Our World is

‘MYSTICAL’

This ‘Mysticism’

ELUDESthe Laity

However, ….. ,

It obliges the

“DEEP-MEDITATING”mind

‘MUSIC’Is no exceptionTo this ‘mystic’WORLD ORDER

I have hypothesizedThat …….

A ‘Pre-Historic’ MUSICHad permeated down

our culturesAs a ‘jigsaw puzzle’,

in the most‘Mysterious’ manner !

One ‘tessellating piece’remains in the form of

‘MUSICAL FRACTIONS’Along the Western

Musicological culture

Another ‘interlocking piece’Had come downin the form of

Sama Vedic ‘TONES’Along the INDIAN

Musicological culture

The WestAlways handled music only as

Mathematical ‘Fractions’,Not knowing how to

organize them as the ‘tones’Of an Octave !

As opposed to this,The Indians handled musiconly as The ‘Tones’ of a

perceptual octave,Not knowing what‘Musical Fractions’are all about !

The ‘Divine Irony’, however,Is such that

This ‘Pre-Historic’ MUSICWould get unveiledONLY IF these

two tessellating pieces are‘RE-ASSEMBLED’ !!

The ‘CLUES’ for re-assemblyhad been passed down

In the form of ‘Sumerian Pantheon’ of the West

And the‘Oral Musicological Traditions’ of India

Firstly, …… The WESTERN ROUTE

Sumerians worshipped‘SIMPLE FRACTIONS’

As their pantheon ofTwelve Main gods

The ‘WESTERN ROUTE

Please see Next Slide, for some Examples

Another mysteriousCultural Process !

The ‘WESTERN ROUTE

The ‘Ancients’ worshipped Natural Numbers

Between ‘1’ and ‘12’ as

‘SACRED’

The ‘WESTERN ROUTE

They shunned Natural Numbers

Between ‘13’ and ‘18’ as the

‘Devil’s Domain’

The ‘WESTERN ROUTE

The ‘Ancients’, however, regarded Number “22”

As MOST SACRED,As it symbolized

The INFINITE creations of GOD

The ‘WESTERN ROUTE

I experimented by formulating

‘SIMPLE FRACTIONS’,By using Natural Numbers

Between ‘1’ and ‘12’(Somewhat similar to the

Sumerian gods)

The ‘WESTERN ROUTE

These are shown in the Next Slide

I found that ONLY 22 such Fractions are

Mathematically feasible

The ‘WESTERN ROUTE

These ‘22’ FractionsHappen to lie

between ‘1’ to ‘1/2’i.e. The LOWER and UPPER

Limits of an octave,( as shown in the next slide )

The ‘WESTERN ROUTE

1/1

1/2

11/1210/11

9/108/9

7/86/7

5/69/11

4/57/9

3/4

8/115/7

7/10

2/3

7/115/8

3/5

7/11

4/75/9

6/11

LOCATING THE 22 “SIMPLE FRACTIONS” BETWEEN 1/1 AND 1/2

DEC

REA

SIN

G

OR

DER

O

F

FR

AC

TIO

NA

L

VA

LU

ES

LOWER OCTAVE LIMIT

UPPER OCTAVE LIMIT

7/12

To enable comparison betweenthe Western and Indian traditions, I converted these 22 - Fractions

into ‘TONAL VALUES’And inserted them in an Octave

Characterized by the limits:Lower Octave Limit = ‘0’ and

Upper Octave Limit = ‘22’

The ‘WESTERN ROUTE

(Contemporary musicologycalibrates the octave only

Between the limits of ‘0’ and ‘12’ )

(please see next slideTONAL Details are shown in RED colour)

The ‘WESTERN ROUTE

(However, ancient Indian musicologistsHad always calibrated the octaveBetween the limits ‘0’ and ‘22’)

1/1

1/2

11/1210/11

9/108/9

7/86/7

5/69/11

4/57/9

3/4

8/115/7

7/10

2/3

7/115/8

3/5

4/75/9

6/11

ASSIGNMENT OF TONAL VALUES TO THE 22 “SIMPLE FRACTIONS”

(0)

(22)

(2.76)(3.03)

(3.34)(3.74)

(4.24)(4.89)

(5.79)(6.37)

(7.08)(7.98)

(9.13)(10.11)

(10.68)(11.32)

(12.87)

(14.35)(14.92)

7/12

(16.21)

(17.11)(17.76)

(18.66)(19.24)

INC

REA

SIN

G O

RD

ER

O

F T

ON

AL V

ALU

ES

THE LOWER OCTAVE LIMIT

THE UPPER OCTAVE LIMIT

I have now Tabulated theseTONAL VALUES

(Please see next slide)(Please see next slide)

The ‘WESTERN ROUTE

(For ease of reference,Let us call them as

“The Family of 22-Fractions”)

NOTE FRACTION TONAL VALUE

S 1/1 0.00

R1 12/11 2.76

R2 11/10 3.03

R3 10/9 3.34

R4 9/8 3.74

R5 8/7 4.24

R6 7/6 4.89

G1 6/5 5.79

G2 11/9 6.37

G3 5/4 7.08

G4 9/7 7.98

M1 4/3 9.13

NOTE FRACTION TONALVALUE

M2 11/8 10.11

M3 7/5 10.68

M4 10/7 11.32

P 3/2 12.87

D1 11/7 14.35

D2 8/5 14.92

D3 5/3 16.21

N1 12/7 17.11

N2 7/4 17.76

N3 9/5 18.66

N4 11/6 19.24

S’ 2/1 22.00

continued

The Family of 22-FRACTIONS

Let us now look at

The INDIAN scenario

The ‘INDIAN ROUTE’

