Structure of Mohras

Tālam & Layam related topics
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shankarank
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#1 Structure of Mohras

Post by shankarank »

The below from fellow forum member, Nick triggered me to delve into this:

I think this was discussed somewhere ( probably kORvai thread - by @mridhangam - not able to locate it.
Nick H wrote:
11 Aug 2019, 15:32
There is a formula by which a mridangist can compose it, on the spot, for any thalam, even if it not in their memory. Of course, I have forgotten it :oops: :oops: .
If you observe here for miSRa capu - https://youtu.be/uU9YAALt828?t=6540 ( Video Rec. of Sri Arun Prakash playing the Mohra - we discussed the kOrvai that follows in the Structure of Korvai thread ), Instead of 4 16(s), he does a 12, 16, 12, 16 to occupy 2 Avartas.

In the higher kALam reckoning ( 8 mAtras per beat), all tAlAs come to even number of mAtRas per Avarta and that is handy.

Here is one scheme that retains some EVEN symmetry - I am not saying mOHras cannot go beyond this. Leaving it to higher experts.

We start with a scheme (A, B, C are integers):

2*A + B + 4*C = N * (mAtra count per Avarta of the given tALam) - Where N can be as low as (1/4) , (1/2) , 1, 2 , 4 - depending on the speed of execution.

For sUlAdi tALAS we can use N = 1 and then scale it to lower or higher speeds. 1 - kALAI here and caturaSRA naDAI. For cApu tALAS - choose an appropriate N - most likely 2 or 4 for shorter tAlAMS.

where 2*A + B + 4*C is executed in the order A, B , A, 4*C . The reason for saying 4C will become clear soon.

A, B , A, 4*C - this pattern is executed 2 times.

For the third time it goes like:

A , B , A + 2*C, A + 2*C, A + 3*C , 3*C , [2*C]

The first two rounds and the third together make for a total of 4 rounds - i.e. 4 times the starting structure : 4 *(2*A + B + 4*C )

In other words - the third round pattern's time duration = twice the time period of starting structure pattern.

Now lets analyze the structure of 4*C for the case where 4*C is 16. It is usually (popularly) a dramatic - cApu expressing one like talAngu-dhin-ta-talAngu-thom(16). 2*C in the last part is done (popularly) as talAngu-thom(8). 3*C is done as talAngu-dhin-ta-thom (12). The last [2*c] in square brackets is actually a part of 3*C - with thom cut off because thom goes away with reaching a samam or an eDuppu - and that is : talAngu-dhin-ta - after which any following kORvai is started.

Now we said A , B , A 2*C, A + 2*C, A + 3*C , 3*C , [2*C] goes for two rounds of the basic starting pattern.

So 4*A + B + 12*C = 2 *(2*A + B + 4*C) --> B + 12*C = 2B + 8*C --> B = 4*C

So listing the constraints: With A, B, C as integers. In the 8 mAtras per beat setting - where tagutarikiTataka - goes for 1 beat.

1) 2*A + B + 4*C should equal N( mAtra count per Avarta of the given tALam). N is 1, 2, 4 etc - enough to fit one round of the pattern.

2) B should be divisible by 4 - since it has to equal 4*C.

3) The pattern chosen for 4*C ( which is equal to B in duration) , should be modifiable to similar sounding patterns in durations 2C and 3C. As explained above.

4) (3) above puts a minimum value on C - which should be 4 mAtRas - in the 8 mAtRas per beat setting. Less than that, patterns for 2C and 3C cannot be set appropriately.

5) (3) above Also restricts C to even integers - as executing to odd mAtra positions with 3C is impossible.

Based on this we can work out for rUpakam ( the ordinary usage) and khanDa cApu easily - next post!.
Last edited by shankarank on 18 Aug 2019, 22:18, edited 1 time in total.

sr_iyer
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#2 Re: Structure of Mohras

Post by sr_iyer »


shankarank
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#3 Re: Structure of Mohras

Post by shankarank »

Thanks. What a providence? His nephew Sri Ananthakrishnan ( a disciple of his!) taught my brother - coming home for the class.

