108 basis rAgAs/ The extended mela system/ dvi madhyama ragas
Ramasubramanian Ramakrishnan
Here is a mathematical development of how you can get
108 mela kartha(basis ragas) system, which captures some
ragas like hindustani lalit. For those interested in
shruti-bedam, hindustani lalit can be gotten by
shifting notes of subapantuvarAli and Ahir-lalit
can be gotten by shifting mAyAmAlava gowlA, as
another nettor remarked recently. Why not more
such ragas with both the madyamas? Read on!
I heard that someone (Mr.X) has discovered this 108
system earlier and composed in a few new ragas. Since
the number 108 matches with Mr.X's dicovery, I am
guessing that it is the same system. If someone knows
details on Mr.X and this system, please post.
-----------------------------------------------------
How do we get 72 melakarthas? Let's develop this using
a keyboard.
-------------------------------------------
| | | | | | | | | | | | | | |
| | | | | | | | | | | | | | |
| | | | | | | | | | | | | | |
| | | | | | | | | | | | | |_2|
| |_2| |_4| | |_7| |_9| |11| | |
| | | | | | | | |
| 1 | 3 | 5 | 6 | 8 | 10| 12 | 1 |
| | | | | | | | |
|____|____|____|____|____|____|____|____|
repeat
{
1 = Sa
2 = Ri1
3 = Ri2, Ga1
4 = Ri3, Ga2
5 = Ga3
6 = Ma1
7 = Ma2
8 = Pa
9 = Dha1
10 = Dha2, Ni1
11 = Dha3, Ni2
12 = Ni3
} until (all keys are exhausted)
Assuming we live with the assumption of equivalence of Ri2, Ga1
etc, we have the following mathematical explanation for the 72
mela scheme:
Let's forget about the keys numbered 6,7 and 8 for now.
Consider 2,3,4,5:
If 2 is chosen as Ri (Ri1), we have three choices for Ga (3,4,5).
If 3 is chosen as Ri (Ri2), we have two choices for Ga (4,5) and
if 4 is chosen as Ri (Ri3), 5 is the only possible Ga. Hence,
there are six possible combinations of Ri and Ga.
Applying the same formula to Dha and Ni among (9,10,11,12),
we have six possible combinations of Dha and Ni.
Now, key 8 is Pa, which is a fixed note. Hence choosing Ma from
(6,7), we have 6 x 6 x 2 = 72 possible scales with unique
set of SRGMPDNS, leading to the 72 melakarthas. Now, many
janya ragas can be considered janya of one of the 72 melas.
Some bAshanga rAgAs are better explained in a 72x72 extended
melakartha system. This scheme still does not capture rAgAs
like hindustani lalit or ahir lalit. How can we fix this?
Consider choosing two of the three notes (6,7 and 8):
-If 6,8 are chosen, we get the 36 "shuddha madhyama" rAgAs.
-If 7,8 are chosen, we get the 36 "prati madhyama" rAgAs.
-Why are we obsessed with retaining Panchama?
If 6,7 are chosen, we get another 36 rAgAs. Call them
"dvi-madhyama" ragas, if you like. These 36 will capture
rAgAs such as lalit and ahir lalit. What is so special
about retaining Pa? We have the concept of madhyama
shruti, right? Here, we go then. An extended melakartha
scheme with 108 basis rAgAs. Hindustani ragas like lalit
and Ahir lalit occur naturally as melas in the 108 system!
Are there other ragas like lalit?
* For those breaking their head over janya-janaka relationship,
there is more headache for janya ragas without panchama.
* Now, newgroupish stuff: Here is a unique opportunity.
Interested folks can compose in all 108 and reach
higher than Mount Everest for the first time!
Mathematically yours,
Subu
Raghunath K. Rao
>
>-If 6,8 are chosen, we get the 36 "shuddha madhyama" rAgAs.
>-If 7,8 are chosen, we get the 36 "prati madhyama" rAgAs.
>-Why are we obsessed with retaining Panchama?
