What is chatusra tisram?

Tālam & Layam related topics
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nmn1974
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#1

Post by nmn1974 »

Hello All,

I think my subject is self-explanatory :-) Could anyone please explain what is chatusra tisram? Can this be sung in any pallavi? Also can this be extended to chatusra khandam/misram or similar combinations?

Thanks!

rasikaranjan
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#2

Post by rasikaranjan »

Tisram, Chatursram, Khandam, Misram and Sangirnam are kinds of natais or gatis in the parlance of music. It is rhythmic gait. It is measured by beats. Beat containing 3 swaras is called tisram, four=chatursram, five=Khandam, seven=Misram and nine=Sangirnam. Commonly all songs are rendered in Chatursra natai. Kritis like Shankari Sahnkuru (of Shyama Sastri), Vallabhanayakasya Bhakto Bhavami (Dikshitar) etc. are sung in Tisra Natai. Only those who are blessed with the element /gene of laya can sing these natais. Those who are not, sing these kritis in roopaka talam. Conversely, laya experts sing rupaka tala kritis in Tisra natai.

Able and scholarly teachers train children to sing even all varisais in all these natais. All Varnams can be (rather should be practiced) in all natais, at least in Tisra Natai. You would have noticed brilliant laya experts rendering swaras in jet speed, while rendering manodharma swaras, which can be appreciated only by the layagnanis, which some stupid critics call as mad rush or other dim-witted words You would have heard about Shatkala Marar, It is said, marveled by his dazzling control over laya, Tyagaraja swamigal composed the Sriraga Ratnam. (the concluding pancharatnam)
Prof: Sambamoorthy paying high tributes to Mahavaidyanatha Iyer says "The ringing and fascinating character of his voice and his ability to sing to all the six degrees of speed charmed one and all beyond measure. "

Pallavis can be sung in all natais.

nmn1974
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#3

Post by nmn1974 »

Thanks Rasikaranjan.

However, I was referring to the technique of singing a pallavi in chatusra tisram. I have heard this term very frequently, but would like to know what it means and how one would execute this in a pallavi.

Could any of the laya experts please help?

Nick H
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#4

Post by Nick H »

It simply translates to four three --- so, expressed thus, it is a nonsense!

So there must be something missing, or assumed.

Let's take the full description of tisra nadai "adi" talam as a possible example:

Tisra Nadai Chatusra jathai Triputa talam

Indicating that

--- the tala is triputa, ie it consists of one laghu, followed by two druthams.

--- the length of the laghu is four counts (clap plus three fingers)

--- each of the counts, four in the laghu, two in each drutham, is subdivided into three pulses.

chatusra, in this context: the number of counts in the laghu[s]

tisra, in this context, the number of pulses in each beat.

In the palavi context, I can only think that it is to do with singing in different speeds, which can be done 1st, 2nd, tisra, 3rd, 2nd-tisra. First, second and third are chatusra (unless the palavi is in another nadai anyway) and are simple doublings; tisra is moving from four beats per count to three or six, ie a nadai change.

Shots in the dark here... maybe some help?
Last edited by Guest on 02 Sep 2009, 02:11, edited 1 time in total.

arunk
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#5

Post by arunk »

I may be wrong. This is basically singing a song that is set in catusra gati, in tisra gati while keeping regular catusra gati tala. Applies to varnams and pallavis.


Arun

srinivasrgvn
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#6

Post by srinivasrgvn »

nick H wrote: Tisra Nadai Chatusra jatai Triputa talam
Did you mean jathi?

Nick H
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#7

Post by Nick H »

Yes... Thank you, I did.

Post edited :)

vasanthakokilam
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#8

Post by vasanthakokilam »

arunk wrote:I may be wrong. This is basically singing a song that is set in catusra gati, in tisra gati while keeping regular catusra gati tala. Applies to varnams and pallavis.
Arun
Such cross-rhythms is my understanding of chatusra tisram as well. There have been some other discussion about this elsewhere. ( Essentially nothing changes at a fundamental level )

Arun, I am intrigued about what you say regarding 'varnams and pallavis'. I am always unsure of what 'tisram' singing in varnams and pallavis refers to.

