INDIAN MUSICOLOGY REVISITED
“ SADJA-GRAMA ” SCHEME 1
AS
PER
BHARATA
Muni,
SADJA-GRAMA SCHEME
IS
THE
EARLIEST
FORMAT INHERITED by us DIRECTLY from the
SAMA
VEDA 2
EARLY MUSICIANS PERCEIVED ‘MUSIC’ TO CONSIST OF
ONLY TONEs
‘7’
(SWARAs), namely …. , 3
PRONOUNCED
SADJA = RISHABHA = GANDHARA = MADHYAMA = PANCHAMA = DHAIVATA = NISHADA =
‘S’ ‘R’ ‘G’ ‘M’ ‘P’ ‘D’ ‘N’
AS
(Sa) (Ri) (Ga) (Ma) (Pa) (Dha) (Ni) 4
SADJA-GRAMA
LOWER LIMIT
UPPER LIMIT
OCTAVE
S
S' R3
3
G2
M4
P4
D3
2 4
4
3
SEVEN SWARAS
N2
2
S' 4
4
THE
ARE GIVEN IN
5
SADJA-GRAMA
LOWER LIMIT
UPPER LIMIT
OCTAVE
S
R G R3
3
G2
M M4
P4
2 4
EACH
P
4
D D3
3
N N2
2
S' S' 4
4
UNIQUE SRUTI-CONTENT AND THESE ARE NOT EQUAL
SWARA
HAS
A
6
SADJA-GRAMA
LOWER LIMIT
OCTAVE
D3
2 4
3
4
THESE
ARE
N2
2
(S’)22
P4
(D) 18
M4
(D) 16
G2
(P) 13
(M) 9
(G) 5
(R) 3
(S) 0
R3
3
UPPER LIMIT
S' 4
4
THE
“SEATs” FOR
EACH SWARA
7
SADJA-GRAMA
LOWER LIMIT
UPPER LIMIT
OCTAVE
S
S' R3
3
G2
M4
P4
2 4
EACH
SWARA
LIMITS
FOR
4
D3
3
N2
2
‘LOWER’ ‘UPPER’ HAS
IT’s
S' 4
4
and
SRUTI-CONTENT
8
SADJA-GRAMA (A
SIMPLIFIED
SCHEME
REPRESENTATION )
SWARA-RANGE FROM
TO
“SEAT” OF THE SWARA
SADJA (LOWER)
-18.00
0.00
0.00
RISHABHA
0.00
3.00
3.00
GANDHARA
3.00
5.00
5.00
MADHYAMA
5.00
9.00
9.00
PANCHAMA
9.00
13.00
13.00
DHAIVATA
13.00
16.00
16.00
NISHADA
16.00
18.00
18.00
SADJA’ (UPPER)
18.00
22.00
22.00
SWARA
9
this
is
the
‘TRADITIONAL VIEW’ About SADJA-GRAMA
10
What does my research work Reveal ?
11
‘Ancients’ of the WEST as well as the EAST Worshipped Numbers From ‘1’ to ‘12’ As ‘SACRED’
12
When Numbers From ‘1’ to ‘12’ Are analyzed mathematically Only ‘22’ fractions Can be formulated
13
I had
transformed these 22 fractions into the Tonal domain And assigned values In an octave calibrated Into 22 equal segments
(Please see the results In the tabular format)
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continued SERIAL
FRACTION
SRUTI VALUE
SERIAL
FRACTION
SRUTI VALUE
1 2 3 4 5 6 7 8 9 10 11
1/1 12/11 11/10 10/9 9/8 8/7 7/6 6/5 11/9 5/4 9/7 4/3
0.00 2.76 3.03 3.34 3.74 4.24 4.89 5.79 6.37 7.08 7.98 9.13
12 13 14 15 16 17 18 19 20 21 22
11/8 7/5 10/7 3/2 11/7 8/5 5/3 12/7 7/4 9/5 11/6 2/1
10.11 10.68 11.32 12.87 14.35 14.92 16.21 17.11 17.76 18.66 19.24 22.00
15
I found that the ‘sruti values’ Indicated in RED colour Were very close to the ‘Traditional Sruti values’ of The Sadja-grama format (Please see the following table)
16
continued FRACTION
SRUTI VALUE
Traditional Sadja-grama values
SERIAL
FRACTION
SRUTI VALUE
1/1
0.00
0.00
12
11/8
10.11
1
12/11
2.76
3.00
13
7/5
10.68
2
11/10
3.03
3.00
14
10/7
11.32
3
10/9
3.34
15
3/2
12.87
4
9/8
3.74
16
11/7
14.35
5
8/7
4.24
17
8/5
14.92
6
7/6
4.89
18
5/3
16.21
7
6/5
5.79
19
12/7
17.11
8
11/9
6.37
20
7/4
17.76
9
5/4
7.08
21
9/5
18.66
10
9/7
7.98
22
11/6
19.24
11
4/3
9.13
2/1
22.00
SERIAL
5.00
9.00
Traditional Sadja-grama values
13.00
16.00 18.00
22.00 17
I interpreted that the ‘Traditional Sruti values’ of Sadja-grama Were the “ROUNDED - OFF” Values of six tones Belonging to the family of “22 Fractions”
18
The first thought That would appeal to a ‘Rational’ mind is that It is a mere “CO-INCIDENCE”
19
I researched further In the realms of What is known as ‘Madhyama-grama’ and ‘Murchanas’ To discover and get Convinced that Some “MASTER-HAND” Had conceptualized this ‘DESIGN’
20
I HOPE MY VIEWER IS WITH ME ON THIS
VERY
‘SIGNIFICANT’
DEVELOPMENT ??
21
I AM TALKING ABOUT
BETWEEN
TOTALLY
TWO
UNRELATED
ENTITIES ??
22
THE ‘22 - FRACTIONS” BASED ON AN
ANCIENT
CULTURE
( AND DETERMINED BY USING CONTEMPORARY MATHEMATICS )
Vis-à-vis ANCIENT
INDIAN ‘SHASTRAs’ OF MUSIC ?? 23
To know more details On my relevant research work on ‘Madhyama-grama’ And ‘Murchanas’, Please read my blog Exclusively made for these subjects.
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CONTACT
ME
Tele: 91 20 30441256 Mobile: 9890266845, 9850121834 E-Mail:
[email protected],
[email protected] Web site: http://www.22sruti.com
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