As regards, his triSra bhava arudhi, the ending kArvai for tarikiTathom is elongated in the last section as tarikiTa(4)thom(6) . That the tinkering of silence achieves wonders is well known ;) :D

So the 4*C could be changed as 2*D + 2*S - where S (Thom) is silence and hence amenable to elongation in the smaller patterns. D will have newer constraints.

So I qualified my logical layout with the term "EVEN" symmetries ;) :mrgreen: . I mentioned that , as I could in khanDa cApu elongate the kARvai to get something that doesn't fit my scheme.

tAngiTatarikiTA(8) tAngiTataka-tarikiTAtaka (12) tAngiTatarikiTA (8) tarikiTathom(6) tarikiTathom(6) - here B = 4*C still holds.

Two times = 80.

tAngiTatarikiTA(8) tAngiTataka-tarikiTAtaka (12) , tAngiTatarikiTA (8) tarikiTathom(6), tAngiTatarikiTA (8) tarikiTathom(6), tAngiTatarikiTA (8) tarikiTa(4)thom(6), tarikiTa(4)thom(6), tarikiTa(4)

Total = 80.

tarikiTa(4)thom(6) = 10 IS NOT 3*C - where C = (12/4) = 3.

shankarank
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#4 Re: Structure of Mohras

Post by shankarank »

For khaNDa cApu, the one that fits the EVEN scheme ( or caturaSra bhAvam) will be :

tAngita (4)-dhitAngiTAtagutarikiTAtaka(16) - tAngita (4)- talAngudhin-ta-talAngu-thom(16) - 2 times

Total = 80.

and the last round:

tAngita (4)-dhitAngiTAtagutarikiTAtaka(16) - tAngita (4)-talAngu-thom(8) - tAngita (4)-talAngu-thom(8) - tAngita (4)-talAngudhinta-thom(12) talAngudhinta-thom(12) - talAngudhinta (8)||

Total = 80

shankarank
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#5 Re: Structure of Mohras

Post by shankarank »

if taka-thom (4) by itself is accepted as arudhi unit - then miSRa cApu goes to C=2 , stretching the limits.

tAngitataka(6)tAngiTatarikiTA(8)tAngitataka(6)taka-thom-taka-thom(8) - 2 times

56

tAngitataka(6)tAngiTatarikiTA(8)tAngitataka(6)taka-thom(4) tAngitataka(6)taka-thom(4) tAngitataka(6) tarikiTA-thom(6) tarikiTA-thom(6)- tarikiTA(4) ||

56

tarikiTA-tom(6) -is 3*C = 6.

and taka-thom-taka-thom(8) = 4*C = B = tAngiTatarikiTA(8) - the middle phrase.

shankarank
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#6 Re: Structure of Mohras

Post by shankarank »

I will sunset the symbhol "C" forever. :)

As explained in video posted by @sr_iyer in -> #2 - the last part is two arudhis represented as 2*(D + S) where S is the silence measure for "thom".

I will introduce additional symbols E+T for the arudhi of last round, with no presumption about its relation with any other component.

So first pattern : A, B, A, 2*(D+S) - two rounds

Last pattern : A, B , A , (D+S), A , (D+S), A, (E+ T), (E+ T), E.

2*(2*A + B + 2*D+2*S) = 4*A + B + 2*(D+S) + 3*E + 2*T

As expected 4*A cancels out.

2*B + 4*D + 4*S = B + 2*D + 2*S + 3*E + 2*T

B + 2*D + 2*S = 3 * E + 2*T = (time measure 1 round of basic pattern ) - 2*A.

The arudhi of the last round 3*E + 2(T) - 3 patterns with 2 silences (T) in between. T can be a new value depending on what is needed to reach samam.

