What is chatusra tisram?

Tālam & Layam related topics
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vasanthakokilam
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Post by vasanthakokilam »

I understand now. msakella, balaji and mridangamkid are all saying the same thing (msakella does not agree with the term 'chathusra-tisram' and provides a much clearer label. )

What nmn wrote in post #18 which I expanded upon in post #21, is not chathusra-thisram but the regular gathi switch. This is what Arun also opined.

( I think Balaji will take back his preface in post #19 'nmn you are right ...' when he gets a chance to revisit this thread ).

mridangamkid, I assume your demos are consistent with what wrote in your post #29. Post #29 and akellaji's use of the word 'break' helped me see that you three 'm's ( msa, m and mk ) are stating the same thing. ;)

I like msakella's distinction

"units running in each Kriya should be called Gathi "
"the units running in each break should be called Nadai"

Even if this distinction is not universally recognized, in normal gathi switches the two units are the same and hence the two terms mean the same thing.
And in this chathusra-tisram case, the units are different and let us use the distinction and call it as akellaji did: Chaturashra-gati-trisra-nadai

So the terminology for the sequence for the switch and back will be as follows if I understood akellaji right

Chaturashra-gati-Chaturashra-nadai
Chaturashra-gati-trisra-nadai
Chaturashra-gati-Chaturashra-nadai

We will treat chathusra thisram just as a short hand way of saying 'Chaturashra-gati-trisra-nadai'

( I am completely un-confused now.. I am coming after anyone who manages to change this. :) )

vasanthakokilam
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Post by vasanthakokilam »

Hope this picture captures the main idea

Image

msakella
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Post by msakella »

Dear brother-member, vasanthakokilam, If you go through the following step-wise definition you can very easily understand the inconsistency of our bother-member, mridangamkid.
Chaturashra-trisram: 1. Say ‘thakita’ - 3 syllables four-times arriving at 12 syllables in Rupakam. 2. Among them make the ‘tha’ only audible and the remaining ‘kita’ inaudible. 3.Thus, you can pronounce four ‘thas’ only.
Chaturashra-khandam: 1. Say "thadhiginathom"- 5 syllables twice arriving at 10 syllables in Khanda-chapu. 2. Among them make the ‘tha’ only audible and the remaining ‘dhiginathom’ inaudible. 3. Thus, among the two ‘thas’ we have to accommodate four ‘thas’ in double the speed.
Even your diagram does not suffice. So, I have made the following modifications with the help of figures as I am unable to draw a diagram I require. amsharma
1 - - - 1 - - - 1 - - - || - 3 beats and 4 in-between spaces of Rupaka-tala-Chaturashra-gati.
1 - - 1 - - 1 - - 1 - - || - 4 beats and 3 in-between spaces of Trisra-nadai.
1- - - -1- - - - 1- - - -1- - - - || - 4 beats and 4 in-between spaces of Chaturashra-nadai.

vasanthakokilam
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Post by vasanthakokilam »

akellaji: I did not realize the nature of step 3. I should have caught on to that based on what you wrote in post #30.

Please see if this picture is same as what you depicted.

Image

sr_iyer
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Post by sr_iyer »

Leaving aside the technical correctness of the nomenclature "chaturashra tishram" for the moment, since one of the questions was with regard to pallavi rendition, I would like to add:

If the pallavi takes 1 Avartanam in the base speed (in chaturashra gati),
rendering the pallavi once in the chaturashra tishram formulation makes it stretch to 1.5 Avartanams

(Note: the chaturashra tishram formulation discussed in the posts above divide 'each tishra group recited in chaturashra gati' into four units -- an alternative used is to divide 'each tishra group recited in chaturashra gati' into two units -- note that this is just a kAla variant of the formulation discussed in previous posts, where changing kAla induces speed variations in geometric progression by factors of 2)

Hence, for a pallavi defined in base speed of chaturashra gati, performers render the pallavi _twice_ in chaturashra tishram formulation for it to integrally span eDuppu to eDuppu (in 3 Avartanams).

Singing the pallavi in tishra gati on the other hand would require 3 iterations for it to span eDuppu to eDuppu (in 4, 2 or 1 Avartanas of tALa reckoning, depending on kAla of tishra gati. In many cases, artistes use the tishra gati such that 3 iterations in tishra gati occupy 2 Avartanas of tALa reckoning. Sri TNS has shown all the kAlas of tishra gati in some of his multi speed pallavi renditions)

Chaturashra tishram creates an illusion of changing from chaturashra gati to tishram, while actually this is effected using tishra-groups and factor-of-two divisions thereof in chaturashra gati itself - it is easy to see that for certain chosen kAlas in each formulation (chaturashra tishram and tishra gati), the speed scaling factors for chaturashra tishram would be 0.75 and that for tishra gati would be 0.6667, while the time scaling factors for these two formulations would be 1.5 and 1.33 respectively. These factors for the two formulations, which may be quite close, require accurate calibration of tALa reckoning to readily identify the formulation or perceive the difference in formulations, especially in live concerts without replays :-)

The chaturashra tishram formulation is useful in certain eDuppus where tishra gati transition may be difficult (if not impossible)

2 kaLai pallavis with eDuppu of samam (0-skew), arai (1/2 beat skew) etc are conducive to easy changeover to tishra naDai. For 2 kaLai pallavis that have 1/4 or 3/4 type of eDuppus, or 4 kaLai pallavis that have 1/8, 3/8, 5/8 or 7/8 eDuppus, it is difficult to change to tishra-gati, except to use the fastest kAla of tishra-gati. In such cases, chaturashra tishram is useful.

