Conceptual Overview
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CONCEPTUAL
OVERVIEW
Contemporary music (of the West & the East) Is limited to the design of “12 Tones”
However, Contemporary Indian Carnatic music traditions Claim that there are Many more ‘tones’ in actual use, duly integrated with their ‘Ragas’
but….. , These are NOT ‘defined’, ‘quantified’ & ‘adopted’ on a sound musicological basis
Great ‘seers’ of medieval India indicated the existence of
‘22 TONEs’ In
Music
But …. , Not much evidence was adduced in support of their Contentions.
My research work in pursuit of this ideal had been somewhat Fruitful. I had narrated the details, in my Book :
MY
BOOK
A
BRIEF SUMMARY Of My “FINDINGs”
OUR “ANCIENT MUSIC” WAS FOUNDED ON 22 ‘Simple Fractions’
These
22
‘Simple
Fractions’
were derived from the Natural Numbers between ‘1’ and ‘12’
The “Ancients” worshipped
These Natural Numbers between ‘1’ and ‘12’ as “Gods” (for
some unknown reasons)
‘Sumerians’ known
the earliest civilization ( 4000 B.C. )
worshipped Their gods/ goddesses as 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, and 60 (For details use my link: http://sumeriangods.blogspot.com/ )
I
have established that these are eventually reducible to The numbers from ‘1’ to ‘12’ only
Therefore, there must be something very “ SPECIAL ” about these Numbers between ‘1’ and ‘12’ !
The
“Ancients” shunned
The Numbers between ‘13’ and ‘18’ As “Devil’s
Domain”
The
The as
“Ancients” glorified
Number
‘22’
“INFINITY”
(i.e. SUM of all things Created by GOD)
I, therefore, Confined my ‘Examination’ To the numbers Between ‘1’ and ‘12’ And SHUNNED Numbers between ’13’ and ’18’
I discovered that Only “22” fractions Can be formulated Mathematically Between ‘1’ and ‘12’
ONLY
These are the 22 ‘Simple Fractions’
‘mathematically between
feasible’
‘1’ and ‘12’
When these 22 mathematical Fractions are converted as ‘tones’ in the
22 Pitch (Sruti) Octave, they
acquire the following tonal values !
(please see next slide)
FRACTIONs
TONAL VALUEs
FRACTIONs
TONAL VALUEs
(in 22-pitch scale)
(CONTINUED)
(in 22-pitch scale)
1/1
0.00
11/8
10.11
12/11
2.76
7/5
10.68
11/10
3.03
10/7
11.32
10/9
3.34
3/2
12.87
9/8
3.74
11/7
14.35
8/7
4.24
8/5
14.92
7/6
4.89
5/3
16.21
6/5
5.79
12/7
17.11
11/9
6.37
7/4
17.76
5/4
7.08
9/5
18.66
9/7
7.98
11/6
19.24
4/3
9.13
2/1
22.00
I discovered
‘six ( out are
(the
that
fractions’
of These
“22 Fractions” )
“seeded” into ‘Sadja-grama’
earliest
musical scheme
‘rounded-off’ (see
of
the
India)
forms, like this ! next slide)
in
Sadja-GRAMA
TONEs
(“Rounded-off” values)
Sadja (Tonic)
Nearest members of the Family of ‘22- FRACTIONS’
0.00
1/1
Rishabha
3.00
2.76
12/11
Gandhara
5.00
4.89
7/6
Madhyama
9.00
9.13
4/3
Panchama
13.00
12.87
3/2
Dhaivata
16.00
16.21
5/3
Nishada
18.00
17.76
7/4
22.00
2/1
Sadja octave׳
It could be a ‘trivial’ coincidence ! Therefore, I decided to extend My study to cover The other Ancient Musicological formats, known as
“MADHYAMA-GRAMA” and “MURCHANAs”.
