1. BkE-DevalKB-HinduMusicalScale&22Srutis-0018

TAT TWAM ASI

EX BIBLIOTHECA INDICA Dr. h.c. ALFRED SARASIN

THE HINDU MUSICAL SCALE

AND

THE TWENTY-TWO SHRUTEES

BY

KRISHNAJI BALLAL DEVAL (Retired Deputy Collector).

ITÄTS-BIR aLIO

BASEL

(All rights reeerved.)

CONTENTS.

1: Introduction by Mr. E. Clements C. S. ... ... I-IV

2. Preface by the author. ... ... V-VIII

3. The object of the Brochure ... 1-4 4. The constitution of Musical sound, Enropean and Hindn, views compared ... ... 4-15

1 Sound ... ... 4

2 Musical sound ... ... 4

3 Harmonics ... 5

4 Nodal points and Ventral segments ...

5 Reflection of sound ... ...

. 6 Sympathetic Resonance ... ... 9

Printed at the " ARYA BHUSHAN PRESS " 7 Pitch ... ... ... 9

BY 8 Laws of the vibrations of strings aud of artificially NATESH APPAJI DRAVID produced harmonics ... ... 10

and published by 9 Simple ratios of consonant notes ... ... 11

KRISHNAJI BALLAL DEVAL at Poona, 10 Beats ... ... ... 12

11 Resultant notes or difference notes ... ... 13 5. The positions and vibrations of the seven notes of the Diatonic Scale and the octave, worked out mathemati- cally ... ... ... 16-24 H1 (C1 ) and #2 (C2) ... ... ... 16

Incl, Tee. W 517 A (F) ... 17 ... ... ... ... . ... ...

q (G) ... ... 18 ... ...

.54, 1015 (D) and (A) ... ... ... ... 19

• Perfect and imperfect concords ... ... ... 19 Katalog (E) and fa (B) ... ... ... ... T (E ) and fa (B)ngain, 21 ... ... ... ...

Notes and summary .... 21 ... ... ... The Evolution of the Hindu Diatonic major and minor scales-The कोमल स्वरसप्तक and तीव्र स्वरसप्तक and Ellis' cents . . ... ... 23 The Evolution of the Finer Hindu Mnsical. Scales- The Chromatic ard a still finer scale of 22 Shrutees ... 34

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. Table A. Indian Diatonic Major Scale or afa araaar ... 26 7. Table B. Indian Diatonic Minor Scale of 5 Flat notes or कोमल स्वरसम्क .... INTRODUCTION. ... ... .... ... 27 8. Table C. The Indian sharp and flat notes or तीव्र कोमल स्वरसप्तक-अचल थाट ... ... 28 9. Table D. The scale of 22 Indian notes or the zia scale. 29 The work accomplished by Mr. Deval, it would hardly be'+ 10. The Diachord. ... ... 31 an exaggeration to say, marks an epoch in the history of Indian. ... ... 11. The Shrutees. Different views Music. As he tells us, many treatises have already been written ... ... ... ... 31-44 Mr. Sahasrabuddhe on the subject, but those who have heard Indian Music and who ' ... ... ... 32 Mr. Chinna Swami Mudliar ... have sufficiently keen musical perception to appreciate the ... ... . 34 Raja Surendra Mohan Tagore 34 smoothness and beauty of the intervals used, must have laid; ... ... Capt. Day and Mr. Ellis down some of those books after reading them with a feeling of .... ... ... ... 35 Raja Ram Pal Singh ... bewilderment. If Mr. Deval's results are accepted, the Indian ... ... ... ... 38 Mr. Pingle scale which is several thousand years old will stand out as the ... ... 39 ... ... ... ... The conclusion ... most perfect example of a natural untempered scale. ... ... 39 ... ... ... A ppendix A. A note by Mr. Chhatre That Mr. Deval's 22 Shrutees are the correct ones may in ... ... ... 45 Appendix B. Extracts from European writers on the the first place be presumed from the fact that he has studied importance of Melody ... the latest European literature on the subject of the formation ... ... ... 48 of scales, and has spent eight years in testing the notes used by various singers in order to ascertain the exact intervals which the singers endeavour to produce .: As he tells us, he has. been guided by the principle laid down by old Indian writers on Music, that the simplest ratios are always the best. Secondly it will be found that although Mr. Deval did not test his Shrutees throughout by the harmonic intervals 5:4, 6:5, and 7:6 which may be called the major third, minor third and septimal third, they are clearly built up from those intervals .*

The major thirds. The minor thirds. The septimal thirds: 1. Sa : ti. gal' 2. a.k.ri : a.k. ma. 1: Sa : K. ga. 1. K.fi .: ti.ga.(nearly) 3. K.ri. : K.ma .. 2. m.ri. : K. ma. 2. ti. ri. : a.k. ma .. t.

4. ti. ri. : ti. ma. 3. ak. ga. : t.t. ma. 4. ti. ga. : pa. 3. k. ga. : ti.ma. ( ,;) 5. K.gal: pa/i: 5. K. ma. : k.dha. 4. K.ma .: ak.dha.(,, ) 6. K.ma. : m. dha .. 7. t.t.ma. : ak. ni. 6. ti. ma. : ti.dha. 5. t.t.ma .: m.dha.(,,) 6. k.dha .: ti. ni. ( ,; Exact septimal 8. pa. : ti. ni. 7. pa. : K. m.

5. k. dha. : Sa. 8. m.dha. : Sa. 1. k.ga. : ak. ri. sevenths.

6. ak. ni. : m. ri. 9. ak. ni. : k.ri. .

7. K. ni .: ti. ri. 10. ti. ni. : ti. ri .: ... 2. pa. : ak. ma. 12. t.t ni. : ak.' ga. 3. k.ni. : ak.dha.

Indeed the importance attached to the Septimal intervals, III that is those derived from the seventh harmonic, places the music of India in the first rank of intellectual developments of use of considerably more than 22 Shrutees has kindly sung the Musical art. Some writers on Harmony have elaborated over to me 83 Ragas and Raginis and given me the names of theories based upon the supposition that the Subdominant, the notes used in them. It appeared to me that the extra ( corresponding with Komal Madhyam ) and dominant Shrutees used were chiefly those necessary to give the exact seventh ( that is, Atikomal Madhyam ) are for all practical septimal intervals in some of those cases which I have marked purposes the same note. No one who has attentively listened . 'nearly ' in the footnote. An additional ' Atikomal Gandhar' to Indian Ragas could entertain such an idea for a moment, as of 280 relative number of vibrations was also used but in one the septimal seventh is very much flatter than the ordinary Raga only. Mr. Deval tells me that some singers use a similar seventh, the interval 7:6 being easily distinguishable even by septimal ' Atikomal Nishad '. The ' Atikomal Nishad ' chosen the untrained ear from the interval 6:5. by him is however a vital necessity as the fourth above

The 22 Shrutees are as Mr. Deval points out a selection Madhyam and if the Shrutees are to be restricted to 22. I am

from the total number of Shrutees used in Indian Ragas and afraid one must give up these two septimal notes, pleasing

Raginis, Mr. Deval had not only to ascertain what Shrutees though their effect must be acknowledged to be.

were made use of by different singers but also to pick out the The intervals between each Shrutee and the next as given 22 which might justly be considered essential. It was after in Mr. Deval's table D are of no great significance. Perhaps his choice had been made that I had the good fortune of hear- some day a list of Ragas as sung by some great singer will.be ing of his researches. I then suggested that to perfect his given showing the intervals between the notes used in each theories an inquiry should be made into the nature of the Raga. Such a list would show that the Ragas are built up Gramas and the musical constitution of the Ragas.The first scientifically from the major, minor and septimal intervals. inquiry he has completed. His paper on the subject makes The list in table D as I have observed is merely the sum total out a good case for the proposition that the Gramas correspond of the Shrutees used as essential notes in all the Ragas and with the registers of the human voice. The question of the Raginis, and it is of no practical interest to any one, to take an Gramas is therefore purely a question of pitch. No complete. example, that Madhya Rishab and Tivra Rishab are separated by scientifie examination of the Ragas has yet been made. The: the interval 81 : 80. Madhya Rishab is used in some Ragas subject is involved in great difficulty on account of the fact corresponding in tonality with our B flat major or D minor that musical science in India has been handed down from one: keys ; Tivra Rishab is the fifth from Pancham and is used in generation to another mainly by oral teaching. The result is other Ragas in the manner one would expect from : that that no two singers can agree as to the intervals to be used in connection. the Ragas and Raginis; even in the case of Ragas whose names My examination of the Ragas is sufficient to satisfy me are known to every Hindu household there are differences of that it is quite incorrect to say that the feeling of tonality is opinion. Mr. Krishnaji Mahadev Gokhale of Miraj who makes absent from Indian music. The feeling of tonality is some- times disguised by the pedal bass, and to European ears" this is

AI

a defect, but that the feeling is there is shown by the progres. sions used and in particular by the final cadence. Old Hindu tical with the Doric Mode. If the identity is accepted, it theorists had a special name, ara FT for the note on which a follows (1) that B flat is the fifth above E flat and is a relation particular Raga should end. of G, (2) that A flat is the fifth above D flat and is a relation It is noteworthy that primary harmonics bevond the of F. It also follows that in the ancient soles until the time seventh are not recognized. In European music with just of Pythagoras, tuning exclusively by fifths or thirds was un- tuning the nearest approach we have to a true seventh is.the known, the simplest intervals, which are obtained by fifths and augmented sixth ; with tempered tuning we continually use thirds combined, being used. It is only in a system like the sevenths which depend for their validity not upon harmonics European, where transposition from one fixed key to another, but upon their asthetic effect. Those writers who discourse and extensive modulation is practised, that tuning by a long upon the 17th harmonic as furnishing the interval of the minor series of fifths, tempered or otherwise, is likely to lead to any- ninth and diminished seventh, are in my humble opinion deal- thing but confusion. The Indian Tivra scale substitutes F ing with harmonic fictions, for I find it hard to conceive that sharp for F and the fifth above D for the A in our major

any reasoned and cultivated musical system should go beyond scale, thus producing the smoothest and most harmonious scale

the seventh harmonic. I have heard an Indian musician sing possible, one in which every note is in primary or secondary

a Raga which he called Shuddh Todi, and in which he made harmony with G. This scale appears to be identical with

use of notes corresponding with F sharp, G, Septimal A flat Syntono-Lydian Mode.

rand B. The effect was wonderfully pleasing. In another Indian Musicians owe a great debt of gratitude to Mr. : form of the same Raga, the ordinary A flat was used instead Deval, for, now that the Shrutees are known, it will be possible of.Septimal A flat. The latter appeared to be an inferior com- to construct harmoniums which will be in tune with Indian

i.bination possibly because the interval from Septimal A flat to Music. The tempered harmoniums now in use which have a B: being nearly a minor third is easier to sing and smoother in painful effect upon Indian ears will then be discarded. I have

effect than A flat to B which approximates to a Septimal third. no doubt that with the advent of properly constructed keyed

Mr. Deval's 22 Shrutees appear to throw considerable light instruments, Indian Music will enter upon a new era of pro- gress and development, possibly in the direction of harmony, on the question of the constitution of the Ancient Greek Modes for harmony is already extensively practised in the form of and will, I have no doubt, prove of the highest interest to irregular Arpeggios. This progress will be hastened by the European Scientists. In his book on the "Sensations of invention of a simple musical notation ; and for that purpose Tone "Prof. Helmholtz expresses doubt whether the Greek also Mr. Deval's researches will be of the utmost value. Modes were built up from the relations of F or those of G, and he suggests that they may possibly have been built up from Belgaum, E. CLEMENTS. both. If the Komal notes of Mr. Deval's scale are taken with 2/4/11. Sa and Pa, as in the scale which he calls the Indian Diatonic Minor Scale, a scale is obtained which is in all probability iden:

List of abbreviations.

Names of the seven notes of Corresponding European the Hindu Musical Scale. names. Old notation. Tonic Solfa.

ष. C ... Do.

ऋषभ ... D Re. ...

ग. गांधार Mi. ... ... E ...

म. मध्यम Fa. ... F ... पं. पंचम G Sol. ... ... धेवत ... A ... La. ... नि. निषाद ... B Si. ...

अ. की. अतिकोमल को. कोमल Do not accurately correspond with मध्य > European notation. See Preface pp. ती तीव्र VI, VII and tables A. B. C. D त.ती. तरती्र

• The author has followed the usual practice of calling Taor C. If H is taken to be F, the note to which it approximates in pitch, the Indian and European names may be made to correspond, ar. . being translated 'low flat,' को. 'flat,' म. 'low,'ती. 'natural,'and न. ती. 'high.': Thus म. धै. would be 'low D,' त. ती. नि. 'high E,' ती. नि.E natural' को. म. 'B fat.'

PREFACE. ERRATA.

Two years ago I publisbed a small brochure entitled " Music Page Line Incorreot. Correet. :. East and West " dealing mainly with the scientific value of the 2 .17 he the Hindu musical scale and the question of " Shrutees." But :18 tMr. Mr. further study of the subject has enabled me to state more fully 8 16 by the string from the string my humble views and hence the present pamphlet. I read 14 12 10×2 specially Capt. Day's Book on " Music of Southern India " 19 13.3 1 which was suggested to me by Sir J. W. Muir Mackenzie, the late 3 omit Revenue Member of the Government of Bombay. He has a 21 3 fine ear for Music. About 3 years ago Ihad an opportunity omit=4555 of explaining the subject to Sir J .. W. Muir Mackenzie, when f 25 laid before him my views, and practically demonstrated them 22 7 omit ln=&1' with the help of Professor Abdul Kareem, an artiste of great 23 Englis English renown on this side of India. I also perused with great interest 27 Table B 9 F FL and profit the late Mr. A. J. Ellis' paper on the " Musical Scales 27 Tablo B: 10 को. पंचम of the World. " Besides the valuable light thrown on the 28 Table O: 9 F1 F subject by these treatises I had also much and: invaluable 10 F Fsh. enlightenment from Helmholtz's " Sensations of Tone " a 30 14 Oents number Cents, name & kind -- masterly work on the Science of music. The perusal of these 31 17 मेंडा and other works has served to strengthen the views previously 18 Ghasists Ghasit held by me. The tables of Scales in the present brochure are 40 10 that that that: 41 14. The musical scale The Hindu Musical scale: almost entirely worked out 'afresh, and in some respects differ 11 observes observed from those in the old pamphlet. In that work I had touched 44 29 by the means by all the means upon the question of Shrutees so far only as the Diatonic Scale of seven notes was concerned. In this brochure, I have arrived at a probable solution of the whole question of 22 Shrutees. The paper read in the Kirloskar Sangit Theatre on the Shrutees is incorporated in this pamphlet.