Music was“ENSHRINED”

In Sama Veda as‘SEVEN TONES’

The ‘INDIAN ROUTE’

These were designated as

‘Swaras’And “QUANTIFIED”Within an Octave

The ‘INDIAN ROUTE’

This ‘Grouping’ of SwarasWas called “ SADJA GRAMA ”

SWARASWARA QUANTIFICATIONQUANTIFICATION

SADJA (SADJA (LOWER)LOWER) 0.000.00

RISHABHARISHABHA 3.003.00

GANDHARAGANDHARA 5.005.00

MADHYAMAMADHYAMA 9.009.00

PANCHAMAPANCHAMA 13.0013.00

DHAIVATADHAIVATA 16.0016.00

NISHADANISHADA 18.0018.00

SADJA’SADJA’ ( (UPPER)UPPER) 22.0022.00

The ‘INDIAN ROUTE’

Now let us take an‘INTEGRATED

VIEW’Of the Western and

Indian traditions

I observed that the‘Quantified’ values ofSama Vedic ‘TONEs’

Were the“ROUNDED-OFF” values of

Seven members of theFamily of 22-Fractions

Please see Next Slide

SWARASWARASADJA GRAMASADJA GRAMA

(ROUNDED-OFF (ROUNDED-OFF VALUES)VALUES)

FAMILY OFFAMILY OF

22-- FRACTIONS22-- FRACTIONS

SADJA SADJA ((LOWER)LOWER)

0.000.00 0.000.00

RISHABHARISHABHA 3.003.00 2.762.76GANDHARAGANDHARA 5.005.00 4.894.89MADHYAMAMADHYAMA 9.009.00 9.139.13PANCHAMAPANCHAMA 13.0013.00 12.8712.87

DHAIVATADHAIVATA 16.0016.00 16.2116.21NISHADANISHADA 18.0018.00 17.7617.76SADJA’SADJA’ ((UPPER)UPPER)

22.0022.00 22.0022.00

I observed that the‘tonal’ values of

Another Group known as“MADHYAMA GRAMA”

Were also the “ROUNDED-OFF” values of Five more members of

theFamily of 22-Fractions

SWARASWARA

MADHYAMA MADHYAMA GRAMAGRAMA

(ROUNDED-OFF (ROUNDED-OFF VALUES)VALUES)

FAMILY OFFAMILY OF

22-- FRACTIONS22-- FRACTIONS

SADJA SADJA ((LOWER)LOWER)

0.000.00 0.000.00

RISHABHARISHABHA 4.004.00 3.743.74GANDHARAGANDHARA 6.006.00 5.795.79MADHYAMAMADHYAMA 10.0010.00 10.1110.11PANCHAMAPANCHAMA 13.0013.00 12.8712.87

DHAIVATADHAIVATA 17.0017.00 17.1117.11NISHADANISHADA 19.0019.00 18.6618.66SADJA’SADJA’ ((UPPER)UPPER)

22.0022.00 22.0022.00

I observed that theThe remaining members

Were ‘seeded’ inThe Fourteen Murchanas

(generated from ‘Sadja grama’ and ‘Madhyama grama’, as

Stipulated in Indian Musicology)

Sadja-gramaSadja-grama

MURCHANAsMURCHANAsMadhyama-gramaMadhyama-grama

MURCHANAsMURCHANAs

Rishabha-3 = Rishabha-3 = 9/109/10 Rishabha-2 = Rishabha-2 = 10/1110/11

Rishabha-5 = Rishabha-5 = 7/87/8 Dhaivata-1 = Dhaivata-1 = 7/117/11

Gandhara-2 =Gandhara-2 =9/119/11

Gandhara-3 = Gandhara-3 = 4/54/5

Gandhara-4 = Gandhara-4 = 7/97/9

Madhyama-3 = Madhyama-3 = 5/75/7

Madhyama-4 = Madhyama-4 = 7/107/10

Dhaivata-2 = Dhaivata-2 = 5/85/8

Nishada-4 = Nishada-4 = 6/116/11

In this manner, ….There is

“TOTAL CONVERGENCE”

In the musicological traditions of the WEST and INDIA

Probably the ‘Gods’Worshipped by theSumerians and the

Vedic Indians were the same !This may open up as

a separate domain of researchby itself!

I have also identified several unique “FEATURES” within

the Family of22-Fractions that makes it a

‘class’ apart from ourContemporary classical music

(Please see next slide)

Please peruse Presentation Slides at :http://www.esnips.com/doc/65dd0fff-f143-48ae-b580-8716f52b18a8/

COMPOSING-IN-OUR-ANCIENT-MUSIC-OF-22-TONEs(1)

1. Simplicity of Notes; i.e. ‘Sonance’ within the

Octave2. Simplicity of Intervals between Notes3. ‘Consonance’ within the

Octave4. ‘Assonance’ within the

Octave

Once this ‘pre-historic’ music

Is perfected and practised,Our human race is bound

To experience aNew class of aesthetic and

Spiritual wel-being !

Please peruse Presentation Slides at :http://www.esnips.com/doc/65dd0fff-f143-48ae-b580-8716f52b18a8/

COMPOSING-IN-OUR-ANCIENT-MUSIC-OF-22-TONEs(1)

Please peruseMy BOOK :

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