DELHI UNIVERSITY LIBRARY

DELHI UNIVERSITY LIBRARY

Cl. No. 181.613 No 13 Ac. No. 31587 This book should be returned on or before the date last stamped below. An overdue charge of one anna will be levied for each day the book is kept beyond the date.

INTRODUCTION TO THE STUDY OF MUSICAL SCALES

THE INDIA SOCIETY

3 VICTORIA STREET, LONDON S.W.I.

PRINTED BY A. BOSE, AT THE INDIAN PRESS, LTD., BENAREs. 1943.

TO MAX D'OLLONE

TO ŚIVENDRA NĀTH BASU

5

21

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24

25

26

29

30

31

39

41

42

47

49

50a

( H )

FOURTH PART

The Cycle of Fifths (The musical theory of the Chinese)

Chinese music. 55

The nature and the purpose of music. 55

The Yin and the Yang. 57

The seven degrees of the pentatonic scale. 62

Symbolic representation of the pentatonic scale. 64

The spiral of fifths. 65

Equalized or temperate divisions. 70

Cyclic division into twelve. 71

The lyü. 72

The degrees of the scale. 73

The scale of the lyü. 75

Scale of fifths (The sixty lyü). 77

Symbolism and correspondences of the lyü. 83

Signification of the names of the first twelve lyü. 86

Some correspondences of the twelve first lyü. 87

Correspondences of the degrees of the scale. 88

Western commentaries. 90

Correspondences of the degrees of the scale (tables). 91

FIFTH PART

The relations to a tonic (The modal music of the Hindus)

The Hindu musical theory. 99

The laws of music and their applications. 100

Modal system and harmonic system. 101

The problem of the division of sounds. 103

The theory of elements 104

Sound and vibration. 107

The nine svaras. 108

The tonic and the grāmas (basic scales). 110

( iii )

The diatonic series and the comma diesis. 111

The tonic and the cosmic cycles. 113

The two diatonic scales. 115

The Ga grāma. 116

The scale of nine sounds and the mūrchhanās. 117

The fourteen mūrchhanās. 119

Chromatic and Enharmonic. 121

Acoustic definition of the division of śrutis. 123

Symbolic necessity of the division into twenty-two śrutis. 125

Musical definition of the śrutis. 129

The śrutis. 131

Further subdivisions of the śrutis. 132

Misinterpretations of the śrutis. 133

Western division of the octave into twenty-two intervals. 136

Influence of Hindu theory in Europe. 139

The jātis. 140

The five jātis. 141

Affinities of the musical notes. 143

The modes or rāgas. 145

Affinities of notes. 146

Definition of modes. 148

The periods of the day. 149

The modal or harmonic division of the scale. 152

Harmonic division of the octave. 153

The twenty-two śrutis. 154

SIXTH PART

Confusion of the systems (The music of the Greeks)

Greek music. 159

The theory of the scale. 163

Genus. 166

Perfect group (disjunct). 168

( iv )

PAGE

The Enharmonic. 172

The Chromatic. 180

The Diatonic. 185

Dorian harmonies. 187

Exotic harmonies. 191

The fifteen tones of transposition. 197

SEVENTH PART

The Western scale and Equal Temperament

Western music. 203

The modes of Plain-chant. 208

The eight Gregorian modes. 210

The scale of Zarlino. 212

The major mode. 215

Equal temperament. 218

EIGHTH PART

The scale of sounds

Need for a scale of sounds. 229

"3" cyclic number and "5" modal number. 230

Similarities of the scale of fifths and the scale of proportions. 234

The universal scale of sounds. 237

Numbers of vibrations. 242

Remarks on the scale of sounds. 243

Conclusions. 245

BIBLIOGRAPHY. 247

INDEX. 255

All rights of translation and reproduction reserved by the author.

La novità del suono e il gran lume

The newness of the sound,

di lor cagion mi accesero un disio

And that great light, inflamed me with desire,

mai non sentito di cotanto acume. . . .

Keener than e'er was felt, to know their cause.

"Tu non sèi in terra, sì come tu credi ; . . .

Thou art not on the earth as thou believest ;

"Qui veggion l'alte creature l'orma

( Then said Beatrice ) . . . . . . . . . . Here

dell'eterno valore, il quale è fine,

The higher creatures see the printed steps

al quale è fatta la toccata norma."

Of that eternal power, which is the end

( Dante, Paradiso, Canto Io, v. 82 e segg. )

For which the order of things is made.

( Cary's translation, adapted ).

METAPHYSICAL CORRESPONDENCES

7

note producing vibrations in unison . . . In the Universe there is no

hazard, there is no spontaneity ; all is influence and harmony, accord

answering accord." (Cited by A. Préau, Lie Tseu, in "Voile d'Isis",

No. 152-3, 1932, p. 554-5).

To be able to realize the nature of this accord between the different

aspects of the Universe, we must know the principles which are common

to all these aspects. This is why the theorists of Hindu music assert

that though the subtle correspondences between the laws of nature and

the laws of harmony, between the modes of music and the modes of our

sentiments, can be experimentally discovered, they can be completely

and logically explained only by traditional metaphysics whose source

is in the Veda. As Mr. René Guénon explains :-

"The affirmation of the perpetuity of Veda is directly connected with

the cosmological theory of the primordiality of sound among sensible

qualities (sound being the particular quality of Ether, ākāśa, which is

the first element). And this theory is, in reality nothing else than that

which is expressed in other traditions when 'creation by the word' is

spoken of. The primordial sound is the divine word through which,

according to the first chapter of Hebrew Genesis, all things have been

made. This is why it is said that the Ṛṣis or sages of the first ages

'heard' the Veda. Revelation, being a work of the Verb, as creation

itself, is actually a hearing for him who receives it." (Études Tradition-

nelles, 1936, p. 68, Quelques aspects du symbolisme du poisson.)

According to Kṣemarāja (Commentaries on Śiva Sūtra Vimārṣini,

cited by André Préau, in Voile d'Isis, 1935, p. 350):

"The Bindu, desirous to manifest the thought it has of all things,

vibrates, transformed into a (primordial) sound of the nature of a cry

(nāda). It shouts out the Universe which is not distinct from itself,

that is to say, it thinks it : hence the word śabda (word). Medi-

tation is the supreme 'word' : it sounds, that is, it vibrates submitting all

things to the fragmentation of life; this is why it is nāda (vibration).

This is what is expressed in the half śloka–Sound (śabda) which is of

the nature of Nāda resides in all living beings."

8

INTRODUCTION TO MUSICAL SCALES

Swami Hariharanand Saraswati explains (Siddhant, I 43, Sabda and Artha) the fundamental inter-dependence of sounds and forms :

"The things named and their names are both parallel manifestations resulting from the union of Brahman (the undifferentiated principle) and Maya (appearances) just as waves appear in the sea. From Brahman united with Sakti (Energy = Maya) is issued, in the order of manifestation of the world, on the one hand the Principle of naming : from it the monosyllable AUM, and from AUM all words (or sounds) ; and on the other hand, from Brahman united with Sakti, in the order of manifestation, is also issued the Principle of forms and out of it all the world, living beings, etc."

But, between those two aspects of manifestation, the relation remains close, there is fundamental identity between the principle of names and the principle of forms, as well as between words and objects.