It should be remembered while reading this pamphlet that there are two kinds of tones-the tones of the natural scale

X XI and those of the tempered scale. According to Blaserna the vibrations of these notes are as follows :-- flat, nor Tivra with sharp, nor must Atikomal be confused with

Natural Scale or Just Major. double flat or Tivratar with double sharp. The nomenclature

C D is quite different. As a matter of fact Tivra coincides with sharp E F G A B C 240, 270, 300, 320, 360, 405*, 450, 480. in the case of only one note F sharp, and Komal with flat in the case of four notes D flat, E flat, A flat and B flat. Tempered Scale. 240, 269}, 302} 3203, 3591, 403g, 453, 480. The formulæ embodied in the pamphlet, which have been

It will thus be seen that the above two scales are quite deduced from rules laid down by Sanskrit writers, have been

different. When a European repeats the seven notes of the worked out for me by my learned and esteemed friend Mr.

Modulator, Dho. (d); Ray, (r); Me, (m); Fah, (f); Soh, (s); Nilkanth Vinayak Chhatre B. A., L. C. E., Fellow of the Univer-

Lah, (1); Te, (t); Dho, (d) he necessarily refers to the notes sity of Bombay and retired Deputy Educational Inspector C.D. I take this opportunity of thanking him for the great interest of the tempered scale, which is now universally used in Europe he evinced in discussing the subject and suggesting several in vocal as well as in instrumental music. The Hindoo Musician improvements. I must also express my obligations to my who repeats the seven notes of the natural scale, refers to the friends, Dr. G. K. Garde, the late Hon. Mr. V. R. Natu, natural scale which is given above. The notes in the natural Professor -R. K. Joshi, late of the Fergusson College, Poona, scale are indicated by the letters C, D, E, &c., as has been done G. S. Khare and others, who helped me much by their valuable in Scientific Books, and not by the usual small letter Solfa contribution to the discussion of the subject. notation to prevent ambiguity and confusion. I am, however, I am extremely thankful to Dr. Hamilton who has a very for the present concerned with the notes of the Hindoo Music fine ear and who very patiently heard my demonstration and and as such with the notes of the natural scale only, noted encouraged me to continue my efforts in this line. - Mr. Mac- above. Millan, Assistant Collector, Ahmednagar, kindly came over to The sharp and flat notes :- The sharp and flat notes of the Poona and very sympathetically went through the whole pro- tempered scale are the result of the sub-division of the interval gramme of the last demonstration which took place at the between any two principal notes, into aliquot parts or equal Kirloskar Theatre in Poona and made several valuable sugges- divisions. Such is not the case with Hindoo Music. tions. The interval between C and D or between 24 and 270 I cannot adequately express my gratitude to Mr. E. Clements, vibrations or the length of wire between 32" and 36" is District Judge, Belgaum, who voluntarily and promptly divided into 4 parts which, as measured by Ellis's cents, are not extended his sympathy towards my efforts. He is educated in equal parts, but 85, 27, 70, 22 cents respectively. The notes European Music and has also a very keen appreciation for making up these intervals are called अ. को० क, को० ऋ, म, ऋ, Hindoo Music. He has not only written an intelligent af. #. The Indian word Komal must not be confused with introduction full of appreciation and suggestion but has improved this pamphlet in matter as well as in form and ° Blaserna gives 400 as the vibrations of A, whereas our A is of 405 vibrations, which is exactly the Panchama or the 5th o fD, vibrations 270. has thus made it intelligible to the European as well as to the

XII

Indian public. Not only this, but Mr. Clements has suggested to me that there is a branch of Indian Music which requires THE HINDU MUSICAL SCALE scientific and systematic treatment on similar lines. He has AND convinced me that without the development of this latter branch, the present attempt will be incomplete. I allude to the THE 22 SHRUTEES.

composition of Indian Rag's and Ragini's and especially to BY their notation, a subject which I mean to take up as soon as I can. Mr. K. B. Deval. ( Retired Deputy Collector. ) SANGLI, 10-4-11. K. B. DEVAL. For more than the last eighty years, several attempts have been made to determine the Hindu Musical Scale with mathematical precision, by Indian and European scholars. But hitherto they have not been crowned with success; the solutions arrived at do not satisfy the tests of reason. Neither do they agree with conclusions noted by Sanskrit writers on Hindu Music. Hence it is that I propose to lay: before the public a few thoughts about the Hindu Musical Scale and the lines of its development and progress. It might be stated here at the ontset that the Hindu Musical Scale dates as far back as the Brahman Period which is calculated, according to modern re- searches, to extend from 2500: B. C. to 1400 B. C. It is possible that further researches might modify this date or might, perhaps, carry it still farther back. But we may be certain that our Scale. dates farther back than the Greek Scale which is acknowledged to be: the parent of modern European Scales. Capt. Day in his " Music of Southern India" observes :- "The Historian Strabo shows that the: Greek influence extended to India, and also that Greek musicians of a- certain. school attributed the greater part of the science of music to India." : The antiquity of the Scale apart, the most important point to be noted about it is that it is formed in consonance with the laws. of the constitution of musical sound. : It is a progressive Scale and the lines of its progress are laid down in old Sanskrit works on Hindu- Music. The ancient sages of India, with their austere methois of stuly, meditating for years together in the quiet and tranquil recesses of nature undisturbed by the bustle of human habi-

2 3

tations, have preserved the results of their labours in their precious of Rome, in his valuable treatise on the "Theory of Sound in its works, which excite even to-day the wonder and admiration of the Relation to Music", by a musical scale is meant " the col- cultured world. In recent times the attention of educated Indians lection of all the notes comprised between the fundamental note turned to this Art of Arts, and men like the late Mr. Kunte, Messrs. and its octave, which succeed each other and are intended to Pingale and Sahasrabuddhe, Mr. Banhatti, Raja Surendra Mohun Tagore, succeed each other with a certain pre-established regularity." " The Mr. Chinnaswami Mudliar, have written copiously on Hindu Music. musical scale is always the product of the musical activity of a nation But difficult as the subject is, several points have been enshrouded extending over a number of centuries." Hence to allow such wrong in mystery, e.g. the Shrutees. In some of these recent publications impressions about the Hindu Musical Scale to stand permanently on there appear misinterpretations of shlokas from the Sanskrit. works. record and to suffer them to prejudice the minds of Western and Hence they have given rise to a number of wrong notions about the Oriental Scholars as to the rank which the Hindu Musical Scale Hindu Musical Scale, and consequently about the value of Hindu should take in the musical scales of the world, is neither just nor Music, not only among Indians but also among scholars of the West. reasonable when there exists abundant evidence to disprove the European writers on Hindu Music e.g. Capt. Willard (" Music of above allegations. To elucidate all the difficult points of so diffi- Hindustan"-a paper sent to the Society of Arts in 1834), Sir William cult and scientific a subject as Music requires an amount of Jones (paper on Musical Scales), Mr. Bosanquet (paper read before labour, energy, and talent which is given to but a few ; it is the Royal Society of Arts in London in 1877 on the Hindu Division of a stupendous task, and personally I feel it quite hazardous on he Octave), Mr. Patterson, Captain Day (Music of Southern India), my part to attempt to undertake it. But approaching the subject tMr. A. J. Ellis (paper read before the Society of Arts in 1885 on the with the humility and diffidence of a student, I have pursued my Musical Scales of the World), have come to hold erroneous views about attempts hitherto and I lay before the public the results of my hum- the theory of the Hindu Musical Scale. This might be due partly to ble.labours. their ignorance of the Sanskrit works on Music, partly to the erroneous information supplied to them by recent publications, and partly to 2. It would be proper to state at the outset the laws of the the assumption that the Hindus must have followed a system similar constitution of musical sound which the ancient Sanskrit authors ob- to the equal ' temperament ' system at present in vogue in Europe, served in their works on Hindu Music. In order to make this point In 1885, the late Mr. A. J. Ellis, the distinguished English physi- quite clear, I place in juxta-position the laws observed by Sanskrit writers and those followed by modern scientists of renown. cist, scientist, and translator and editor of Helmholtz's " Sensa- tions of Tone", in his paper on "the Musical Scales of the World" after comparing and examining the Scales of the various nations -among them the Hindu Musical Scale also-came to the following conclusion: " The Musical Scale is not 'one', not ' natural', nor even founded necessarily on the laws of the constitution of Musical sound so beautifully worked out by Helmholtz, but very diverse, very artificial, and very capricious." This I humbly submit cannot be said at least of the Hindu Musical Scale, as. will be seen. from the following. Now as, observed by Professor Pietro Blaserna, of the Royal University;

5

Both make a clear distinction between Sound European Scientists .. Authors on Aryan Music.

and Musical Sound. (b) A note not accompanied (b) श्रवणयोग्यता अनुरणनात्मकस्य by its harmonics may sometimes स्वराख्यस्य दीर्घध्वनेर्वतते.

1. Sound. be sweet, but it is always thin रा. वि. आर्या १४ टीका. and poor and therefore but little (c) शृत्यनंतरभावी यः स्त्रग्धोऽनु-

European Scientists. Authors on Aryan Music. musical. रणनात्मकः । स्व्रतो रंजयति

Blaserna p. 165. श्रीतचिन्त सः स्वर उच्यते।।

(a) Sound in our apprehen- (a) शुति or (नाद) शु= to hear सं. र. स्वराध्याय प्र० ३ शो० २३.

sion is that which is heard and श्रवणयोग्या एव शुनयः। (c) In order that a sound स्वरशब्दस्य व्याख्यामाह :-

therefore our only means of recog- रागविबोध आर्या १४ टीका. may acquire a musical character, मनः श्रोतचित्त स्वतः कारणान्तरनिरपेक्ष

nizing its existence is through the (3) शरवणेद्रियमाह्यत्वाद ध्वनिरेष it must satisfy the essential con- अनुरकं कुर्वेतीति स्वरा:

sensation on our ear. The auditory श्रुतिर्भवेत्-विश्वावसु सं.रं.पृष्ठ१४- dition of being agreeable to the रा. वि. आर्या १४ टीका.

nerve alone can perceive sound. (c) प्रथमश्रवणाचछब्दः श्रूयते व्हस्व- . ear. मात्रक: सा श्रुतिःसंपरज्ञया Blaserna p. 74.

'( Holmes' Vocal Physiology- स्वरावयवलक्षणा।। Ed. 1900-p. 52). -माघ सर्ग १. शोक- १० टीका. also संगीत रत्नाकर; 3. Harmonics. (b) Sound on the other hand श्रुतिर्नाम =स्व्ररारंभकावयवः is produced in our ears and is शब्दविश्ेष:। therefore subjective; but vibra- माघ सर्ग १. शलोक १० टीका, Harmonics defined. In Sanskrit, Harmonics are

tion is objective. It exists in ) May be translated sounling bodies independently of : Strings in vibrating do notonly called अनुरणनात्मकध्वनिः

swing as a whole but have also (a) श्रुत्यनंतरभावी यः स्त्िग्धोऽनु- (a)+(b)1 as follows :- the listener. To a deaf man the Any sound which' रणनात्मकः॥

vibration exists but the sound is heard by the ear -several secondary motions, each

does not. Sound is the result of and is a Shruti भति and' of which produces a sound proper स्वती रजयति श्रोटचित्त सःस्वर उच्यते।।

(e)+(d) a शरति and sound are to itself. A string, when struck, सं. र. शोक २३ vibrations .* one and the same. vibrates first in its entire length, and are perneived, (४) अनुरणनात्मको ध्वनिविशेषो-

Blaserna p. 27. because the ear secondly in two segments ; third-

hears them. ly in three; fourthly in four, and यस्मात् संभवति तादृग्लक्षणो उदीयात्-तथाप्रथंमतंत्री बंधनीया.

2. Musical Sound. so on. All of these motions are रा. वि. आर्या १९ विवेक २. simultaneons and the sounds pro- (a) Musical sound strikes us (a) तंत्री-मेरु-सारी संभ्ेषोद्गवां ये ceeding from them are blended (c) रणद्िराघष्टनया नभस्वतः पृथग्विभिन्नश्रुतिमंडलै: (Harmno. as being even, smooth an l melo- ध्वनयः ते श्रुतयः शुतिशब्द- into one note. The lowest note nics) स्वरः। dious like the tones of all musical वाच्याः।। श. वि. वि. १ आर्या २०. is the loudest and is called the

instruments. Holmes p. 61. fundamental or prime tone, and क्षमाणं महर्ती मुडमुंहुः ॥ the others are called over-tones, माघ सर्ग १ श्लोक १०. upper partial tones or harmonics. वायोराघातेन पृथक् संकीर्ण So does #77 (= vibration ) exist to a deaf mun and gia (= sound ) is the Holmes p. 69. ध्वनद्धिः अनुरणनोर्पद्यमानै: result of ' स्पंदन's. स्फुटीभवंति ..... टीका.

6 7

European Scientists. Authors on Aryan Music. 4. Nodal points and Ventral Segments.

