vasanthakokilam » 21 Feb 2016, 03:33

wow, this is quite deep. Brilliant stuff Shankarank, Uday and others.

Not sure if I understood any of this so my comment may not make any sense... but that has not stopped me before...

a) With GTR, mass causes curvature in space and time. In CM, does the curvature of swaras induce weightiness to the raga?

b) I always wondered about this regarding GTR. The math is too much for me to check it for myself but how much of Newston's laws are still applicable, especially the 3rd law? ( for every force there is an opposing force so momentum is conserved ). So if Mass causes curvature in space and time, does space and time create an equivalent effect on the mass? Doe it even make sense to ask such questions.

c) Extending the above, if in CM curvature causes Mass, does that mass have an effect on the curvature? ( this is more an artistic description and I guess once something is perceived as weighty due to curvature, I can see curvature getting affected by people wanting to make it more of a gana raga until one reaches a gana-curvature equilibrium!!! ).
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VK RAMAN
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#10 Re: The Point - Extension conundrum

Post by VK RAMAN » 21 Feb 2016, 04:44

The word weighty according to me is a misnomer as raga/sound are more of sonic in nature and can sound be vertical and horizontal with variances of super sonic to sonic - I do not if I am making sense at all?
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kvchellappa
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#11 Re: The Point - Extension conundrum

Post by kvchellappa » 21 Feb 2016, 08:03

To add my characteristic frivolity to the discussion, probably all issues will be resolved once a unified theory is found, but until then variety and mystery will give pep to life.
I must add that a faint ray of light has penetrated through my blindfold after reading Uday's comments.
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arasi
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#12 Re: The Point - Extension conundrum

Post by arasi » 21 Feb 2016, 10:20

Super scientific minds...
Wow! In a discussion like this, even a fly on the wall needs credentials to be there!

Yes, it's music which brings us together where brilliant minds co-exist with the rest of us rasikAs...:)
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uday_shankar
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#13 Re: The Point - Extension conundrum

Post by uday_shankar » 21 Feb 2016, 20:52

vasanthakokilam wrote:b) I always wondered about this regarding GTR. The math is too much for me to check it for myself but how much of Newston's laws are still applicable, especially the 3rd law? ( for every force there is an opposing force so momentum is conserved ). So if Mass causes curvature in space and time, does space and time create an equivalent effect on the mass? Doe it even make sense to ask such questions.
This one's hard.

Perhaps we should start our discussion differently. Assertion #1: Gravity according to GTR is NOT a force. Newton's laws were about forces.

So if gravity is not a force what is it ? Answer: It is the bending of spacetime by large masses/energies (BTW, not "space and time" but spacetime, this is extremely important. The notion of the spacetime continuum is central, and follows directly from even special relativity).

So if gravity is the bending of spacetime, why is there an acceleration ? Did we not learn from Newton that only "forces can cause acceleration on masses" (i.e., F = ma, therefore a = F/m, etc..) ?

We say that the so-called accelerated motion in a gravitational field is just the body in a free fall along a geodesic (i.e., the "shortest" path in spacetime between two points), not caused by any force in the Newtonian sense. So the motion of the body, say a ball dropped down from a height, is along a geodesic of the distorted spacetime around the relatively huge mass Earth (with respect to which the ball is practically massless) and it reveals itself to us as an acceleration in "space and time" ! This acceleration is the same for all bodies regardless of their mass. This "free fall" is the "stationary" state in a gravitational field.

I'll think more...it's been a while since I've thought about these things ! Sankarank rekindled an old demon !
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vasanthakokilam
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#14 Re: The Point - Extension conundrum

Post by vasanthakokilam » 21 Feb 2016, 22:00

Thanks Uday. You have latched on to the crux of my question/confusion/lack of understanding (QCLOU). Thanks. See if anything else you can add as you think about this.

Building on what you said, for the question 'why should curvature in space time reveal itself as acceleration to us?', is the following the kinder garten level answer? Newton dealt with non curved space time (Euclidean).

Acceleration = change of velocity over time = change of change of distance over time.

We have both time and space figuring in the calculation of acceleration. If space and time do not change by themselves then you need an external force to bring about a change in them to cause acceleration. That is the case with Euclidean assumption. But If spacetime is warped, the body, as it moves through spacetime, will experience automatic change in space and time and the basic equation above demands that it comes across to us as acceleration. No external force is necessary.

( Bonus QCLOU. If our brain can sense curved space time directly, we would not perceive it as acceleration right? Because curved space time will be the nature as we know it and so as the body moves through it, there is really no change in space or time. So in a way, our brain is biologically limited to perceiving reality as Euclidean and that is why curved spacetime is perceived by us as acceleration? )

Whether the above is right or not, my basic QCLOU even at a more fundamental level is this. Newton formed his three laws of motion to explain Galileo’s measurements and put them in a formal framework. In Galileo’s experiments, as a body rolled down the slope it was always acted on by the same force (its weight), and the effect was to make it constantly speed up. ( from A brief history of time by SH). So in a way Newton's laws were based on the notion of gravity as a force and then he generalized that to any force, including the one you and I can apply to a body at rest to make it to move etc. With Einstein refuting that fundamental assumption, is there a new set of axioms on which fundamental laws of physics are framed after Einstein or we still use piece parts of Newton?