In one Bombay Sisters' varnam in pUrvAngA, they sing Tisram for half and then tisram double speed for the other half and it takes the same time as chathusram. I thought that is quite a neat idea.
Since tisram length is 1 and 1/3 of chathusram and tisram double speed length is 2/3 of chathusram, 1 1/3 + 2/3 = 6/3 = 2 of chathusram. Nice!!

That leads to the obvious conclution that if they had sung tisram for the whole pUrvAngA it would have taken them 1 and 1/3 time to complete the pUrvAngA. Are such things done as well?

arunk
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#9

Post by arunk »

singing tisram for varnam I have heard is an advanced lesson for strengthening one's handle of laya. It is similar what is done in Bombay Sisters example above and I think same is done in pallavis also (i.e. besides anulomam and pratilomam, tisram is also done sometimes).

I should note that here the tala (keeping) remains same but the melody switches gait (thus length of notes changes) i.e. to tisra gati. So this is really singing tisram only - the only additional "caveat" is that tala keeping doesn't reflect tisra gati, and stays in catusra gati (thus perhaps the need for catusra-tisram term in colloquial use). Anyway, this is the opposite of keeping the melody same but changing the tala (say you put 4 cycles of rupaka capu vs. 1 cycle Adi tisra gati) - I wonder if this is what you were referring to in your first para above and "essentially nothing changes..."

Arun

msakella
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#10

Post by msakella »

Dear brother-member, vasanthakokilam, Each and every Varnam cannot be sung in the same manner. amsharma

vasanthakokilam
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#11

Post by vasanthakokilam »

>(say you put 4 cycles of rupaka capu vs. 1 cycle Adi tisra gati) - I wonder if this is what you were referring to in your first para above and "essentially nothing changes..."

Yes, along those lines though I was not thinking of that example. ( side bar: in such cases, the eduppu also sometimes changes , so there is a lateral shift )

The example I was thinking of was in Kalpanaswarams, thani or bharathanatyam ( as practised sometimes in pancha-nadai ), the sub-beat size does not change, the beat interval does not change ( though suspended temporarily ), only thing that is done is the size of the grouping. So take 3 avartha of adi for 24 beats - 24 groups of 4 in chathusram = 96 sub beats. Temporarily set aside the thala avartha, now that we have flattened it to the sub-beat level. Regroup it to 32 groups of three. It is still the chathusram sub-beat length but grouped as a thisram hence chathusra thisram. ( so essentially same as your example ).

So, arun, if chathusra thisram is what I described above, then it is not same as what is done in Varnams or Pallavis, right?

Akellaji: Is your comment in reference to singing thisram in Varnam? Intriguing. Please explain further.

msakella
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#12

Post by msakella »

Dear brother-member, vasanthakokilam, Let it be either any Varnam or any Pallavi for that matter the mathematical application while singing the meterial in Trisra-gati which is already set in Chaturashra-gati, is the same. That is OK. But you wrote ‘In one Bombay Sisters' varnam in pUrvAngA, they sing Tisram for half and then tisram double speed for the other half and it takes the same time as chathusram’. In general, many of our artists choose a Varnam which is mathematically convenient to do such thing. That too they do such things in respect of the Purvanga only but conveniently avoid to do the same in respect of Uttaranga. Once if you look into the Uttaranga of 2 or 3 different Varnas and try to apply the same you can very well understand the implications. amsharma

Venkatachalam J
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#13

Post by Venkatachalam J »

Is it chatusra jathi thisra gathi (or) chatusara gathi thisra jathi

arunk
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#14

Post by arunk »

vk,

What i am referring is the case where sub-beat lengths (or more pertinently the lengths of swaras/notes of the melody) DO change and hence is NOT the same as you thought I was referring.

As you know, there are 2 possibilities in gati switch:
1. Melody remains same (i.e. lengths in time of swaras/notes that make up the melody remains same), but tala keeping (i.e. length in time of avarthana) changes.