The Universe is called in Sanskrit Jagat (that which moves) because nothing exists but by the combination of forces and movements. But every movement generates a vibration and therefore a sound which is peculiar to it. Such a sound, of course, may not be audible for our rudimentary ears, but it does exist as pure sound. Each element of matter producing a sound, the relation of elements can be expressed by a relation of sounds, and therefore we can understand why Astrology, Alchemy, Geometry, etc., express themselves in terms of harmonic relations.

Although those pure sounds, those absolute sounds which Kabir calls "the music inaudible", cannot be perceived by our ears (they may be perceptible for more delicate instruments; and the perception of such sounds is one of the stages in the practice of Yoga), yet we may be able to produce corresponding sounds within the range of vibrations which we can perceive. Among these partial sounds we can establish relations similar to the subtle relations of Nature. These will be only gross relations, but may approach sufficiently the subtle relations of Nature to evoke images in our mind. As explained by Sir John Woodroffe, the learned commentator on Tantric metaphysics (Garland of Letters, p. 77) : "there are, it is said, closely approximate natural names, combined

THE CONFLICT OF MUSICAL SYSTEMS

27

as far as we know, from a need of harmony that the "Ison" was introduced ( ! ) into the Byzantine chant but it was from the necessity of keeping the singers in tune," imply that they have not the slightest idea of those relations which are, properly speaking, the harmony of so-called monodic music and outside of which melody has not much effect or meaning. It would be just as ridiculous to speak of adding a fundamental to a chord, since a chord exists only by relation to its fundamental note.

The "Ison" or "equal" of Byzantine music was called "Chhandovati śruti" ( the measuring sound ) in ancient Hindu music. It is, properly speaking, the standard by which all intervals are measured. No interval, no note, no melody has a meaning unless the "Ison" (Sa) is present. It seems that Occidentals are just as unable to "hear" those relations as Orientals are unable to perceive chords, but this is not a sufficient reason to consider either system of relations as unpleasant and useless. The "Ison" defines the meaning of each note, which can be expressed by a numerical ratio, exactly as does harmony. And melody without "Ison" is just as flavourless as is, for the modern Westerner, melody without harmony. When they disregard the importance of the "Ison", learned and respectable Occidentals only show that they understand nothing of the Eastern music they pretend to study and explain, and that they perceive nothing of its marvellous power.

The "Mesa" was, to ancient Greek music, what the "Ison" is to modern Byzantine music. "For the ancient [Greeks], the A (Mesa) is a directional string whose permanent use constitutes a guiding mark for the ear and a reduction to unity for the mind." ( Maurice Emmanuel, Grèce, Dictionnaire du Conservatoire.) The "Mesa" is "the connecting element of successive sounds, . . . . the connecting agent of all the melodic forms of the octave." (Gevaert, Problèmes d'Aristote.)

Orientals often make remarks similar to this: "The Beethoven symphonies are very interesting, but why have all those chords been introduced spoiling the charm of the melodies ?" From

THE CONFLICT OF MUSICAL SYSTEMS

33

THIRD PART

MEASURE OF INTERVALS AND HARMONIC SOUNDS

MEASURE OF INTERVALS AND HARMONIC SOUNDS

41

The Scale of Sounds.

Suppose that we collect all the intervals which, in ordinary practice, are used in modes (rāgas), as well as in chords, in relation to a note considered as the tonic. When comparing these intervals, we shall find a certain number of points within the octave, each of which corresponds to a perfect relation with the basic note, though they may not have harmonious relations between themselves. When we apply the same process to each of the notes of the diatonic scale (Sa or Ma grāma), in relation to each note we shall obtain a certain number of points, some of which will coincide with those of other notes, and some of which will not. We shall thus have a number of distinct points within the octave, and we can then see whether they bring out a simple division of the octave and whether the points which form an harmonic interval with one note are also in harmonic relation with other notes.

By trying all the possible combinations of the minor tone, the major tone, the major half-tone, and all the intervals resulting from their sum or their differences (the minor half-tone is the difference between the minor tone and the major half-tone ; the limma is the difference between the major tone and the major half-tone ; the maximum tone (8/7) is the difference between the ditone (2 major tones) and the minor tone, etc.), we get a division of the scale which is of nine intervals for the major tone, eight for the minor tone and five for the diatonic (major) half-tone. These intervals are separated from each other by one comma (81/80 = 5 savarts), except for a discontinuity of 8 savarts between the notes of different name (C and C sharp ( Sa and Komal Re), E and F (Ga and Ma), etc.). If we compare this scale to the key-board of the piano or organ, for each key, black or white, we shall have several notes separated from each other by one comma (5 savarts). But, between the highest note corresponding to a certain key, A (Dha) for example, and the lowest one corresponding to the next key, flat B (Ni Komal), there remains an interval of 8 savarts.

6

MEASURE OF INTERVALS AND HARMONIC SOUNDS

43

Ex : Ḋ# = Ḟb (Gab) (komal)

The sign -- indicates that the note is lowered by two commas.

Ex : D-- (Re--)

The sign - indicates that the note is lowered by one comma (81/80 =5 savarts).

Ex : E-(Ga-)

To these signs are added, as previously explained, between ++ and #, the sign ½ and, between b and --, the sign ¾. The major tone, the minor tone and the diatonic half-tone are thus divided in the following way :

In the major tone :

A (Dha) + ++ ½ # L- L+ b ¾ -- - B(Ni)

44

INTRODUCTION TO MUSICAL SCALES

or

A(Dha) + ++ 1/4 b L- L+ b 3/4 -- B(Ni) +

In the minor tone :

D(Re) + ++ 1 # L b 3/4 -- E(Ga) +

MEASURE OF INTERVALS AND HARMONIC SOUNDS

45

or

D(Re) + ++ E(Ga)

major half-tone -- limma -- minor half-tone -- limma -- major half-tone

L b

In the diatonic half-tone :

major half-tone, 16/15 - limma, 256/243- - - minor half-tone, 25/24 -

E(Ga) + ++ F(Ma)

-- minor half-tone, 25/24 limma. 256/243 -- --major half-tone 16/15

In practice, we shall indicate the exact tuning sign above the note, and the general indication sharp (#) or flat (b) (tivra (r) or komal (K)) beside the note as customary.

But, in the Indian notation, as the doubt cannot arise, we shall, generally, indicate the exact tuning sign only.

We then shall have Bb, Bb, Bb. Bb, etc., (komal Ni#, NiL-, NiL+, Nib, etc.).

A# would be identical to Bh, A# identical to Bb, A# identical to Bb, etc...

In this way is realized a division of the octave into fifty-three intervals, allowing us to play accurately, i.e. without beats, all the

FOURTH PART

THE CYCLE OF FIFTHS

What we hear is either auspicious or inauspicious; music must not be inconsiderately executed. Seu-ma T'shyēn.

Preliminary Note - In this short account of Chinese music we have abundantly drawn on the admirable work of M. Maurice Courant, published under the title "Chine et Corée" in the "Encyclopédie de la Musique et Dictionnaire du Conservatoire" (Fondé par Albert Lavignac), Paris 1924, Section : Histoire de la Musique, Vol. I, p. 77 to 241. All the translations from Chinese authors are those of M. Maurice Courant except where otherwise specified. The sentences borrowed from M. Maurice Courant's work are indicated by the letters (M.C.) whenever they occur.