. The above Sanskrit piece mark- European Scientists. Authors on Aryan Music.

ed (c) translated by Sir W. Jones runs as follows :- A string when rubbed is in a श्रुतिमंडलै: Ventral segments state of rapid vibration; at the and the consequent production

x x "Nârad sat watching extremities where it rests on two of harmonics as defined by Bla-

from time to time his large bridges, it appears to be at rest. serna were observed by Nârada in

Veena ( sonometre or monochord) Bat when the middle part is exa- vibrating strings which were set

which by the impulse of breeze, mined, it is found that the string free to vibrate by the breeze.

yielded notes that pierced succes- loses its sharpness of out-line. What an amount of patient

sively the regions of his ear, and It appears sensibly thickened and and careful observation must

proceeded by musical intervals. " this thickening reaches its maxi- have been bestowed in the time

Pingale's treatise, p. 251. mum at about the middle of the of Magha when the poet could string which proves that each describe the celestial musician

It need hardly be noted here particle of the string performs a Nârada as having detected by

that the great sage Narad to and fro movement in direction his eyes and ears these ventral

perceived these Musical intervals perpendicular to the length of the ( otherwise called harmonics ) as string. Vibrations of this sort segments and harmonics !

arising from the whole length of are called transverse. The most Somanâth refers to harmonics

simple form of a vibration is that in his रागविबोध In Aryas 30 the wire set free to vibrate on its. in which the whole string vi- and 31 he gives their importance;

own account and creating natural brates simultaneously in one he calls them स्वयंभू notes.

nodes and ventral segments as single vibration. This effect can easily be obtained by leaving the स्वस्मावेव भवंतीति स्वयमुव: And again distinguished from artificial nodes in commentary to आर्या 34,

and segments which it is neces- string quite free. The note thus he states मेरुगतस्व्र यंभूस्वरपंक्तिपामा-

sary to produce ( as will be seen obtained is called the funda- ण्येन। स्व्रयंभू tones means harmo-

in the sequel) in the construction mental note. x x nics or upper partial tones which

of the Musical Scale .* tive channels in regular order or succession, Whether we interprete the adjectival compound qualifying the Swaras in the Jonesian way or we do it tions from works on Music, we can well understand that the Poet makes Narada

Gayan Samaja. Narada's Veena is called werafrTr Page 22 of "Hindu Music" in the method of Mallinath who draws out the meaning giving accurate quota- observe with amusement the action of the wind on the lute and note the same महती is the name given to the ब्रह्मवीणा of Narada in the stanza phenomena ( Nodal points, Ventral segments and upper partial tones ) as a modern European physicist may well observe with all the precision of his quoted here. latest advanced notions of the theories of sound. Here we have in the clear poetic way of Magha, noted down a fact which, The foregoing interpretation of the Shloka has been accepted and found to

ought to arrest our attention. Narad is descending from the heaven to the be correct by Prof. V. G. Vijapurkar M. A., Prof. V. K Rajwade M. A., Mr. earth and the wind strikes his big lute the Mahati. He was observing his Vinayakrao alies Annasaheb Patwardhan, Sardar K. C. Mehendale, Mr. Raddi instrument with the Murchhana of the several Gramas displayed or unfolded by Shastri of Elphinstone High School and other Sanskrit Scholars.

the several Swaras ( upper partial tones ) each showing on the string its It would be interesting to note here that while Harmonics were un-

distinct successive ventral segments. Sir William Jones seems to have under- observed by the Europeans as admitted by Blaserna till the latter half of the

stood the word Shruti in the ordinary meaning of ear and not as the primary last century, it was a matter of common knowledge to the Hindoos at least

tone going to build up the secondary or upper partial or over tones. He inter- as far back as the 6th century. Magha makes a passing reference to it in his

prets Mandala to mean regions or more scientifically, the encircling channels Sishupala-vadha which is a poem merely of general interest, which fact proves

( of the ear ). According to him the various Swaras pierced the various recep- that in the days of Magha general readers of poetic literature were expected to be familiar with the phenomena.

8 9

European Scientists. Authors on Aryan Music. 5. Reflection of sound. But if the string be touched in are heard when the whole string European Scientists. Author on Aryan Music. the middle, a note which is resting.on two fixed bridges is double in pitch, which practical made to vibrate. He warns musi- ECHO-The best understood सं. र. पान ३५ कोहल. आानंत्यं हह श्रुतीनां च सूचयन्ति musicians call the octave of the cians to always test the correct- of all the cases of reflection is that which is called ECHO. विपश्चितः। fundamental note, is obtained. ness of their notes, wherever -Blaserna, page 43. यथाध्वनिविशेषाणाममानं गगनोदरे॥ The string in this case vibrates possible, by referring them to these टीका-नेषां अतिसूक्ष्मभागकल्पनया Sमानम्. in two parts in such a way that the point touched remains at rest. स्वयंभू harmonics. The reflection of sound has been This fixed point is called a node utilized in various ways. Nature वितक्षयाSSनन्स्यं दर्शितम् of the vibrating string and has and art have combined to solve been produced artificially by some problems not unknown in इयत्य: प्रतिपद्यन्ते न तरंगपरम्पराः॥

tonching the string at the point history. The celebrated " ear of रागविबोध, विवेक २, आर्या ३२

indicated. . Successively higher Dionysius" is well known; it is and higher notes can be obtained a sort of hole excavated in the by the string by touching it at a rocks near Syracuse where the third, a fourth, a fifth of its least sound is transformed into & length, etc. etc. deafening roar. Similar pheno- .(Blaserna, Chapter I, pages mena are often met with under 11-14). the large arches of bridges, via-

By the figures ducts, &c. &c.

given in the 6. Sympathetic Resonance. margin Bla- Experiment shows that. when- अष्टम्येकादश्योः सार्योरुर्ध्व समापर- serna has ever a body vibrates, other bodies ध्वनितः ॥ shown the placed near it, are able to enter तत्तैः समाः सपसमा: स्वयंभुवो मुक्त्त- different modes of into a state of vibration on this तन्त्रीजाः । condition only that such bodies टीका-तन्तैशित॥XX मंद्रप मध्यसम- .vibration which a string assumes shall be capable by themselves of मध्यमानां स्वयंभूत्वाद्धंतो: तैः मंद्र- - in different cases when it vibrates producing the same note. पंचमादिभि: समाः। सटृशनादाः मुक्क्कतंत्री as a whole or into 2, 3, 4 &c. parts. In the first case no node Blaserna, Ch. II, p. 49. जा: मुक्ता: वामहस्तांगुलिश्ेषरहिता: या: तंत्र्यः प्रथमादयश्चतस्त्रः ताम्यो जाताः is formed, in the others we have सपक्षमा: अनुमंद्रष ड्जानुमंद्रषड्जमंद्र- one, two, three, &c. nodes. The parts of the string between the मध्यमा: स्व्रयंभुन: ज्ञयाः इति शेषः॥ नीचोच्चस्थानकृत एवैषां भेदो न रूपभेद nodes which contain these points of maximum movements are 7. Pitch. इत्यर्थ: ॥ रा. वि. वि.२ आ. ३२.

called ventral segments. This is what we have in शरुतिमंडलै:स्वरैः What is the limit of audible According to Sanskrit writers

of Magha. connds? Does our ear perceive as there are five divisions of sound. & note any number of vibrations

10

European Scientists. Authors on Aryan Music. European Scientists. Authors on Aryan Music.

whatever or is our perception con- मतंगमते तु-सूक्ष्मश्चैवातिसूक्ष्मश्च व्यक्तो- The notes of this harmonic se- नीचोच्स्थानकृत एवैषां भेदो न रूपभेव: fined between certain limits? S व्यक्तश्च कृत्रिम := सूक्ष्मनादो गुहावासी ries are not notes taken at random. Twenty or twenty-five vibra- हृदये चातिसूक्ष्मक: &c. पंचानामपि सा- They are very agreeable to the इत्यर्थ:

मान्येन गीतोपयोगित्ये पासे हस्कंत्र- ear in relation to the fundament- रा. वि. वि. १ आर्या २१. टीका ..

tions just take place per second in order to produce appreciable मूर्धस्थाने एव गीतोपयोगित्वमाह अत्र al note, and have great import- अत्यनंतरभाव्री य: स्िग्धोऽनुरणनात्मक: ance as we shall see in the sequel स्व्तो रंजयति श्रोतुश्चितं सस्वर उच्यते.

note. The notes that are too low गानाश इति। in the theory of musical instru- सं. र. आर्या २६.

are badly heard and those that are रा. वि. वि. १ आर्या ११. ments.

too high are unpleasant. एवं पंचसु त्रयाणां गानोपयोग्यता।

Blaserna, pp. 66-67. रा. वि. आर्या १२-१३. अधराधर तीव्रा स्तास्तज्जो नाइः श्रुतिमर्तः।'

The well-known voice of a नादाSतिसूक्ष्म: सूक्ष्मभ्र पुट्टोऽपुषभ टीका-तंत्र्योऽधराधरास्तीवा उच्चोच्चध्वनयो भवंति.

single singer embraces about two कृन्रिम:।। इति पंचाभिर्धा धत्ते पंचस्थानस्थित: Tones increase in Pitch in the तंत्रीतंतुस्वरी ज्ञेयस्तदैर्ध्यव्यस्तमानतः।

octaves. In the case of a woman क्रमात् ॥। (५) inverse ratio of the length of the तंतुस्थौल्येऽि विज्ञेयस्तंतुसौक्ष्मयेऽप्ययं

a little more. व्यवहारे खवसौ त्रेधा हदि मंद्रोऽभिधीयते। Wire. विधिः ॥ शेष लीलावती

कंडे मध्यो मूर्मरि तारो द्विगुणश्चोत्तरोत्तर:11७। यथा शरीरे शरुतयः उत्तरोत्तरोच्चा: उ-

सं. र. पान ३२. स्पदन्ते तथा वीणायां. . अधराउच्या उत्पद्यन्ते-इति स्वारस्यम्। 8: Laws of the vibrations of strings and of artificially (सं. ८. प्र. अ. प्रकरण ३ श्रोक १३.).

produced harmonics. But it may be noticed that (in वायुःसोपानपरपरामिव आरोहात् अत्र

Blaserna, pp. 71-72. human voice) the larynx rises for हत्कंठ मूधस्थानेषु मरुताघाताभि-

(1) When the whole string the production of high notes. व्यक्तानूनादान् कुरुते=(विवृणोति)

vibrates in one vibration, it अभिव्यज्यते । अत्र तंत्री शब्देन त्डु- रा. वि. आर्या १३. टीका ..

gives `its lowest note which द्वो रवो लक्ष्यते। 9. Simple ratios of consonant notes. is called the fundamental

If the whole string be touched note. The whole vibrating length of It may be established as one संवादि स्वरा: Sanskrit writers call:

in the middle with a finger, a the string resting on the of the fundamental principles of notes which bear simple ratios to

two fixed bridges ( 6) gives a our mnsic that the ear can endure higher note is obtained, which each other संवादि स्वर and the fol --

practical musicians call the note (षड्ज) which in English notes, be they simultaneous or successive, on this condition-viz :- lowing extracts will show the im-

octave of the fundamental note. is called the fandamental note. that they should bear. simple portance which has been given to-

(2) If the string be divided द्वाविंशीस्थ: षड्ज: द्विगुणसमः । ratios to each other in respect of these simple-ratio-bearing-notes

रा. वि. वि. १ आर्या २१. the number of their vibrations per ( otherwise called संवादि स्वर) by by touching it with a finger or a feather into two, three, four, &c. second, that is to say, that the the Aryan authors of music as a मध्यस्थानस्थ: षड्ज: = द्विगणित- parts, higher and higher notes षड्ज: द्विगुणप्रायः ratio of the number of vibrations science, and by musical compo --

are obtained which form that A note double of the funda- per second of the notes should be sers.

which is called " En-harmonic" mental is obtained, if the wire is expressed by low numbers. Blaserna. Chp. 5 sec. 2. संवादिनां समाजो रंजनकारी भवेदिति series. halved. [ रागविबाध ]- न्यायात् ।

:12

European Scientists .. Authors on Aryan Music.

निरत नि्ः्शंकादिभिरिहापि संवादि सान्निध्यम्। रा. वि.१८. The werd न्याय may be trans- lated by the English word ' law.' टीका-संवाद=एककार्यत्वं येषामास्ति तादृंश्ानां समूहः (समाज:) सहावस्थितिः इति यावनू रंजनकारी रंजको भवेत् इति लोकमघातः। Blaserna divides consonant in- Sharangdeo also in his Sangit tervals or simple ratios into 4 Ratnakar (संगतिरत्नाकर) defines groups. consonant sounds and divides 1 Unison or: octave शुद्ध संवाद them into 4 classes. [रा. वि. वि. १ आ. २२ ]. 2 Perfectly consonant संवादी. सं. र. म. अ. प्रकरण ३ श्लोक ४९.

3 Consonant अनुवादी. चतार्वेधा: स्वरा वादी संवादीच विवाधापे। 4 Dissonant निवादी अनुवादीच वादीतु नयोगे बहुलःस्वरः॥

10. Beats. सं. र. पा. ४९.

When two notes not exactly of The Aryan and Sanskrit the same pitch and bearing intri- authors also describe in similar cate ratios are sounded together terms the unpleasant effect pro- (a new phenomenon is observed duced on our ear by the combina- known by the name of beats ) a tion of notes bearing intricate sound is obtained of varying loud- ratios, which notes go by the name. ness, now strong and now feeble, and very marked jerks or shocks विवादिस्वर एकश्रुत्यंतरितौ (having a difference of only one Shrutee are perceived. These shocks are -or a quarter or a third of a note ) -the beats &c. &c. विवादिनौ वैरिणौ मिथोभवतः। 'If one of the two notes be Two more resultant notes are also heard riz: 40 ( 64-24) and

slightly altered unpleasant beats (आर्या ३८ रा. वि. विवे.) 28 (64-36); the last or rather the half of it riz: 14 introduces the are heard and they. " spoil the टीका-विवादिनं लक्षयति-XX septimal harmony in our music.

harmony." Blaserna Chapt. V, संवादि अनुवादिजनितरागरक्तिविना-

Sec. 4, 5 and 6. शकत्वात् विवादिनौ भवतः । विवादित्वं यथा-ऋषभस्य गांधारः॥

12 13 European Scientists. Authors on Aryan Music. European Scientists. Authors on Aryan Musie .. निर्त निःशंकाड़िभिरिहपि संवादि farama note as defined by Sha- सान्निध्यम्। rangdeo पृष्ठ ४२ शोक ४९ टीका। रा. वि.१८. The werd arry may be trans- विवदनादिवाहि। विवशन नाम वाद्या- lated by the English word ' law.' दिि: स्वरैरुत्पाद्यमानरक्ते: विनाशकर्ल टीक्ा-संवाद=एककार्यतं येषामस्ति (bere र्ति means harmony. रंजन" नेादृंदानां समूहः (समाज:) सहावस्थतिः -pleasure &c. &c. )

इति यावन् रंजनकारी रंजको भवेत् इति 11. Resultant notes or difference notes. लोकप्रघातः । Blaserna divides consonant in- Sharangdeo also in his Sangit Blaserna in sec. 6 Chapter 5. After describing the Veena (n. .Whenever any two notes bear- stringed instrument of the time. tervals or simple ratios into 4 Ratnakar ( aitoat ) defines ing simple ratios are combined, of Nârada) the author of Râgavi- groups. consonant sounds and divides besides these two notes a low bodha in Arya 19 and in its com -. 1 Unison or octave शुद्ध संवाद them into 4 classes. note is very clearly heard (i. e. mentary gives instructions as to. सं. र. प्र. अ. प्रकरण ३ शोक ४९. when two notes making 200 and how to tune the 4 strings on the 2 Perfectly consonant aaet. चनुार्वैधा: स्वरा वादी संवादीच 250 vibrations per second are said instrument. 3 Consonant अनुवाठी- विवादयापे। sounded, a third note correspond- 4 Dissonant निवादी- अनुवादीच वादीतु नयोगे बहुलःस्दरः। ing to 50 vibrations per second is अनुर्भद्रषड्जमहेनुमंद्रे पं द्वितीयका तंत्री।

