Unique number of Janya Ragas

[violinvicky]

All:
We all know that 483 janyas are possible for a given melakartha, resulting in the sum of 483x72 = 34776 janya ragas. However it is also fairly obvious that swaras of Mohanam could easily have been Janya of Hari kambodhi or Sankarabharanam or Kalyani or Vachaspathi or... ! Hence the above number has a lot of redundancies.

Here is a link that I come across which cracks this problem and concludes that the number of unique janya raga to be 26864: http://rudiseitz.com/2013/03/15/janya-r ... -or-26864/

Author's (Rudi Seitz) explanation arrives at this number using probability theorem/ sheer number crunching (which is commendable in itself), while the comments of a mathematical professor, a certain Narayanan Santhanam, in the post discussion of this article explains this problem using Polynomial functions/ probability and combinatorics !! He even has a formula for this which is called as "Janya Polynomial" : [ (1+4y+6y^2) + 4x(1+4y+3y^2) + 6x^2(1+2y+y^2) ]^2 (1+2x+2y+2xy) (1+x+y+xy)

Of course there is the argument of Janyas with same swaras can still be sung/ perceived differently as its parent's bhavam/ other unique applications can be used to establish their individual identity. For example, When Madhyamam is not sung at all and if I do an aalapana with just Sa Ri Ga Pa Dha Ni of Major scale, One can still make out if I am singing Sankarabharanam (Over emphasize on Sa Ri Ga) or Kalyani (repeated gamakam on Ni touching the adjacent Sa) etc., But with my limited exposure to carnatic music I have not seen any authoritative explanation/ theory behind this. I would be certainly looking forward to tap the knowledge available here on this angle from the perspective of establishing uniqueness of redundant janya ragas. If you know of any such pairs/ groups, please let me know.

But for now, I am happy in knowing a number (26864) for the problem that has haunted me in a long time and thought of sharing this here.

With Love
Vicky

PS: If this is not the right forum/ category/ topic, please feel free to move it to the right section.

[mriganayanee]

Wow! Could you elaborate on that polynomial...some link?

[Rsachi]

What a discovery!!!!
So each raga will now be reduced to a mere number like a jailbird!
Mohana, in all his conceit and kApAlin glory, will henceforth be called Qaidi, sorry Janya, number 17329.
Maybe we should get GOI to straightaway allocate UID to these janya chappies, it will be some Aadhar when they fall on bad days.
Amma, are you listening to this matter of utmost importance and pride to TN?

[keerthi]

Congratulations to Rudy on his work at arriving at a number. However I have to place on record a few observations. I mean them in the best spirit.

1. Historicity of rAgas - The understanding of the rAga as a unique scala [ArOha-avarOha combination] in a janaka-janya scheme framed within the 72 mela scheme is woefully modern. The understanding of a rAga as a scale,is in itself an inadequate understanding of the notion of rAga and raga-based music.


2. Exhaustive lists of janya rAgas - The achilles heel of this metric is that it is unlikely to be sensitive to vakra rAgas.The difference between nATakuranji [smgmndnpdnS/Sndmgmpgrs/mgs]and upAnga khamas [smgpdnS/Sndpmgrs] won't show up. bhASAnga rAgas don't even fit into the picture. The first paragraph of Rudy's post acknowledges this fact. There are many books that have emerged since the beginning of the last century that attempt to list all potential janya rAgas; some in a mElakarta wise arrangement, some giving alphabetical lists. It is important to ask oneself the purpose of such an investigation; and its relevance to music and musicology.


Hence the number that warmed the cockles of Violinvicky's heart is not an exhaustive number of janya rAgas, but the number of upAnga non-vakra (varjya) janya rAgas alone.

[cmlover]

As Keerthi has rightly pointed out imprisoning Ragas in the Melas is modern. A vast majority bhashanga ragas have broken out of the fetters as are the vakra ragas whose name is myriad. Again many ragas are phrase based and the aro/avaro has no relevance. Hence if the question is as to how many ragas can exist under 22 shrutis the correct mathematical answer is infinite, not even counting the Gamaka variations!