-----
Asides: Of course, there is another style of transitioning to tishra gati in a chaturashra gati pallavi, where each speed transition occurs from arudi to arudi, in which case the fractional eDuppus cited above do not prove challenging, assuming that the arudi is right on the beat that starts off the uttarAnga of tALa (which only in the rarest of cases like some of Mali's pallavis is not the case, where there is a small skew between the beat and the kArvai that marks the musical-arudi)

We have discussed a pallavi set in chaturashra gati in its basic form, and with this, the difference between chaturashra tishram (not a gati variation) and a genuine gati transition to tishra gati. In some pallavis sung by GNB and TRS, the pallavi is in tishra gati in its basic form and they transition to chaturashra gati (the genuine gati transition).
Last edited by sr_iyer on 06 Sep 2009, 13:58, edited 1 time in total.

msakella
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Post by msakella »

vk - Very nice. This absolutely depicts our problem. Thank you. This can only be justified by naming it after ‘Chaturashra-trisra-chaturashram’ but not ‘Chaturashra-trisram’ at all. amsharma

arunk
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Post by arunk »

I now see the difference and perhaps not surprisingly this all boils down to the same 2 different kinds of switching from a true catusra/quaduple pattern (i.e. 1,2,4,8, ...) to something that is a tisra/triiple pattern (1,3,6...) - which we have discussed umpteen times in the forum earlier. That it STILL took so many posts, and still IMO may not be simple to digest for most folks (me included of course) is one of the many things I personally find frustrating about tala and laya related issues in CM!! It is one of the reason laya related topics turn me off almost instantly (except for occasions like this) - but this could be just my problem!

I can see why there is a need to differentiate "catusra-tisram/catusra-tisra-catusram" from "tisra gati" . For example, even aside the more obvious case of varnams and pallavis, even regular krithis switch to something like this - albeit very locally as in within an avarthanam (say 32 = 9*3 + 5, or 24 = 3*8 or 6*4). Considering these local variations as true gati switches is bizarre.

However, if this switch to a triplet grouping is NOT too localized, I fail to see why this is NOT a tisra gait from a pure rhythmic (laya) standpoint. If the song switches to a triplet grouping for say an entire sub-portion AND the rhythm matches it as such, isn't it in tisra gait in that portion? Note that i am purposely using the word gait here in the true rhythmic sense and not the cm specific restricted meaning implied by the above posts. From this viewpoint, addition extra connotation to the word "tisra gati" thus disallowing its use to this (or differentiating with naDai which means exactly the same as gati in the literal sense) - seems to only add more confusion to the mix.

I think the root of the problem is the use of words like gati and naDai to mean something different or more than what they intuitively convey. It could have been say tisra blah vs. tisra blih and we may not be in the same boat :) !!!

Arun
Last edited by arunk on 06 Sep 2009, 19:12, edited 1 time in total.

Nick H
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Post by Nick H »

Maybe "what do people mean when they say..." is more appropriate than "what is..." for this kind of question.

The fact that "technical" terms are banded about between rasikas doesn't mean to say that we use them "correctly". Even musicians and teachers belonging to different schools have different definitions and understandings. The absolute can be hard to come by!

vasanthakokilam
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Post by vasanthakokilam »

Thanks sr_iyer for the elaboration. Makes perfect sense. This following point of yours is worth highlighting: To get in sync with the thala avartha, it will take 2 repetitions in chathusra-thisram and it will take 3 repetitions with regular thisram.

Until shown otherwise:

Let the picture in post #35 be the correct pictorial representation of what is commonly called chathusra-thisram, now that it has been approved by msakella and commented on further by sr_iyer.

Arun: See if you caught on to the 0.75 and 0.6667 differences in sub-beat duration between chathusra thisram and the regular tisram. This 0.75 is indeed different from the numerous other discussions we have had in the past.

arunk
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Post by arunk »

I am not saying there is no difference - there is certainly difference although this seems exactly what we have discussed (inner-division changes vs. inner division does not change). 0.75 => 3/4; 0.66 => 2/3 i.e. 4/3 normalized to < 1. I do believe it is still the same as what we have discussed before.

My gripe is entirely with confusing terminology which stems from overloading of well known words. But I also realize this is somewhat unavoidable in languages or lingo.

Arun

vasanthakokilam
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Post by vasanthakokilam »

Arun:

Your point about confusing terminology is understood and acknowledged. Going beyond that,

- Our previous discussions were definitely about "inner-division duration changing vs. inner division duration not changing".
( My picture in post 33 is not correct for chathusra-thisram. That does illustrate a case of inner division duration not changing but that is probably something else, not pertinent here.
I was a bit confused about your statement "(say 32 = 9*3 + 5, or 24 = 3*8 or 6*4). Considering these local variations as true gati switches is bizarre.". That gave the impression that you
are interpreting such local variations as chathusra thisram . It turns out that is not the case )
)

- What I felt new is within the domain of 'inner-division duration change'. We have two different changes, one is chathusra thisram ( 0.75, 1.5 etc. ) and the other is regular thisram ( 0.667, 1.33 etc. )

- And you also talk about 'triplet' grouping in relation to gait. The idea here is not to change the inherent grouping in the song but to sing it as is, using the new sub-division duration. This grouping business is just a mathematical device to arrive at the right sub-division duration.

Just want to sure all loose ends are tied up...

I think we are on a convergence on chathusra-tisram which is quite remarkable given the history of discussions on gathi related topics :)

=================================

Now, here is where there may still be a disconnect among many of us. ( may be not but let us explore, being in agreement for too long is no fun ;) )

- Though that difference of 0.75 vs 0.667 may seem academic when viewed strictly in numerical terms, I think the logical derivation ( how we got to .75 ) and the resulting aesthetics make them two distinct things.

