Composing In Our Ancient Music Of 22 Tones

PART - 1

WHAT DO I MEAN BY “ ANCIENT MUSIC OF 22 TONEs ” ?

A

BRIEF

OVERVIEW

The “Ancients” worshipped

Natural Numbers between ‘1’ and ‘12’ as “Gods” (for

some unknown reasons)

‘Sumerians’, The earliest civilization Known to our Historians (i.e. 4000 B.C.) ,

Worshipped Their 12 Main gods/ goddesses as numbers: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, and 60 (For

details see my link:

http://www.esnips.com/web/GODSOFSUMERIASYMBOLIZEOURANCIENTMUSIC

I ( in

have already established my

earlier

‘blogs’ )

that these are eventually reducible to The numbers from ‘1’ to ‘12’ only

A

MATHEMATICAL

The viewers please note

FACT !

may that

Only “22” fractions Can be formulated Mathematically Between ‘1’ and ‘12’

ONLY

22 ‘Simple Fractions’

‘mathematically feasible’ between

‘1’ and ‘12’

These 22 mathematical Fractions Transferred on to the

22 Pitch (Sruti) Octave, would

acquire the following tonal values !

(please see next slide)

NOTES

FRACTIONs TONAL VALUEs

NOTES

(in 22-pitch scale)

FRACTIONs TONAL VALUEs (CONTINUED)

(in 22-pitch scale)

SADJA

1/1

0.00

MADHYAMA – 2

11/8

10.11

RISHABHA – 1

12/11

2.76

MADHYAMA - 3

7/5

10.68

RISHABHA – 2

11/10

3.03

MADHYAMA - 4

10/7

11.32

RISHABHA – 3

10/9

3.34

PANCHAMA

3/2

12.87

RISHABHA – 4

9/8

3.74

DHAIVATA – 1

11/7

14.35

RISHABHA – 5

8/7

4.24

DHAIVATA - 2

8/5

14.92

RISHABHA - 6

7/6

4.89

DHAIVATA - 3

5/3

16.21

GANDHARA –1

6/5

5.79

NISHADA -1

12/7

17.11

GANDHARA –2

11/9

6.37

NISHADA - 2

7/4

17.76

GANDHARA – 3

5/4

7.08

NISHADA – 3

9/5

18.66

GANDHARA --4

9/7

7.98

NISHADA – 4

11/6

19.24

MADHYAMA - 1

4/3

9.13

SADJA “

2/1

22.00

PART - 2

SOME UNIQUE FEATUREs Of the Family of 22 FRACTIONs

UNIQUE

FEATUREs

1. Simplicity of Notes; i.e. ‘Sonance’ within the Octave 2. Simplicity of Intervals between Notes 3. ‘Consonance’ within the Octave 4. ‘Assonance’ within the Octave 5. ‘Gamaka’/ ‘Andolan’ in the Indian context

UNIQUE

FEATURE - 1

SIMPLICITY OF NOTEs i.e. ‘Sonance’ Within the Octave

SIMPLICITY OF NOTEs i.e. ‘Sonance’ Musicologically speaking, These “22-Fractions” are the

“ SIMPLEST FAMILY OF FRACTIONS ”

SIMPLICITY OF NOTEs i.e. ‘Sonance’ The digits either in the Numerator or in the Denominator

do

NOT

exceed

‘12’

SIMPLICITY OF NOTEs i.e. ‘Sonance’ WHAT

IS

ITS

RELEVANCE ?

SIMPLICITY OF NOTEs i.e. ‘Sonance’ This “simplicity” conforms to the famous doctrine of The ancient Philosophermusician

Pythagoras

of

Samos

SIMPLICITY OF NOTEs i.e. ‘Sonance’ “ Number and ratio Should be expressed

MOST

elementally In

music ” --(PYTHAGORAS

OF

SAMOS)

SIMPLICITY OF NOTEs i.e. ‘Sonance’ “ COMPLEX FRACTIONs PRODUCE

DISCORD ” --(PYTHAGORAS

OF

SAMOS)

SIMPLICITY OF NOTEs i.e. ‘Sonance’ AS

OPPOSED

TO THIS

DOCTRINE,

CONTEMPORARY MUSIC CONSISTS OF “COMPLEX” FRACTIONs !