THE CYCLE OF FIFTHS

57

who sings becomes straight and displays his moral influence, and,

when he himself comes into motion, Heaven and Earth respond,

the four seasons are in harmony, stars and planets are orderly, life

is sustained in all beings." (Yò kī). This is why the mastery and

ordinance of music are the first duties of statesmen because, "if it

is given to the dukes and ministers to hear the lyŭ of each month

in the court's assemblies, they will become able to move Heaven and

to accord themselves to the Earth influx." (Pào Yè, about 77 A. D.)

The Yīn and the Yâng.

Since the Chinese musical system has as its only aim the estab-

lishment of contacts and mutual reactions between apparently un-

connected aspects of manifestation, it is essential for us, in order

to understand its applications, to have an idea of the knowledge that

the Chinese had of metaphysical reality, and an idea of the book

which sums up that knowledge, the Yī kīng. Though it may seem

a digression, it appears necessary to give here a very short

account of it.

Composed by the mythical Emperor Fó-hī in the fourth mil-

lenium before the Christian era1, the Yī kīng has been and still

remains the inexhaustible source whose form conditions all Chinese

metaphysical thinking.

All manifestation issues from two principles supplementary and

concordant, one positive, spiritual, active, male and warm, the Yâng,

the other negative, material, passive, female and cold, the Yīn.

These two terms correspond to the Sanskrit Linga and Yoni which

symbolize Śiva and Śakti, that is, Puruṣa and Prakṛti, Being

and Matter. •

1. cf. "Orient et Occident", by René Guénon, note p. 70.

"The exact date for the existence of Fo-hi1 is 3468 before the Christian

era according to a chronology based upon the exact description of the condition

of the sky at that time ; let us add that the name of Fo-hi is used, in reality,

as a designation for a whole period of Chinese history."

8

THE CYCLE OF FIFTHS

61

calamity, the moon, the thief, hardness of the heart, the den,

the music, the thorny bush, the fox.

Kèn (the mountain) is : stop, the fox, the hand, the boy, the path

the stone, the door, the monk, the finger, the mouse, solidity,

the nose, the tiger, the wolf.

These trigrams, combined two by two, form 64 hexagrams

which allow the representation of all the aspects of existence. It is

through them that we can study and bring into practice the laws of

correspondence between the different aspects of the world and,

in the particular field of music, understand the modalities according

to which the fifths, in succession, will allow us, following their

hierarchical development, to reach all the planes of the visible and

invisible world, to influence spirits, celestial emperors, elements and

seasons, and to regulate the destinies of the Empire. This is pos-

sible because "rites and music rise up to Heaven and surround the

Earth, act upon the principles Yîn and Yâng and communicate with

the manes and heavenly spirits." (Yò kī). According to the words

of the Emperor Hyáo-Wên (477-499) : "Music . . . shakes Heaven

and Earth, moves the spirits, brings into accord the two cosmogonic

principles, penetrates men and manes."

The correspondence of the trigrams and the musical notes appear

of a different nature according to the method used to determine

this correspondence, each method being valid in its own field. The

comparison, for example, can be based on their symbolism isolated or

in combination, or it can be based on the analysis of the structure

of the trigrams and the relative position of full lines and

broken lines as comparable with the structure of tetrachords

and chords.

The peculiarity of the trigrams is that, whatever may be the

way in which they are manipulated, the results, which are thus

obtained, endlessly various as they are, will always be in conformity

with some aspect of reality.

70 INTRODUCTION TO MUSICAL SCALES

Equalized or Temperate divisions.

Considering the first series of fifths, we can obtain, beyond the

six perfect tones,

I. C (Sa), II. G (Pa), III. D (Re),

IV. A+ (Dha+), V. E+ (Ga+), VI. B+ (Ni+),

the six imperfect tones,

VII. F# Ma tivra), VIII. Db (Re komal), IX. Ab (Dha komal),

X. Eb (Ga komal), XI. Bb (Ni komal), XII. F+ (Ma+),

alternatively considered as male and female.

If we neglect the small difference between the thirteenth fifth

and the octave, we obtain the equalized chromatic division into twelve

half-tones on which are based all "temperaments" or equalized

divisions of sound, space and time.

The six perfect tones can be represented by the sides of the

inscribed hexagon. If we divide the side of the hexagon (which is

equal to the radius) first into two, then into ten parts, this will lead

us to the division of the circle into twelve, then 60 parts, divisions

always employed for the representation of the world's movement

within a closed circle. Occidentals use this division for the measure-

ment of circles and angles (60 × 6 = 360 degrees) and, consequently, for

astrology and astronomy (12 Zodiacal signs, etc.).

They use also a similar division for time into twice 12 hours,

60 minutes, 60 seconds, etc., all divisions which are said to have

been borrowed from the Chaldeo-Assyrians. Europeans also divide the

sound octave into 12, but do not proceed with the logical implicati-

ons of this division as do the Chinese.

In reality, the physical laws which are applicable to sounds

are not particular to them, but are those which regulate all the

normal rhythms of the Universe, and those "positive" minds, which

smile at such conceptions, might be very embarrassed if Saturday

did not come every eighth day, if the days no longer had 24 hours

(12 × 2), the hours 60 minutes, and if the relation of the sun and the

INTRODUCTION TO MUSICAL SCALES

78

major tone 9/8

(large tone)(small minor third)(trihemitone)minor third (major tone + apotome)(small major third)(major third)ditone 9/8 × 9/8 = 81/64

51.14

(51.99)57.0762.8568.7674.6379.6885.5391.4097.37102.31

157,464 = 39/64 = 243/128 or II of III

157,136... = 286/244155,344... = 231/38153,253... = 240/315151,190... = 259/337149,155... = 278/389147,456 or 213/3 of IX = 33 × 218141,581... = 270/384139,968 = 37 × 26

32/23

35/267314/222326/241338/260350/279393/214312/283383/282345/271334/26

THAI-TSHÚ

.....shí-shí.... .... .... ....KYÁ-CHÖNG.... .... .... ....KÚ-SYÊN

D(Re) Shāng

.....D+(Re+)D++(Re##)Eb(Ga#)Eb(GaL)bEb(Gab) ShāngE--(Ga--)E-(Ga-)E(Ga)E+(Ga+) Kyō

III

(LVI)XV XVII XIX LI X XII XIV XVI V

11

12131415161718192021

THE CYCLE OF FIFTHS

81

(small sixth) (harmonic sixth) (fifth + major tone = 27/16) (large sixth) (small minor seventh) (seventh harmonic) (minor seventh) (minor seventh)

210.47 216.34 222.21 227.24 228.08 233.11 238.98 244.85 250.72 255.76

109,103... = 230/39 107,634... = 249/331 106,185... = 268/338 104,97 = 38 × 24 104,757... = 287/365 103,563... = 222/34 102,169... = 241/316 100,794... = 260/338 99,437... = 279/340 98,304 = 331 × 215

330/281 385/250 344/269 38/24 356/288 315/288 327/243 389/261 351/280 310/215

kya-hing .... .... NÂN-LYÛ .... kyê-kong .... .... yi-hán WÛ-YI

A--(Dha --) A-(Dha-) A (Dha) A+ (Dha+) Yü A++ (Dha++) # Bb (Ni#) # Bb (Ni-) # Bb (Ni+) # Bb (Nib) Yü

XXI XXXIII XLV IV (LVII) XVI XLVIII XL LII XI

43 44 45 46 47 48 49 50 51 52

11

FIFTH PART

THE RELATIONS TO A TONIC

Fifth Part

THE RELATIONS TO A TONIC

The Hindu Musical Theory.