- With thala beat remaining constant, it still makes sense to keep two things separate:

1) The gathi of the thala resulting in one inner division - this remains the same unless indicated explicitly by a kriya change
2) For a given gathi, a different inner division is employed while singing. This does not imply a gathi change. Also this is different in magnitude from a 'power of 2' kAlam change of the gathi.

It looks to me that keeping these two concepts separate has musical value.

If I am cornered to answer why it has musical value, my answer would be along these lines. It is about 'inner division frame of reference'. Musical aesthetics and frame of reference have a lot to do with each other. ( In melody, resolution is about consonance and in rhythm it is about stress alignment ). Getting out of resolution so you can get back to resolution is one aspect of musical aesthetics.

If you buy into the above distinction, then you can see that item 2 provides for another level of 'getting away from resolution', affording possibilities of different resolution schemes resulting in different aesthetics.

msakella
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Post by msakella »

Accordingly even to the 2nd variety of the 29th post of mridangamkid it justifies if it is named after ‘Pakshini-gati-khanda-nadai-dviguna-chaturashra-nadai’ just like 'tilakaashtha mahishabandhanam' of Tenali Ramakrishna. amsharma
Last edited by msakella on 07 Sep 2009, 07:04, edited 1 time in total.

vasanthakokilam
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Post by vasanthakokilam »

This is probably a case of me not knowing when to stop. The mathematical curiosity got the better of me, especially after msakella termed this C-T-C

C-T-C involves three steps:

the C step which yields 1/4
the T step which yields 1/4 x 3
the C step which yields 1/4 x 3 x 1/4
to yield a subdivision duration of 3/16 which is indeed 75% of the chathusra duration which is 1/4

If Chathusra Khanda is Chathusra Khanda Chathusra, then it is C-K-C to yield ( 1/4 x 5 x 1/4 = 5/16 ) as the sub-division duration

Extending further,
thisra - khanda - misra - 5/21
chathusra - thisra - khanda - 3/20
khanda - thisra - chathusra - 3/20 ( same as C-T-K )
khanda - thisra - khanda - 3/25
misra - khanda - chathusra - 5/28
etc.

===================

Generalizing the above, and without consideration for human possibility or musical aesthetics:

It is P-Q-R where P, Q, R can each be { 3, 4, 5, 7, 9 }

That gives 125 possible combinations but not all of them yield unique sub-division duration values.

The sub division duration, expressed as a fraction of the thala beat duration is Q / ( P x R ).

P x R yields 15 unique possibilities: 9, 12, 15, 16, 20, 21, 25, 27, 28, 35, 36, 45, 49, 63, 81

Combining this with the 5 possible values for Q reduces our possibilities to 75 fractions

But there are 20 duplicates among the 75.

That brings the number of unique sub-division durations to 55.

This 55 includes the base gathi ratios of 1/3, 1/4, 1/5, 1/7 and 1/9. So if we exclude those, we have 50 extra possibilities for subdivision variations

====================

Here are the low, middle and high... for sub-division duration expressed as a fraction of the beat duration ( I did not want to burden you all with all the 55 )

0.037037, 0.047619, 0.0493827, 0.0612245, 0.0617284,...............

0.16, 0.178571, 0.183673, 0.185185, 0.1875, 0.190476, 0.194444, 0.2, 0.238095, 0.25,.................

0.45, 0.466667, 0.555556, 0.5625, 0.583333, 0.6, 0.75, 0.777778, 1

msakella
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Post by msakella »

vk - Excellent elaboration. Very nice indeed. amsharma

vasanthakokilam
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Post by vasanthakokilam »

akellaji: Thanks.

Let me push my luck and offer the general model, again setting aside considerations of human possibilities and aesthetics. I will leave the derivation as an exercise to the reader ;) ( I will post the derivation details if some of you want to see it )
==========
For a genuine Gathi Switch: Let O be the original gathi and N be the new gathi . Both O and N can take values { 3, 4, 5, 7, 9 }

A switch from O to N requires 'N' repetition of the pallavi line to get in sync after 'O' tala cycles. The subdivision duration switches from 1/O to 1/N
e.g 4 to 3 switch requires 3 repetitions of the pallavi line to get back in sync after 4 thala avarthas
5 to 9 switch requires 9 repetitions of the pallavi line to get back in sync after 5 thala avarthas
etc.
==========

A switch from O to P-Q-R requires P x R repetitions of the pallavi line to get back in sync at O x Q thala cycles. The subdivision duration switches from 1/O to Q / ( P x R )

e.g 4 to 4-3-4 switch requires ( 4 * 4 = 16 ) repetitions of the pallavi line to get back in sync at ( 4 * 3 = 12 ) thala cycles: 4 Repetitions in 3 thala cycles
9 to 3-5-7 switch requires ( 3 * 7 = 21 ) repetitions of the pallavi line to get back in sync at ( 9 * 5 = 45 ) thala cycles : 7 Repetitions in 15 thala cycles.
3 to 4-5-7 switch requires ( 4 * 7 = 28 ) repetitions of the pallavi line to get back in sync at ( 3 * 5 = 15 ) thala cycles : 28 Repetitions in 15 thala cycles
etc.
==========

sr_iyer
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Post by sr_iyer »

VK: Good work at modelling. I would make a minor modification in your statement (already captured BTW in your examples) as:

A switch from O to P-Q-R requires (P x R)/(HCF of O and P) repetitions of the pallavi line to get back in sync at (O x Q)/(HCF of O and P) thala cycles.