सं. र. पा. ४९ .- heard. This number is 4th part मंद्रं संच तृतीया चतुर्थिका मध्यमं 10. Beats. of 200 or the half of the half). मंद्रम् ॥ १९ ॥ This note is called the resultant रा. वि.वि. २- When two notes not exactly of The Aryan and Sanskrit or difference note. Its pitch or' If translated it is as follows :- the same pitch and bearing intri- authors also describe in similar strength or the number of vibra- The first string should be so cate ratios are sounded together terms the unpleasant effect pro- tions is equal to the difference (a new phenomenon is observed duced on our ear by the combina- between the two combined notes. tuned as to give the fandamental note. The second to give its 5th;' 'known by the name of beats ) a tion of notes bearing intricate This thirdnote is agreeable to the 3rd to give the octave, and .sound is obtained of rarying loud- ratios, which notes go by the name. the ear, because it arises or is the result of two combined notes the 4th to give F. the fourth ness, now strong and now feeble, विवादिस्वर एकश्रुत्यंतरितौ (having which bear simple ratios to each of the octave. Now supposing a difference of only one Shrutee the fundamental note gives 24 and very marked jerks or shocks other. It, theretore, forms a vibrations per second, we find? are perceived. These shocks are or a quarter or a third of a note ) consonant: part of any one of the- two notes combined and thus out the: following vibrational; the beats &c. &c. supports harmony. values of the 4 notes combined. If . "If then several notes be combined" Now if we: :slightl otserves Blaserna "it is not enough to C or षड्ज=24 find out the. :are he select those which by themselves will valnes . of harmor give an agreeable harmony ; it is ne- G or q4T=36 12 the result- cessary further to examine the resultant C'or SET=4812' ant notes' notes and to see how these will behave For मध्यम=64 16 they are as in relation to the combined notes.". -noted in the: margin,

14 15

European Scientists. Authors on Aryan Music. between notes bearing the ratio of an octave; eniar=

The discovery of these resultant This very same principle has perfect concord, ratio of 2 : 3, STIT = imperfect concord,

motes was made towards the all along been strictly observed ratio of 4 : 5 or 5 : 6; faare = dissonance. They lay

middle of the 18th century and both by the celebrated Rishi down that the rule of perfect concord should be observed

is generally attributed to the strictly in forming musical scales. The lengths which will be

celebrated violinist Tartini. Narada ( who is called the father of music ) during the Vedic period given for the several notes in the Diatonic scale below, are those

and also by instrumentalists and of the wire of the Diachord, whose length, I take to be 36 inches;

composers of subsequent periods. each inch being further divided into 20 subdivisions,

x How the first two resultant which I call lines. I also take 240 vibrations for the funda-

notes form into the lower octave mental note aT. In the Diachord are two strings or wires, resting

of the fundamental note 4=12 on two fixed bridges, one at each end. When experiments are to be

how the 3rd note viz: of 32 vibra- made, we have to tune one string to give out a note which may

tional value forms into lower be called the fundamental note. The other string is to be tuned

octave of F"= 4 = 32 and how so that it may be in full unison with the first. When the two strings are thus tuned, then the moveable bridge is to be moved these 3 support the original 4 about for producing the required notes. Its height must be such notes and how they thus contri- as to leave no distance whatsoever between the string and the bridge, bute to the harmony of the whole instrument, may be more easily yet not pressing the string upward. One of the strings is to be left free to vibrate on its whole length, giving the fundamental heard and enjoyed than described. note, while the different notes required are to be produced on the

The next most simple ratio द्वाविर्शास्थ: षड्ज: द्विगुणसमः पूर्व other. On moving the bridge to the distance required for producing

that can be imagined after बड्जेन। मध्य स्थानस्थ: षड्जः। a note, the string is to be pressed very lightly to the edge of the unison is that of 1 to 2. This यथा पूर्वोक्तस्थापनया, मध्यषइजेन- bridge with the finger-nail, so as not to increase the tension is the ratio called that of the सह मंद्रषड्जस्य मेरुस्थस्य संवाद in the least. Then the exact note will be produced on sounding the (agreement complete) साशुद्धेति. string. To get the exact note on the given length, it is necessary -octave. निश्चयः। रा. वि. वि. १ आ. २१, २२. that there should not be any disturbing element such as increased tension caused by pressing the string downward to the bridge. This depends on the accuracy of the instrument. 3. From the foregoing comparison of the fundamental laws of the constitution of musical sound, adopted by modern scientists, How the positions and vibrations of the 7 notes of the Diatonic and those observed by our old Sanskrit writers, it will be clear that Scale and the octave, have been settled with mathematical precision in constructing their musical scale the Aryan authors proceeded on is shown below. scientific lines. How from these laws the Diatonic scale of seven notes, or the Fataar was formulated may be noted below. It may be stated that the rule of perfect concord and of harmonics was strictly observed in the construction of the musical scale. An explanation of the ordinary terminology in Sanskrit musical works would help towards understanding the subject: 5=fixed bridge; moveable, fret=सारिका; शुद्धसंवाद=unison or the relation

16 17

#1 (C) and #, (C, ). तंत्रीततुस्वरो ज्ेय: सद्ैर्ध्यव्यस्तमानतः। -0

१. मेरुडिलष्टतुर्यतंत्रीरवे सः षड्ज: (शेष 'लीलावनी)

अभिव्यज्यते. Rule ( 3 ) The pitch of a note or its vibrations are inversely pro-

(रागविबोध-वि. १ आर्या २१). portional to the length of the wire. This,rule is a legitimate inference from the above Rule (1) The whole length of two rules. Rale ( 1 ) permits us to take any length the wire between the for the Fandamental Note ( F. N. ) and according to two fixed bridges gives Rale (2) if the length is halved the pitch is doubled, and the fundamental note. if the length is doubled the pitch or the number of स1 (c1). vibrations is halved. If therefora ird length is taken

Let the length of the pitch or the number of vibrations prolnced will be

the wire be 36", the trebled. Or by generalization :

note produced be call- Rule ( 4) The pitch varies inversely as the length and vice cersa. ed #1 (c1) and let its The above four rales may therefore be put in the form

vibrations be 240 per of a simple Formula for convenience of working and

second. ready reference. Let V,=Vibrations or pitch of the note on wire l, inchos 2. मध्यस्थानस्थ: षड्ज: द्विगुणसम long. u"=The vibrations or pitch of wi (c1) the F.N, here 2 18 ... (रा. वि. ). =240 : 480 नि Rule (2) The note produced on =The length of the wife of the F. N, here ()8 (8) .1814 455%

half the length is in =36 Inches=36". Ba नि (7)a B 19} : value equal to 1 (c1) Then : and in pitch or vibra- VAxl .= uxt .... (A) A (6) 211 405 450 tions it is double the Vi=wx2 fundamental note .... (B) 24 (F. N.) (5) 1 = 36" .. (C) म (4) 27. The note produced on the The Seven Notes: i (c.) to H2 (c2). 4/3 3/2

length 18" is therefore. therefore if Vx=2u : (3)6 28 Eb 3032 -ai or c1 itself, but one octave higher. Let this. ... (D) 5'4 281 note be called 2 or cg to distinguish it from c1 म (F D (2)

or a1, the F. N .; then ४. मध्यस्थानस्थ: मध्यमः । (रा. वि.) 1 .9/8 (1) 36 . 32 the vibrations of ag or- उभयो: षडूजयोर्मध्ये मध्यमं स्वरमाचरेत्। 240 270 300 : 320 360 -..-. Cg are double i. e. (संगीत-पारिजात.) ; 2 x 240 = 480 per Rule (5 ) The note (. For the fourth note ) is produced at the प ध नी स1 Ratios second. middle of the Fundamental Note and its octave. Vibrationg 3 Notes

18 19 The note # is therefore produced at half the length of #1 (c1) and aa (cs) orat }(36"+18")=} (54") =27". 36 In other words the note of the wire 27" or 27" inches V= 240× 24 = 360= Vibrations of q (G )

of the executive part of the wire will give out the 4th 36 3 note or # (F) and by Rule (4) formula (B) the pitch or vibrations of # (F) are eqnal to 320. or the Vibration's of q ( G ) are The formula ( B ) is :- % of its #1 or F. N. and Here u = 240, 1 = 36 & ln = 27 .. (C) Vn = 240 x = 320 = Vibrations of 36 240 213 And formula (O) is : - 360 24

1 =240 × 3 3 or the length of q is g of its a, (c, ) or F. N.

4 =T X 36 These facts may be noted down under Rule ( 8 ) below :-

or the length of is of the length of the F. N. and Rule (8) The length of the wire of 4 ( G ) or the fifth note is of that the vibrations of # are of the F. N. and it may be of a1's (c1 ) wire and its vibrations or pitch is of that

. laid down :- of स1 (c). ttule ( 6 ) Thai the length of the wire of a ( F) or the 4th note is री (D) and ध (A). of that of the Fundamental Note and the ribrations of- ६. स-प-स-ममुख्या: संवादिन: स्वरा एकसंश्रयाः परायः। (रा. वि.) (F) are $ of the vibrations of the Fundamental Rule (9) In the interval of a given octave, a1 (C1 ) with q(G ) and Note 1 ( c1 ). (F ) with H2 (.Cg ) form perfect concords; it may be q (G). noted that Fri (C1 ) with ( F ) and 4 ( G ) with as ( Cg ), ५. त्रिभागात्मकवीणायां पंचमःस्यान्तवमिमे। (संगीत-पारिजात.) the inverted interval, form imperfect concords.

Rule (7) The fifth or ( G) note is produced on } or f of This rule is very important and is mide use of in finding ont whole length of the wire. The former note is one octare the lengths and vibrations of the other notes fr, ( D), T(E ), &c. &c. higher than the latter. According to Rule (1) any length may be said to give the The length of the wire is 36". Therefore a length of fundamental note and its Ta will be the 5th note from it. This 12" or 24" will give the fifth note q (G ). Bat we want iaw or q will form a perfect concords with it .* This gives us the the length between 18" and 36"-the two limits of following consonant notes. the octave. Therefore the length 24" is that which we F. N. H1 (c1). Consonant note 4 ( A ) or # (F). require and it will give out the note q (G). स C1 q G Let us apply the formula ( B) and (C) to the case of ₹D नी B स2 C2

VA = u x 7 ........ (B) स, 0 qg G2 or q G Substitute the values u = 240, 1 = 36 and in = 24 e As I proceed to show, T3 (Ez) is not a perfect pancham with v (A); nor is #2 (F2) with fa (B).

20 21

Let us take q (G ) itself as the starting or fundamental note; then. its o or fifth will be D in the higher octave. which may be its H or the fifth note. Therefore the length of A x 28=x == 183f and the cibrations of fa. called fr, D2. Apply the formula (B). V,=u ; Here u =360, l= 24 and l=j x 24; .. =16 ग (E) and नि (B).

Rule ( 7). Substituting the values of u, l, and lA again

V .= 360 x2: = 540. Bule (12) If the vibrations of (E) be taken at 300 ( and there is a

540 are the vibrations of fr, or fr (D) in the: 2nd octave. reason for doing so ) in place of 303g as obtained in

Therefore the vibrations of f in the first octave are=} x540 = 270 Rule ( 2 ) above, then

Vide Rule ( 2 ). .. (C); u= 240, 1=36 and V# =300 Formnla (C is- : 240X36 =111 ; substituting u = 240, l = 36 and 300 =281 Hence the length of =28f and its pitch=300. V .=: 270, we have [ The ( E.) obtained by the foregoing process has 3032 vibra- 1, = 240 × = 32. Hence- tions and bears with the F. Note a complicated ratio viz. 81 : 64. The Rule (10) The length of tr (D) is 32 inches and its vibrations are T (E ) obtained as the fifth harmonic when reduced by two octaves 270 or the length is & l and vibrations & u. has 300 vibrations and bears with the F. Note the simple ratio of

a (A). 5 : 4; and it sounds more consonant with it. It is clearly heard on the

Rule (11) The length of tf is 32". If we take this as the starting bass string. ( the fourth, giving ar or F. Note ) of the Vina.

note, then its H is 4. Therefore the length of is of Sanskrit writers have adopted this in preference to the other. They

32=211 by Rule (8) and its vibrations are of 270=405. tested their notes by harmonics ; the author of urfaara clearly lays . down: मेरुगतस्वयंभूस्वरपंक्तिमा माण्येन। रा. वि.विवेक २ आर्या ३५ टीका] ग (E) and नि (B) The 'length of ( A) is 21} and its vibrations are 405. नि (B).

Let us take v as the fundamental note ( Rule 1 ) ; then Rule (13) If (E) is taken as the fundamental note, then fa (B): (E) or T.ut in 2ud octave becomes its iT4 or the 5th becomes its y the fifth in the same octave. note (Rule 9). Therefore its length is =} x 21} and: .. 300 x = 450 = the vibrations of fa by Rule (8); vibrations = x 405; but these are for Ta. Therefore according to Rule (2) The length of T is = 2x } x 211 and the length is x283x == 193=19)

=2x40_284=281. .. The vibrations of f = 450 and the length of fa = 191. and the ribratims of = } x x 405= 1215 = 303. Notes and Summary. 4 नि (B). 1. The lengths and vibrations of ar, (c1) and ar2 (c2) are directly

The length of r is 289 and its vibrations 3031 ( Rnle 12) .- derived from Rules 1-2-3 which are based on the directions distinctly

If we take ar as the Fundamental note, then fa becomes laid down in old Sanskrit. works on Music-रागविवोध, संगीत-पारिजांत and संगीत-रत्नाकर.