Sorry, shankarank, this is getting into more physics than music..but hopefully it is only a small detour.
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shankarank
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#15 Re: The Point - Extension conundrum

Post by shankarank » 13 Mar 2016, 10:46

https://www.youtube.com/watch?v=s06_jRK939I explains it succinctly in a short video - how the detection mechanism works.

Briane Greene's books are a good read - especially for people outside the area of expertise.

As regards the connections I drew - the one that treats a swara as an extension rather than a point is not an analogy - as frequency is just as valid a physical quantity as much as space ( positions of particles ) is. Hence the concept is seminal to any measurable quantity.

Whereas the curvature caused by mass Vs the weightiness of extended swaras is just analogy - the weightiness of music is just an attribute - a particular way of intonation is say pregnant with musical expression.
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shankarank
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#16 Re: The Point - Extension conundrum

Post by shankarank » 13 Mar 2016, 10:51

Here is the discussion on the beauty aspect of it:

http://www.thehindu.com/opinion/op-ed/f ... 290056.ece
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shankarank
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#17 Re: The Point - Extension conundrum

Post by shankarank » 13 Mar 2016, 11:20

The more fundamental argument I want to pursue is - by choosing to make them extensions did Indian music transcend the infinities ( equivalent of singularities in physical theories) caused by the cycles of fifth ( Cantor set?) etc?

By being obsessed with the point position of a pitch - did Western music make an irrational choice ( pun intended) by resorting to the equi-tempered scale using the "12th root of 2" factor? Can we call them Kriya centric?

Conversely can we call Indian musical systems viSrAnti centric and assert our difference more philosophically?
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shankarank
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#18 Re: The Point - Extension conundrum

Post by shankarank » 14 Mar 2016, 09:31

SrinathK wrote:It is both infinitesimal and infinite -- more than everything and less than nothing.

Does this start sounding familiar to you?
Are you implying the bindu-nAda tatva? your being more a Zen now :)

nAda bindu kalAdi namO nama - tirupugazh.

http://www.youtube.com/watch?v=vRFdbCDK1jc - the way MSS sings slightly off beat - (Minus) the way we all ordinary mortals sing = Carnatic music. What a verve and comfort with the flow!

Carnatic music is created when the nAda obscures and obfuscates the bindu!

Also:
bindu nāda vaśaṅkari śaṅkari ( kriti : ambA nIlAyadAkshi )

SrinathK wrote: By the way, S and P can have some gamakas on them -- the jaaru and the vibrato are two of them. The usage however does not compromise on their fundamental positions and only a vibrato can be sustained on them for any length of time.
Now we have to distinguish the Sruti - S vs the swara S then? That distinction is then applicable to all other note positions ? - but then as Srutis they can be only be the Adhara Sruti of a graha bEda not the full swara by themselves ?
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Nick H
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#19 Re: The Point - Extension conundrum

Post by Nick H » 14 Mar 2016, 14:32

shankarank wrote:By being obsessed with the point position of a pitch - did Western music make an irrational choice ( pun intended) by resorting to the equi-tempered scale using the "12th root of 2" factor? Can we call them Kriya centric?
Isn't it more chord-centric? Haven't the intervals in Western music evolved so that notes sound good when harmonies are involved?
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shankarank
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#20 Re: The Point - Extension conundrum

Post by shankarank » 14 Mar 2016, 21:58

Chord-centric is still usage of 3 kriyAs instead of just one.. but not a continuum? Well you could say CM is chordified naturally ( and statically) with S - P - <the other note> can't you? :lol: Plus the tampura produces other notes like R, G etc!
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#21 Re: The Point - Extension conundrum

Post by Ramasubramanian M.K » 17 Mar 2016, 05:18

Acknowledging that the above discussion is beyond my "pea-brain" I am reminded of the late Veena Dhanammal's quote about the Lec dems/discussions at the Music Academy during the December season( MA was started in the late twenties and Dhanammal died in 1938 so that she may have been privy to not more than 10 seasons:
Adu Ennanga academi le sangeethathai patri pesarangalame --adile pesarathukku enna irukku".
I am not against the scientific enquiries into Music but all these refinements cannot make up for lack of conditioning of the ears to note the subtleties. Knowing that the Sa Ga(anthara gander)Ma(suddha Madhyamam) Pa relationship as a 1:1.25:1.33: 1.50 frequency ratio relationship does not in any way help me enjoy Bahudhari or Nagaswarali better. But it helps me in understanding WHY the Ga in Sankarabharanam has LESS latitude than in Kalyani which has the same Gandhara. HOW: The interval between Ga and Suddha Ma(in Sankarabharanam is one-twelfth of the base Sa-- too narrow to permit oscillations wheres in Kalyani the prathimadhyamam is further apart and hence the liberty in 'asaippu" of Ga in Kalyani.
Likewise the occasional prayogam of a note below the Suddha Daivatam in Panthuvarali or Saveri(attempted by GNB in his raga alapanas ) is equally enjoyable without one knowing that the Dha is Ekasruthi Daivatam!!