HCF of course is the highest common factor (aka the greatest common divisor, GCD)

One minor advantage of readily getting the tala Avartanas thusly is to work out other permutations in presentation -- e. g., in the common way of singing the 'chaturashra tishram', we have mentioned it takes 1.5 tala Avartanas to sing what could be accomodated in one avartana of base-speed rendition of pallavi. This is equivalent to 4 to 4-3-2 switch as per your model. Now, an option is to sing the 'chaturashra tishram' twice to accomodate 3 avartana cycles as I mentioned earlier. Another option is to sing 'chaturashra tishram' once, followed by a single iteration of double-speed rendition of pallavi (this double speed or second kAla would account for 0.5 Avartana). This 1.5 + 0.5 avartanams yields back an integral number of cycles. For added effect, the pallavi can be rendered thrice in the double speed, yielding 1.5+0.5+0.5+0.5 again yielding the integral number of cycles. (I must add that these formulations have been used by master performers)

vasanthakokilam
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Post by vasanthakokilam »

sr_iyer: Adding the GCD makes it solid. Thanks. As you wrote, I used the GCD to reduce the results to the basic form in the examples.

What you say about different ways of getting to the integral number of cycles makes sense.
Your example would amount to one repetition of 4 -> 4-3-2 followed by 1 or 3 repetitions of 4 -> 4-4-8 ( so to speak )

Nick H
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Post by Nick H »

(sometimes I wish I was good with numbers)

Tangentially, I was reading an interview with Delia Derbyshire the other day. She was a pioneer of electronic music, and, among many other things, created the actual sounds for the Dr Who theme tune.

She spoke of the passion for creativity that she had had all her life, and that, with such a passion, it was necessary to have a discipline. She said that, as disciplines go, numbers make a pretty good one!

(sorry to interrupt)

gn.sn42
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Post by gn.sn42 »

sr_iyer wrote:Another option is to sing 'chaturashra tishram' once, followed by a single iteration of double-speed rendition of pallavi (this double speed or second kAla would account for 0.5 Avartana). This 1.5 + 0.5 avartanams yields back an integral number of cycles. For added effect, the pallavi can be rendered thrice in the double speed, yielding 1.5+0.5+0.5+0.5 again yielding the integral number of cycles. (I must add that these formulations have been used by master performers)
This does open up a number of possibilities. Do you know of compositions where such variations have been explicitly coded, or is this purely a pallavi/ musician's performance thing? The reason I ask is we can imagine a long and complicated pattern of such changes, with multiple levels etc., that add up to a musical effect in a way that is difficult to pull off ex tempore. (And with the composition fixed, I can further imagine some interesting cross-rhythm games will be played by the musicians, compulsively creative as they are.)

sr_iyer
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Post by sr_iyer »

The generic possibilities could be independently worked out and then applied to the pallavis, rather than work out the possibilities on a per-pallavi basis.

To get familiar with the possibilities, one could start practising them on simpler pieces like varNams or even varisais. Many may know of the following ways of applying such forumations, but even so, I would state them as follows.

The key practical thing in 4-3-2n formulation is to tighten the kAlapramANam.

E. g. consider the first sarali varisai which is simply the ArohaNam and avarOhaNam of a krama sampURNa rAga (say mAyAmALavagauLa). In order to get a feel of chaturas'ra tis'ram + double speed for pallavi rendition that I referred to in post 47 in the context of pallavis, one could begin by singing this varisai as:

s,, r,, g,, m,, p,, d | ,, n,, s',, | s'ndpmgrs ||

(To establish a frame of reference for timing, you could take this up after singing the varisai as
s, r, g, m, p, d, n, s', | s', n, d, p, | m, g, r, s,|| which in turn can be sung after its immediately lower speed if felt useful)

Here the ArohaNa krama is in the 4-3-1 model and the avarOhaNa krama is in 4-4-4 model (as per nomenclature of akellaji and vk)

This would stabilize one's sense of kAlapramANa while giving tis'ra kArvais (elongations or pauses of three) without speeding up. All saralis can be sung this way. The phrases in the ascent could be sung in tis'ra kArvai formulation and the descent could be in normal double speed.

E. g.
s,, r,, s,, r,, s,, r |,, g,, m,,|s,, r,, g,||
, m,, p,, d,, n,, s',, | s'ns'ns'ndp| s'ndpmgrs||


Next, each of the sapta tALa alankAras could be taken up.

I am not going to notate wrt the angas of the tALa, but just to give an idea in dhruva tALa (note: each cluster of triplets will not align with each Avartana but the close of the alankAra will bring us back to integral number of Avartanas)

s,, r,, g,, m,, g,, r,, s,, r,, g,, r,, s,, r,, g,, m,,
r,, g,, m,, p,, m,, g,, r,, g,, m,, g,, r,, g,, m,, p,,

so on until

p,, d,, n,, s,, n,, d,, p,, d,, n,, d,, p,, d,, n,, s',,
Then immediately followed by
s'ndpdns'ndns'ndp
ndpmpdndpdndpm
so on until
mgrsrgmgrgmgrs

The end of the alankara should bring it back to an integral number of Avartanas.

If one can sing all the alankaras this way in a tempo tight way (without speeding up the groups of 3), one can proceed to the 4-3-2 model. An initial practice would be to sing second speed of varisais in 4-3-1 for ascent as well as descent, instead of the composite manner as indicated above )

Then, one could render the entire pUrvAnga of varNam in 4-3-2 for practice (instead of the composite 4-3-1 followed by 4-4-4 indicated above)

To start with, take a varNam which starts with a kArvai of 2 (or multiples thereof) - e.g the popular Adi tALa varNas in mOhanam, vasantA, s'ankarAbharaNam, s'ahAnA, madhyamAvati etc. It is then easier to transition into 4-3-2 by stretching the starting note - say of 2 units to 3 (note: in the 4-3-2 model, kArvais of 2 get stretched to kAravis of 3). Once the mind stabilizes that speed, it is easy to include a divide-by-two split for the successive notes that may have single unit durations or odd multiples of single unit. (It is difficult initially to accurately stretch 1 to 1.5, and easier to calibrate by having to stretch 2 units to 3, use the resultant speed to split the odd-unit-durations dyadically to the resulting fractional ones -- this is an aspect that will be obvious upon practice)

These are practice exercises for the 4-3-2n alone. Note that 4-3-4 would pose greater practical challenges to maintain kAlapramANam and it may be prudent to stop with 4-3-2 for musically aesthetic reasons.