3*E + 2*T is what Sri Srinivasan refers to as "periya" arudhi - a single bigger one.
<<Corrected : as suggested by @sr_iyer in Post #7 below >>

Now in all known arudhis , even the triSra , khanDA , MiSra - All go with B and 2*(D+S) as equal time measure.

with 32 count reckoning:

triSRA bhava : 10 , 6, 10 , 6

khANDa Bhava : 6, 10, 6 , 10

miSRa bhava : 2, 14, 2, 14

Then 2*B = 3*E + 2*T = 2*(2*(D+S)) - i.e the big arudhi at the end occupies twice the period of the two small arudhis that basic start pattern ends with.

But there is a counter example where B != 2*(D+S).

khaNDa cApu: (20 mAtras per Avarta - higher kALAM)

6,16,6,12 = 40 -> with 2 Avartas for one round.

two rounds = 80.

which in the last round will go as 6, 16, 6+6, 6+6, 6+10, 10, 8 = 80.

Here 10, 10, 8 will be executed as arudhi like 8,2,8,2,8 = 28.

E = 8, T=2.

3*E+2*T = 28 = 16 + 12 = B + 2*(D+S)

So some variation is possible in some cases.
Last edited by shankarank on 19 Aug 2019, 21:12, edited 3 times in total.

sr_iyer
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#7 Re: Structure of Mohras

Post by sr_iyer »

Read through your progression of thoughts/models/symbols. Thanks!

A small typo in one portion:
shankarank wrote:
19 Aug 2019, 10:19
E + T is what Sri Srinivasan refers to as "periya" arudhi - a single bigger one.
Using your symbols, this should actually be (E+ T), (E+ T), E

Your post later (as quoted below) indicates the correct formulation
shankarank wrote:
19 Aug 2019, 10:19
Then 2*B = 3*E + 2*T = 2*(2*(D+S)) - i.e the big arudhi at the end occupies twice the period of the two small arudhis that basic start pattern ends with.

SrinathK
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#8 Re: Structure of Mohras

Post by SrinathK »

I suggest a notation is far easier to read. For very basic work, one need not even consider the various syllables, but just write down the beats with t and , .

For a beginner's introduction, there must not be too much jargon (any jargon must be clearly explained and not taken for granted) and there must not be too much analysis either.

I suggest a video that covers a mohra slowly and then works up to concert speed would be far easier to grasp.

sr_iyer
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#9 Re: Structure of Mohras

Post by sr_iyer »

To use simple melody or swara based notation to indicate the parts of a mO(h)rA, let us try to start with some simple varisais – it’s a somewhat unconventional approach, but easier to notate. Let us note that the aesthetics of a mora should not be compared to that of a korvai (which has more complex and exact arithmetic patterns). Take any sampurna raga like mayamalavagaula or kalyani, and adi tala.
Component A: S,RGMPDN
Component B: S’,NDPMGR
Component C1: DP,M
Component C2: GR,S
Let us piece together the components in the order
A, B, A, C1, C2,
A, B, A, C1, C2
A, B, A, C1
A, C1
A,
C1, C2, C1, C2 --
for the last portion, let us use the same duration of C1, C2, C1, C2 with the pattern DP,M - G, - PM,G -R, - MG, R || (s… -- actually this leads-in to final-korvai))


With this, we get something like
S,RGMPDN - S’,NDPMGR - S,RGMPDN – DP,M – GR,S
S,RGMPDN - S’,NDPMGR - S,RGMPDN – DP,M – GR,S
S,RGMPDN - S’,NDPMGR - S,RGMPDN – DP,M
G,RGMPDN – DP,M
G,RGMPDN
DP,M - G, - PM,G -R, - MG, R || (s… -- actually this leads-in to final-korvai)

The aesthetics of a mOrA is partly associated with higher-speed or mEl-kAlam, one speed above what we sing melodically in (second speed) swaras or the varisais above. With that in mind, please listen to the initial portions of YouTube link in post #2, mapping the above structure to the components uttered as double speed (double of melodic second speed swaras) rhythmic solfeggio, Note that the swaras indicated above are just to map to the mOrA structure rather than having any stand-alone merit as swaras.

shankarank
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#10 Re: Structure of Mohras

Post by shankarank »

-> #7 @sr_iyer . True. E+T I took it as a component of the periya arudhi. Sri Srinivasan referred to the 2*(D+S) as two arudhis - in tamizh as iraTTai arudhi.