[violinvicky]

@ Rsachi: My post in no ways discredited the aesthetics of (any) janya ragas. For all the subjectivity in carnatic system, I think ultimately it is also defined on a scientific platform and any step towards understanding existing voids should be perceived constructive. Would you also seethe in rage that the Melakarta system in itself is tagged and that Charukesi is just 26 or Panthuvarali is just 51. There are merits in tagging, bringing in order through categorization and even over-expensive reverse engineering to find which number a karta finds itself on the chart using concepts like Katapayadi Sankhyayai. So if tagging Mohanam as //Qaidi, sorry Janya, number 17329// helps identify a given Janya's time and space, why not?

@ Keerthi/ cmlover:
First and foremost my idea of sharing this post was not to pigeon hole the janya system as being mere methodical derivatives of a melakarta.
The whole post/ article is about the dubious deal of the number 34776 and how it can be meaningfully optimized to 26864. The number 34776 in itself is applicable only on - what you called "the modern context of upanga non-vakra (varjya) janya raagas". This naturally restricts all further discussions in this domain within that super set. So re-iterating this given criterion is as redundant as the number 34776 while assuming that this marks the end of Janya universe is naive.

For all the rhetoric of vastness of the janya system being polluted by optimizing the number of janyas (Sorry the number of upanga non-vakra (varjya) janyas) et al, I have not seen any inputs on how two different sets of "sa ri2 ga3 pa dha2 sa" can be sung differently to qualify as a janya of karta A or karta B independently. My quest for knowing independent existence of two or more raagas with same set of arohana/ avarohana has been futile so far. So I do believe there is merit to the optimization that was done.

While I thought the mathematical rigor in perfecting fallacies should be shared, it seems I happen to be robot misfit among rasikas. So I shall stop.

With Love
Vicky

[Rsachi]

Vicki,
For sure, I do not throw cold water on scientific experiments or mathematical analysis per se. They are interesting and I follow them quite well.

I was only joking that a matter of musical aesthetics was being subjected to such permutational analysis. This is the boon or bane of the multiverse of knowledge we live in. As Osho once joked, man will not be satisfied until he creates God in a test tube!

Sugar is sweet. But someone did scientific analysis and extracted sucralose which has sweetness without the calories. A good discovery indeed. So maybe analytical endeavours have some meaning even in music, it is just that it doesn't excite me.

I am happy to imagine that Mohana existed before someone tagged it in the janya analysis, and Mohana gave much pleasure to a lot of singers and listeners in folk and classical and far eastern music for ages.

Please don't stop your analyses or efforts to share. In the multiverse we all live in, we will always get some nasty responses, but why stop in our tracks if we are enjoying our journey? And there are quite a few rasikas here who engage in 'puzzles'. So you're most welcome, Vicki! And you know, I am going to throw the number 26864 at some musical nerd in the not so distant future for sure, and shall mention you to them too.
Ciao

[harimau]

@ Keethi/ cmlover:

For all the rhetoric of vastness of the janya system being polluted by optimizing the number of janyas (Sorry the number of upanga non-vakra (varjya) janyas) et al, I have not seen any inputs on how two different sets of "sa ri2 ga3 pa dha2 sa" can be sung differently to qualify as a janya of karta A or karta B independently. My quest for knowing independent existence of two or more raagas with same set of arohana/ avarohana has been futile so far. So I do believe there is merit to the optimization that was done.

While I thought the mathematical rigor in perfecting fallacies should be shared, it seems I happen to be robot misfit among rasikas. So I shall stop.

Vicky

Last December. Sri S R Janakiraman presented a lec-dem on "S R M P N S Ragas" at the Sri Parthasarathy Swamy Sabha.

He was not able to cover all of them for lack of time but did manage to cover quite a bit. I don't know/remember if among those ragas that he covered any two or more shared the same swaras. But theoretically, there should be 72 of the S R M P N S ragas. It is left as an exercise to the reader to determine which among these 72 share swaras, how many such groups exist, what are the names of these "identical looking" ragas, etc.

[vasanthakokilam]

Why the negative reaction to Vicky's post!

This kind of technicalities and math heavy calculations are not foreign to CM. ( think thalaprasthara and serial numbers that Akellaji talks about in the laya side of the house ). This article by Rudi is a contribution on how to arrive at the non duplicate count for that particular class of Janya ragas. All the other points mentioned about ragas being not scales etc are all valid and well known and in fact are acknowledged in the source article by Rudi as well. The main point is there are a couple of different approaches to this problem that are outlined there, which by no means is easy or trivial.