‘Five’ more Fractions Were found “seeded” in Madhyama-grama in their ‘rounded-off’ forms, like this ! (see
next
slide)
Madhyama-GRAMA TONEs Nearest members of the (“Rounded-off” values) Family of ‘22- FRACTIONS’
Sadja (Tonic)
0.00
1/1
Rishabha
4.00
3.74
9/8
Gandhara
6.00
5.79
6/5
Madhyama
10.00
10.11
11/8
Panchama
13.00
12.87
3/2
Dhaivata
17.00
17.11
12/7
Nishada
19.00
18.66
9/5
22.00
2/1
Sadja octave׳
The Remaining 11 Fractions Were “seeded” in the ‘Murchanas’ (see next slide)
Sadja-grama MURCHANAs Rishabha-3 = 10/9 Rishabha-5 = 8/7 Gandhara-2 =11/9 Gandhara-3 = 5/4 Gandhara-4 = 9/7 Madhyama-3 = 7/5 Madhyama-4 Dhaivata-2 Nishada-4
= 10/7 = 8/5 = 11/6
Madhyama-grama MURCHANAs Rishabha-2 Dhaivata-1
= 11/10 = 11/7
This
“QUEER
is
a very
PHENOMENON”
As
my calculations are based On modern mathematics And their relevance is getting related to Some data contained in Indian Musicological records of
200 B.C.
vintage !
Let
us
look
from another angle!
What is so “SPECIAL” About finding some 22 Fractions In the early forms of Music ?
Please note that this Family of “22-Fractions” Are the “SIMPLEST FRACTIONS” From the mathematical view point
This “simplicity” conforms to the famous doctrine of The ancient Philosopher-musician
Pythagoras
of
Samos
PYTHAGORAS’s
DOCTRINE
“ Harmonization should not be Enforced : It should be
picked out from Nature, as
the mathematics whole integers ”
of
PYTHAGORAS’s
DOCTRINE
“ Numerosity Should Governed by
be
strict arithmetical economy In
music ”
PYTHAGORAS’s
DOCTRINE
“ Number and ratio Should be expressed
MOST
elementally In
music ”
AS
OPPOSED
TO THIS
DOCTRINE,
CONTEMPORARY MUSIC CONSISTS OF “COMPLEX” FRACTIONs !
PYTHAGORAS
STATED
THAT:
“ COMPLEX FRACTIONs PRODUCE
DISCORD ”
‘clanging of metals’ ‘roar of a jet engine’ Are few examples of “COMPLEX FRACTIONS” And consequent ‘Discord’ Contained in sound
EXAMPLEs of CONTEMPORARY MUSIC “TEEVRA MADHYAM” “KAKALI NISHADA” “ Ab”
(HINDUSTANI MUSIC) - 45 / 32 (CARNATIC MUSIC)
(WESTERN ‘ET’ MUSIC)
- 243 / 128
- 1571527 / 990000
HOW IS THE MUSIC FOUNDED ON THESE ‘SIMPLEST FRACTIONS’ DIFFERENT From
contemporary
Music ?
MUSIC
FOUNDED ON THESE ‘22 SIMPLE FRACTIONS’ Generate HARMONY, As
they are picked out From NATURE
The
‘RESOURCE - BASE’
OF
22 TONEs IS
MUSIC
LARGER
IN TERMS OF NUMBER OF TONEs AND THEIR ‘CONSONANCE - RICHNESS’
However….., To feel its true experience, the following TWO ‘canons’’ Should be strictly observed
FIRSTLY, While
composing
melodic phrases, Intervals between successive Notes should also be strictly maintained as
“simple - FRACTIONS”
THESE
ARE THE PERMISSIVE SEQUENCES BETWEEN THE “22- Fractions”
R1
S
R2
G1
M1
R3
G2
M2
R4
G3
M3
R5
G4
M4
R6
D1 P
D2 D3
N1 N2 N3 N4
S׳
INTERVALS
INVOLVING
“LEAPS”
BEYOND SUCCESSIVE NOTEs ARE ALSO PERMISSIBLE, ONLY WHEN THESE ARE COFIGURED AS
“SIMPLE
FRACTIONs”
I
HAVE
ALSO
PREPARED
A SIMILAR
“ LEAP - NOTEs NETWORK ” GIVING
ALL SUCH COMBINATIONS (Please see two examples in the following slides)
R1– SWARAs: NETWORK
N1
M1
N1 D2
P
N2
D3
S N3
M3
M1
N4
R1
G1
D2
N2
P M3
S D3
N3
N4
G1 M1
P
R2- SWARAs
D2
M1
D1
N1
N2 P
D3
M1 S
N3
M3
NETWORK
N4
G1 R2
G2
D2
N1
N2
P M2 M3
S D3
G1 M1
N3 R2 N4
M2
P
SECONDLY, We presently experience “Consonance” existing between ‘Sadja’, ‘Panchama’ and ‘Sadja (octave)’ ONLY By activating a Drone As the sruti base.