> If 6,7 are chosen, we get another 36 rAgAs. Call them
> "dvi-madhyama" ragas, if you like. These 36 will capture
> rAgAs such as lalit and ahir lalit. What is so special
> about retaining Pa?
^^^^^^^^^^^^
Well, of course one couldn't say the same thing about retaining Sa :-).
If one sits down and derives the fundamental 12 notes based on the principle
of octaves, then the Panchama is of course critical. So I think retaining
the Pa in melakarthas *is* justifiable. Although the 108 melakartha
seems mathematically attractive, I think it is over-generalizing the
basis for deriving janya ragas. Why stick to 108, why not consider all
combinations of choosing 6 notes from the remaining 11 (excluding Sa),
i.e. create a basis of 11!/(6!*5!) = 462 melakarthas? Because it overspecifies
the requirement. Of these 462, a large part will not sound pleasant to the
ear!
If one were to derive an alternative melakartha system, a thumb rule one could
use is that a separation of more than 3 notes (eg. more than R1 to G3)
should not be allowed in creating a melakartha. Of course, janya ragas can have
such large jumps, but these are derived by simple varja relationships with
appropriate melas. The 72 mela system is partially based on a similar principle but maybe a more general system can be derived that includes Hindustani ragas
(like lalit and Ahir lalit that you mention). I haven't worked out the details
fully, but maybe it will lead to a different mela system, with more than 72
ragas. Maybe, it will even lead to the same 108 raga system that you suggest.
More on this later when I get around to doing it.
BTW, I think I have heard of the 108 mela system before (don't remember who
or when), but I do recall that it did not add much. I mean, to my knowledge
no new beautiful ragas were discovered :-(.
------------------------------------------------------------------------
_____ ___ _______
K. RAGHUNATH RAO /____/ \ /__/\ /______/\
email : rr...@chitra.ece.iit.edu | __ \ /| / _ \ \ / ___ \ |
sleepy (res) : (312)791-9428 | |__) |/ / /_\ \ \ | / | \ | |
sleepier (off) : (312)567-3407 | __ /\ | ___ | | | | | | | |
| | \ \ \ | / | \ | | | | |_| | |
It is the intonation and not | | |\ \ \ | | | | | | | \/__/ |/
the intention that matters!! |_|/ \_\/ |_|/ |_|/ \______/
------------------------------------------------------------------------
SOMASUNDHAR VENKATASUBRAMANIAN
>
>Here is a mathematical development of how you can get
>ragas like hindustani lalit. For those interested in
>
>-If 6,8 are chosen, we get the 36 shuddha madhyama rAgAs.
>-If 7,8 are chosen, we get the 36 prati madhyama rAgAs.
>-Why are we obsessed with retaining Panchama?
raagas. Retaining panchamaas thus was much less an
obsession than a requirement. But yes, why should
a kartha be sampoorna-sampoorana...is reasonably
valid IMO.
> If 6,7 are chosen, we get another 36 rAgAs. Call them
> dvi-madhyama ragas, if you like. These 36 will capture
> rAgAs such as lalit and ahir lalit. What is so special
> shruti, right? Here, we go then. An extended melakartha
> scheme with 108 basis rAgAs. Hindustani ragas like lalit
> and Ahir lalit occur naturally as melas in the 108 system!
Ahir lalit type raagas to be a kartha??
In the present scheme (72), these raagas are a
still there as a part of vakraas, isn't it??
By making Dwi-madhyamaas as karthaas(janakaas), are we
getting at some new janyaas, which has this particular
swara flavours?? If so, are those janyaas (which naturally
would come only as a part of the vakraa in the present scheme)
already not included.
But ofcourse if a need for making Dwi-madhyamaas as
karthaas is substantiated, then for sure one can say
that, "there can't be more than 108 kartha raagas"
So in that sense, this generalized kartha scheme is
interesting.
But it gives the whole idea of sampoorna-sampoorna,
sampoorna-panchama etc,, etc.. type classification,
a different taste.
Being a vakraa raaga is in no way lesser in any sense
of melody compared to proper janyaas or karthaas, IMO.