SINCE the remotest antiquity there has existed in India, besides a general theory of sounds, a theory of musical modes which seems to have been the source from which all systems of modal music originated. The Hindu theory is not, like other systems, limited to experimental data; it does not consider arbitrarily as natural certain modes or certain chords, but it takes as its starting point the general laws common to all the aspects of the world's creation.

Starting from metaphysical principles, the Hindus have recreated the theory of sounds. They have analysed and classified all the possible ratios and relations between sounds. The result is, obviously, an astronomical number of theoretical chords, modes and combinations, of which few only are utilized in practice; the others, however, remain accessible for the day when new conditions, or the inspiration of musicians, may require new modes or new musical forms

The Hindu classification deals once and for all with the subject of musical relations. It is the necessary basis of any serious study. All other classifications are, beside it, child's play. Unfortunately its approach is difficult, no systematic study of it has been made in any modern language, and we cannot here start this enormous enterprise1. But, without going beyond the limits of the classifications utilized today in Hindu music, we can find

1. "Music, in which the Hindus excelled. has not as yet been the object of special studies. The refinements of a too scholarly theory have paralysed the researches of the Europeans." (Sylvain Lévi; at the word 'India' in the "Grande Encyclopédie".)

101

which pleases people. Gāndharva music always follows the rules of the theory." Rāmāmātya, (Svaramelakalānidhi, II. 7, 8, 9, edit. Ramaswami Aiyar.)

Modal system and Harmonic system.

1. Hindu muṣic, p. 340,

THE RELATIONS TO A TONIC

119

The Fourteen Mūrchhanās.

The mūrchhanās of Sa grāma are : (modern notation)

1. Uttaramandrā

Re Ga Ma MaL+ Pa Dha+ Ni Sa ReL+ Re or Sa Re- GaL (Ga+) Ma Pa Dha NiL+ (Ni) Sa

2. Rājanī

Sa ReL+ Re Ga Ma MaL+ Pa Dha+ Ni Sa or Sa(ReL+) Re Ga Ma (MaL+)Pa Dha+ Ni Sa

3. Uttarāyata

Ni Sa ReL+ Re Ga Ma MaL+ Pa Dha+ Ni or Sa ReL+ (Re+)GaL Ma MaL+ (Pa+) DhaN Sa

4. Śuddha Ṣaḍjā

Dha+ Ni Sa ReL+ Re Ga Ma MaL+ Pa Dha+or Sa Re- GaL (Ga+) Ma Pa- DhaL(Dha)NiL+ Sa

5. Matsarīkṛta

Pa Dha+ Ni Sa ReL+ Re Ga Ma MaL+ Pa or Sa Re Ga Ma(MaL+) Pa Dha NiL+ (Ni+) Sa

6. Aśvakrāntā

Ma MaL+ Pa Dha+ Ni Sa ReL+ Re Ga Ma or Sa(ReL+) Re Ga+ MaL- Pa (DhaL)Dha+ Ni Sa

120 INTRODUCTION TO MUSICAL SCALES

7. Abhirudgatā

Ga Ma Maᷫ Pa Dhaᷫ Ni Sa Reᷫ Re Ga or Sa Reᷫ (Reᳫ)Gaᷭ Maᷫ Pa Dhaᷭ(Dhaᷫ)Niᷭ Sa

The mūrchhanās of Ma grāma are :

8. Sauvīrī

Pa Dha Ni Sa Reᷫ Re Ga Ma Maᷫ Pa or Sa Re- Ga Ma (Maᷫ)Pa Dha Niᷫ (Niᷫ) Sa

9. Hāriṇāśva

Ma Maᷫ Pa Dha Ni Sa Sa Reᷫ Re Ga Maᷭ or Sa (Reᷫ)Re Ga Maᷭ- Pa (Dhaᷭ)DhaᷫNi Sa

10. Kalopanatā

Ga Ma Maᷫ Pa Dha Ni Sa Reᷫ Re Ga or Sa Reᷫ (Reᷫ)Gaᷭ Maᷫ Pa Dhaᷭ(Dhaᷫ)Niᷭ Sa

11. Śuddha Madhyā

Re Ga Ma Maᷫ Pa Dha Ni Sa Sa Reᷫ Re or Sa Re- Gaᷭ(Gaᷫ) Ma Pa- Dha Niᷫ(Niᷫ) Sa

12. Mārḡī

Sa Reᷫ Re Ga Ma Maᷫ Pa Dha Ni Ṣa or Sa (Reᷫ) Re Ga Ma (Maᷫ)Pa Dha Ni Ṣa

THE RELATIONS TO A TONIC

121

13. Pouravi

or

Ni Sa Re+ Re Ga Ma MaL+ Pa Dha Ni orSa Re+ (Re+) Ga Ma MaL+ (Pa+) Dha NiL+ Sa

14. Hṛṣyaka

or

Dha Ni Sa ReL+ Re Ga Ma MaL+ Pa DhaorSa Re Gab (Ga++) Ma+ Pa Dhab (Dha++) Ni Sa

To the mūrchhanā scales are to be added the scales made on the basis of tetrachords, which are directly obtained on the Viṇā and other stringed instruments. Such scales have generally their two tetrachords indentical.

There are also other scales obtained by changing the śruti of the tonic. A certain number of them are described in the Saṅgīta Ratnākara.1

Chromatic and Enharmonic.

If, leaving aside the details of tuning, we assemble the notes of the different mūrchhanās, we get a chromatic scale which corresponds to what the Westerners call the "harmonic" form of the chromatic scale.

Sa ReK Re GaK Ga Ma MaT Pa DhaK Dha NiK Ni Sa

C Db D Eb E F F# G Ab A Bb B C

But, if we are careful of tuning particularities, we can find that, to transpose all the mūrchhanās in the same pitch, we require,

1. The interpretation of a few of these is given by Paṇḍit Firoze Framjee in his "Theory and Practice of Indian music", pp. 33 to 107, 16

126

INTRODUCTION TO MUSICAL SCALES

eye,

which sees everything : circles which we shall have to cross,

before

we can reach the final resorption into absolute knowledge.

The

Arabic division of the octave into seventeen intervals

is

also based on considerations of symbolism connected with

Musalman

esotericism. This by no means excludes their physical

actuality.

The fact that the Arabs divide the octave into

seventeen

intervals does not imply that those intervals are

bigger

than the śrutis, as many Westerners have lightly considered.

Those

divisions refer, necessarily, to identical notes, in conformity

with

the needs of musical expression, because they are the repre-

sentation

of metaphysical realities corresponding to the very nature

of

sounds, as well as of all other aspects of the three worlds.