-> #8 @SrinathK - wanted to first establish an all ecompassing framework to understand the restrictions. And also used the actual sounds, initially. I do see that some of the sounds like dhitAngita have four or double mAtras per syllable and matra -> syllable correspondence is not one-to-one. Will put out a glossary with your suggested method for most common phrases.
Last edited by shankarank on 19 Aug 2019, 21:21, edited 1 time in total.

sr_iyer
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#11 Re: Structure of Mohras

Post by sr_iyer »

shankarank wrote:
19 Aug 2019, 19:33
as two arudhis - in tamizh as iraTTai arudhi.
Yes, and then goes on to define periya arudhi as double of the said iraTTai arudhi

shankarank
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#12 Re: Structure of Mohras

Post by shankarank »

Now sequel to Post #5:
shankarank wrote:
18 Aug 2019, 23:31
if taka-thom (4) by itself is accepted as arudhi unit - then miSRa cApu goes to C=2 , stretching the limits.
If ta-thom (3) is allowed :D - khANDA cApu gets a single Avarta one :mrgreen:

4, 6, 4, 6 - 2 times - 40 count

4,6, 4,3, 4,3, 4,(2+3),(2+3),2 - Total 40 count.

tAngiTa tAngiTAtaka tAngiTa ta-thom ta-thom, tAngiTa tAngiTAtaka tAngiTa ta-thom ta-thom

tAngiTa tAngiTAtaka tAngiTa (4) ta-thom (3) tAngiTa (4) ta-thom (3) tAngiTa (4) taka-thom,(2+3) taka-thom,(2+3) taka (2) ||

Mohra's Academic lower limit with the smallest tALAM Avarta. :lol:

So we mohrafied Sri tyAgarAja's uncavriddhi cipla beats!

shankarank
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#13 Re: Structure of Mohras

Post by shankarank »

shankarank wrote:
19 Aug 2019, 10:19

Now in all known arudhis , even the triSra , khanDA , MiSra - All go with B and 2*(D+S) as equal time measure.

with 32 count reckoning:

triSRA bhava : 10 , 6, 10 , 6

khANDa Bhava : 6, 10, 6 , 10

miSRa bhava : 2, 14, 2, 14

Then 2*B = 3*E + 2*T = 2*(2*(D+S)) - i.e the big arudhi at the end occupies twice the period of the two small arudhis that basic start pattern ends with.
After explaining the 4 bhAvas possible for Adi tALA , Sri Srinivasan ruled out the sankIRANA bhava : https://youtu.be/I-hTiDIJ6-M?t=356

He points out that sankIRNA bhAva , the reTTAi arudhi is 18, then the big arudhi in round 3 will be 36 whereas the tALA itself has only 32.

That implies that the big arudhi in round 3 will have to be twice the period of the reTTAI arudhi - as a rule. Something he indicated as reNDu bhAgam when explaining the structure at the beginning.

If that condition is violated, but other aspects are kept in tact:

Then SankIRNA bhAva arudhi can be done as below (32 count per Avarta):

1, 12, 1 , 18 , where 18 is the double arudhi as 9 + 9. - Two rounds : 64.

Last round:

1, 12 , 1 , 9, 1, 9, 1, (6,6), (6, 6) , 6 || -> ( 34 + 30 = 64)

First 2 rounds:
ta(1)-tAngitatakatarikiTAthom(6) tAngitatakatarikiTAthom(6)-ta(1)-tarikiTAthom tarikiTAthom tAm(6+3)-tarikiTAthom tarikiTAthom tAm(6+3) - Repeat this again.