It looks like Vicky wondered about this in 2005 in a blog article about how to eliminate the duplicates. Rudi picked up that challenge recently and solved it. Why would Vicky not be excited! Great! Congratulations and thanks to both the originator and solver of the problem.

Now sing an alapana in Raga 1357

Though I am only kidding, it should be possible to number them sequentially and have a quick way to arrive at the Arohana/Avarohana given a Jayna serial number. Rudi, take up that assignment!

May be this problem will find a more comfortable home in our Puzzle thread!

[satyabalu]

* Nice way to start an interesting thread.

[rudi]

One could say there are limitless ways of rendering one raga or even one note. So, this was definitely not an attempt to reduce music to mathematics; it was only an exploration of a mathematical question that arises from music. Thanks to Vicky for posing the question and starting the discussion here.

One point that I didn't discuss in the original post was whether the number 26864 has any significance beyond the solution to a puzzle. Is it of any relevance to a practicing musician or rasika? I do think it's interesting to have a sense of the order of magnitude of the possibilities. One could imagine that the calculation turned out differently -- imagine, for example, that after accounting for duplicates there were only 2000 distinct (upanga varjya) janya possibilities. That would still be a huge number to work with, but perhaps it's small enough that a diligent and/or adventurous person could hope to consider each possibility in a lifetime. I see 26864 as similar to 34776 in that they are both too big for any person to systematically explore, and hence virtually limitless from the standpoint of a human musician or listener. Now, I will be happy if I can thoroughly explore just a handful of ragas in my lifetime, but I still find it interesting to have a sense for the scope of possibilities in the modern janya scheme.

Now, as for the assignment of giving each of the 26864 janyas a serial number, I'll start looking into that once I've learned to sing them all

[VK RAMAN]

Once Yesudas mentioned in one of the interviews that it took him 4 years to invent a new ragam and was wondering how many years it would have taken to come out with so many variations of each ragam and good luck to rudi for learning to sing them all

[vasanthakokilam]

Welcome to the forum Rudi. Thanks for the contribution.

Regarding the serial number scheme, I was thinking along the lines of the Katapayadi formula of figuring out the mela number from the first two alphabets reversed and then from that number getting the Aro/Ava. But in this case, may be we can make it even simpler if we are clever enough. May be. Something along the lines of: Is it divisible by N and a few such questions ( I am just making it up ) and outcomes a quick way to figure out the Arohana Avarohana. I have not really given it any thought to see if there is any regularity in the variations of the swaras. But then I also think why would there not be one? Then, the trick is come up with a numbering scheme that makes the job easier to go in the direction of Serial Number to Aro/Ava. ( just like how the cleverly chosen IP addressing scheme helps in quick routing in the internet where as the telephone numbering scheme is not ).

One possible brute force approach is this:

The top level starting point can be just a binary representation of 12 bits for Aro and 12 bits for ava. 0 represents lack of the swara and 1 represents the presence of the swara. With the added constraint that only 7, 6 or 5 of the bits can be turned on on each of the 12 bits.

But this 24 bit number space is really huge and very sparsely populated. That is not for human consumption or remembrance. we just need a numbering scheme in the range of 1 to 26864 that maps to each of the sparsely populated numbers in the 24 bit universe. I can see how that can potentially be done. But we do not want humans to deal with 24 bit monstrosities or requiring an app to convert! We just need a clever scheme to go from the serial number to the Aro/Ava without having to go through the 24 bit number.

I have not paid close attention to the derivation of the max number, but I have a feeling that the clue to the clever numbering scheme lies in the details of the derivation itself.

[vasanthakokilam]

Thinking through this further, we do not necessarily need a numbering scheme that goes strictly sequentially between 1 to 26864. This is all part of the cleverness I mentioned. It can be a larger number as long it is easy to remember.