The

seventeen notes of the Arabic octave can, in reality, be identi-

fied

with seventeen of the śrutis. The śrutis left out are those

which

are least employed, since, following the deterioration of the

cycle,

the scale of tonic C(Sa grāma) is the only one employed in

modal

music. In the ancient law, Hebraic or Hindu, the numbers and

śrutis

of the lost grāmas (scales) are piously kept, but in the new

law

(Islam), they are left out in the general theory because they

are

so rarely used. This is what al-Fārābī explained1 : "the two

cycles

that we have established each contain twenty-two degrees ;

these

are the totality of the notes which are used on the lute,

some

frequently, others more rarely. We shall deal only with the

notes

which are ordinarily used and which, consequently, are the

more

natural." Elsewhere, speaking of the tuning of the Hūrāsān's

ṭunbūr,

he says2 : "the scale of this instrument contains, in this

tuning,

thirty-two degrees ; the doubled notes being ten in number."

The

number seventeen, which was considered inauspicious in

ancient

times, in the Occident as well as in the Orient, has,

on

the contrary, been sometimes taken as representative of the new

gospel,

Christian or Musalman.

Kitābu al-Mūsīqī al-Kabīr, transl. d'Erlanger, p. 25.

ibid., p. 253.

132

INTRODUCTION TO MUSICAL SCALES

10. Vajrikā (thundering, steel, diamond, severe, abusive)

F+ (Ma+)

A. Ga 11. Prasārinī (diffusing, pervading, shy)

F# (MaL-)

12. Prītiḥ (pleasure, love, delight)

F# (MaL+)

Ma 13. Mārjanī (cleansing, adorning, excuse)

G (Pa)

14. Kṣitiḥ (forgiving, destructible, Earth)

Ab (DhaL)

15. Raktā (red, impassioned, coloured, playful)

Ab (Dhab)

16. Sandīpanī (stimulating, inflaming)

A (Dha)

Pa 17. Ālāpinī (speaking, conversing)

A+ (Dha+)

18. Madantī (lust, spring, intoxication)

Bb (NiL+)

19. Rohinī (adolescent girl, lightning, growing)

Bb (Nib)

Dha 20. Ramyā (night, love, pleasure, rest, calm)

B (Ni)

21. Ugrā (sharp, passionate, cruel, formidable, powerful)

B+ (Ni+)

Ni 22. Kṣobhinī (irresolute, agitated)

C (Sa)

Further Subdivisions of the Śrutis.

The śrutis are represented, in practice, by their characteristic notes, but they are, theoretically, regions of the octave. Within the limits of each śruti several positions may be possible, allowing an adjustment of the tuning of the notes according to modes or rāgas. As long as the notes do not trespass the limits of the śruti their expression keeps the same characteristics. This expression will only be the clearer and stronger if, within the limits of the śruti, that note is utilized which forms, with the tonic, the most rational and simple ratio. This leads to the utilization, within the octave, of the fifty-three (and sometimes sixty-six) positions which allow, inside the śrutis, the necessary adjustments of tuning according to modes or rāgas.

The limits of the śrutis are strictly determinate, a fact which has induced the Hindu physicists carefully to differentiate the limma 256/243 = 22.63 savarts from its complement to the minor tone 135/128 = 23.12 savarts (256/243 × 135/128 = 10/9). Those two

140

INTRODUCTION TO MUSICAL SCALES

The

Jātis.

According

to

their

expression,

the

twenty-two

śrutis

are

divided

into

five

families,

or

jātis.

The

different

relations

which

can

be

established

between

these

five

families

allow

the

determination

of

the

notes

in

the

different

modes

(rāgas)

according

to

their

expression.

According

to

the

Saṅgīta

Ratnākara

and

the

Saṅgīta

Parijāta,

the

five

jātis

are

:

First

family

:

Dīptā

(shining,

illustrious)

contains

the

śrutis

:

Raudrī,

Vajrikā,

Ugrā

and

Tivra

(E+

,

F+,

B+,

)

(Ga+,

Ma+,

Ni+,

ReL-)

to

which

correspond

the

rasas,

or

emotional

flavours

:

marvellous,

heroic,

and

furious.

Second

family

:

Mṛduh

(soft),

of

which

the

rasa

is

'love',

contains

the

śrutis

:

Ratika,

Prītiḥ,

Kṣitiḥ

and

Mandā

(E,

,

Ab,

D-)

(Ga,

MaL+

DhaL,

Re-).

Third

family

:

Āyatī

(abundant),

of

which

the

rasa

is

comic,

contains

the

śrutis

:

Krodhā,

Prasāriṇī,

Sandīpanī,

Rohiṇī

and

Kumud-

vatī

(F,

,

A,

,

)

(Ma,

MaL-,

Dha,

NiL+,

ReL+).

Fourth

family

:

Madhya

(moderate);

rasas

:

comic

and

love;

śrutis

:

Chhāndovatī,

Raṇjanī,

Mārjanī,

Raktā,

Ramyā

and

Kṣo-

bhiṇī

(D,

,

G,

,

B,

C)

(Re,

Gab,

Pa,

Dhab,

Ni,

Sa).

Fifth

family

:

Karunā

(compassionate);

rasas

:

pathetic,

odious

and

terrible;

śrutis

:

Dayāvatī,

Ālāpinī

and

Madantī

(Eb,

A+,

)

(GaL,

Dha+,

NiL+).

The

jātis

are

not

scales,

but

analogies

of

expression.

It

is

impossible

to

build

a

scale

in

which

all

the

notes

have

a

similar

expression,

that

is,

in

which

all

the

notes

belong

to

the

same

jāti.

It

is

only

when

the

scale

has

been

built

according

to

the

general

rules

of

proportions

that

it

can

be

seen

whether

it's

dif-

ferent

notes

can

incline

themselves

towards

a

certain

expression,

enter

into

a

certain

jāti,

or

not.

THE RELATIONS TO A TONIC 141

The Five Jātis The tuning of the notes according to mood will, therefore, be :

142 INTRODUCTION TO MUSICAL SCALES

minor half-tone comma limma comma limma comma comma minor half-tone comma limma comma comma minor half-tone comma (MaL-) (MaL+) (Pa) (DhaL) (Dha) (Dha) (Dha+) (NiL+) (Nib) (Ni) (Ni+) (Sa) F F+ G Ab Ab A A+ Bb Bb B B+ C

Āyata (comic) Mṛduḥ (love) Madhyā (comic and love) Mṛduḥ (love) Madhyā (comic and love) Āyata (comic) Karuṇā (compassion) Karuṇā (compassion) Āyata (comic) Madhyā (comic and love) Dīpta (marvellous, heroic, furious) Madhyā (comic and love)

Prasāriṇī Pritiḥ Mārjani Kṣitih Raktā Sandipini Ālapini Madanti Rohiṇī Ramyā Ugrā Kṣobhiṇī Antara Ga Ma Pa Dha Ni

11 12 13 14 15 16 17 18 19 20 21 22 There are two kinds of Jātis. One, as shown here, refers to the classification of the śrutis. The other refers to the classification of the raga-jāti, is called śruti-jāti. The notes used in ascending and descending ; this is called jāti expression : the number of the number of scales according