SIMPLICITY OF NOTEs i.e. ‘Sonance’ EXAMPLEs of

CONTEMPORARY MUSIC “TEEVRA MADHYAM” “KAKALI NISHADA”

“ Ab”

(INDIAN SHASTRIYA SANGEET) (INDIAN CARNATIC MUSIC)

(WESTERN ‘ET’ MUSIC)

- 45 / 32

- 243 / 128

- 1571527 / 990000

UNIQUE

FEATURE - 2

SIMPLICITY OF INTERVALS (i.e. ‘ANTARAs’) Between NOTEs

SIMPLICITY OF INTERVALs BETWEEN NOTEs

The knowledge of 22 Fractions, alone is NOT ENOUGH. We should KNOW certain Rules That defines Melodic sequences in music

SIMPLICITY OF INTERVALs BETWEEN NOTEs

Intervals between successive Notes should ALSO be “simple - FRACTIONS”

SIMPLICITY OF INTERVALs BETWEEN NOTEs

This is feasible Within the Family of 22- FRACTIONs, ONLY !

SIMPLICITY OF INTERVALs BETWEEN NOTEs

I A

HAVE IDENTIFIED NETWORK WHICH ENSURES THAT THE INTERVALS BETWEEN SUCCESSIVE NOTES ARE ALSO “SIMPLE - FRACTIONS”

SIMPLICITY OF INTERVALs BETWEEN NOTEs R1 R2 R3 S R4 R5 R6

G1

M1

G2

M2

G3

M3

G4

M4

D1 P

D2 D3

N1 N2 N3 N4

S‫׳‬

SIMPLICITY OF INTERVALs BETWEEN NOTEs

INTERVALS INVOLVING

“LEAPS”

BEYOND SUCCESSIVE NOTEs ARE ALSO PERMISSIBLE, ONLY WHEN THESE ARE COFIGURED AS

“SIMPLE FRACTIONs”

SIMPLICITY OF INTERVALs BETWEEN NOTEs I HAVE

ALSO PREPARED A SIMILAR

“ LEAP - NOTEs NETWORK ” GIVING

ALL SUCH COMBINATIONS (please see

following three

slides)

SIMPLICITY OF INTERVALs BETWEEN NOTEs COMBINED R1 AND R2 – SWARAs

M1 P

D3

S

R1

G1

N4

D2 P

N3

S D3

R2

NETWORK

G1 M1

N3 R2

G2 M3

N4

M2

P

SIMPLICITY OF INTERVALs BETWEEN NOTEs COMBINED R3 AND R4 – SWARAs

NETWORK

D1

R4

N2 P

D3

R4 M1

S

P G2 R3

N4

N2

G3

M2

S

M1

D3 M2 N4

G3

P

SIMPLICITY OF INTERVALs BETWEEN NOTEs COMBINED R5 AND R6– SWARAs D1

N1

NETWORK N1

R5

P

D3

R6

S

M1

P

S D3

N4

N4 G4 R6

M4

M1

P

UNIQUE

FEATURE - 3

CONSONANCE WITHIN THE OCTAVE

In Indian musicology, ‘Sonant’ (‘Vadi’) is the Note That sets the ‘MOOD’ For the entire range of the Raga (i.e. The melodic structure)

‘Consonant’ (i.e. ‘Samvadi’) is the Image Note of ‘Sonant’ Present in the other half of the Octave.

The ‘Consonant’ (i.e. ‘Samvadi’) Note Helps to extend the mood set By the ‘Sonant’ Note, into the other half of the Octave (which is outside the melodic influence Of the ‘Sonant’ Note).

For evolving a Raga, (i.e. Melodic sequence)

from ( i.e.

any

a

‘Mela-karta’

The

basic

Note

‘Mode’), (‘Swara’)

Can be designated as ‘Sonant’ (‘Vadi’).

Once ‘Sonant’ (‘Vadi’) is designated, The ‘CONSONANT’ (‘Samvadi’) is decided by the ‘9’ / ‘13’ PRINCIPLE as stipulated in Ancient Indian Musicology.

THE 9 / 13 PRINCIPLE “SWARAs WHICH HAVE ‘ANTARAS’ (i.e. INTERVALS) ‘NINE’ or ‘THIRTEEN’ ARE MUTUALLY VADIs / SAMVADIs”

OF

-‘NATYA SASTRA’, (200 B.C.)