Last Round :
ta(1)-tAngitatakatarikiTAthom(6) tAngitatakatarikiTAthom(6)-ta(1)-tarikiTAthom tarikiTAthom tAm(6+3)-ta(1)-tarikiTAthom tarikiTAthom tAm(6+3)-ta(1)-tarikiTAthom tarikiTAthom tA,,aam(6+6)-tarikiTAthom tarikiTAthom tA,,aam(6+6)-tarikiTAthom tarikiTAthom (6) || tAm

The original reTTAi arudhi , the two 9(s) and other 9(s) in last round if executed as (6,3), along with the big arudhi as (6,6-6,6-6) this will sound like a mohra.

The last big arudhi is only 6 short of the - two times the one before, requirement - 30 instead of 36 and will not sound too disproportionate!

And the use of just one Akshara as a beginning phrase (Aramba coRkaL) , if we feel that is inadequate - oTRAi collinum col collE ( even if it is of measure 1 it can count as a phrase)

May be we can call it lakshya mohra ;)

shankarank
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#14 Re: Structure of Mohras

Post by shankarank »

shankarank wrote:
24 Aug 2019, 23:25
First 2 rounds:
ta(1)-tAngitatakatarikiTAthom(6) tAngitatakatarikiTAthom(6)-ta(1)-tarikiTAthom tarikiTAthom tAm(6+3)-tarikiTAthom tarikiTAthom tAm(6+3) - Repeat this again.
<< Correction>>

Now that is doing 9 as 3 *3 - which still retains the triSra bhava only. So it is another version of triSra bhava arudhi, that albeit does not make the whole mohra fit into the rules.

Original triSra bhava arudhi
as explained by Sri Madurai T Srinivasan goes like :

10 , 6, 10, 6

ta,dhi,tAngitataguntarikiTAtaka(10 : ta,dhi, makes 4 rest 6) - tAngitataguntarikiTAtaka(6)-ta,dhi,tAngitataguntarikiTAtaka (10)- tarikiTAthom tarikiTAthom(6 : each 3)

This one follows the rule of normal mohra. - i.e 4*(D+S) = 3*E+2T = 12.

ta,dhi,tAngitataguntarikiTAtaka(10 : ta,dhi, makes 4 rest 6) - tAngitataguntarikiTAtaka(6)-ta,dhi,tAngitataguntarikiTAtaka (10)- tarikiTAthom (3) - ta,dhi,tAngitataguntarikiTAtaka (10)- tarikiTAthom(3) - ta,dhi,tAngitataguntarikiTAtaka (10)- tarikiTAthom,, (5) - tarikiTAthom,, (5) - tarikiTA (2) || thom.

E=2, T = 3 for the final big arudhi.

Another triSra bhava arudhi mohra

4, 12, 4, (6,6) - two rounds 2*32 = 64.

4, 12, 4, 6, 4, 6, 4 6, 3, 6, 3, 6 = 64.

Here E = 6, T =3 . And it obeys all the rules of Mohra.

ta,dhi (4)- tAngitataguntarikiTAtaka tAngitataguntarikiTAtaka (12: each 6 )- ta, dhi,(4) - tarikiTAthom tAm (6) tarikiTAthom tAm (6) - 2 rounds

ta,dhi (4) - tAngitataguntarikiTAtaka tAngitataguntarikiTAtaka (12) - ta, dhi, (4)- tarikiTAthom tAm (6) - ta, dhi, (4) - tarikiTAthom tAm (6) - ta, dhi, (4) - tarikiTAthom tarikiTAthom (6) tAm (3) - tarikiTAthom tarikiTAthom (6) tAm (3) - tarikiTAthom tarikiTAthom (6) || tAm


I will post a potential SankIRNA bhAva lakshya mOhra seperately :?

shankarank
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#15 Re: Structure of Mohras

Post by shankarank »

shankarank wrote:
24 Aug 2019, 23:25
Then SankIRNA bhAva arudhi can be done as below (32 count per Avarta):

1, 12, 1 , 18 , where 18 is the double arudhi as 9 + 9. - Two rounds : 64.