146 INTRODUCTION TO MUSICAL SCALES

Affinities of the Notes

Ahobala

Rasa 1 comic heroism wonder anger love comic compassion

Bharata Śārṅga-deva Ahobala

Birth place Jambū dīpa Śaka Kuśa

Śārṅga-deva Ahobala

Seer (Rṣi) Agni (fire) Brahmā Moon

Śārṅga-deva Ahobala

Family Devas (angels) Ṛṣis (sages) Devas (angels)

Śārṅga-deva

Uttered by : Peacock Chātaka 2 Goat

Nārada Śārṅga-deva Ahobala

Caste Brāhmaṇa (priest) Kṣatriya (knight) Vaiśya (trader) Śūdra (slave)

Nārada Śārṅga-deva Ahobala

Colour lotus green or orange gold

Śārṅga-deva

Deities (Devas) Vanhi (fire) Brahmā Saras-vati

Nārada

Brahmā Fire ..

according to :

Ancient notes Sa Chaturtha (4th) Svarita Re Tṛtīya (3rd) Anudātta Ga Dvītīya (2nd) Udātta Ma Prathama (1st) Svarita Ma T. (F#)

Modern notes

Re Ga Ma Ma T. (F#)

THE RELATIONS TO A TONIC

147

comic disgust terror compassion love

comic love comic love compassion

Krauñcha Śalmali Śveta Puṣkara

Viṣṇu Nārada Tumburu Tumburu

Devas (angels) Pitṛs (ancestors) Ṛṣis (sages) Aṣuras (genii)

Heron Kokila (black cuckoo) Frog Elephant

Brāhmaṇa (priest) Brāhmaṇa (priest) Kṣatriya (knight) Vaiśya (trader) Śūdra (slave) Śūdras (slaves)

white jasmine black yellow all colours

Viṣṇu Śiva Gaṇeśa Sun

Soma Sun

Pa (G) Dha (A) Ni (B) Sa (C) Re K. Ni

Antara Ga Pa Krṣṭa Svarita Dha Pañchama (5th) Anudātta Ni Atisvāra Udatta Kākali Ni other altered notes

In the system of Hanumanta, used by Nārada, Bharata, and Śārṅgadeva, the general tonic is said to have been the Sa (modern Re=D), while the general tonic would have been the Dha (modern

1. In the system of Bharata, this explains the difference in the expressions attributed to the notes.

2 The Chātaka is a mythical bird which lives only on rain drops.

THE RELATIONS TO A TONIC

153

Relation to the tonic C (Sa)

C Sa + ++ 1/4 # L- L+ b 3/4 -- - D Re Interval (between two successive notes) 0 1 2 3 4 5 6 7 8 9

relation to tonic intervals

D Re + ++ 1/4 # L- L+ b 3/4 -- - E Ga 9/8 256/225 15/8 93/80 75/64 32/27 6/5 75/62 128/105 100/81 5/4 com. com. disjunction com. com. disjunction com. com. 9 10 11 12 13 14 15 16 17

relation to tonic intervals

E Ga + ++ 1/4 -- - F Ma 5/4 81/64 32/25 31/24 125/96 320/243 4/3 com. com. disjunction com. com. 17 18 19 20 21 22

relation to tonic intervals

F Ma + ++ 1/4 # L- L+ b 3/4 -- - G Pa 4/3 27/20 512/375 62/45 25/18 45/32 64/45 36/25 90/62 375/256 40/27 3/2 com. com. disjunction com. com. com. disjunction com. com. 22 23 24 25 26 27 28 29 30 31

relation to tonic intervals

G Pa + ++ 1/4 # L b 3/4 -- - A Dha 3/2 243/160 192/125 31/20 25/16 128/81 8/5 50/31 81/50 243/128 5/3 com. com. disjunction com. com. disjunction com. com. 31 32 33 34 35 36 37 38 39

relation to tonic intervals

A Dha + ++ 1/4 # L- L+ b 3/4 -- - B Ni 5/3 27/16 128/75 31/18 125/72 225/128 16/9 9/6 29/16 11/6 50/27 15/8 com. com. disjunction com. com. com. disjunction com. com. 39 40 41 42 43 44 45 46 47 48

relation to tonic intervals

B Ni + ++ 1/4 -- - C Sa 15/8 243/128 48/25 31/16 125/64 160/81 > 2 1 com. com. disjunction com. com. 48 49 50 51 52 53

20

Sixth Part CONFUSION OF THE SYSTEMS.

Greek Music.

IF we try to study Greek music from the works of Western scholars

it is extremely puzzling. A great number of ill-assorted intervals seem to be assembled in genera and modes which appear strange and ill adapted to the necessities of acoustics as well as to those of art. In addition to which, these genera, modes or intervals, are represented by ratios which, although mathematically very accurate, yet differ according to each theorist. When intervals are so ill-determined that such laxity in definition is possible, so much precision in measurement seems rather arbitrary.

If, however, we consider the peculiar position of Greek civilization,

it is easy to find the key of the enigma. But, first, we shall have to repudiate the legend by which we are made to believe that the Greeks invented everything. Far from having invented anything in music, the Greeks received all the elements of their musical system from Egypt and the Near East, a fact which they never attempted to conceal. But where they really showed their originality was when their physicists tried to explain the laws of that music with the help of a theory which they had received from another source, and which, in reality, was applicable to another system. Since the physicists' theory could never coincide with the system as used by the musicians, many compromises had to be invented. This explains the multiplicity of combinations and ratios proposed for each mode according to the fancy of the physicists.

Greek music, as it was actually played by musicians, being of modal form,

is necessarily included in the definitions of ancient Hindu music, because those definitions cover all the possibilities of such music. Greek music, like Egyptian music, most probably

168

INTRODUCTION TO MUSICAL SCALES

Greek denomination Proslambanomenos Hypate hypaton ""Parypate ""Lichanos ""Hypate meson ""Parypate ""Lichanos Mesa Paramese Trite diezeugmenon Paranete ""Nete Trite hyperbolaion ""Paranete ""Nete

Arabic denomination Lowest given Lowest of the principal tetrachord ""Medium ""Highest Lowest of the medium tetrachord ""Medium ""Highest Central sound Disjunctive sound Lowest of the disjunct tetrachord ""Medium ""Highest Lowest of the highest tetrachord ""Medium ""Highest

Modern scale C (Sa) D (Re) E (Ga) F (Ma) G (Pa) A (Dha) Bb (Ni komal) C (Sa) D (Re) E (Ga) F# (Ma tivra) G (Pa) A (Dha) B (Ni) C (Sa)

Ancient Hindu scale Ṁa Pā Dha Ni Sa Re Ga Ṁa Pā Dha kāli Ni Sa Re antara Ga Ṁa

Arabic scale G (Pa) A (Dha) B (Ni) C (Sa) D (Re) E (Ga) F (Ma) G (Pa) A (Dha) B (Ni) C# (Sa T.) D (Re) E (Ga) F# (Ma T.) G (Pa)

182 INTRODUCTION TO MUSICAL SCALES

The two tetrachords are separated by a major tone 9/8.

The Chromatic of the musicians gives, in each tetrachord, the intervals 32/27, 243/224 and 28/27.