(There are many practice exercises for 'genuine' tis'ra gati variations, both with monolithic speed and composite speed at Avartana level, which I will not get into in this post since it is already getting long)

_______

Equipping oneself thus, any pallavi in chaturas'ra gati lends itself to generic exercises such as the transition to 4-3-2 or 1.5+0.5 Avartana formulation.

There are also specific advantages certain pallavis may offer. In case of chaturas'ra gati kAla variations, one may have observed the pallavi that has its pUrvAnga as nI padmulE gatiyani nammiti as sung in khaNDa tripuTa is conducive for a fractal effect.

[This pallavi structure can be understood as take off point after 1/2 beat corresponding to two inner units - the numerals in parentheis below are wrt these inner units:

; nI(3) pa(1) da (1) mu(1) lE (3) ga(1) ti(1) ya(1) nI (3) nam(2) mi(1) | ti (arudi) ]

The end-point of nI padamulE bisects the entire pUrvAnga (9 units out of 18 units that are there from eDuppu to arudi start) and hence can be used for a speed change. It can be sung as nI padamulE in first tempo followed by nI padmulE gatiyani nammiti in second tempo to land at arudi. The next progression is to sing it as nI padamulE in first tempo followed by nI padamulE in second tempo followed by nI padmulE gatiyani nammiti in third tempo to land at arudi.

Coming to similar formulations in 'chaturas'ra tis'ram' :
A pallavi with even-unit-kArvais will be easier for chaturas'ra tis'ram, but this is not a hard requirement. In a case of a pallavi where an aesthetic bisection point can be identified in pUrvAngam, it is possible to effect the 4-3-2 to normal double-speed transition (or the reverse) at the bisection point to include the composite speed effect in the pUrvAngam itself. Of course, the generic method of rendering complete pallavi (pUrvAngam +uttarAngam) in 4-3-2 followed by complete pallavi in normal double-speed can be performed irrespective of presence of an aesthetic bisection point in the pUrvAngam of pallavi.
Last edited by sr_iyer on 09 Sep 2009, 16:24, edited 1 time in total.

gn.sn42
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Post by gn.sn42 »

sr_iyer, thanks - the varisai example is helpful to clarify the process; and the note on the pallavi helps point out some interesting possiblities. I'll think about these and look for examples as I'm listening.

I still am intrigued by the potential use of this technique in composed music - there should be some interesting things that can be (or perhaps have been) done here.

sr_iyer
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Post by sr_iyer »

I agree with you that use of these possibilities in precomposed music (without or with sAhityam) would be enriching. Of course, gatibhEdam has been used in compositions of pApanAsam s'ivan and UttukkADu (and Sri BMK in his gatibhEda tillAnA). We know about iDadu padam starting out in caturas'ra gati and transitioning to tis'ra gati in caraNam (tiruvaDiccilambugaL) and grouping the inner tis'ra gati units into fours in the line starting dhimi taka tarikiTa in caraNam. I am not aware of 4-3-2n in composed music -- jatiswarams, tillAnas and orchestral pieces can (and perhaps have been, as you say) fruitfully employ the more complex techniques (not restricted 4-3-2n). Requires good performer(s) to ensure that melody is not compromised due to rhythmic complexity. Of course, many tani (percussive) employ complex multilayered concepts. With respect to the multispeed possibilities we spoke about, a lot of performers have used the melodic material in varNams to present it in different speeds in varied ways, sometimes compositing varied speeds within each Avartana. E. g. Mali presenting viribONi or ninnukOri in caturas'ram + slow tis'ram + fast tis'ram in each Avartana. I have also heard some ciTTasvaras in BMK's renditions introducing gatibhEdams to tis'ram, or his rendition of select lines of his tillAnas (e. g. kuntalavarALi) in multispeed renditions including slow and fast tis'ra naDai.
Last edited by sr_iyer on 09 Sep 2009, 15:52, edited 1 time in total.

vasanthakokilam
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Post by vasanthakokilam »

sr_iyer: Excellent write up. Though I had the math worked out, until I tried your basic sarali varisai I did not appreciate the aesthetics. Now I realize why you wrote earlier that this chathusra thisram is a tisram illusion. When I tried the basic saraLi exercise, I could get the syncopation effect when all I was doing was triple speed chathusra swara lengths ( grouped in thisra kArvai of course ). I felt it is a grade easier than the genuine thisram.

BTW, to keep my thoughts right, please see if the following is correct for your basic saraLi exercise in the O -> P-Q-R notation

Initially, both Aro and Ava is : 1 -> 1-1-1 ( subdivision duration = 1 / ( 1 * 1 ) = 1)
The 3/4th avartha would be: 1 -> 4-3-1 ( subdivision duration = 3 / ( 4 * 1 ) = 3/4 )
The 1/4th avartha would be: 1 -> 4-4-4 ( subdivision duration = 4/ ( 4 * 4 ) = 1/4 )

( You already provided the P-Q-R for the last two )

This is definitely a very minor thing but a doubt nonetheless. When you wrote "to get a feel of chaturas'ra tis'ram + double speed,", did you actually mean to say "to get a feel of chaturas'ra tis'ram + triple speed"? Triple with respect to the starting point which was one solfa syllable per beat to that 1/4th avartha being in 4 solfa syllables per beat.