2. Tala keeping remains same (i.e. length in time of an avarthana remains same) but melody changes (i.e. lengths in time of swaras/notes that make up the melody changes).

In BOTH cases, across the switch, the duration of say any particular portion of melody would be different RELATIVE to the duration of avarthana as kept in tala.

But IMO, this is not as significant as the question "does the duration of particular portion of the melody" CHANGE in time i.e. # of seconds it takes across the switch?

Say sarasuDa in that rendition was done so that one avarthana of 2-kalai took 16 seconds (so one 1 second per "tap" in 2-kalai). There are 32 "swaras" in first line of the pallavi ( s , r , g , rg r, , , ... <=> sarasuDa ninnE kOri ) . In catusra gati, then 32 swaras take 16 seconds i.e. 2 swaras per tap i.e. 2 swaras per second. When doing second speed in catusra gati, now 32 swaras take 8 seconds i.e. 1/2 the tala or 64 swaras are fit in that 16 second avartana.

When doing tisram, the first 24 swaras of the pallavi are sung in the same 16 seconds while putting the same 2-kalai tala (1 tap per second). Thus the first line of the pallavi which fit in 16 seconds, now will stretch beyond the 16 seconds. So this is the case #2 above.

What you were referring to is where the sarasUDa ninnE kOri STILL takes 16 seconds after switch, but the tala keeping changes so that one avarthana shortens to 12 seconds (?not sure about math (16/32)*24 = 12)

In any case, catusra tisram is really not that special. I believe it is #2 above - which is basically one way of doing gati switch.

Arun
Last edited by arunk on 02 Sep 2009, 18:10, edited 1 time in total.

Nick H
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#15

Post by Nick H »

1. Melody remains same (i.e. lengths in time of swaras/notes that make up the melody remains same), but tala keeping (i.e. length in time of avarthana) changes.

2. Tala keeping remains same (i.e. length in time of an avarthana remains same) but melody changes
I think that is aniloma and pratiloma, which two words I have probably mangled, and quite likely got the wrong way around --- not nadai change. Can both come under gati?

arunk
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#16

Post by arunk »

Nick I think you are right. I am not 100% sure but I think in the usual/common case anulomam and pratilomam, the gati/naDai remains same - and so it is "time stretching and contracting" over same gati/naDai. So spread what took in say 1 cycle (at the start of pallavi) of the tala to 2 cycles of the same tala in same tempo, and on the other end do it in 1/2 and even 1/4th cycle (thus repeat 2 and 4 times to fill a cycle). But if we generalize, then this above doing tisram while keeping tala constant also should fall under anulomam.

Now of course I also want to say that I am not 100% if this is indeed what is called catusra tisram :)

Arun
Last edited by arunk on 03 Sep 2009, 02:43, edited 1 time in total.

cmlover
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#17

Post by cmlover »

VK
what is the caveat?
One can do these for any thaaLam. The mridangist can easily play three avarthams for four cylcles of thaaLam without any difficulty..

vasanthakokilam
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#18

Post by vasanthakokilam »

CML, by caveat, I am referring to the test in my post #21 above "1) If ( Thala avartha count x BN ) is divisible by NN, then "BN NN" switch is feasible". This is a requirement for non fractional convergence on each repetition of the pallavi line. ( non fractional convergence means each cycle in NN should finish on a BN sub-beat and not a fraction of a BN sub-beat )

That is, when the singer is doing "Misram" while you are keeping the thala in "Sankeernam" for a pallavi which is originally set in Kanda Jathi Triputa thala sankeerna nadai, the singer's pallavi frame would not finish on your chathusram count. It will fall in between a sub-beat . Such practical difficulties aside, yes it is mathematically possible and who knows, for our laya experts, it may not be a super big deal ;)

FYI, in the above example for Khada-Triputa, each avartha in Misram consisting of 81 misra swaras will fall on 104.14285714285714285714285714286 th sankeerna swara. :)

The same sankeerna misram technique will work out fine without fractions for Tisra-Triputa, Khanda-Ata, Chatusra-Jhampa, Khanda-Roopaka, Mishra-Eka and Chatusra-Dhruva thalas.

arunk
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#19

Post by arunk »

I am still confused :) - vk what you explain was what I thought would happen for catusra tisram but Balaji sir's explanation confused me.