A totally new concept Of “ASSONACE” would be Perceived within this Family of 22- Fractions
‘Spectral
ASSONANCE’
exists in certain ‘TRIADs’ of these 22-FRACTIONS. This should be observed with PRECISION (please
see
next
slides)
“ASSONANCE” WITHIN ‘22- FRACTIONs SACRED NUMBERS
12
S’ N4
11 10
S’
7
P D1
D3 N3
9 8
N1
S’
M2 M4
P D2
N2
M1 G2 G3 G4
M1 M3
G1 R2 R3 R4
R5 R6
R1
S S
S S
S S LEGEND
THERE ARE PLENTY OF SUCH ASSONANT ‘TRIADs’
S
SADJA
P
PANCHAMA
R
RISHABHA
D
DHAIVATA
G
GANDHARA
N
NISHADA
M
MADHYAMA
S’
SADJA (OCTAVE)
“ASSONANCE” WITHIN ‘22- FRACTIONs SACRED NUMBERS
12
S’ N4
11 10
S’
7
P D1
D3 N3
9 8
N1
S’
M2 M4
P D2
N2
M1 G2 G3 G4
M1 M3
G1 R2 R3 R4
R5 R6
R1
S S
S S
S
S
This Renders
‘PHENOMENON’ the whole system
“ ASSONANCE - RICH ”
These ‘22-FRACTIONs’ project incredible “MYSTICISM” ( A HINDU Point of View! )
Please observe : The Family is seated in the Holy “PRANAVA” Form ! (next
slide)
S S S S S S
R3
R5
G2
G4
M3
M4
P D1
D3
D2 N3 S’
M1 M2
P
N2
G1
G3
M1
S’
R2
R4
R6
R1
S’
N1 N4
S’
S’
S’
Ancient sages of India believed that the Human body Resembles
the three musical And they contain
octaves
22 ‘satvic’ nodes In each Octave (i.e. Centers that Promote Spiritual Harmony and Peace of mind !)
These
‘satvic
nodes’
energized ONLY music of
22
by
are the
‘simple fractions’
On the contrary, listening to music
based on other tones
with heavy “DISCORD” content, might activate only our ‘rajasic’ / ‘tamasic’ nadis ( i.e. “Indulgence needs” of our body ) and cause incalculable “harm” in the long run !!
I,
THEREFORE, LOOK FORWARD TO GREATER PARTICIPATION FROM THE SOCIETY OF MUSIC LOVERS IN SPREADING ‘AWARENESS’ ABOUT THIS UNIQUE DISCOVERY
I
have developed this theme Further to discover that A great treasure of “Ancient Music” is remaining uncovered as yet
Please peruse My BOOK :
MY
BOOK
CONTACT
ME
Tele: 91 20 30441256 Mobile: 9890266845, 9850121834 E-Mail: [email protected] Web site: http://www.22sruti.com POSTAL ADDRESS A-7 / 103, FLORIDA ESTATE, KESHAV NAGAR, MUNDHWA, PUNE-411036
OVERVIEW
Contemporary music (of the West & the East) Is limited to the design of “12 Tones”
However, Contemporary Indian Carnatic music traditions Claim that there are Many more ‘tones’ in actual use, duly integrated with their ‘Ragas’
but….. , These are NOT ‘defined’, ‘quantified’ & ‘adopted’ on a sound musicological basis
Great ‘seers’ of medieval India indicated the existence of
‘22 TONEs’ In
Music
But …. , Not much evidence was adduced in support of their Contentions.