Question on your excellent write up on "nI padamulE".

>nI padamulE bisects the entire pUrvAnga (9 units out of 18 units that are there from eDuppu to arudi start)

If the eDuppu is 1/2 beat, how did you get 18 units from eDuppu to arudi start? I know you wrote before that chathusra thisram is easier than regular thisram for non-samam eduppu pallavis, I realize I am missing something, so I thought I will ask. Thanks.

sr_iyer
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Post by sr_iyer »

Reference your question on pallavi --

Consider the pallavi rendered in 2 kaLai (note: had abstracted out this kaLai instantiation in post 51 to keep things generic). Each beat has two kaLai subdivisions and each kaLai subdivision has two inner units in slow duration (this is the duration quantified in my break-up). So 1/2 beat skew works to 2 such inner units. Adding 2+18 yields twenty inner units in slow duration which is associated with the khaNDa jAti laghu. In this case, actual tis'ra gati would be easy. This is because the 1/2 beat skew starts on the kaLai subdivision-beat upon which it is easy to start a ta-ki-Ta genuine tis'ra gati. In practice, when an even number of units is available to start the pallavi line, psychologically, a performer uses the easy tis'ra kArvai in 4-4-4 domain he currently was in, to start uttering the first syllable during transition, then back project this duration using his conception of musical/rhthmic proportions in the pallavi line, to scale any subsequent odd-units into 4-3-2.

Just to clarify on the fractions posing challenges to genuine tis'ra gati...

In a 1 kaLai, a 1/2 beat skew makes it difficult to transition to tis'ra gati (except for the fast tempo thereof-- in the absence of a demonstrable medium, I use subjective terms like 'fast' :-) --- you can use the following example to extend the understanding to the other fractions in my previous post. As an example, consider a 1 kaLai 1.5 eDuppu akin to brOvabhArama (a 1.5 eDuppu is no different from a 0.5 eDuppu in this context of illustration). It is difficult to transition to medium or slow tempo tis'ra gati starting from this eDuppu since the ta-ki-Ta cannot be mounted on any tangible beat. Yes, the fast speed tis'ra gati makes this possible. In this case, you could easily utter a fast ta-ki-Ta in the gap between the 1.5th and the next integral beat (the ring finger) and continue the utterances through the tALa cycle at that speed. Why do I say difficult (for tis'ra gati in the next-slower speed) and not impossible? -- By extension it is possible to subsample this fast ta-ki-Ta starting at the halfth beat by a factor of two and practice and perfect it, but this is heavily syncopated with no syllable falling on any tangible beat. Moreover, starting the utterance as a tis'ra gati is easier than real-time transitioning to it from another naDai - the performers would, with a very high probablity, adjust and manipulate the music and tALa reckoning based on their knowledge of alignments and deviate from the kAlapramANa (absolute time or wall clock time). This practice (mounting the tis'ram on fractions previously indicated wrt kaLai) is best avoided and even discouraged by performers. In such cases, caturas'ra tis'ram is sometimes taken up. BTW, caturas'ra tis'ram could be more difficult than tis'ram, since it would be required to split the 4-3-1 into 4-3-2 dyadically and maintain this kAlapramANam in sync with the tALa reckoning. The varisai is easy since it is 4-3-1. And 4-3-4 is tougher than 4-3-2, and I have not seen it used in pallavi multispeed renditions.

PS: Your other questions in post #54 well taken. I have edited my original post #51 by just adding a qualifier to state the context of (my thought process in) 'double speed', as well as a suggested starting point before embarking on the composite speed of rendering the first varisai.
Reference your question on pallavi -- I have provided some info in words in post 51 as well, on the association of the 1/2 beat take off points vis-a-vis inner units. This association might have been somewhat cryptic in my previous (unedited) post -- to infer this (without the added qualifying words for association), one has to factor in that the semicolon corresponded to two inner units as per conventional notation.
Last edited by sr_iyer on 09 Sep 2009, 22:30, edited 1 time in total.

gn.sn42
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Post by gn.sn42 »

vasanthakokilam wrote:When you wrote "to get a feel of chaturas'ra tis'ram + double speed,", did you actually mean to say "to get a feel of chaturas'ra tis'ram + triple speed"? Triple with respect to the starting point which was one solfa syllable per beat to that 1/4th avartha being in 4 solfa syllables per beat.
I think "double speed" is indeed what sr_iyer is referring to. If we take the (base) arohanam and then apply "chatusra tisram" it will take up 1.5 avartanas. Then if you take the (base) avarohanam and double the speed, it will take up 0.5 avartanas. The notation clarifies this, I think.

By the way, I like your terminology and model - when I read it I feel I can understand it; but I need a bit of time and effort to internalize and start using it. It appears to be a powerful and flexible model for these transitions.

vasanthakokilam
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Post by vasanthakokilam »

gn.sn42: Thanks for raising that question. As a side effect, we got a great lesson from sr_iyer on how these things work in practice.

sr_iyer has addressed your question substantially. When I read your question, the first composer that came to my mind was OVK as well. There is an album by TNS of OVK compositions. What a great match-up!!

While pondering your question, I thought of the following:

sr_iyer had nicely built up the kaNakku from Sarali to varnam to pallavi. And you were wondering about pre-composed music. And the biggest one of them of course is the krithis.
As Sri. Srikantan says, traditional thinking is krithis represent the rakthi bhakti sangitam. Whereas this would be rakthi kaNakku sangitam ;)
That is on a lighter note of course, but that may point to the standard thinking on the differences in aesthetic goals of pre-composed music vs manodharma music.

Not that they can not be reconciled, I am sure people can relate to bhavam/emotion induced through music that provides for kaNakku based speed variations.