Here are my stream of consciousness type thinking. Taking the IP addressing scheme as a guide, why not come up with a '.' notation with each segment coding for how many swaras in Aro and how many in Ava and for each which of the 12 are used. So, strictly as an example that I just pulled out of thin air, 12.6.82.34 can signify the 12th mela 6 can be a unique number that says whether it is 7-7, 7-6, 7-5, 6-6, 6-5, 5-5, 5-6, 5-7 etc. If that count is less than nine then 1 digit is enough, if not we need 2.. Just along those lines.

This is not a big departure from our current and conventional lines where we say the mela name and then audava-shadava etc. and then state the varja swaras for the aro/ava. That pretty much defines the syntax of the janya raga. But this numbering scheme is just a short cut so we do not have to say all those things, just like how we remember shankarabharanam to be 29.

The main thing is, it should be easy for humans to comprehend and not for machines.

We will call it simply the Janya Raga Address, JR Address to be short.

Then we can say, sing an alapana for the JR Address 28.4.54.23. Out comes a melodious Madhyamavathi!!

An IP address is hard to remember. That is why we have domain names like rasikas.org, Similarly, JR addresses are not easy to remember, that is why we have Raga names. So like DNS, we will have RNS. Raga Name Service that will translate back and forth between Raga name and its JR Address.

Also, it does not need to have to be 4 levels, it can be smaller but then we need to be prepared for the future and bringing in other types of Janya ragas into the mix. So instead of cornering ourselves to JRv4 and later confusing everyone by coming up JRv6, we can think ahead to possibly accommodate other janya raga types. But that is all for bonus points.

OK, I better stop now.

[rudi]

Oh no! I thought the numbering challenge was a joke but already we are getting involved in it!

So, what comes to mind as numbering scheme is [mela #].[arohanam deletions].[avarohanam deletions]. In this scheme, Madhyamavati could be represented as 28.gd.gd, meaning we start with mela #28 = Harikambhoji and omit ga and da from both the ascent and descent. This scheme doesn't account for duplicates, so you could get the same from 22.gd.gd, for example.

If you wanted to do it all with numbers, you could assign a unique number to each deletion possibility. For example: [0:(no deletion), 1:r, 2:g, 3:m, 4:p, 5:d, 6:n, 7: rg, 8: rm, 9: rp, 10: rd, 11: rn, 12: gm, 13: gp, 14: gd, 15: gn, 16: mp, 17: md, 18: mn, 19: pd, 20: pn, 21: dn].

In that scheme, Madhyamavati would be 28.14.14

[vasanthakokilam]

Rudi: Good job. Thanks for playing along. There is elegance in the simplicity of your scheme. By coding the varja, it is much simplified.

It will be a bit hard to remember the sequential mapping of the two digit numbers to the deletions.
What if we do this! Let us keep with the familiar numbering of swaras with s = 1, r = 2,...High s = 8 This way the M is 4 and P is 5 which we all know as the fourth and fifth. (With them well known and instantly recollect-able, 3 and 6 can ride on that recollection. 2 and 7 have to be learned by rote which is manageable after a few times of doing this..

The single swara deletion will be same as yours plus 1.

Two swara deletions would be: 23:rg, 24:rm, 25:rp, 26:rd, 27:rn 34:gm, 35:gp, 36:gd, 37:gn, 45:mp, 46:md, 47:mn, 56:pd, 57:pn, 67:dn
Now madhyamavati would be 28.36.36
In some rare cases where even the high S is omitted like Kurinji and Navroj, we can accommodate that also since we have a number for high Sa.
Kurinji will be 29.78.78
Navroj will be 29.678.678

(once)This (is) conquered, we need to do something about the 1 to 72 numbering of mela. The top 36 and bottom 36 are so intuitive. But the rest is a mess. Given a number it is hard to quickly recall what it is, other than the familiar 29, 28, 22,15, 8, 65 etc. which we have learned just through use. We need a scheme, even if it is multiple levels, that can help us quickly recall the swaras of that mela.

[makham]

All the above is futile because while talking about the swarasthanams we are dealing with a crude discrete approximation of what is essentially continuous in nature. The digital sampling of the analog spectrum was done mainly for documentation and dissemination purposes. I too indulged in arithmetical magics with our system before SSI told me to abandon any such attempt. He said "tomorrow I will create a new swara called shuta panchamam with a frequency slightly less than that of the standard panchamam and come up with another 72 mela ragas. How will you handle such developments?" Similar views were expressed by Prof William Skelton of Colgate University.