Anyway what you explain above from what I can tell this is standard catusra gati to tisra gati switch (and if true, a separate label like catusra tisram adds more confusion to me! ). If the mridangist plays a rhythm that is in line of the target gati (i.e. tisram), then the tala keeping is somewhat irrelevant to the musical aspect isnt it? It isnt completely irrelevant as it does play a role to ensure that the avarthana cycle remains the same

Arun
Last edited by arunk on 04 Sep 2009, 17:00, edited 1 time in total.

msakella
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#20

Post by msakella »

vasanthakokilam wrote:FYI, in the above example for Khada-Triputa, each avartha in Misram consisting of 81 misra swaras will fall on 104.14285714285714285714285714286 th sankeerna swara. :)
vk - Leave alone the Chaturashra-trisram, but in Khanda-triputa carrying 9 Kriyas, each Avarta in Mishram arrives at the total of 9 x 7 = 63. But I am unable to arrive at a total of 81. I am also confused. Of course, our birth right is to make others confused or to become ourselves confused. Then only people think us stalwarts as per our tradition. But, I am still more surprised to know when did you learn my Talaprastara even without my knowledge and got this little number ‘104.14285714285714285714285714286’ to make me still more confused. amsharma

mridangamkid
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#21

Post by mridangamkid »

From what I understand, Chathusra thisra is merely playing a chathusra pattern in chathusra nadai however after ever 3 (thisra) beat.

The best/easiest example is using Rupaka thalam, if we play a normal 4 beat pattern.... thakadhina.... in Adi thalam Chathusra Nadai, it will fit perfectly, as shown

http://www.sendspace.com/file/1ptdls

This is just me saying "Thakadhina" in different speeds in Adi Thalam Chathusra Nadai

Now if you do the exact same thing as above but in Rupaka thalam it will be as follows

http://www.sendspace.com/file/zgsduw

If you'd notice, when I said "Tha dhin dhin na, thaka dhin din na, dhina dhin dhin na, thatha dhin dhin na", I had to repeat it thrice, rather than once or twice as I would in a normal 8.

Now in Chathusra-Thrisa, though it may not sound like it, I will still be in normal Chathusra nadai, however I am subdividing it into 3. The reason why this is so controversial however, is because at first I play a note after every 3 beats "THA tha tha KA ka ka DHIN dhin dhin NA na na". (Capital letters only being audible), however once you go into double speed, it will go into 1.5, then .75, and so on and so on.

If you'd notice now, I will play what I payed before in Adii -chathusra and Rupaka Chathusra... however this will fit perfectly as if it would in Adi thalam.

http://www.sendspace.com/file/mftabh

The same can be done in Kanda Chapu if you divide thakadhina into 5, and same with mishra and sankeerna into 7 and 9 respectivly.

As always, please tell me if I made any mistakes or am confused at all (it wouldn't be the first time).

vasanthakokilam
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#22

Post by vasanthakokilam »

Mridangamkid: Thanks. I listened to them. Still have to digest..

My posts above are based on what nmn wrote. With Arun's comment, I am now officially confused as to what chathusra thisram is. I thought Balaji agreed with nmn. I will sit by and wait for mridangam and mridangamkid to sort this all out for us.

Death and taxes are considered the only certainties in life but we should add 'nadai terminology confusion' as a third item :)

akellaji: That is quite funny :) No thalaprasthara knowledge on my part, except for the serial number looking scary number in my post. I was explaining to CML that ( 81 * 9 /7 ) gives this large fraction and not an integer.

>but in Khanda-triputa carrying 9 Kriyas, each Avarta in Mishram arrives at the total of 9 x 7 = 63. But I am unable to arrive at a total of 81.