My research work in pursuit of this ideal had been somewhat Fruitful. I had narrated the details, in my Book :
MY
BOOK
A
BRIEF SUMMARY Of My “FINDINGs”
OUR “ANCIENT MUSIC” WAS FOUNDED ON 22 ‘Simple Fractions’
These
22
‘Simple
Fractions’
were derived from the Natural Numbers between ‘1’ and ‘12’
The “Ancients” worshipped
These Natural Numbers between ‘1’ and ‘12’ as “Gods” (for
some unknown reasons)
‘Sumerians’ known
the earliest civilization ( 4000 B.C. )
worshipped Their gods/ goddesses as 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, and 60 (For details use my link: http://sumeriangods.blogspot.com/ )
I
have established that these are eventually reducible to The numbers from ‘1’ to ‘12’ only
Therefore, there must be something very “ SPECIAL ” about these Numbers between ‘1’ and ‘12’ !
The
“Ancients” shunned
The Numbers between ‘13’ and ‘18’ As “Devil’s
Domain”
The
The as
“Ancients” glorified
Number
‘22’
“INFINITY”
(i.e. SUM of all things Created by GOD)
I, therefore, Confined my ‘Examination’ To the numbers Between ‘1’ and ‘12’ And SHUNNED Numbers between ’13’ and ’18’
I discovered that Only “22” fractions Can be formulated Mathematically Between ‘1’ and ‘12’
ONLY
These are the 22 ‘Simple Fractions’
‘mathematically between
feasible’
‘1’ and ‘12’
When these 22 mathematical Fractions are converted as ‘tones’ in the
22 Pitch (Sruti) Octave, they
acquire the following tonal values !
(please see next slide)
FRACTIONs
TONAL VALUEs
FRACTIONs
TONAL VALUEs
(in 22-pitch scale)
(CONTINUED)
(in 22-pitch scale)
1/1
0.00
11/8
10.11
12/11
2.76
7/5
10.68
11/10
3.03
10/7
11.32
10/9
3.34
3/2
12.87
9/8
3.74
11/7
14.35
8/7
4.24
8/5
14.92
7/6
4.89
5/3
16.21
6/5
5.79
12/7
17.11
11/9
6.37
7/4
17.76
5/4
7.08
9/5
18.66
9/7
7.98
11/6
19.24
4/3
9.13
2/1
22.00
I discovered
‘six ( out are
(the
that
fractions’
of These
“22 Fractions” )
“seeded” into ‘Sadja-grama’
earliest
musical scheme
‘rounded-off’ (see
of
the
India)
forms, like this ! next slide)
in
Sadja-GRAMA
TONEs
(“Rounded-off” values)
Sadja (Tonic)
Nearest members of the Family of ‘22- FRACTIONS’
0.00
1/1
Rishabha
3.00
2.76
12/11
Gandhara
5.00
4.89
7/6
Madhyama
9.00
9.13
4/3
Panchama
13.00
12.87
3/2
Dhaivata
16.00
16.21
5/3
Nishada
18.00
17.76
7/4
22.00
2/1
Sadja octave׳
It could be a ‘trivial’ coincidence ! Therefore, I decided to extend My study to cover The other Ancient Musicological formats, known as
“MADHYAMA-GRAMA” and “MURCHANAs”.