[rudi]

vasanthakokilam, yes, your adjustment makes the scheme easier to work with. For the melas themselves, one possibility that comes to mind is just to list the swara types in the order RG.M.DN. So, for example, 13.1.13 would be R1 G3 M1 P D1 N3 or Mayamalavagowla. Combining the mela and janya schemes, Madhyamavati would be 23.1.22:36.36

[vasanthakokilam]

Awesome rudi. That works. We are done! .. Well, we will see

Even those among us who are not warming up to all this math better be impressed with one aspect of this scheme. The purvanga-uttaranga symmetry of some of the melas are very obvious in this compact notation.

Thodi : 12.1.12
Mayamalavagowla: 13.1.13
Karaharapriya : 22.1.22
Shankarabaranam: 23.1.23

Quite impressive compared to 8, 15, 22 and 29 which obscures all this beautiful symmetry ( though the difference of 7 among the numbers should give some clues to that implicitly).

Thinking in terms of purvanga/uttaranga symmetry, this is really a short hand for the full representation. In the full version the purvanga consists of srgm and uttaranga consists of pdns. But in a mela since s and p are unchanging, the above scheme is correct. But we can run into issues when we move to janya ragas where p can be omitted. ( more on this later below ).

The full scheme then for the above four ragas are
Thodi : (1.12.1)(1.12.1) : (1.12.1)(1.12.1)
Mayamalavagowla: (1.13.1)(1.13.1) : (1.13.1)(1.13.1)
Karaharapriya : (1.22.1)(1.22.1) : (1.22.1)(1.22.1)
Shankarabaranam: (1.23.1)(1.23.1) : (1.23.1)(1.23.1)

This obvisouly represents more than the 72 melakarthas of Venkatamakhin. This accomodates for Aro and Ava to have different swaras. Like the omitted swaras as in Dikshithar Sampradaya of Asampoorna melas as well as Aro and Ava having totally different swarasthanas for the same scale degree ( E.g M1 in Aro and M2 in Ava etc. ). ( more on the omitted swaras below )

There is the obvious syntactic overhead. We can do something about that.

If the context is clear that we are working with the 72 sampoorna melas of Venkatamakhin, we can then do two stages of simplification.

First stage is to leave out the second part after the ':'

Thodi : (1.12.1)(1.12.1)
Mayamalavagowla: (1.13.1)(1.13.1)
Karaharapriya : (1.22.1)(1.22.1)
Shankarabaranam: (1.23.1)(1.23.1)

This syntax with the parts grouped like above makes the purvanga/uttaranga split obvious and also makes the role of 'pa' to be the base of the uttaranga very obvious, as opposed to some fuzzy concept of 'pa' being in the middle of the octave! This role of 'pa' as the base of the uttaranga has some important implications for symmetry which we can talk about later.

( as a side bar, we hear people hum sa-pa-sa. They should really hum sa-ma , pa-sa if they care about purvanga-uttaranga split. In my opinion we all should care and I will be glad if students are taught to do this as opposed to sa-pa-sa, to get their voice in order and for checking their swarasthanas. Of course, if the song they are going to sing does not have ma then they should not.)

Second stage simplification is, In melas, s and pa do not change, and so we can leave that out too without creating any ambiguity

Thodi : (12.1)(12.1)
Mayamalavagowla: (13.1)(13.1)
Karaharapriya : (22.1)(22.1)
Shankarabaranam: (23.1)(23.1)

It is better to preserve the high Sa for symmetry purposes since it is the uttaranga counterpart to the purvanga M.

The above short hand is to be used only for melas and not for janyas as we will see below.

Thinking through this explicit representation of symmetry, let us extend it to Janya Ragas also. With the benefit of standing on the shoulders of the above scheme, an equivalent representation for JR address is to make very good use of '0'. Let '0' represent absence of a particular swara position. So each swara position can take one of 4 values: 0, 1, 2 or 3

If we work within the Venkatamakhin sampoorna mela, we can use the middle representation above and use 0 for the missing swaras.

Madhyamavathi : (1.20.1)(1.02.1) ( wow again, look at that mirror symmetry between purvanga and uttaranga )
Abhogi : (1.22.1)(0.20.1)