As you and sr_iyer covered, jatiswarams, tillAnas and orchestral pieces can definitely make use of these for good effect.

Here is the main point I wanted to write about as a possible direction of thinking for your question. There may actually be not that much difference in aesthetic goals between those sub-genres.

What we are basically talking about is syncopated speed variations in pre-composed music.

Manodharma aspects including niraval readily accommodate such things. What is the equivalent of niraval in pre-composed music? It is of course Sangathi. May be that is one place where chathusra-thisram type speed variation can find its place. In many thyagaraja krithis, the sangathis are built up with speed variations. You see a pattern where he sometimes speeds up the pUrvAnga while maintaining uttaranga and vice versa in other krithis or both in some krithis. They are normally 'power of 2' speed variations which are not normally syncopated. And Thyagaraja was a master at using off-beat and syncopated constructions. I do not see why chathusra-thisram type speed variation can not be accommodated in such sangathi construction. It is really not even gathi-bedam as sr_iyer observed earlier, just an illusion while still in chathusram.

gn.sn42
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Post by gn.sn42 »

Yes, sr_iyer has given us quite a bit of useful and thought-provoking information.

I'll set about listening to all the OVK I can find! :) That should be fun. And I appreciate your point about sangathis, especially in Thyagaraja's compositions. There are definitely speed variations in many cases, and I'll need to listen to those more carefully and try to understand how they work. I agree that many of them are probably multiples of two (Thyagaraja's beat tricks are hard enough as they are - in my imagination he's standing there grinning as musicians screech round each next corner).

TNS/OVK should definitely be a good combination - could you give me details on this album?

vasanthakokilam
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Post by vasanthakokilam »

sr_iyer: That answers my question about the 'nI padamulE' pallavi. I got the split mixed up. Thanks for clarifying it. The rest of your additional description is very informative, as always. Much appreciated.

gn.sn42: I understand now where the 'double speed' vs 'triple speed' difference comes from. The first step of the exercise uses a 0.75 - 0.25 split whereas the second step uses the 1.5 - 0.5 split. sr_iyer is referring to the second step when he mentioned 'double speed'. I mistook that as a reference to the first step. Thanks.

vasanthakokilam
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Post by vasanthakokilam »

sr_iyer, I just read your PS in your post #55 and the additional notes in your post #51. Understood.

I tried the step-wise process you suggested to get to the chathusra tisram. I used the step 3 below to get that 1/4th split right. It was initially hard to go from two 0.5 splits to three 0.25 splits.

This is what I did. ( All the avarthanams below are of the same time duration.)

1) s r g m |p d |n s' ||s' n d p|m g |r s ||

2) s, r, g, m,| p, d,| n, s', ||s,' n, d, p,|m, g, |r, s, ||

3) s,,, r,,, g,,, m,,,| p,,, d,,, |n,,, s',,, ||s,,,' n,,, d,,, p,,,|m,,, g,,, |r,,, s,,, ||

4) s,, r,, g,, m,, p,, d | ,, n,, s',, | s'ndpmgrs ||s,, r,, g,, m,, p,, d | ,, n,, s',, | s'ndpmgrs ||

5) s,, r,, s,, r,, s,, r |,, g,, m,,|s,, r,, g,||, m,, p,, d,, n,, s',, | s'ns'ns'ndp| s'ndpmgrs||

The third step set the stage for the syncopated fourth and fifth step by changing from chathusra karvai to thisra karvai as per your plan.
Though I got the kAlapramANam reasonably tight after 9 or 10 tries, I found it hard to do steps 4 and 5 while keeping the thalam. I brought in a metronome program to keep the thala.

I put in my own syllables to each swara in step 1 for a 16 syllable pallavi. Step 4 and 5 sounded awesome like a real pallavi .

It is a fun exercise :) Thanks sr_iyer.

sr_iyer
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Post by sr_iyer »

Vk, you are welcome. Just so that there is no confusion in the notation you are expressing, I would recommend that you ensure that all Avartanas in your sequences 1 through 5 occupy the same time-duration. If this is not the case (let us say, in your post, you intended that Avartana time-duration in #1 is half of #2 is half of #3), please indicate that explicitly in your post so that I can mentally map your notation without any gap.

As an example, I would normalize and express (a) first, (b) second and (c) third kAlam in notation by fixing say four inner units per kriyA, and indicate: (a) --- s,,, r,,, g,,, m,,,|p,,, d,,, |n,,, s',,,|| (b) --- s, r, g, m, p, d, n, s', | s', n, d, p, | m, g, r, s,|| and (c) --- srgm pdns s'ndp mgrs| srgm pdns'| s'ndp mgrs|| (Akin to how books normally notate varNams and Krtis set in 1 kaLai ...)

This is a minor point -- just to avoid any gap.

Having normalized the notation thus, I would recommend that for all the numbered items in your post (esp for # 4 and 5), you could use an Avartanam that spans 6 to 8 seconds to get a feel, i.e. about three fourths to a one second to a kriyA. (It is not intended that you use 2 kaLai, in which case, the exercise would be easier)

_________________


To hear a sample of caturas'ra tis'ram used in a performed pallavi, please refer to http://www.mediafire.com/?sharekey=b016 ... f6e8ebb871

I excerpted just the multispeed rendition part from a pallavi I found at sangeethapriya, rendered by Sri LGJ (in a duet with Sri N Ramani).

The pallavi is in khaNDa tripuTa, 2 kaLai. eDuppu is 1/4. (I have retained the initial announcement by the maestro, cut out the initial niraval portion and spliced the initial part directly into the multispeed rendition part. The maestro declares quite precisely, that the take off point is 'half a division of the first beat where every beat has two divisions'. These divisions are the kaLai subdivisions. This makes it a 1/4 beat skew, i.e. 1/4 eDuppu).