Last round:

1, 12 , 1 , 9, 1, 9, 1, (6,6), (6, 6) , 6 || -> ( 34 + 30 = 64)

First 2 rounds:
ta(1)-tAngitatakatarikiTAthom(6) tAngitatakatarikiTAthom(6)-ta(1)-tarikiTAthom tarikiTAthom tAm(6+3)-tarikiTAthom tarikiTAthom tAm(6+3) - Repeat this again.



Last Round :
ta(1)-tAngitatakatarikiTAthom(6) tAngitatakatarikiTAthom(6)-ta(1)-tarikiTAthom tarikiTAthom tAm(6+3)-ta(1)-tarikiTAthom tarikiTAthom tAm(6+3)-ta(1)-tarikiTAthom tarikiTAthom tA,,aam(6+6)-tarikiTAthom tarikiTAthom tA,,aam(6+6)-tarikiTAthom tarikiTAthom (6) || tAm
For a true sankIRNA bhava which is 4+5 pattern:

First 2 rounds:

ta(1)-tAngiTataka tarikiTAthom(6) tAngiTataka tarikiTAthom(6)-ta(1)-ta,dhi, tAngiTa tarikiTAthom(4+5)-ta,dhi, tAngiTa tarikiTAthom(4+5) - Repeat this again.

Last Round:

ta(1)-tAngiTataka tarikiTAthom(6) tAngiTataka tarikiTAthom(6)-ta(1)-ta,dhi, tAngiTa tarikiTAthom(4+5)-ta(1)-ta,dhi, tAngiTatarikiTAthom(4+5) -ta(1)-ta(1)-ta,dhi, tAngiTatarikiTAthom(4+5)-ta(1)-ta,dhi, tAngiTatarikiTAthom(4+5)-ta(1)-ta,dhi, tAngiTatarikiTAthom(4+5) || tAm

Now the final big arudhi for 30 is negotiated with a "ta" prefix , leaving the rest of the formation as having a sankIRNa bhava. But as a total count it is not divisible by 9 , and hence not the double of the initial reTTai arudhi.

Here A = 1 and that itself provides an adjoining pattern in the final round already doing a (1) (9) , (1) (9) first two - and the last (1) adjoins , what is now suggested as a new (1)(9) which repeats 3 times to make 30.

This thought came from the khaNDa bhava arudhi and miSra bhAvA arudhi - where the big arudhis go for 20 or 28 aksharas respectively in a 32 akshara per Avarta setting.

There what is being done is a tIRmAnam to cover the total aksharas: 20 -> 6(1)6(1)6. 28 -> (8)(2)(8)(2)(8) - but if we were to spell out a 5 or 7 in either we have to prefix it with ta.

(1,5)(1)(1,5)(1)(1,5) -> 20
and

(1,7)(2)(1,7)(2)(1,7) -> 28

So with 30 what I have done is

(1,4+5)(1,4+5)(1,4+5) without a kARvai i.e T = 0.

If not it can also be done as :

(4, 1 + 5) (4,1 + 5) (4, 1 + 5) - where the phrase used will be :

ta,dhIm,, (2,2,1) tAngiTatarikiTAthom (5) - ta,dhIm,, tAngiTatarikiTAthom - ta,dhIm,, tAngiTatarikiTAthom.

This sounds as a continuation pattern to ta,dhi,tAngiTatarikiTAthom the phrase used for sankIRNam.

And of course the ta,dhi, can be made higher kala (speed) as tarikiTAthom, (4) for effect etc.

Here to get a number divisible by 3 after removing an even number which can act as a kArvai in between 3 repetitions is available only with 30 - 12 = 18. as 30 - 2 , or 30 -4, or 30 - 6 or 30 - 8 - none of them divisible by 3.

But 18, 6, 6 sounds like a triSra bhavam.

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