22 23

2. Rule 4 expresses in the form of formulæ the resnlts of 9. I give below Table A, the Diatonic Major Scale तीव्र स्वर समक the atove rules. The formula which are derived from formula A showing the number of Shrutees assigned to each: note,t the are given below for the convenience of ready reference. V. x 1 =ux 1 ...... (A) number of vibrations, lengths of swire ofthe Diachord, the number of Mr. Ellis' cents," the musical intervals between any V .= u .... (B) where Vn= Vibrations of the length I two consecutive notes of the scale, the ratios of each note with the

where u=Vibrations of length l, which fundamental note, and the Englis .names of the intervals and

are respectively 240 and 36" notes :- 10. Now on looking at this table it will be seen that there are (D) The rules are not discoveries of new truths in the science of three kinds of musical intervals viz. 8:9, 9:10 and 15:16. In

the theory of Music. But they prove that these truths were known to the scale the interval 8:9 occurs three times, 9:10 occurs twice and

Sanskrit writers on Music several centuries ago. 15:16 occars twice. The seven intervals form two trichords : the intervals between a and ft, R and , and T and forming the 3. Rule (5) gives the length of (F) the 4th note as prescrib- first trichord ; while those between q and y, y and fa, and fa and a, ed by arofaara. Rule. (6) notes down the length and vibrational forming the second trichord. Each interval of the first trichord exactly value of (F) as worked out from the rules. tallies with the corresponding interval of the second trichord. The 4. Rule (7) determines the position of q (G), the 5th note, its length on the diachord and its vibrations .: Rule (8) notes down interval between and 4 (8:9) stands as a neutral zone between the two trichords. It is interesting to see that these intervals are evenly the length and vibrations of q (G) the fifth note in general in any distributed. The interval between a and fr (8:9) which is the octave. largest, occurs between q and y of the second trichord. The smaller .: The positions, length and vibrations of , (c1), (F), (G) and interval between fr and " (9:10) of the first trichord also lies between 2 (c,), the 4 principal notes which have consonance of the first and fa of the second trichord. The smallest interval 15:16, which order, are thus marked down, worked out and settled. It now re- lies between and # also appears between ra and af ( octave ) of the mains to find out the same of the remaining notes viz. a (D), (E), second trichord. The total of Mr. Ellis' cents for these intervals (A) and fa (B). This is done by the rule of aanarr of the 5th is 1200. note q (G ) which may be called the rule of perfect concord. 11. Similarly we might note with interest the Diatonic Minor 5. Rule (9) describes in full the rule of perfect concord and Scale (कोमल स्वर सप्क,) shown in Table B given below. It consists of how it. may be used in finding out satisfactorily every thing eight notes including the npper Octave, like the Major Scale afa required to be known of the remaining 4 notes-f, , y and fa. 6. Rules (10) and (11) show how the lengths and vibrations of The assignment of Shrutees in Colmmn 2, to the different notes. is ++ fr and y may be found from those of y (G) by applying the rule of based on the following Arya (आर्या) in रागविबोध (विवेक १. आ. २१) :- ऋषभस्तृतीयसार्यो ग्भपंचम्यां नवम्यां मः। perfect concord. 7. Rule (12) and (13) show how the lengths of T (E) and fa(B) पस्तु त्रयोदशीस्थ: बोडशी, अष्टादशी च ध, नी। द्वार्विशीस्थ: पड्जो द्विएुणसमः पूर्वषड्जेन ॥। are determined, the first by imperfect concord with ar (Ci) and For the explanation of the word ma, I would draw the attention of the the second by perfect.concord with a (E). reader to Paragraphs 17 and 20. 8.The lengths and vibrational values of all the notes in an By dividing the interval between the fundamental note of value one

octave are thus found ont, by means of rules distinctly laid down (1) and its octave of double the value i.e. two (2), into 1200 cents, according to his method, Mr. Ellis has' devised a system for measuring the various in old Sanskrit works on Hindu Music such as रागविबोध, संगीत-पारिजाव intervals. : This system, into the details of which we need not go at present, and संगीत-रस्नाकर he used for testing the scales of the world .. It would be gratifying to learn, that the Hindu Musical scale stands this test of cents admirably

24 25

स्वर सपकं hefiil be seen that in place of major second at. ft, 204 cents is thus split up into two smaller ones of 92 and 112 msjsr third major sisth ar. y. and major seventh ar. f., cents respectively, making a total of 204 cchts. The tume ratio are inserted .: reShundin flat notes or कोमल स्वरा It is 15 : 16 is again introduced in the second half er the scale botween "; very interesting to note that the seven musical intervals are the qand y. And the results are similar, IW this manner we same as those of the mijor Soale, but are differently distributed. have got ar. f. and its eorresponding iana note ( consonant) in the So also are the ratios of each note with the fundamental note. second half viz. sr. w. Again similarly we divide the larger The total of cents assigned to these intervals also comes to 1200. interval of 9 : 10 as before by the introduction of a There are different modes (ErT ) and modulets (mirfrofr ) which smaller one of 15: 16. Thus we get ar. TT. of 288 are sung in the notes of this Diatonic Minor Scale. 12. It will be seen from the Diatonic Mijor Scale ( Table A) vibrations, af. . being of 300 vibrations. The interval between' that the smallest interval is 15:16 that between and , and faand t ; if. ft. and ar. IT. becomes 15 : 16, and has 112 cents; and that and this interval is used in forming our Chromatic Scale of twelve between at. IT. and aff. TT. becomes 24 : 25 and has 70 cents. These notes. Perhaps here a question may be asked as to why. this two smaller intervals make up the 182 cents which was the number particular interval of 15:16 is used in formulating the chromatic for the second larger interval of 9 : 10. Similarly we have intro- scale of twelve notes. To this question the simple answer is as duced को. नि. between ती. घै. and ती. नि., with 432 vibrations and follows. When we look at the seven musical: intervals of the having a ratio of 15 : 16 with 112 cents. The interval between Diatonic Major Scale we find that out of these seven,. tive are को. नि. and सी. नि. is 24:25 with 70 cents. Thus we have in place large intervals and two are the smallest viz. those of 15:16 of the seven notes of the Diatonic Scale, or eight including the upper between and #, and fa and a. Siuskrit writers have termed octave, the following twelve notes of the Chromatic Scale the musical Scale as " a ladder "-सोपानपरंपरा (संगीतरल्नाकर, viz. 1++2+1+1q+2¥ + 2+1 =12. aTr 3, w( \ ). They have formel out of this Diatonic Major Between # and q which with a form the backbone of onr scale, we Scale of seven notos a Chromatic Scale of twelve notes, by insert a note called afr. A. This note is the oth harmonic of and putting four more smaller notes or steps. They have also styled. therefore forms sIgT with it. a and q are kept fixed and unchange- , the fourth note or step of the Diatonic Scale, as aras ; this is able. [षडूजपश्चमयोरविकृतत्वात्। vide रा. वि. वरि. ३ आर्या ८टीका.] Now the smallest step of the musical ladder. Now it is evident that by inserting smaller intervals of 15 : f6 between the larger ones of in introducing minor notes the smaller ratios or intervals will 8 : 9 and 9 : 10, we have introduced four araw or flat notes into the have to be utilized. Thus we get a method for developing our two trichods or halves of the scale, two in ench; making in all eleven Scale by introducing minor notes. intervals for 12 notes. In order to show that these intervals are just 13. Proceeding thus, while forming our Chromatic Scale oftwelve and mathematical, Mr. Ellis' cents are given, and each interval is notes, the smallest interval 15:16 is introduced between the four given its English name. The total of these cents for the notes of the Diatonic Scale having larger intervals viz. 8:9 and 9:10. The interval between ar and af. ff. is 8: 9. This is the biggest step. various intervals is 1200. These are the very notes of the Chromatic An interval of 15:16 is introduced between these two notes. Thus is Scale of twelve notes which we actually sing and play. It is to be obtained a third note called af. ff. with 256 vibrations, a being noted here that the twelve frets which are fixed on the Satar ( aar )" of 240 vibrations. Now a stands to ar. R: in the ratio of 15:16, as 3TT uTE, are intended to give out the twelve notes of this and ar- f. stands to ar. fe. in the ratio of 128:135. Assigning Chromatic Scale aud not any other. The foregoing resnlts are given Mr. Ellis' cents to these intervals, we get for 15:16, 112 cents; in Table C. and for 128: 135, 92 cents. The 'larger interval of 8 : 9 having 4

TABLE A. तीव्र स्वरांचे स्वर-सतक (वरील षड्ज धरून भठ स्वरांचे). Indian Diatonic Major Sca'e.

.1 2 4 5 6 7 8 9 11

Ratio of Vibrating

Names of Notes. Vibra- Musical leach note

tions. Interval Its name. with the length of

Funda Its name. wirerequired

mental for each Note.

Note.

Shrutees. Serial No. Ellis' cents.

Ellis' cents. Inches-lines

1: 0 षड्जor 0 240 8:9 Major 2nd 204 36 26

2 3 ET or D 270- 9:10 Minor 2nd 8: 9 Major 2nd; 9th Har- : monic ...

3 5 गांधार or E .... 300 182 : : 5 Just Major 3rd; 5th 204 32

15 : 16 Diatonic Semitone 112 Harmonic

मध्यम or F 386 28-16 lines

4 9 320 Just and Pythago-

13 8 : 9 3 : 4

5 पंचम or G Major 2nd 204 rean fourth ... 498 27

360 2: 3

16 8 :!

405 Major 2nd 204 Just and Pyth. Fifth 24

..

6 धेवत or A 3rd Harmonic ... 702

... 16:27

7. 182 Pythagorean major!

18 निषाद or B 9 : 10 Minor 2nd

450 15 6th; 27th Harmonic. | 906 21-63 lines

... Just major 7th; 15th

15 : 16 Diatonic semitone 112 Harmonic 1088 19-4 lines ...

8 22 षड्ज or C' 480 1200 Octave . 1200 18 कोमल स्वरांचे स्वर-सप्तक (वरील षड्ज धरून आठ स्वरंच) भैरवी थाटाचे. Indian Diatonid Minor Scale of 5 flat notes or 8 notes including the Fundamental. note the Fifth and Octave. .

1 2 3 4 5 6 7 8 9 10 11

Ratio of each note Vibrating

Names of Notes Vibra.| Musical Its name. with the Its name. length of

tions. Interval Funda- wire required

menta for each

Note. Note

Ellis' cents | Inches-lines Remarks.

Ellis' cents.

1 षड्ज or C. 240 1 15:16 Diatonic semi- 112 36

2 256 tone. 27

को. ऋषम or Dflat. 3 को. गांधार or E f. 288 8: 9 Major 2nd. 204 15 : 16 Diatonic semitone. 112 33-15

Just Minor 3rd

4 Serial No. 4 320 182 316 30-0

को. मध्यम or F. 9:10 . Minor 2nd. 5 : 6

को. पंचम or G. Major 2nd. 204 3 : 4 Just fourth. 498 27-0

5 360 8: 9 2:3 Just fifth. 702 24-0

को. घेवत or A f. 384 15:16 Diatonic semi- 112

tone.

8: 9 204 5:8 814 22-10

: 7 को. निषाद orB स. Major 2nd. Just minor 6th.

432 5 :9 Just Minor 7th. 1018 20-0

9:10 Minor 2nd. 182

8 षडूज or C'. 480- (Sometimes called acoute.)

1200 1:2 Octave. 1200. 18-0

ABLE D. 28 ( Referrec to at page 30 pars 9. )

Indian Chromatic Scale of twenty-two Nees, or the Shrutee Scale.

1 2 3 4 6 7 8 9 3 5 7 10 11 2 9

Name and kind | Name of noter fusicai in- terval Iying Ratio of each Its Ellis' centa it Nusical in with oquivalents. in Vibrations bet ween enci aoguvalents, et ween eacl aasigned to note with the Ita Name, Ellie' Fundamental u Vibrating leneth for each nate. Harutee Name of notes. Vibratione betwea/ Ita Jen Glened to pote with the ta Name. Ellis' oach intarval red No. Ellie' cents Ratio of encL Fundament Vibrating length sach intertal un Tor anch pota. 6-12 सतिनाम, जाति. Noto. Note. 19-4 24-0 20-0 21-67 18-0 22-1 28-1 27-4 30-0 32-0 : 10 a Remarke. nches. Lines Enchen-linen for each N डंदोपती, मध्या. q or C. 240 Inches. Linea. 02 0 : 21 Submimid. 36 -- 0 5 (13) 360 Just Fifth:3rd Harma 702 24-0 1200 204 316 386 814 906 112 1088 दवापती, करुणा. Subminor S 590 9 अ. को. Sopti 252 85 20 : 21 63: 64 Septimpa. Subminor Second. 27 85 34-5# (14) मईंसी, करणा भ. को. पे. Septi 378 20 : 21 85 787 22-174

को. प. DI 33 -- 15 mal AL 16:25 Grave Sub-Fifth: (2) रैजमी, मध्या, Diatonic or Just (15) रोहिणी, भयता- को. घे.Al 384 63 : 64 Septimal Cor 25th Harm, 256 15 : 16 112 5:8 Just Minor 6th, 814 22 -- 10 nor fth | 1018 Smal sem (3) रसिका, सूदु. seinitone. 2663 4:25 Small e 70 (16) रम्बा, मध्या. 24 : 25 70 म. क. low D : 10 Minor second. 182 32-8 T. N. low A. 400 Just Major Gth. 884 21-12 t miDor att jor ladiith Just fourth. Jut aft Juest minor ard Diatonie somi- रोट्री, दीमा. 22 Pythagorean Ito name. major nis (4) 22 80 : x1 ती. क. D. 270 80 : 81 Comms oaus 204 8 : Major second 204 32-0 )रमा, रीमा ती. धे.A. 405 Comma of D 204 16 : 2 Pyth. Major Gth 906 2163

कोषा, भायता. भ. को. गं. low Ef 2841 248 : 256 Pyth .! 90 41

27 : 82 Pyth. Minor Third 294 30 -- 71 (18) सोमिनी मध्पा. 243 : 256 Pyth, Li 90 अ. को. नि. low Bf, 426 996 20-5 80 : 81 Comma o 22 Juat Minor Third. (19) सीव्रा, दीमा. 80 : 81 Comme of D Just dimini 7th 22 9:10 2 : 3 8 :191 5 : 6 : 3 : 32 : 45 Just tri-ione:4 7 4 6 Junt major frd 16 : 27

जियिका, दीमा, ो. मं. Ef. 288 316 1018 Fundar 5: 30-0 को. नि. BL 5: Acute Minor 7th 20-0 16 : 16 432 tal Note, each note with the 24:25 70 (7) .70 मसारिणी, भायता. 300 4: 25 Smalt e ती. मं. E. 4: Just Major Third : 386 28-16 (20) कुमुदसी, भायता, सी. नि. B. 150 8:15 Just Major 7th, 1088 19 --- 4 182 -204 $182 $204 Comma of Da 204 6 92 (8) म्रीती, मृड्. 303 22 455 70 112 स. ती. गं. high E 80:81 Comma onus. 5th HArm. Pyth. Mejor Third. 28-9 (21) मंदा, बडु 22 204 64 : 81 त. ती. नि. bigh B. 80 : 8 408 204 128 : 243 Pyth, Major 7th. 1110 112 1121 112 112 1121 Ellis' centa.