‘Five’ more Fractions Were found “seeded” in Madhyama-grama in their ‘rounded-off’ forms, like this ! (see
next
slide)
Madhyama-GRAMA TONEs Nearest members of the (“Rounded-off” values) Family of ‘22- FRACTIONS’
Sadja (Tonic)
0.00
1/1
Rishabha
4.00
3.74
9/8
Gandhara
6.00
5.79
6/5
Madhyama
10.00
10.11
11/8
Panchama
13.00
12.87
3/2
Dhaivata
17.00
17.11
12/7
Nishada
19.00
18.66
9/5
22.00
2/1
Sadja octave׳
The Remaining 11 Fractions Were “seeded” in the ‘Murchanas’ (see next slide)
Sadja-grama MURCHANAs Rishabha-3 = 10/9 Rishabha-5 = 8/7 Gandhara-2 =11/9 Gandhara-3 = 5/4 Gandhara-4 = 9/7 Madhyama-3 = 7/5 Madhyama-4 Dhaivata-2 Nishada-4
= 10/7 = 8/5 = 11/6
Madhyama-grama MURCHANAs Rishabha-2 Dhaivata-1
= 11/10 = 11/7
This
“QUEER
is
a very
PHENOMENON”
As
my calculations are based On modern mathematics And their relevance is getting related to Some data contained in Indian Musicological records of
200 B.C.
vintage !
Let
us
look
from another angle!
What is so “SPECIAL” About finding some 22 Fractions In the early forms of Music ?
Please note that this Family of “22-Fractions” Are the “SIMPLEST FRACTIONS” From the mathematical view point
This “simplicity” conforms to the famous doctrine of The ancient Philosopher-musician
Pythagoras
of
Samos
PYTHAGORAS’s
DOCTRINE
“ Harmonization should not be Enforced : It should be
picked out from Nature, as
the mathematics whole integers ”
of
PYTHAGORAS’s
DOCTRINE
“ Numerosity Should Governed by
be
strict arithmetical economy In
music ”
PYTHAGORAS’s
DOCTRINE
“ Number and ratio Should be expressed
MOST
elementally In
music ”
AS
OPPOSED
TO THIS
DOCTRINE,
CONTEMPORARY MUSIC CONSISTS OF “COMPLEX” FRACTIONs !
PYTHAGORAS
STATED
THAT:
“ COMPLEX FRACTIONs PRODUCE
DISCORD ”
‘clanging of metals’ ‘roar of a jet engine’ Are few examples of “COMPLEX FRACTIONS” And consequent ‘Discord’ Contained in sound
EXAMPLEs of CONTEMPORARY MUSIC “TEEVRA MADHYAM” “KAKALI NISHADA” “ Ab”
(HINDUSTANI MUSIC) - 45 / 32 (CARNATIC MUSIC)
(WESTERN ‘ET’ MUSIC)
- 243 / 128
- 1571527 / 990000
HOW IS THE MUSIC FOUNDED ON THESE ‘SIMPLEST FRACTIONS’ DIFFERENT From
contemporary
Music ?
MUSIC
FOUNDED ON THESE ‘22 SIMPLE FRACTIONS’ Generate HARMONY, As
they are picked out From NATURE
The
‘RESOURCE - BASE’
OF
22 TONEs IS
MUSIC
LARGER
IN TERMS OF NUMBER OF TONEs AND THEIR ‘CONSONANCE - RICHNESS’
However….., To feel its true experience, the following TWO ‘canons’’ Should be strictly observed
FIRSTLY, While
composing
melodic phrases, Intervals between successive Notes should also be strictly maintained as
“simple - FRACTIONS”
THESE
ARE THE PERMISSIVE SEQUENCES BETWEEN THE “22- Fractions”
R1
S
R2
G1
M1
R3
G2
M2
R4
G3
M3
R5
G4
M4
R6
D1 P
D2 D3
N1 N2 N3 N4
S׳
INTERVALS
INVOLVING
“LEAPS”
BEYOND SUCCESSIVE NOTEs ARE ALSO PERMISSIBLE, ONLY WHEN THESE ARE COFIGURED AS
“SIMPLE
FRACTIONs”
I
HAVE
ALSO
PREPARED
A SIMILAR
“ LEAP - NOTEs NETWORK ” GIVING
ALL SUCH COMBINATIONS (Please see two examples in the following slides)
R1– SWARAs: NETWORK
N1
M1
N1 D2
P
N2
D3
S N3
M3
M1
N4
R1
G1
D2
N2
P M3
S D3
N3
N4
G1 M1
P
R2- SWARAs
D2
M1
D1
N1
N2 P
D3
M1 S
N3
M3
NETWORK
N4
G1 R2
G2
D2
N1
N2
P M2 M3
S D3
G1 M1
N3 R2 N4
M2
P
SECONDLY, We presently experience “Consonance” existing between ‘Sadja’, ‘Panchama’ and ‘Sadja (octave)’ ONLY By activating a Drone As the sruti base.