248/224 (35.36 savarts) can be identified with the large half-tone (27/25 = 33.42 savarts), one comma larger than the major half-tone, and 28/27 (15.3 savarts) belongs to the same śruti as the minor half-tone (25/24 = 17.73 savarts). The tuning is therefore :

In the vulgar chromatic, the interval C A+ (Sa Dha+) is a trihemitone (major tone + limma = 32/27). In the softened chromatic, C A (Sa Dha) is a minor third (major tone + major half-tone = 6/5), therefore one comma larger than in the vulgar chromatic.

The tone G A+ (Pa Dha+) was, in the vulgar chromatic, a major tone (9/8). G A (Pa Dha), in the softened chromatic, becomes a minor tone.

This minor tone is divided, according to Didymus, into a major half-tone and a minor half-tone (16/15 × 25/24 = 10/9), but, according to Eratosthenes, it is 19/18 × 20/19 = 10/9 which stands for an equal division, and is called by the Arabs weak chromatic. According to Ptolemeus, the minor tone is divided as : 5/14 × 28/27 = 10/9. This is yet another scale, and called by the Arabs strong chromatic.

CONFUSION OF THE SYSTEMS

195

We can find here a remarkable confirmation of the theory by which it is stated that, the fundamental modes being connected with the cosmic developments of the cycle, only those modes which are related to the cosmic condition of a certain period appear natural during that period. In India, as in Europe, the ancient Dorian mode (Bhairavi), the mode of E (Ga), has slowly given place, as basic scale, to the mode of D (Re), Kāfi, only to be, in turn, replaced by the mode of C (Sa), Bilāval.

When we study in greater detail the significance of the notes according to Hindu theory, we shall understand why the major mode was formerly rejected. We shall see that its intervals express materialism, sensual egotism, hardness and other qualities which could not be given a dominant place in Art so long as it was subordinate to considerations of an intellectual and spiritual order.

When we want to pass from the abstract theory of the great perfect system to musical practice, we immediately notice the discrepancy. All these modes were, in reality, in use before their classification was made, and this way of bringing different modes within the frame of one scale, however clever it may be, does not really, nor in fact can it ever, fully correspond to the reality of modal systems. Therefore, the tuning of the notes in the general scale corresponds only approximately to the actual tuning for each mode. The tuning of all the notes in a mode, is done in relation to the tonic of that mode, and any note cannot arbitrarily be chosen as fundamental; or, if this be done, the modes so obtained can only be pseudo modes which, although they may outwardly appear as different modes, are only plagal forms of the original scale.

For any of these pseudo modes to become a real mode, it would be necessary to adjust the tuning of each note so as to establish, with the new tonic, the ratios which would justify this function. At first sight the notes might appear the same, but, in reality they present differences of one or two commas. This changes their expression and allows for the establishment of logical ratios.

208 INTRODUCTION TO MUSICAL SCALES

The Modes of Plain-Chant.

Very little is known to-day about the modal forms used in

Europe during the Middle Ages. There remain very few documents and no means of comparison with actually existing modal systems.

In the Middle Ages, the musical systems were not isolated from each

other as they later became. It seems, for example, that, in Spain, when Alfonso X the Wise introduced the teaching of music into the University of Salamanca, points of comparison were numerous between Christian art as codified by Saint Ambrosius and Saint Gregory, ancient art as explained by Boetius, and Arab art as defined by Avicenna in conformity with Greek tradition.

The re-

forms of Guido d'Arezzo had not as yet ruined popular art and that rich musical folk-lore which the troubadours were hawking from one end of Europe to the other, and of which few people now realize the importance, the richness and the beauty.

In our times

traces of it are rare and have never been studied by a musician having sufficient knowledge of modal music.

It is mostly in the

Nordic countries that some remnant of this "pre-harmonic" art of the West has survived, and the transcriptions attempted by Grieg, imperfect as they are, can give us at least an idea of this powerful and vigorous art now almost lost.

The only trace of mediaeval music which has kept some vital-

ity in the West is the religious music called plain-chant codified by Saint Gregory, and which, although extremely simplified, has kept, to our day, a system similar to that of the Greek Doristi (the Dorian modes and its plagal forms).

The main difference is

that the modes develop upwards instead of downwards and that the fundamental of the first tone is the seventh of the Doriar mode, the D (Re), (we have seen that the Dorian mode was the mode of E (Ga)).

The conjointed tetrachord, which contains an

augmented fourth, having become an integral part of some of the modes, we may often get an idea of what the practice of Greek modes was more easily from the simplified Gregorian modes than

THE WESTERN SCALE AND EQUAL TEMPERAMENT 209

from the theory of the Doristi which was made too abstract by a desire for symetry.

Imported from the East by Gregory the Great (540-604), who, on return from his post of ambassador in Constantinople, codified them in his famous Antiphonary, the eight modes of plain-chant are a transcription of Byzantine modes similar to the eight modes in which the Patriarch Severus of Antioch had already, in the fourth century, published tropes. Unfortunately, during their journey to Rome, these modes had lost the essential element of their differentiation, namely the measuring element, the pedal of the tonic, the Byzantine "Ison", essential element of all modal music, in relation to which each tone and the expression of each note is defined. These melodies are thus devoid of a basis and have a character ill-defined and an absence of expressiveness rather peculiar. Besides, their classification is as arbitrary as it is incomplete, because it has, as its principle, the permutation of the tonic, inspired of the Greek Doristi, a system which, being based on the peculiar concordance of certain modes, can be utilized as a means of classification, but can in no way be considered as the basis of modal structure. This is why the modes of plain-chant do not represent the system of metaphysical correspondences that Saint Gregory thought he had rediscovered. Therefore Dante wrote that Saint Gregory "laughed at himself when he opened his eyes in heaven," and rejected the classification given by him. Saint Gregory had not at all understood the basis of the system he pretended to adopt. He was a violent enemy of pre-Christian culture and whenever he could get hold of ancient books he had them burned; this was obviously not the best way to understand them. The modifications he brought into the modes and the substitution of heptachords for tetrachords are not justifiable and serve no purpose.

Although, on account of these deformations and of the lack of certain elements, they are deprived of their true expression, the Gregorian modes are, nevertheless, by their structure, real modes and, because of this, keep a certain appearance by which their use

27

THE WESTERN SCALE AND EQUAL TEMPERAMENT

211

Second mode (plagal)

(Yavanpuri Toḍi)

Dha Ni Sa Re Ga Ma Pa Dha or Sa Re GaK Ma Pa DhaK NiK Sa

Third mode (authentic)

(Bhairavī) (first Dorian)

Ga Ma Pa Dha Ni Sa Re Ga or Sa ReK.GaK.Ma Pa DhaK.NiK.Sa

Fourth mode (plagal)

(Aśvakrāntā mūrchhanā) (first Dorian)

Ni Sa Re Ga Ma Pa Dha NiK Ni or Sa ReK GaK Ma MaT DhaKNiK Ni Sa

Fifth mode (authentic)

(Gaur-Sārang) (Hypolydian)

Ma Pa Dha NiK Ni Sa Re Ga Ma or Sa Re Ga Ma MaT Pa DhaNi Sa

Sixth mode (plagal)

(Khammāj)

Sa Re Ga Ma Pa Dha NiK Ni Sa

212

INTRODUCTION TO MUSICAL SCALES

Seventh mode (authentic)

(Matsarīkṭa mūrchhanā)

F Pa Dha Ni Sa Re Ga Ma Pa or Sa Re Ga Ma Pa Dha NiḰ Sa

Eighth mode (plagal)

(Kāfi) (Phrygian)

Re Ga Ma Pa Dha Ni Sa Re or Sa Re GaḰ Ma Pa Dha NiḰ Sa

The first and the eighth modes are forms of the Phrygian mode, the third and the fourth are forms of the first Dorian, the fifth mode is a form of Hypolydian, the sixth and the seventh modes belong to the group Hypophrygian-Ionian-Hyperlydian.