() माजनी, मध्या. $15 7:28 6 : 2 21at Harm., Sub F. 4:471. 27 -- 84 243 : 256 Pyth. Lit TABLE C. 90

(10) सिसी, मुदु, mal F. 320 3 : 64 eptimna 27 90 3: 4 Just and Pyth, 498 37-0 (22) उरोवती, मध्बा. 480 498 1:8 Octave, 1200 .18-0 5 Dlnionle semi Dlstonie wemal- Diatonis s Amall vemiton Dintonie semt- Bmdt Limma Dlalo'le se Its name. 8mall Betnitone. (11) रका, मष्बा. ती. म. Fs. 128 : 135 337} Largert. 92 32 : 45 Fourth. nerfect Fourth 590 25-12 Total carridn 20 ir to 702 16 (12) संदीपनी, भावता. 2025 : 2048 5th Harm. 16 स. ती. म. High Fs. 341} wlin'snh in C' ao ratta in Col. & are teken from thie table of Harmonica on 128 : 135 Largert. 45: 64 Dimi. Fifth. 610 25-6 135 Total from : 16 or GI. 92 J 498 24 : 25 15 : 15 : 15 702 24-0 15 : 16 15 : 16 Diatonle sami- 128 1 15 : 16 (13) भालापिनी, करुणा 360 24 : 25 128 : 135 204 2: 702 Fifth. Junt and Pyth. Grand 1200 15 : 16 240 25G 270 . 337# along with the musical consonance in the notes, there is elao e cor Note :- The Sanskrit writers heve essigned names to each one of the ttwo Shrutees, indicating the particular emotion, ( or tar ) effected by the particular note. As the twenty-two notes for the twenty-two Shrutees have now bedd in the above Tatle, it is easy to sesigu the names. It will be seon that re is alao e corresponderd the otions effected by them. Experts like Prof. Abdul Kareem do actually aing these twenty-two notes, for several modes and modulets. 405 360

The following notes ere alao used by experts, ar. ent. #t. of 280 vibrzh i.ch is the 7th Harmonic of #, and it has its curresponding a. ai. fr. of 420 vibrations which is fifth above a. Tir. . (280 vibr. ) ; 3- Gt. F. Of 501 115 ich is minr . a. of 307 1/5 vibratidlich is minor third of et. R, and it has its corresponding w. eft. far. which G ... 3 OT A fI 384

in ffth above it ; a. if. s. of 345 3/5 3/5 vibrationa which is third from t. t. Tites are used by some experts for some Ragas, Twenty- by Rabimatkhan and Bhayasabeb Joshi ; the Dagari and the Nohari as sung by Pr Alladbia and Gokhule brothers ( who both are in the service of the Kolhupur Durbar ) and Beveral syatems in the Faratio. A accepted by aimost all the systems of Indian Musie. There are sereral syster ogun, .. g. tbe Goburbari, as sung b ms in the Karnatio. All these systems accopt the St, thongh thei rbari, as sung by Abdul Kareem, the Kandusr s , thongh their several advocates differ as to the combination of the several Notes. .RvTRorF fl. 320 .मध्यम or F. r or G Trre or B .. 450 waa or A को. सबम D fI ... RTH or D ... tert or E ... 300 notes as well as the notes themselves used in several Modes and Modulets, I add that further research proves that the first and fourteenth are reelly septimal notes of 252 and 378 vibrationa respectively a respectively and are therefore really " flatteno " as the name arfa niaer indicates, T Ore 480 1 .FTrTor B fl: 432 4 को. माधार Efl. 288 12 13 3

. Note for column 10-each inch is divided into 20 "lines.' pTe glikh nemos of the-mr

30

9. Now when we look at the intervals newly obtained in our Uhromatic Scale of twelve notes ( Table C), we find that another int rval smaller than 15 : 16 which we get in the Diatonic Scale, , in its appearance twice, and that is 24 : 25. It must not be uverlooked, because it is an interval lying between two consecutive notes of the musical scale viz. Fr. s. and ar. . which form part of nonics. Therefore this interval has been considered as an "uportant and the most suitable interval to be put in for the purpose t evolving a still finer scale. The same process which has been uscribed above for the Chromatic scale of twelve notes, has been llowed in developing the scale of twenty-two notes or ia scale as fined in arifaara. For purposes of easy reference, Table D of the twenty-two Shrutee scale is given below, with the musical intervals, lengths of wire of the Diachord, Mr. Ellis' cents number of Shrutees ' degrees' ( as called by Mr. Ellis ), and names of the note etc.

10. From this table it will be seen that when the smaller inter- $ef of 24 : 25 having 70 cents, is put in between a (240 vib.) ar. ft (256 vib.), another note called sr. ar- ft (250 vib.), Esaring the simple ratio of 24:25 and having 70 cents makes its opearance. In the same way a third H. fr (266} vib.) appears between को. रि and ती. रि. Similarly two संवादि (consonant) notes are introduced in the second half of the scale viz. sr. ar and #. . It is to be clearly noted bere that these notes अ.को. रि. को. रि and म. रि, in the first half of the scale, and अ. को. ध, को. ध, and म. ध in the second half are called by सोमनाथ author of रागविबोध as विकृत स्वराs, and are recognised by him. [Vide. श्रुति Table in Dr.Banhatti's बालसंगीतबोध, Pt. III, Page 16.] In the same way अ. को ग. and त. ती. ग and the corresponding अ. को. नि and त. ती. नि have been introduced newly. It is already stated that like #, 4 is also to be kept unchanged -(faaa ); and the two are to form the back-bone of the scale. The interval between wand q which is the largest viz. 8:9, cannot therefore bo neglected. Therefore the Aryan authors divided the same into four parts and assigned notes which are considered as fagsars or modifications of y and not of q [vide yra Tahle in Mr. Banhatti's book.] These notes are अ. को. म, को. म, ती. मं, and त. ती. म, having. th intervals of 24:25, 128:135, and 125:128 respectively, with 70, 92, 42 cents respectively, making up a total of 204 cents whicha are

31 32 assigned to the higher interval of 8:9 lying between a and q. In this manner we havegot 1+4+4+4 +1 4+4 ¥ +4 fa+ deflect it only to such an extent as will give him the exact l# ( upper ), making up a total of 23 notes including the octave. note required, which will tally accurately with that given out in the These results are given in the following Table D. Diachord. This can be attained only by long and patient study. Even gifted specialists like the late Bande Ali and his disciples Chunna 11. All the lengths given for the notes in these tables are and Murad, Bharkhat Ulla, Haidur Bux, Antubua. Sadhale those of the wire of the Diachord and they must not be confounded, and Vishnupant Joshi ( Pakhwajis ) required years of constant with lengths of strings of playing instruments, such as Been, practice to train their ears and fingers to get the exact. notes Satar etc. The difference between the instrument fixing with ease. The Diachord is the exact standard of measurement scale like a Diachord and a playing instrument consists in for accurately determining the musical scale ; in other words this, that in the playing instrument the height of the strings or wires it affords us a means to measure musical notes, just as we have above the frets necessarily varies from one to five milli- the rain gauge, the thermometer, the barometer etc. But the metres, as has been shown by Mr. Ellis in his examination, playing instrument, unless it is played upon by a specialist, is not of several oTrs and the arT of Tanjore sent to him by the standard by which the musical scale can be accurately gauged, Cap. Day. Unless we leave some margin for height, an as the skill of the player must be taken into account. The Sans- instrumental player cannot move the fingers from the different krit authors clearly intended this, as they distinctly state the exact frets freely and with ease ; and he cannot produce increased tension divisions of the length of the wire, for producing the different notes in order to have different shades, and मेंडा (mends) and घसिद viz. a, #, 4, and #. They do not obviously intend that there should ( ghasits ) required for different modes (IrT) and modulets (rof be any height whatsoever between the speaking string and the But it is to be observed that when the player puts pressure upon moving fret. Had this been the case, then the laws laid down by the string when bringing it down to the fret, the increased tension them ( given above ) would have given incorrect results. They 'due to the pressure must per force increase the pitch. But in pre- intended the construction of the musical scale. paring an instrument of scale, which is in other words a Diachord, we must not leave any height whatsoever between the speaking 12. After having thus obtained these scales, let us now consider string and the moving bridge. Now when we have prepared the the Shruti problem. Among notable recent writers who have: above scale, we are to note down the different speaking lengths of attempted to solve the question, may be mentioned Mr. Bhavan- the different notes, on the wire of the Diachord. When rao Pingale, Mr. Balawant Trimbak Sahasrabuddhe, and Raja an instrument player wishes to set the frets to the instrument Surendra Mohun Tagore. I will consider the methods of Messrs. to a particular scale, he must keep this Diachord by [his side; Pingale and Sahasrabuddhe, first; and then examine the Raja's and taking into account the tension caused by the pressure of method. They have taken it for granted that like vibration his finger on the string, he must see whether the note a "Shrutee" was the "unit" of measurement of the long interval on the playing instrument tallies exactly with that given ont lying between a fundamental note and its octave and that 22 Shrutis by the Diachord. He must also while practising attune his were 22 subdivisions of equal value. This is not the case. A Shrutee ear or voice to the different notes of the scale produced on- the which is a sub-division of a note, may be a quarter or a third of a Diachord, and not the playing instrument ; because the latter is note &c. &c., according to the position it occupies in the interval likely to misguide him. So also while prodncing different fanra between any two consecutive notes. Earrs or modified notes by mends (#) on the same fret on his playing 13. For the purpose of comparing the Shrutee Scale with the instruments, he must not deflect the string indiscriminately; he should exact Scale (FaT wa) they divided the entire length of the executive part of the wire into 44 units. I quote Mr. Sahasrabuddhe. " If a

33 34

monochord" says Mr. Sahasrabuddhe " be taken and a space equal to It is well-known that notes increase in pitch in the inverse ratio 44 units be measured and the bridge- shifted to this point, the string when struck will yield a note ; if we start with this note as the tonic of the length of the wire. And applying this law, we easily determine

or: keynote and run through the gamut by shifting the bridge ( the the several lengths of the executive part of the wire which, when sounded, will give the 7 notes of both the Shruti Scale (Mr. Sahasra- Sanskrit writers affirm ) the following facts will be observed. Sa will be produced at the distance of 44, Ri at 40, Ga at 37, Ma at 35, buddhe's) and the exact Scale. These lengths are :-

Pa at 31, Dha at 27, Ni at 24 and Sa again at 22, but the latter Sa : Shrutce scale as explained by Exact Hindu will be twice as intense as the former." Mr. Sahasrabuddhe. Scale. (Table A) C=the whole length तेषां श्रुतयः क्रमतो वेदा रामा दृशौ तथाम्बुधयः। HT=the whole length

निगमा दहना: पक्षावेव हार्विशतिः सर्वाः ।।१६॥। D=8 तर्यायां ससम्यां तासु नवम्यां शुतौ त्रयोदश्याम्। E=$ समदशीविशीद्वाविशीधु च ते स्फुटाः क्रमतः।१७॥ F=4 G=% × x x द्वाविशीस्थ: षड्रजो द्विगुणसम: पूवेषड्जेन ।। २१। A=1 रागविबोध. f= or 11 B=r6 Mr. Sahasrabuddhe has based the above theory on the wrong सा"=or! interpretation and application of Aryas 16 & 17 and the latter part of Arya 21 of रागविबेोध quoted above. It will be found that each one of the intermediate notes of the

Exact Hindu Scale- CDEFGABC Shrutee Scale as explained above bears a complicated and rather "24, 27, 30, 32, 36, 401, 45, 48. higher ratio with the fundamental note and that none of the lengths

Mr. Sahasrabuddhe's- Sá Ri Ga Ma Pa Dha Ni Sá shewn on the left side gives out notes which are obtained in the "22, 26, 29, 31, 35, 39, 42, 44. FT-aH (Table A) and which we actually sing and play. But the And now when actual comparison is made by finding the fact is otherwise. Our artistes actually sing and play notes which ratios of the fundamental note with each of the successive 7 notes of bear simple ratios with the fundamental note. the Shrutee scale thus wrongly demonstrated, we find none of the notes (except the octave) bears those simple ratios which our 14. Mr. Chinna Swami Mudliar M. A. of Southern India, wrote a

Hindu Scale as well as the European exact scale bear. This is quite large volume entitled " Oriental Music," but has left untouched the plain from the following comparative table. question of was or Shrutees as being a very complicated and intri- Shruti scale as explained cate one. How the labours of Messrs. Pingale and Sabasra- by Mr. Sahasrabuddhe. The Hindu Exact Scale. buddhe, were not productive of successful solution, I have already

C=24=1 shown above. Raja Surendra Mohan Tagore also attempted to determine the position of the twenty-two Shrutecs. He divided the D=h= E =; 4 =* whole speaking length of the wire into two halves, the whole length giving the a or fundamental note and the half giving the a', the G=af= octave ; both these notes are correct. Again he divided the first A=196 =27 half into two equal parts, each being one-fourth of the whole length. The first quarter (of the wire ) he subdivided into nine equal parts सा'= 0'=18=2 calling each part a Shrutee. At the end of the ninth part is sonnd- ed a note ( at } of the wire ) which is correct. In the next quarter 5

35

of the wire he made thirteen equal subdivisions, each being also called a Shrutee. Thus in all he got the twenty-two' Shrutees. Let us now see whether according to the Raja's apportionment we get the other notes correctly. Now there are three Shrutees for ar. fr. of the Diatonic Major Scale. (Vide. रागविबोध आर्या २० and २२). Accord- ing to Raja Surendra Mohan Tagore's division, three Shrutees would mean three parts out of the nine equal parts in the first quarter of the whole speaking length of the wire ; the length of these three parts would come to rs part of the whole wire ( } wire divided into 9 parts, each part = {x }=3; three such parts would mean =;= x 3 =; part of the whole length ). Thus the ar. rr. will be prodnced, on the i1 part of the whole wire, according to Raja Surendra Mohan Tagore's method; i. e. ar. fr. will be produced on a length of 33 (= x}}=33) inches. But as we have seen, the musical interval between सा and ती. रि. is 8: 9; the pitch of ती. रि. is g of सा ; 80 If we inverse this ratio of pitch, we get the length required. [ 36x g=32 inches ]. Thus we get 32 inches as the length for ar. fr. Consequently Raja Surendra Mohan Tagore's ar. fr. is flatter or arae than the just Major Second which we actually sing and play; the interval also is smaller than the correct one. Similarly incorrect results might be obtained for the other notes, by following Raja Surendra Mohan Tagore's method. 15. I now proceed to show how Cap. Day and Mr. A. J. Ellis, in their attempts to find out the positions of the twenty-two Shrutees, were not successful, perhaps misguided, partly by the erroneous in- formation of recent publications and partly by the assumption that the Hindu writers have followed or are inclined to follow the equal 'temperament' system of Europe in developing their Chromatic Scales. The lines on which Mr. Ellis tried to solve the question of the Shrutees may be seen from the following extract from his paper read before the Royal Society of Arts in 1885. Cap. Day also was similarly misled, and he follows Mr. Ellis' division. Mr. Ellis follows the lines sug- gested by Raja Surendra Mohan Tagore, whose methods I have already referred to. .In his paper Mr. Ellis says :- "Now we do not know precisely what a degree is. And hence Mr. Ellis for simplicity translates Atikomal by Double flat and any representation of these differences with exactness is impossible. so on. As I have already stated this is a very loose and inaccurate But we may obtain a tolerably approximate notion thus: suppose rendering. the fixed notes to have been those already described in the old C.