The pallavi, indicated in 4 inner units per kriyA-beat (or 2 inner units per kaLai-beat) of 2 kaLai khaNDA tripuTa, is:
, s p m g , , - (r) m g s , , , - r s , , , , (d)- n| s , , , , - s' , , | d p , , m g r s || n- (pallavi wraps around from eDuppu here as s p m g , , again)

Note: The underline indicates swara in the lower octave. The italic coloured swaras in brackets do not have any tangible duration towards tALa-unit count and have been only indicated to show the key grace notes involved in transitions. The hyphens show the spits between phrasings.

In the portion (spmg,, -> mgs,,,-> rs,,,,->n) ... notice the progression from 3 to 4 to 5 units of kArvais in the pUrvAngam forming a yati pattern, leading into the arudi subsequently. The prefixes of the single units swaras that lead into these associated kArvais in the pUrvAngam taper from 3 to 2 to 1 single unit swaras accordingly.

Approximate timelines (started with higher resolution, but later annotated at lower granularity of indicated time-lines:-). This annotation is just indicative to help the reader map the obviously perceived speeds, and different audio players may show +/- 0.5 seconds difference I think...

1:23.5 to 1:37.75 base speed in 2 kaLai
1:37.75 to 2:01.75 slow (1/2 of base peed)
2:01.75 to 2:20 iteration 1 caturas'ra tis'ram
2:20 to 2:38 iteration 2 caturas'ra tis'ram
2:38 to 2:50.5 iteration 1 base-speed
2:50.5 to 3:03 iteration 2 base-speed
3:03 to 3:26.5 four iterations of fast (second wrt base) speed

Followed by return to base speed -- this is actually a composite formulation of speeds in pUrvAngam (base followed second speed of pUrvAngam) -- not important for elaboration for our context here ...

PS: Have excerpted only the relevant portion from sangeethapriya clip and uploaded purely for illustrative purposes. If there is any inadvertant copyright violation, please let me know.
____
More later. I will also briefly comment on why caturas'ra tis'ram is used in some naDai pallavis (i.e. non caturas'ra naDai pallavis) later ...
Last edited by sr_iyer on 14 Sep 2009, 18:08, edited 1 time in total.

gn.sn42
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Post by gn.sn42 »

sr_iyer, thanks for the terrific annotated example. (As far as copyright is concerned, this is a textbook example of fair use - you've excerpted a small portion to illustrate your article, edited it to focus on one aspect, annotated it, and provided credit.)

vasanthakokilam
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Post by vasanthakokilam »

sr_iyer, I just got back to this thread. In the 5 steps in my post, yes, all the avarthanams are of equal length. I have added a note to that effect. I did not understand clearly what you were saying with the "---" ( three dashes ) before each step. What does that signify?

Thanks for the annotated example. I have listened to that a few times but it requires a few more listens to get the feel for chathusra thisram right. Thanks for marking the times with much care and accuracy. That helped a lot.

vasanthakokilam
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Post by vasanthakokilam »

gn.sn42 wrote:TNS/OVK should definitely be a good combination - could you give me details on this album?
gn.sn42, I looked for the official title of the album but I could not find a definitive one online. One or two looked promising but I could not get the song list to verify.
May be others will know. I have the songs and listen to it quite frequently and I know it came from an album.

SrinathK
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Re: What is chatusra tisram?

Post by SrinathK »

Ok, I just looked at KBMK's lec dem up there and I realized the Sri mahAganapatiravatumAm recording of Lalgudi sir is using it.

It is very simple in principle. There's just one more detail.

He's just singing triplets (t,,k,,d,,m,,) in chatushra nadai at 8 counts or 16 counts a beat - this is no different from counting triplets at 4 counts a beat - just the speed got doubled or quadrupled. 

Basically 1) t , , k | , , d , | , m , , || (counting 3 patterns in chatushra nadai) became

2) t,,k,,d, | ,m,,t,,k | ,,d,,m,,|| next degree of speed (8 counts per beat)

If that's too much just do the above in 2 kalai and it's the same thing, just at 50% tempo.

One can do this for 16 counts per beat if one is good enough. What that looks like is this

t,,k,,d,,m,,t,,k | ,,d,,m,,t,,k,,d, | ,m,,t,,k,,d,,m,,||

If you don't get it, do it in 4 kalai at 25% tempo and you'll see it's the same thing as example no. 1.

But do not openly stress the commas. If you say t k d m - you sound as though you are counting in groups of 4, while you are in fact taking 4 triplets in a group.

There is a laya exercise of counting patterns of 3,4,5,6,7,8,9 notes in chatushra nadai, which is basically this. Its in AMS exercises and taught as a basic laya lesson. At 4 counts a beat the concept is simple. The difficulty only arises at much slower or faster degrees of speed.

Similarly they can actually be done for any nadai.

SrinathK
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Re: What is chatusra tisram?

Post by SrinathK »

From the other thread : viewtopic.php?f=8&t=29132#p339093 - A demo of K Gayathri doing chatushra tisram and tisram for a pallavi

viewtopic.php?f=8&t=29132#p339236 - Some more points

All possible cross pattern variations :

viewtopic.php?f=8&t=29132#p339251
viewtopic.php?f=8&t=29132#p339252
viewtopic.php?f=8&t=29132#p339255
viewtopic.php?f=8&t=29132#p339258
viewtopic.php?f=8&t=29132#p339260

Sath
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Re: What is chatusra tisram?

Post by Sath »

Just saw this great, concise explanation here by Shri Sunil:
https://www.youtube.com/watch?v=FJBJNdZZVf8

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