A totally new concept Of “ASSONACE” would be Perceived within this Family of 22- Fractions
‘Spectral
ASSONANCE’
exists in certain ‘TRIADs’ of these 22-FRACTIONS. This should be observed with PRECISION (please
see
next
slides)
“ASSONANCE” WITHIN ‘22- FRACTIONs SACRED NUMBERS
12
S’ N4
11 10
S’
7
P D1
D3 N3
9 8
N1
S’
M2 M4
P D2
N2
M1 G2 G3 G4
M1 M3
G1 R2 R3 R4
R5 R6
R1
S S
S S
S S LEGEND
THERE ARE PLENTY OF SUCH ASSONANT ‘TRIADs’
S
SADJA
P
PANCHAMA
R
RISHABHA
D
DHAIVATA
G
GANDHARA
N
NISHADA
M
MADHYAMA
S’
SADJA (OCTAVE)
“ASSONANCE” WITHIN ‘22- FRACTIONs SACRED NUMBERS
12
S’ N4
11 10
S’
7
P D1
D3 N3
9 8
N1
S’
M2 M4
P D2
N2
M1 G2 G3 G4
M1 M3
G1 R2 R3 R4
R5 R6
R1
S S
S S
S
S
This Renders
‘PHENOMENON’ the whole system
“ ASSONANCE - RICH ”
These ‘22-FRACTIONs’ project incredible “MYSTICISM” ( A HINDU Point of View! )
Please observe : The Family is seated in the Holy “PRANAVA” Form ! (next
slide)
S S S S S S
R3
R5
G2
G4
M3
M4
P D1
D3
D2 N3 S’
M1 M2
P
N2
G1
G3
M1
S’
R2
R4
R6
R1
S’
N1 N4
S’
S’
S’
Ancient sages of India believed that the Human body Resembles
the three musical And they contain
octaves
22 ‘satvic’ nodes In each Octave (i.e. Centers that Promote Spiritual Harmony and Peace of mind !)
These
‘satvic
nodes’
energized ONLY music of
22
by
are the
‘simple fractions’
On the contrary, listening to music
based on other tones
with heavy “DISCORD” content, might activate only our ‘rajasic’ / ‘tamasic’ nadis ( i.e. “Indulgence needs” of our body ) and cause incalculable “harm” in the long run !!
I,
THEREFORE, LOOK FORWARD TO GREATER PARTICIPATION FROM THE SOCIETY OF MUSIC LOVERS IN SPREADING ‘AWARENESS’ ABOUT THIS UNIQUE DISCOVERY
I
have developed this theme Further to discover that A great treasure of “Ancient Music” is remaining uncovered as yet
Please peruse My BOOK :
MY
BOOK
CONTACT
ME
Tele: 91 20 30441256 Mobile: 9890266845, 9850121834 E-Mail: [email protected] Web site: http://www.22sruti.com POSTAL ADDRESS A-7 / 103, FLORIDA ESTATE, KESHAV NAGAR, MUNDHWA, PUNE-411036
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