From: krisna@cham.cs.wisc.edu (Krishna Kunchithapadam)
Newsgroups: rec.music.indian.classical
Subject: More information on Vivadi ragas
Date: 6 Apr 92 19:33:22 GMT
Followup-To: rec.music.indian.classical
Organization: Dept. of CS, Univ. of Wisconsin, Madison

In my earlier article, I tried to clarify some of  the  questions
about  Vivadi mela ragas. Some of my statements were probably not
quite clear. I would like to clarify them and present  some  more
information on this topic.

When I said that Sudha Ga/Ni and Shatsruthi Ri/Dha were Vivadi to
the  swaras  with  which  they share their swara sthanas, I meant
that  Sudha  Ga/Chatusruthi   Ri,   Sudha   Ni/Chatusruthi   Dha,
Shatsruthi  Ri/Sadharana Ga and Shatsruthi Dha/Kaisiki Ni are the
pairs which are assigned the same swara sthanas.

The following is a table of the sruthis used  in  Carnatic  music
and  has  the  frequency  ratios  of these sruthis to the Aadhara
Shadja.

Please note that the names of the sruthis (Chatusruthi) and their
notation  (numbering)  is  different  from  that used for swaras.
Hence (r3 is the Trisruthi Rishabha and is quite  different  from
R3 which is the Shatsruthi Rishabha swara).

-----------------------------------------------------------------
  Sruthi                    Notation F-ratio   Used in raga
-----------------------------------------------------------------
  Shadja                    sa       1         All ragas

  Ekasruthi Rishabha        ra r1    256/243   Gowla
  Dvisruthi Rishabha        ri r2    16/15     Mayamalavagowla
  Trisruthi Rishabha        ru r3    10/9      Bhairavi
  Chatusruthi Rishabha      re r4    9/8       Kalyani

  Sudha Gandhara            ga g1    32/27     Ganamurthy
  Komal Sadharana Gandhara                     Bhairavi
  Sadharana Gandhara        gi g2    6/5       Kharaharapriya
  Anthara Gandhara          gu g3    5/4       Sankarabharanam
  Chyutha Madhyama Gandhara ge g4    81/64     Devagandhari

  Sudha Madhyama            ma m1    4/3       Kuntalavarali
  Tivra Sudha Madhyama      mi m2    27/20     Gowlipanthu
  Prati Madhyama            mu m3    45/32     Kalyani
  Chyutha Panchama Madhyama me m4    64/45     Varali

  Panchama                  pa       3/2       All ragas with Pa

  Ekasruthi Dhaivatha       da d1    128/81    Saveri
  Dvisruthi Dhaivatha       di d2    8/5       Mayamalavagowla
  Trisruthi Dhaivatha       du d3    5/3       Kambhoji
  Chatusruthi Dhaivatha     de d4    27/16     Kalyani

  Sudha Nishada             na n1    16/9      Kanakangi
  Komal Kaisili Nishada                        Bhairavi
  Kaisiki Nishada           ni n2    9/5       Kharaharapriya
  Kakali Nishada            nu n3    15/8      Sankarabharanam
  Chyutha Shadja Nishada    ne n4    243/128   Kuranji
  Tivra Kakali Nishada

  Tara Shadja               sa       2         All ragas with Sa
-----------------------------------------------------------------

Sudha Gandhara and Komal Sadharana Gandhara,  Sudha  Nishada  and
Komal  Kaisiki  Nidhada & Chyutha Shadja Nishada and Tivra Kakali
Nishada are the same sruthis,  they  just  have  different  names
based on the ragas they occur in.

This table does not give the frequencies of  Shatsruthi  Rishabha
and  Dhaivatha.  This  is  because, continuing the progression of
Eka, Dvi, Tri, Chatu sruthis, we require that Shatsruthi Rishabha
have a frequency ratio of 6/5 and that Shatsruthi Dhaivata have a
frequency ratio of 9/5. This makes Shatsruthi Ri and Sadharana Ga
identical  &  Shatsruthi  Dha  and  Kaisiki Ni identical. The 22-
sruthi system does not make any finer distinctions between  these
two  sruthis whereas the differences actually exist and musicians
intuitively take into account this  difference  while  performing
these  sruthis.  In  fact,  some  texts  on  Indian music, do not
distinguish  between  Chatusruthi  Rishabha  and  Sudha  Gandhara
(which  led to the same swara sthana for these two sruthis in the
12-swara system). The same is the  case  for  Shatsruthi  Ri  and
Sadharana  Ga,  Chatusruthi Dha and Sudha Ni & Shatsruthi Dha and
Kaisiki Ni. The above table seems more  accurate  since  it  does
distinguish  between  some  sruthis  that  share  the  same swara
sthana.

               Vadi, Anuvadi and Vivadi intervals.
	       -----------------------------------

The way musicologists classify intervals as samvadi or  otherwise
is by frequency-ratio multiplication.

(1) The Sudha Madhyama and Panchama intervals  (4/3  and  3/2  f-
ratios  rspy)  are  classified as Samvadi. The product of these 2
ratios is 2, which signifies an octave. This is  the  reason  why
drone  instruments  are tuned to Sa-Pa-Sa or Sa-Ma-Sa. Both these
settings capture the 2 Samvadi intervals.

Any two other sruthis which are separated by frequency ratios  of
3/2 or 4/3 are Samvadis of each other.

The following table gives a list of all  Samvadi  Sruthis  (using
the  22-sruthi  notation).  On  the left are those pairs whose f-
ratio is 4/3 and on the right are those pairs with f-ratio 3/2.

-----------------------------------------------------------------
                    ratio = 4/3   ratio = 3/2
-----------------------------------------------------------------
                                  r1 d1
                    r2 m4         r2 d2
                                  r3 d3
                    r4 p          r4 d4

                    g1 d1         g1 n1
                    g2 d2         g2 n2
                    g3 d3         g3 n3
                    g4 d4         g4 n4

                    m1 n1         m1 p
                    m2 n2
                    m3 n3

                    p m1
-----------------------------------------------------------------

(2) Chatusruthi Dhaivatha and Sudha Gandhara, Trisurthi Dhaivatha
and  Sadharana Gandhara, Dvisruthi Dhaivatha and Anthara Gandhara
and Eka Sruthi Dhaivatha and Chyutha Madhyama Gandhara constitute
Anuvadi intervals. Their f-ratio products is 2.

(3) The intervals between  the  Rishabha  and  the  corresponding
Nishada  sruthis are all Vivadi intervals. Once again the product
of the f-ratios of these sruthis is 2.

An confuing point to here is that the above rules  only  describe
Vadi,  Anuvadi  and  Vivadi  intervals,  not sruthis or swaras as
such. I am not sure how these rules can be applied to swaras.  My
impression  is  that  concordance  or  discordance  of sruthis is
determined by their frequency ratios -- if  the  notes  are  very
close,  their  f-ratio is not that of small integers and they are
discordant, if the f-ratio is that of small integers, these notes
are concordant.

The above table and rules  do  not  answer  all  questions  about
sruthis and Vivadi melas. I request more  information  about  the
topic  of  sruthis  from others.

-- Krishna


+---------------------------------------------------------------+
|    Krishna Kunchithapadam		krisna@cham.cs.wisc.edu	|
|    Department of Computer Sciences				|
|    University of Wisconsin, Madison				|
+---------------------------------------------------------------+
Newsgroups: rec.music.indian.classical