THE 9 / 13 PRINCIPLE THIS Is

PRINCIPLE,

the fundamental for formulation

therefore,

GUIDE of the

‘MELODIC STRUCTURE’ WITHIN THE FAMILY OF 22 FRACTIONs .

THIS ANCIENT “PRINCIPLE” , IN OUR REVISED CONTEXT, WILL BE

“9.13 / 12.87”, because…….

We apply rules with mathematical PRECISION !!

IT TO

IS

AMAZING

NOTE THAT THE

FAMILY

‘22-FRACTIONs’ THIS

“NEAR

“PRINCIPLE”

OF

OBEY WITH

PERFECTION” !!

( PLEASE SEE THE NEXT SLIDE )

THE “9.13 / 12.87” RULE

PLEASE

OBSERVE

AS

TO

QUALIFY EXACTLY • • • • • • • • • • • • • • •

HOW

TO

A

PAIR

BECOME

OF

TWO

VADI AND

SWARAs

SAMVADI !!

9.13-antara (intervals) 12.87 antara (intervals) S (0.00) ----- M1 (9.13) S (0.00) ----P (12.87) R4 (3.74)---- P (12.87) R3 (3.34)—D3 (16.21) G1 (5.79) ----D2 (14.92) R5 (4.24) --N1 (17.11) G3 (7.08) ----D3 (16.21) R6 (4.89) --N2 (17.76) G4 (7.98)----N1 (17.11) G1 (5.79)---N3 (18.66) M2 (10.11)- N4 (19.24) G2 (6.37)---N4 (19.24) P (12.87)---- S’ (22.00) M1 (9.13)—S’ (22.00) D3 (16.21)—R3’ (25.34)* P (12.87)----R4’ (25.74)* N1 (17.11)---R5’ (26.24)* D2 (14.92)- G1’ (27.79)* N2 (17.76)---R6’ (26.89)* D3 (16.21)--G3’ (29.08)* N3 (18.66)---G1’ (27.79)* N1 (17.11)--G4’ (29.98)* N4 (19.24)---G2’ (28.37)* N4 (19.24)--M2’ (32.11)* S’ (22.00)----M1’ (31.13)* S’ (22.00)---P’ (34.87)* Note: - The fractions marked with * are to be rationalised by subtracting 22.00. {e.g. 25.34 (R3‘) – 22.00 = 3.34 srutis}

UNIQUE

FEATURE - 4

ASSONANCE WITHIN THE OCTAVE

ASSONANCE

WITHIN

‘Spectral the

22 FRACTIONs

ASSONANCE’

exists in certain ‘TRIADs’ within family of 22-FRACTIONS.

This should be observed with PRECISION

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

THIS IS A ASSONANT

TYPICAL ’TRIAD’

S

SADJA

P

PANCHAMA

R

RISHABHA

D

DHAIVATA

G

GANDHARA

N

NISHADA

M

MADHYAMA

S’

SADJA (OCTAVE)

ASSONANCE

WITHIN

22 FRACTIONs

There are plenty of Such Assonance Triads Within the Family of 22 Fractions !

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

ASSONANCE

This Renders

WITHIN

22 FRACTIONs

‘PHENOMENON’ the whole system

“ ASSONANCE - RICH ”

UNIQUE

FEATURE - 5

‘GAMAKA’ / ‘ANDOLAN’ In the Indian context

‘GAMAKA’ / ‘ANDOLAN’ Traditions in Indian music differs from the West, in following aspects:  Transition from Note to Note is smooth and ‘curved’  NO simultaneous playing of Notes in the form of chords (i.e. Vertical music is NOT played)  Notes are oscillated with respect to their mean position. This is known as ‘Gamaka’ or ‘Andolan’.

‘GAMAKA’ / ‘ANDOLAN’

However, the Indian performers should Be cautious NOT to alter the mean position of such Gamaka oscillations from the stipulated ‘swara-sthaanas’. Otherwise, the ‘Sonance’, ‘Consonance’, ‘Assonance’ and ‘Dissonance’ aspects would get adversely affected leading to heavy DISCORD !

When all these unique features Of 22 Srutis Music are observed with precision, the levels of overall MELODY achieved would acquire a ‘QUANTUM JUMP’

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