> Are there other ragas like lalit?
>
<...>
>
>Subu
>
>----------------
<...>
The names gourishree, thodishree etc.. are surely sounding
nice. It will be interesting to know some janyaas of these
raagas (hearing it ofcourse....arithmetically writing down
the various stuff isn't really a problem.)...and thereby
knowing better the relevance of making "**shree's" as
karthaas.
Just my views....
--cheers
Somsundhar
Ajay P Nerurkar
: -If 6,8 are chosen, we get the 36 "shuddha madhyama" rAgAs.
: -If 7,8 are chosen, we get the 36 "prati madhyama" rAgAs.
: -Why are we obsessed with retaining Panchama?
: If 6,7 are chosen, we get another 36 rAgAs. Call them
: "dvi-madhyama" ragas, if you like. These 36 will capture
How do you propose to deal with raags like Nand that take Ma1,Ma2 and Pa ?
--
Ajay
Ramasubramanian Ramakrishnan
In article <3t47b0$l...@azure.acsu.buffalo.edu>, a...@cs.buffalo.edu (Ajay P Nerurkar) writes:
|> How do you propose to deal with raags like Nand that take Ma1,Ma2 and Pa ?
|>
|> Ajay
Please post the aaroh, avaroh of Nand. Does this raag use Ma1, Ma2
and P in succession?
Coming to those suggestion on the importance of retaining Pa in this
thread, one should remember that Pa gets its importance from the fact
that
(Frequency of Pa) = 1.5 * (Frequency of Sa).
Sa becomes Pa, if Ma1 is shifted and interpretted as Sa .
(I guess dwi-madhyama ragas have to go with madhyama
shruti, i.e. set Sa,Ma1,Sa in the shruti potti).
Now, here is my argument for those who want to retain Panchama
at any cost. If those who formulated the 72 scheme decided to
call Ma1 as madhyama and (Ma2, Pa) as shuddha panchama
and prati panchama, we would have had a different set of 72
melakarthas. Who knows? They could have justified this if
madhyama is interpretted as a central note, which has to
be unique :)
I guess a 462 mela system is justifyable too if you can identify
some ragas that CAN NOT fit in the current system, but can in the
new system. IMO, the point of 108 is that it captures ragas like
lalit, which do not fit in the 72 system. One has to understand
that the 72 mela system is mathematical too. There are some melas
that "suck". So, why shoot the 108 system down thinking that some
of these ragas will suck? I am sure there was opposition for the
72 mela system as well, when it was formulated. Of course, the
current status of these ragas = their scales. It is necessary
for these scales to qualify as ragas and for these ragas to be
"familiarized" by some popular (future) prodigious musician
like koteeswara Iyer or Dr. BMK! Thanks to Nurani Chandrasekar
for the info that the 108 system has already been proposed and
explored. I would love to listen to (late) Shri. Kalyanaraman's
work.
Lalit and Ahir Lalit DO NOT fit in the 72 scheme even as vakra,
bhAshAnga (any other?) ragas. They use both the madhyamas in
succession in both aarohanam and avarohanam. How about
Hem-lalit folks? Is it a dwi-madhyama raga? I have not
listened to this one long enough..
On a related note, ragas like behog, hamir kalyani, sAranga,
which use two madhyamas (though may not be in succession) seem
to have a hinduatani origin. Of course there are several other
ragas in hindustani like the kedar, hamir families, shuddha
saarang, ramkali, etc that use both the madhyamas. IS THERE
ANY CARNATIC RAGA (meaning originated in carnatic) THAT USES
BOTH THE MADHYAMAS? (not necessarily in successtion)
Subu
Ajay P Nerurkar
: Please post the aaroh, avaroh of Nand. Does this raag use Ma1, Ma2
: and P in succession?
Here you are,
Aaroh : S G MmP D N S'
Avaroh : S' NP Dm PG MP RS
or
MRS
Legend : R = Re2, G = Ga3, M = Ma1, m = Ma2, D = Dha2, N = Ni3
--
Ajay