Correct. Let me explain. This is all in the context of what nmn1974 wrote. I was confused by that originally as well. Khanda-triputa in Sankeerna is 9*9 = 81 sankeerna aksharams. If you recite these 81 syllables in Misram, it will take ( 81 * 9 / 7 ) sankeerna aksharams.

mridangamkid
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#23

Post by mridangamkid »

Well I really hope not to confuse anyone, and I especially don't want to confuse anyone by giving anyone false information.

Let us go back to Mridhangam sir's post where he talks about rupaka thalam (I am purposely using rupaka always because I find it the easiest).

Sir asks us to say "Thakita" in Rupaka thalam. If we do this it will fit 4 times.

Now emphasize the "tha" in Thakita.

Now make it such that only the Tha is audible while the "kita" is inaudible.

With this you can say "Tha" four times and make it fit into Rupaka thalam. That (as I understand), is the very very basic form of Chathusra Thisra.

From that you just elaborate into more complex lessons, the problem is keeping it balanced and keeping it on thalam.

If you want to know Chathusra Kanda, do the same for Kanda chapu

Say "Thadhigina thom" in Kanda chapu, such that you say Thadhigina thom twice in one cycle.

Now emphasize the "tha"

Then make "Tha" the only one audible.

With this you will say Tha 4 times within 2 cycles. Double the speed and you will say it 4 times in 1 cycle.

This is the most basic form of Chathusra Khanda....


Is this correct? Because perhaps I understood wrong from my teacher

msakella
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#24

Post by msakella »

mridhangam wrote:take Rupaka Talam and say thakita thakita thakita thakita for one avartanam taking it to 12. Change each thakita to thakadimi thakajonu thakadimi thakajonu ..it is chatusra tisram.
Dear brother-member, mridhangam, If you have to spell out four-trisra-breaks, ‘thakita thakita thakita thakita’, in one avartanam of Rupaka-tala taking it to 12, it is only Chaturashra-gati divided into four-trisra-breaks. Later, in place of these four-trisra-breaks, if you have to again accommodate four ‘thakadimi thakajonu thakadimi thakajonu’ they are Chaturashra-breaks. Some are used to make a difference between Gathi and Nadai that while the units running in each Kriya should be called Gathi the units running in each break should be called Nadai. Even though this is not agreeable to one and all and even if this is applied here, this should be called Chaturashra-gati-trisra-nadai-chaturashra-nadai as there are three steps of usage in this kind of rendering. But, how any one can justify in calling it as Chaturashra-trisram I do not understand. There is nothing wrong in doing any kind of acrobatics but one kind of discipline should always be maintained and, more over, it should properly be defined in every respect without any ambiguity for the posterity. Due to some flenatics (fenatics+lunatics) our kids have already been sufferring a lot in this respect and it is the duty of each and every individual to fully stop it at one point or other even for the sake of our kids. amsharma

vasanthakokilam
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#25

Post by vasanthakokilam »

>Well I really hope not to confuse anyone, and I especially don't want to confuse anyone by giving anyone false information.

mridangamkid, you did not cause any confusion for me...( at least not yet ;) ). This terminology confusion is quite common in any "Nadai Switch" discussion. We will look to Sri. msakella, Sri. Balaji and you to offer the definitive answers on 'what to call what' about the things that are practiced in the field.

I am still processing your info and demos which are very much appreciated.

vasanthakokilam
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#26

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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#27

Post by vasanthakokilam »

Hope this picture captures the main idea

Image

msakella
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#28

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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#29

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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#30

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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#31

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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#32

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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#33

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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#34

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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#35

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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#36

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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#37

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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#38

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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#39

Post by msakella »

vk - Excellent elaboration. Very nice indeed. amsharma

vasanthakokilam
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#40

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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#41

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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#42

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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#43

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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#44

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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#45

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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#46

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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#47

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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#48

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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#49

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
Posts: 396
Joined: 02 Feb 2010, 23:56

#50

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.

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