35 36 of the wire he made thirteen equal subdivisions, each being also called a Shrutee. Thus in all he got the twenty-two Shrutees. Let us Scale, so that Cto D, Fto G, and G to A, have each 204 cents, and a now see whether according to the Raja's apportionment we get the degree of such an interval should be a quarter of that amount, or ol other notes correctly. Now there are three Shrutees for ar- fr. of cents. The interval D to E, or A to B, has only 182 cents, and but the Diatonic Major Scale. (Vide. रागविबोध आर्या २० and २२). Accord- only 3 degrees, so that each degree has 603 cents. Finally, the in- ing to Raja Surendra Mohan Tagore's division, three Shrutees would terval E to F, or B to C, has 112 cents, and only 3 degrees, honce mean three parts out of the nine equal parts in the first quarter of the one of these degrees has 56 cents. The modern Bengali division gets whole speaking length of the wire ; the length of these three parts over the difficulty thus : The C string is divided in half, giving the would come to r part of the whole wire ( 4 wire divided into 9 parts, Octave ; the half nearest the nut is again halved giving the fourth, each part = x =>; three such parts would mean =; rx 3=y F. The part between the nut and Fis divided into 9 equal parts, part of the whole length ). Thus the afr- ft. will be produced, each giving a degree ; and the other part from F to the Octave, is on the 11 part of the whole wire, according to Raja Surendra Mohan divided into 13 equal parts, each giving a degree. From these indi- Tagore's method; i. e. afr. ft. will be produced on a length of 33 cations it is possible to calculate the value of each degree and assign ( =3ª x }=33) inches. But as we have seen, the musical interval the notes. In the following table I give the num ber of degrees and between सा and ती. रि. is 8: 9; the pitch of ती. ि. is g of सा ; 80 the calculation of their value on botb plans, old and new, with the . If we inverse this ratio of pitch, we get the length required. names of the 19 Indian notes assuming that pitch varies inversely as [ 36 x $=32 inches ]. Thus we get 32 inches as the length for the length of the string as shown by the position of F and the Octave ar. ft. Consequently Raja Surendra Mohan Tagore's ar. fr. is and that any errors thus arising have been corrected by ear :- flatter or ara than the just Major Second which we actually sing Indian Chromatic Scales. and play; the interval also is smaller than the correct one. Similarly Degrees ... 1 2 3 4 G 8 incorrect results might be obtained for the other notes, by following Notes C Dff Dfl D Eff Efl Raja Surendra Mohan Tagore's method. Old .. 0 51 102 153 204 264% 3251 386 49 90 204 31G ,259 374 15. I now proceed to show how Cap. Day and Mr. A. J. Ellis, New 0 15 11 12 13 15 10 in their attempts to find out the positions of the twenty-two Shrutees, Degrees . ... 9 10 14 Notes Esh F Fsh Fssl Affl Afl were not successful, perhaps misguided, partly by the erroneous in- Old ... 442 498 549 G00 651 702 753 804 formation of recent publications and partly by the assumption that New ... 435 498 543 589 637 685 736 787 the Hindu writers have followed or are inclined to follow t.he equal Degrees ... 10 17 18 19 20 21 22 'temperament' system of Europe in developing their Chromatic Scales. Notes Afl A Bffi Bfl B Bslı ... ... Old ... 804 966% 1027% 1144 The lines on which Mr. Ellis tried to solve the question of the Shrutees 855 906 1088 bEsc! may be seen from the following extract from his paper read before the New ... 787 841 890 952 1011 1070 1135 Royal Society of Arts in 1885. Cap. Day also was similarly misled, The only valnes agreeing in each are C, D, F, while new Ffl is and he follows Mr. Ellis' division. Mr. Ellis follows the lines sug- the just Minor Third, a mere accident. The 9 degrees from C to F gested by Raja Surendra Mohan Tagore, whose methods I have vary from 49 to 63 cents and then there is a sudden break, after already referred to. . In his naner Mr Wllia an- which the 13 degrees from F to the Octave vary from 45 to 65 cents. This is the first intelligible presentment of the Indian scale which I have been able to effect. It will be seen that C,Dfl,D,Efl,E,F,Fsh, G, Afl, A, Bfl, B are represented pretty well by our equally tempered th notes, but that the 7 intermediate notes Dffi, Effl, Esh, could only be

37 38

tempered on the Quarter-tone system nsed iu Syria. Hence, in the Shruti ends and not where it begins. According to the rule usual transcription, these 7 notes are indentified with some of the given in aary of tuning strings and placing the twenty- others, possibly Dffl with DA (not with C), Eff with Ff (not with. two frets, each indicating a Shrutee, the first fret or Shruti D), Esh with F ( as usual ), Fssh with Fsh ( not with G), Affl with or " degree " is to be placed after the zero (0) or the fixed Afl ( not with G ), Bffl with Bf ( not with A), and Bsh with C ( as bridge on which the whole length of the wire or the vibrating usual ). These comparisons necessarily injure the original character length rests, and when sounded gives the fundamental note. Accord- of the music, and give it a harmonisable appearance which is entire- ingly the correct and proper way of assigning or marking shrutees is ly foreign to Indian music." that noted in the Table D; and is different from that adopted by Mr. 16. But our method of dividing a whole tone either of 204 or Ellis. By this process, the figure (0) comes on a or C, the first 182 or 112 cents into four, three or two tones as the case may Shrutee on the second note, and the twenty-second Shrutee exactly be, is not to make equal divisions, as has been supposed and done by comes on the octave a', giving 1200 cents. And according to Mr. Mr. Ellis ; but the divisions are to be made in accordance with the Ellis, the twenty-second Shrutee comes on a. ar. f. or B sharp, intervals lying between two consecutive notes. For instance the inter- having 1135 cents only. val betweon a and af. f, the first and second note of our Major Dia- 18. Similarly Mr. Ellis made another experiment. He heard tonic Scale is S : 9 with 204 cents. Now snppose we want to Raja Ram Pal Singh playing on his warr (Satar)-a playing instru- divide this greater interval into two smaller ones or. tones. ment, at four different settings. With the aid of a tuning fork, and Then we introduce between स and ती. fि, a third note called को. रि. assisted by Mr. Hipkins, a noted musician, he observed and took or D flat, which bears to the fundamental note ar the ratio of 15 : 16, down cents for each note of the Diatonic Scale at each setting and because this same ratio or musical interval already lies between the got the following results. third and fourth note and #, or between the seventh and eighth Scales set by Raja Ram Pal Singh. note, fa and af, of our Major Diatonic Scale. This done, the three notes स, को. , and ती. रि. will have the following two musical First and Fourth setting :- Obs. 1st. 0 183 342 533 685 871 1074 1230 intervals lying between them. If ar has 240 vibrations in a second 4th 0 174 350 477 697 908 1070 1181 of time, ar. fr. has 270 vibrations, the interval being 8: 9. When New 0 204 374 498 685 890 1070 1200 ar. ft. with 250 vibrations is introduced between the two notes, then Notes. C D E G A B C the three notes ar (240 vib.), ar. fr. (256) and at. ft. (270 vib.) Second setting :- stand to one another in the ratio of 15: 16, and 128 : 135; having Obs. 0 183 271 534 680 872 983 · 1232 New 0 259 :1011 112 and 92 cents respectively, 'in all making up 204 cents. But 204 498 685 896 . 1200 Notes C D Eff1 F G A Bf1 C this has not been done by Mr. Ellis. He has divided the whole tone of 204 cents into four equal parts and has assigned 51 cents to each Third setting :- Obs 0 111 314 534 686 828 1017 1198 part. This is evidently incorrect and these notes obtained by equal New 0 99 316 498 685 787 1011 1200 divisions are not actually sung in practice. Similarly are obtained Notes. C Df1 Ef1 F G Af1 Bf c wrong results for other notes also. Fifth setting :- 0 90 366 490 707 781 1080 1087 17. Again in assigning each subdivision to a Shrutee or Obs New 0 99 374 498 685 787 1070 1200 "degree" of the twenty-two cycle, a wrong start is generally made by Notes ... C Df1 E F G Af1 B c some writers ; because the first Shrutee or degree ( though it begins from the (0) on which a is marked ) is to be marked where the first These results when compared with the cents, put in my Diatonic Major table will show that the cents obtained by Mr. Ellis have not

39 40 been correct ones. The observations noted in the first line of the first setting do not tally with those of the second setting, nor those of the in the Diatonic Major Scale. This point is cleared thus. As third setting with those of the fourth setting. Even the cents observed explained hy Sanskrit writers a Shrutee is any andible musical for the Octave (a) differ for all the four settings. But there is no note given by plucking the wire agninst the bridge; or to speak in wonder that such varying results were obtained. Because Mr. Ellis terms of the scientist of the West, Shrutee is the smallest musical himself says that the setting of the frets was a "pure matter of ear interval, lying between any two consecutive notes of the musical and memory"; and " the frets were moved somewhat hastily and scale. I may make myself clear by giving an example. The musical perhaps were not arranged with the accuracy that would have been interval between a and af. fe. of the Diatonic Major Scale (of eight attained by a professional musician." notes including the octave ) is 8: 9. This interval was first 19. I may state in brief that attempts were made in three direc- divided into three smaller ones, each being called a Shrutee. The tions or ways to solve the question of Sbrutees. Messrs: Pingale author of रागत्निबोध first laid down that that ती. रि. has three Shrutees, and Sahasrabuddhe among others tried to solve the question by divid- But for developing this Diatonic scale into the Chromatic scale of ing the whole speaking length of the wire into forty-four (44) equal twelve or twenty-two notes, it was also laid down that and units, and then trying to assign the positions of the twenty.two are to be kept unchanged (aTfaaa). Therefore the eight Shrutees Shrutees. The faults of their method have been explained above. of ar and q (four for each) had to be distributed among the other Raja Surendra Mohun Tagore divided the string into two equal notes, after retaining one for each (one for a and one for q ). Thus parts, which again were subdivided into equal parts, each containing to distribute the remaining six Shrutees among the other notes, it a varying number of equal units which he designated as the Shrutees was necessary to divide the interval 8:9 between ar and afr. R. into I have already shown the erroneousness of this method. Mr. A. J. four faad Fats, each called a Shrutee. Under these circumstances Ellis divided each interval into as many egual parts as there were it will be easily seen that a Shrutee is not a unit of measure- Shrutees e. g. 4, 3, or 2. I have shown above how this method too does ment, as has been supposed to be the case by several writers; but not give a satisfactory solntion. The reasons as to why Mr. Ellis could it is an interval lying between any two consecutive notes, and as such not get satisfactory results in all his experiments were: first, is liable to be subdivided into as many smaller intervals as there may as he admits, the original treatises on Hindu Music were not accessible be raza Fats, or modifications of tones. Shrutees may be more than to him. Secondly, the experiments were made on fretted instru- twenty-two also, this number being the one generally accepted, some ments. In these instruments, the pressing of the wire or string down Sanskrit authors recognising 42, some 66 and some saying that they to the fret increases the tension, thereby increasing the pitch. The are innumerable. height of strings above the frets in different instruments varies largely, 21. It will thus be seen that in forming the Chromatic Scale of say from 4 to 6 millimetres. Again in playing the same notes on dif- twenty-two Shrutees, the same method of introducing smaller ratios ferent occasions, the same performer is likely to commit mistakes on or intervals is observed, as that pursued in forming the scale of account of defect of ear or want of proficiency. And, as is admitted twelve notes. The rule of perfect concord on which Sanskrit writers by Mr. Ellis himself, "it is exceedingly difficult to determine the put so much emphasis, has been strictly observed in all the minute differences of pitch between notes with qualities of tones so scales. It will also be clear how the Chromatic scale of twelve different as those of plucked strings and tuning forks." notes has been formed out of the Diatonic scale of seven notes, and 20. Now it may be asked that the ras (Shrutees ) in the table how the scale of 22 notes or the Shrutee scale has been worked out of 22 Chromatic notes or the Shrutee Scale (Table D) do not from that of twelve notes. I have already explained the methods apparently correspond to those assigned for each of the 7 notes which the Sanskrit writers have adopted for evolving higher and finer scales. It is to be noted that these scales which are worked

41 42 out strictly on the lines laid down by our Sanskrit authors arel fndian writers like Messrs. Kunte, Pingale, Sahasrabuddhe, Ban- constructed on a thoroughly scientific basis ; and they fally (throngh hatti, Chinna Swami Mudliar, and Raja Surendra Mohun Tagore their intervals ) satisfy the test of the system of cents adopted br, among others; and also to the works of European writers like Sir Mr. A. J. Ellis. The theory of the Farerae or Diatonic Major scale William Jones, Capt. Day, Messrs. Bosanquet and A. J. Ellis, for . has already been propounded above. From all this it will be evident that the Sanskrit writers were fully cognisant of the laws the valuable light of information and criticism which they throw upon of the constitution of musical sound, which have been approved of the subject. To the study of Hindu Music which these writers by modern science ; that they worked out their scales not " arbitra- made and to their labours for regenerating and encouraging this Art rily " but on definite and regular fixed laws; and that in formulat- of Arts, I humbly and respectfully add my share, infinitesimally ing their scales they were led not by ".atrificial" ideas, and were small though it is. As endeavours in this direction are carried guided not by " capricious " suppositions, but proceeded on precise and pursued further, it is quite possible that more light will be . rules and principles. thrown on the subject; and perhaps the results which I have obtained at present might undergo modification. I stand open to 22. By means of the Diachord and these tables which have been correction. worked out from Sanskrit writers, the Musical Scale can be deter- mined with mathematical precision. The Diachord with its moving 24. I cannot conclude without making an appeal to the public bridge gives us an accurate means of determining the several notes in the interests of this Art of Music. At present, broadly speaking, correctly ; and the notes of the instrumentalist or vocalist can be the Art is confined to two classes, professional Musicians-Vocalists tested by referring them to those produced on the Diachord. Like or Instrumentalists-and the operatic ( aina ) stage. And if the the tuning forks of the West which are used for testing the correct- excellence of the Art is to be found anywhere, it must be admitted to ness of the notes, the Diachord with its moving bridge serves exist among the Professional Musicians only. All credit is due to the same purpose. The ear, which at present chiefly guides the them, because in spite of the absence of material encouragement in musician-instrumentalist or vocalist-is not always an infallible test. of the correctness and justness of the notes; it is liable to vary in recent times, they alone have still preserved and protected this ancient and richly developed Art from total extinction. Our Hindoo religion, Diachord. its capacity of adjudgment. Hence the great importance of the which is so comprehensive in its relation to life as to hardly leave any subject outside the sphere of its influence, has done not a little, in fact 23. The experiments which I made with the Diachord, were it has done the utmost, by means of the numerous rites and conducted with the assistance of Prof. Abdul Kareem, an expert pro- ceremonials which embody music as a part of their programme, to fessional vocalist of renown. The results of the experimonts which I preserve, cultivate and develop this Art. The great stimulus which have been making for the last few years, have been verified by him. Institutions like the Gayan Samaj of Poona and other centres, and And it is no small satisfaction to me, and I believe, as well as to the the Gandharya Maha Vidyalaya of Lahore ( the Academy of Indian public, that the results of my study of the theory of the Hindu Music, conducted by Pandit Vishnu Digamber Paluskar ), have given Musical Scale as propounded by the old Sanskrit writers have been ap- to the study of this Art by creating a wide interest among the people, proved of and amply corroborated by eminent professional artistes must be candidly acknowledged. All these attempts are surely com- like Prof. Abdul Kareem. It might be stated here that but mendable, but looking to the steady and slow decline of this Art for the kind help and open-hearted assistance of the Professor, I in recent times, it must be recognised that they are insufficient for the should not have been able to lay these few ideas before the public. I purpose in view. The blind imitation of the Westerns which was the cannot but here express my heartfelt obligations to the works of modern besetting sin of our educated people about 50 years ago, has had its evil effects on Music also as on other spheres of activity. No other