In my younger days brash as I was ,once I asked Musiri Mama about these technicalities-Typcal of that generation's attitudes,he asked me "Therinju enna Ahanam(Why do you need to know) implying that would the explanation help one better in enjoying the music?

I do not want to be misconstrued as against the spirit of scientific enquiry--i it enhances one's listening pleasure so be it!!!
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#22 Re: The Point - Extension conundrum

Post by RaviSri » 17 Mar 2016, 18:26

Likewise the occasional prayogam of a note below the Suddha Daivatam in Panthuvarali or Saveri(attempted by GNB in his raga alapanas ) is equally enjoyable without one knowing that the Dha is Ekasruthi Daivatam!!
MKR, in Saveri not just the dhaivatam, but in certain prayogas the gandharam and nishadam too have a lower value than its so-called parent mela Mayamalavagaula. This is how Brinda-Muktha sang 'Sri Rajagopala'. In the pallavi itself the nishadam is at a very much lower sruti. Subbarama Dikshitar in corroboration says in SSP in the Saveri section that the gandharam and nishadam are very much lower. 'eppDiyenrAl, gAndhArathai sAdhAraNa gAndhAra stAnathilum, niShAdathai kaishiki niShAda stAnathilum piDikka vENDum'. Not only this, throughout that song the prayoga DNDP occurs, both in the Dhanammal family version as well as in the SSP. Tiger, once at the end of an acrimonious ragha lakshana discussion at the Academy, sang Saveri with SRGMPDNS intact and remarked, 'enga ammA (meaning Dhanammal) ipDitAn pADuvA. idula sAvEri irunduda illiyA?' These old lakshanas have been shaved off from Saveri in order to attach her to Mayamalavagaula intact by the latter day musicians. This has happened to a lot of other ragas like Begada, Reetigaula, Sahana etc.

It is also worth mentioning that the rishabha is almost the ShaDja itself. S.Ramanathan used to say, 'sAvErila, sA vE ri'.
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shankarank
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#23 Re: The Point - Extension conundrum

Post by shankarank » 18 Mar 2016, 09:59

Sri MKR - decades of such discussions ended up with a conclusion by one Musicologist that Mridangam is not music. Once we reach that kind of a conclusion - then one should expect all hell to break loose! :lol:

I also used that line (of Dhanammal) in another long post in this section in reply to 'bombal' ( I presume Bombay Sri Balaji - what I gather from rest of his posts) - who made a similar quotation sourced from PMI. You are welcome to refer back.

Once that is said - the musicologist's writings become data - and concerned others like me become processors. Previously us rasikas were data for him!.

You know, they ( the dukkrinkaraNes sitting in Chennai) should send a naivete Phd student of theirs to spend time with long time rasikas like you and Dr VKV to observe you all listen to music driving in the quite mountains of Poconos or New Mexico. And any knowledge produced should have acknowledgments and the publications should list your name too!! Your embodied knowledge is not just data for them and you are not some rats under a microscope. Subjectivity is always bandied about - but then there is something called shared cultural experience where there is a good agreement among many as to what is good music - that then transcends that somewhat.

And as regards the primacy of people like you over a Mylapore Sabha goer - Chennai is a noisy place ( figuratively I mean - there is too much noise baggage to filter out) and the passion towards things musical from being far away makes it special!!

Connoisseurs have not been made part of the study. Your mileage with Spool tapes should count for something.

Ravisri, happy to see heavy weights back posting. The word ViSrAnti, was an education from you long back in the older forum and it kind of explained my experiences as a rasika up until that point. I didn't quite get a chance to acknowledge that - now I do. I could then make sense of why I liked a bEgada varNam as a teenager ( with only a sketchy knowledge of music) rendered by TNS in a thatched roof pandal in a corner of a large plot with thorny bushes in madipAkkam (or nanganallur) about late 80s/ early 90s - with scratchy audio at best!.
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#24 Re: The Point - Extension conundrum

Post by arasi » 23 Mar 2016, 09:51

Your teenage recollections brings no less an ambiance than the vintage stuff an MKR tale conjures up! There is quite a bit of "shared cultural experience' there!
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#25 Re: The Point - Extension conundrum

Post by shankarank » 08 Jul 2016, 09:26

In the dhanyAsi rAga Alapana of Dr BMK that varsha posted in Sangita Kalanidhi 2016 thread

https://archive.org/details/04TArakaman ... halaRAmdAs

- at around 05:20 - 05:37, 05:47 etc. the brighas when looked at from kAveri delta perspective do have a dissonance ( bit of a pisuru). Something more evident with Dhanyasi.

But then he is true to his own words as he explains in his voice culture : https://www.youtube.com/watch?v=3ccGhf4Y-cw at 07:30 thru 08:37 that each note should stick on to its sruti even in fast brighas. Obviously he sees them as points whereas rest of the carnatic world sees them as extensions and smoothen them out!

His carnaticism is heavily in the laya faculty more than the melodic approach.
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