43 44

institution succumbed to the passion so completely as our Dramatic be easily seen from the impatience which the theatre-going andience Stage. The harmonium and piano of the West soon took the place of shows towards scientific and correct Indian music. The harmonium the Veena, Bin and the Sarangi and the musical precision and rich not only vitiates the taste of the audience, but it is bound to falsify melody of old soon gave place to imperfect and graceless music. the ear of the stage-singer himself. A good and expert professional Instruments of the harmonium family with fixed keys which reign singer will never tolerate the harmonium as an accompaniment to his supreme at present on our stage, are based on the European Temperate performance. It must also be borne in mind that it is the stringed Scale, which is admitted by European musicians themselves to be a instrument that forms the nearest approach to the human voice. The defective scale. As observed by Professor Blaserna, "it is an in- Honourable Sir J. W. Muir-Mackenzie, late Member of Council to correct scale. It has destroyed many delicacies and has given to the Bombay Government, who was a keen connoisseur of music, in his music, founded on simple and exact laws, a character of almost coarse speech delivered on the occasion of the Prize Distribution Ceremony approximation." These are instruments with fixed keys, they restrict of the Poona Gayan Samaj, observes : " I don't appreciate the port- a musician by compelling him to choose a note out of a fixed scale. able harmoninms much talked of by the Secretary from the Swadeshi and that too arranged on an approximation to natural tones. Again point of view as they were not in harmony with Indian Music. " the notes on the piano or harmonium die away rapidly and do not While some Europeans are themselves condemning the adoption of the give rise to overtones which are the essentials of rich and good music. temperate scale-on which are based instruments of the harmonium Aroha ( ascent), Avaroha (descent ), Murchchhana ( a quarter-tone ), family-as being productive of evil results and destroying the purity, Mends, or Ghasits-all these are necessary for the proper execution fineness, and delicacy of music, we are, strangely enough, engaged in of a Raga or Ragini; and in the very nature of things, they cannot, reproducing and perpetuating those very defects in India and impairing be had on the harmonium or piano. Yet our musical pieces which the high nature of our music ! It is high time that our eyes were are composed in accordance with the rules of Indian Music, are sung opened to the mischief being constantly done by the introduction and on the stage in accompaniment with these instruments ! For example, use of instruments bisel ou the European temperate scale. The stage the singer of दरबारी कानडा (a Raga), obtains on the harmonium not is only a type of cases where the evil is spreading and minifesting the counterpart of his Raga, but quite a different tune; and the itself prominently. The remely must be appliei externally to the result is the creation of imperfect music and ludicrous incongruity. pirt most affected, and internally to the root canse of the disease .. And yet, it is this incongruity which i enacted and The stage must be freed from the passion for the harmonium, and the tolerated on our dramatic stage, right after night ! As Professor Blaserna rightly observes, "music founded on the temperate scale people must be awakened to encourage and foster the art of Indian. must be considered as imperfect music and far below our musical sensi- Music. All those interested in the re-generation, preservation and bility and aspirations. That it is endured and even thought beautiful development of this Art of Arts, must labor for the cause and render only shews that our ears have been systematically falsified from in- help by the means in their power. fancy."* How truly do these remarks hold good in our case, may o Hon. Mr. Muir Mackenzie explained to me that vocal music and music on instruments of the violin family is sung and plyed in the sxact scale by con- noisseurs only in Europe. But I would add that the tempered scale has been adopted in Europe to suit the exigencies of instruments with fixed keys. Its advantages for the European system which is dependent on transposition and unlimited modulation from one key to another are felt to far outweigh its dis- advantages, and there is very little probability of a return being made to the natural scale in the near future in Europe. At the same time Indian Music which is not dependent on extensive modulation has no need whatever for a tem- pered scale.

46 APPENDIX A. Shrutees of the Hindt Musical scale. That the notesso evolved are correct: A Note by Mr. Nilkanth Vinayak Chhatre, B. A., L. C. E. and are the same as those used in the several Ragas and Raginees at the- late of Bombay Educational Department. present day, is borne out by the testimony of artists like Professor- R. B. Deval, retired Deputy Collector, has laid the musical world Abdul Karim &c. The correct idea of a Shruti is that it is not a unit of under deep obligations by placing before them in the accompanying brochure measurement, but it is an interval lying between any two consecutive. all the facts and figures regarding the evolution of the principal tones notes ( See paras 20, 21 ). Each such interval (Shruti ) is distinguished. and intertones of the Hindu Musical scale, as sung at the present day by by a distinct name and is thought to appeal to certain emotions. The

eminent masters of the science and art of Hindu Music ( Vide Tables verses of the Vedas which are sung in honour of certain Vedic deities at A, B, C, & D). The evolution is not capricious but based on rules given certain sacrifices in India were characterized by the introduction of in old Sanskrit worke on Hindu Music, such as Sangit-Ratnakara, Raga- suitable distinct Shrutis as leading notes ( Sahasrabuddhe-Sangitsar Part. vibodha &c., The rules are few and simple -- 1 Page 54).

१ मेरुश्रिष्टतुर्यतंत्रीरवे सः षड्जः अभिव्यज्यते। The Diachord is the instrument on which the intervals or the severali notes are evolved and marked. The Diachord is useful for testing the: २ मध्यस्थानस्थ: मध्यमः। उभयो: षडजयोम्ये मध्यमं स्वरमाचरेत्। accuracy of a musical note and ono of the pattern of Mr. Deval which is- ३ द्वावविशीस्थ: षड्ज: द्विगुणसमः। simple in construction, may very proftably be supplied to each college or- त्रिभागात्मकवीणायां पंचमस्स्यास्तदभिमे। class wherever Hindu music is taught systematically. सपसम मुख्या: संवादिन: स्दराः। .. मेरुगत स्वयंभू स्वरपंक्ति प्रामा ्येन। It will be interesting to find out and compare the notes which were-

तंत्रीतंतुस्वरो ज्ञेयस्तदैर्ध्येव्यस्तमानतः। used in musical pieces sung at sacrifices in old Hindusthan, Greece and. 19 तंतुस्थौल्येऽपि विज्ञेयस्तंतुसाक्ष्म्येप्ययं विधिः। Rome and in modern Church services. The field is wide and full of hope. and may lead to results as important as those of Comparative Philology. षड्रजपंचमयोरवविकृतत्वात्। १ स्वरसोपान परंपरा। The essential basis of musio is melody and this is contained admit --

How these simple rules are used in the evolution of the musical scale, tedly in the Hindu scale to its full extent. This has been the main charm of the Hindu system of music for thousands of years in the past and. is fully explained in pages 9 to 22 and the tables A, B, C, & D.t How will continue to remain so for a number of years in the future, if the: anxious the people wera to give their Musical scale the sanction of Nature is seen by their adopting the third note (E) of 300 vibrations readiness of the people to use harmoniums and other tempered instru-

in place of 3031 vibrations, for this was evolved as the 5th Harmonic. ments for teaching the gamut is checked betimes by all the civilized world. The 22 Shrutis which are used in the musical pieces of Hindus- For some reason or other the efforts of well intentioned enquirers have now been mathematically calculated and fixed by Mr. Deval and. both European and Native to get at the correct idea and measure of the there is no doubt that his Diachord will serve as a useful guide in notes of the Hindu scale had hitherto proved futile and unsatisfactory. constructing & harmonium or tuning a pianoforte to the natural and. ( See paras 14, 15 &e. ) Mr. Deval's claim to admiration lies in grasp- - just scale of Hindu music. ing the whole difficult situation and in ingeniously applying the Sanskrit rules in a systematic manner to the evolution of the Hindu scale of the The rhythmic movement of suceessive notes which is the soul of"

principal 7 ( 8 including the octave ) notes and in suitably interposing 15 Hindu music or natural scale has a charm peculiar to itself. This is-

additional notes into the intervals between them and thus evolving 22 melody. It is free from trammels of consonant chords and harmonic

notes (23 including the octave ) corresponding to the long known 22 combinations which have so great a charm for the European ear. Hindu. Music lacks this. Hindu music is, however, rich in the wealth of a more

• Vide also 'सपस्वर व श्रुति' by Mr. N. V. Chhatre B. A., L. C. E. p. 7. pliant melody which has the privilege of appealing touchingly to the: emotions.

47 48

Each Shrati is allotted to a peculiar emotion as its name (IAT, TT or suitable encouragement, for this is one of the platforms on which all the like clearly shows. If Hindu Music wants harmony European music, persons of whatever caste and position and shades of thought may meet to our ears; lasks melody. Here is the case of a blind man and a lame as equals and share the pleasure of company without losing their man so aptly illustrated in sop's Fables. Let us assist each other. individuality. Now that Mr. Daval hat evolved the Shruti ssale, musical inetruments I beg to close the introduction by congratulating Mr. Deval again may be tuned accordingly; and these will give Europeans a correct idea for his ingenious evolution of the Hindu Musical Scale and the 22 of Hindu masical charm and a happy way opaned out for a suitable. Shrutis. exchange of musical wealth by one nation to the other. The field of. Hindu music is very wide and to appreciate it corractly and completely one must hear the professors of the art. .The charms of menda (3). APPENDIX B. and ghasit (dffe ) are realized only when they are properly rendered. on stringed and wind instruments. Keyed musical instruments howso- ' The essential basis of music,' as Helmholtz rightly observes, 'is ever perfect in their construction are by their very nature unfit for such melody.' And, as has beon observed by my learned friend Mr. Chhatre execution. These मेंडs and घसीटs should be. heard by lovers of musi in his note to this brochure, this ( melody ) has been the main charm of from the masters of the art. They have spent their lives upon them. Their the Hindn system of music. The same opinion has been distinctly race is fast dying out for want of support. Let it be mentioned however expressed by many European Scientists and Musicians of note; and I have to the credit of the Hindu public and the Native States in India that they, added in this appendix extracts from their writings on the importance of have been and are making efforts to preserve this Art of Arts from decay melody in music. and final extinction by holding annual gatherings of musicians and enter "The object of this introduction will be gained if we, for a little taining the services of those wh> are the best among them. I give. while, allow ourselves to forget the glory and splendour of our below a list of famous professors as far as my knowledge goes and modern harmony, in favour of those melodic systems which once satisfied raquest the readers of Mr. Deval's pamphlet to extend the list by sug- the great nations of classical antiquity and still content those hoary gesting to him the names of other people they may know of. civilizations of the East which preserve so much that is really ancient in 1 Miya Aladiya Khan their present daily life. Capt. Day shows an interesting resemblance 2 Miya Haidar Baksh Antoba Sadhale, pupil of of Kolhapur Durbar. between the leading modes of old Greece and Asia Minor and certain 3 Kudhosing. favourite modes of the Hindus. There is no sure evidence of an intimate 4 Balkiishnaboa of Ichalkaranji. musical connection between these countries and India, a few scattered 5 Bhayyasaheb Joshi, references in classical writers excepted, but the relationship of sister Vishnupant Joshi pupil of Nasarkhan of Baroda Aryan langusges may have been paralleled by a relationship of musical 6 7 Bhaskarbawa Bakhale pupil of Faiz Mahammad. types sufficient to justify a theory of descent instead of one of imitation. " 8 Rahimatkhan son of Haddukhan. Hipkin's Introduction to Capt. Day's Music of Southern India, P. 11. 9 Gokhale brothers of Miraj and Kolhapur Darbar. "This is the musical scale which is established in nature-the most 10 Shoshanna of Mysore. pleasing to all ears and the most accordant with the philosophy of music. 11 Inayat Hussain of Hyderabad Deccan. This scale in its exact proportions is also the most natural and easy for 2 Parasaheb of Culcutta. a human voice-that most wonderful of all musical instruments-in any 13 Indatkhan of Gwalior. he violin too can give accurate intonation, But the ordinary 14 Professor Abdul Karim of the Deccan. an and other keyed instruments do not produce this scale of 15 Muradkhan Binkar of Gwalior. of the voice in exact tune. It may be easily seen that if Before taking leave of my readers I beg to suggest that every effort made perfectly correct in one key some of the notes must of should be made by Europeans and Natives to preserve this dying Art by e incorrect, by a degree or two in all the other keys. They

49

are therefore called imperfect. Mr. Graham, in his 'Theory and Practice of Musical Compositions' shows the great injustice and the great injury to music, which arises from the frequent endeavour to form the voice-a perfect instrument-according to the false intonation of such instruments as these. General Thompson says: 'It may be hoped that time is approaching when neither singer nor violinist will be tolerant of a tem- pered instrument. Singers sing to the pianoforte because they bad bad ears; and they have bad ears because they sing to the pianoforte."" John Curwen: A Grammar of Vocal Music, 26th Edition, page 40. "But I consider it a mistake to make the theory of consonance the essential foundation of the theory of music, and I had thought this opinion was clearly enough expressed in my book, The essential basis of Music is melody. Harmony has become to Western Europeans during the last three centuries an essential, and to our present taste, indispens- able means of strengthening melodic relations; but finely developed music existed for thousands of years and still exists in ultra-European nations without any harmony at all." Helmholtz ' Sensations of Tone', Author's Preface, 3rd Edition. "The proper succession of single musical sounds is called melody. Some study of melody is absolutely essential to a good singer." Dr. John Curwen ' A Grammar of Vocal Music' 26th Edition. "The greater freedom in musical intervals, melodic systems allow, must be reckoned as compensating in some measure for the want of harmonic combinations of which our European music has such inexhaus- tible wealth." Hipkin's Introduction to Capt. Day's Music of Southern India, Pp. 11, 12. "Since a sweet note is already a harmony, the influence of the recog- mized musical concords is not something absolutely new bnt the extension of the same harmonising process." Prof. Bain-' Ha yony.'

yeffort Art by