The scale of Zarlino.

After numerous changes, mostly due to the attempts of theorists to adapt an incomplete and ill-understood Greek theory to an altogether different musical practice, the scale which was to be the basis of Western modern music was finally established by the Italian Zarlino (1540-1594) on the ruins of popular music.

"What are, according to the generally accepted theory of Zarlino, the elements of our modern system ?" asks Fabre d'Olivet.1 And he answers : "On seven diatonic sounds, C, D, E, F, G, A, B, (Sa, Re, Ga, Ma, Pa, Dha, Ni), three, C, F, G, (Sa, Ma, Pa) are correct : one D (Re) is alternatively correct and incorrect, being con-

1. Ea musique expliquée comme Science et comme Art. p. 41.

THE WESTERN SCALE AND EQUAL TEMPERAMENT

223

The failure of modern musicians to realize any effect from their transcriptions of Greek or Oriental modes comes from the fact that they always saw them through temperament, which disfigured their intervals and flattened their coloration, reducing practically everything to one unique mode, the temperate chromatic. We should not forget that, although it is comparatively easy to recognize a known mode or melody in its temperate approximation, it is often extremely difficult, if not impossible, to imagine its colour and expression if one has never heard its real intervals.

Unfortunately, instead of realizing, by contact with Greek or Eastern modes, the deficiencies of their own musical notations, many Western musicians, aided by their convenient evolutionist prejudice, prefer comfortably to consider that these modes, which they are unable to play, are "primitive", of small interest, and could add nothing to the achievements of modern Western music.

EIGHTH PART

THE SCALE OF SOUNDS.

Eighth Part

THE SCALE OF SOUNDS.

Need for a Scale of Sounds.

FOR the comparative study of the different musical systems, as well as for a correct execution of each one, it appears necessary to establish a scale of sounds which will allow a clear and accurate notation of all the usual intervals, an immediate ap-preciation of their nature and relative value. With the help of an accurate notation, the reproduction of the different scales on an appropriate instrument becomes very easy.

If we collect the intervals utilized in the different systems, we can see that their number and their combinations are not un-limited in practice. We have seen, while studying the Hindu theory, that the number of acoustic ratios having a distinct signi-ficance in relation to one sound considered as tonic is only twenty-two. But, by the permutation of that tonic, or simply by the permutation of the ratios between the different notes, the number of the different sounds within one octave is raised to fifty-three principal sounds, to which are added, in certain systems, either six secondary ones, — bringing the total division to sixty sounds, — or twelve quarter-tones, — giving a total division of sixty-six distinct sounds. This scale can be identified with the scale of fifths if the Pythagorean comma (5.88 savarts) is assimilated to the comma diesis (81/80=5.4 savarts), which means an approximation of one hundredth of a tone. This division is by no means arbitrary. It corresponds to the ideal structure of the octave. This is why it can be established on the basis of any one of the systems, either by the progressive rising of the notes in a series of modulations within the scale of Zarlino, or by the combinations and permuta-tions of the intervals necessary for melodic expression in the

THE SCALE OF SOUNDS

233

THE SCALE OF SOUNDS

233

THE SCALE OF SOUNDS

233

THE SCALE OF SOUNDS

233

THE SCALE OF SOUNDS

233

THE SCALE OF SOUNDS

233

THE SCALE OF SOUNDS

233

THE SCALE OF SOUNDS

233

THE SCALE OF SOUNDS

233

THE SCALE OF SOUNDS

233

THE SCALE OF SOUNDS

233

THE SCALE OF SOUNDS

233

THE SCALE OF SOUNDS

237

The Universal Scale of Sounds.

( 53 harmonic or cyclic intervals + 12 quarter-tones = 65 notes )

near-intervals in savarts

5

Notes

C (Sa) +

SCALE

CYCLE

HARMONIC SCALE

exact savarts

with ratios C (Sa)

exact savarts

serial number of fifth

5.88 (Pythagorean comma) 11.74

12th

17.61

24th

23.48

36th

28.52

48th

34.48

7th

19th

with ratios C (Sa)

81/80 (comma diesis)

5.4

128/125 (46/45) 1

10.33 (9.55)

25/24

14.24

256/243 (135/128)

17.73

16/15 (2187/2048)

22.63

27/25

28.03 (28.52)

33.42

135/124

36.89

intervals with C (Sa)

comma

2 commas

quarter-tone

minor half-tone

limma

major half-tone

large half-tone

3/4 tone

10

14

18

23

28

33

37

C (Sa) +

1/4 #

L- L+ b 3/4

1 2

3 4

5 6 7

The ratios within brackets are approximate ratios.

238

INTRODUCTION TO MUSICAL SCALES

CYCLIC SCALE

exact savarts, ratios with C (Sa), serial number of fifth

40.35, 46.12, 51.14, 57.07, 62.89, 68.76, 74.63, 79.68, 85.53, 91.4

31st, 43rd, 2nd, 14th, 26th, 38th, 50th, 9th, 21st, 33rd

31/2, 348/29, 33/28, 314/213, 336/219, 338/221, 25019/214, 39/221, 331/225, 338/229

49, 68, 83, 41, 80, 79, 4, 83, 93

HARMONIC SCALE

exact savarts, ratios with C (Sa), intervals with C (Sa), near-intervals in savarts, Notes

40.36 (41.39), 45.76, 51.14, 56.07 (57.99), 61.10 (62.15), 65.39, 68.88, 73.79, 79.18, 82.67, 86.12 (84.58), 91.51

800/729 (11/10), 10/9, 9/8, 256/225 (8/7), 59049/51300 (15/13), 93/80, 75/64, 32/27, 6/5, 75/62, 8000/6561 (243/200), 100/81

small tone, minor tone, major tone, large tone, small minor third, triminitone, minor third, small major third

41, 46, 51, 56, 61, 65, 69, 74, 79, 83, 87, 92

-, -, -, D (Re), +, ++, 1/4 #, #, L, b, 3/4, -, -

8, 9, 10, 11, 12, 13, 14, 15, 16, 17

THE SCALE OF SOUNDS 239

97.37 102.31 108.17 114.04 119.91 125.78 130.815 136.68 142.55 148.42 153.46 159.42 165.19

345/271 3/2 6 316/25 338/27 344/28 340/28 363/28 311/217 338/236 385/255 347/274 369/29 318/238 380/247

45th 4th 16th 28th 40th 52nd 11th 23rd 35th 47th 6th 18th 30th

102.31 (102.66) 134.70 (135.73) 148.06 (146.13) 165.79 (164.81)

96.91 102.31 107.21 111.15 114.64 119.54 124.94 130.36 134.70 139.18 142.67 148.06 152.97 158.36 161.85 165.79

5/4 81/64 (19/15) 32/25 31/24 125/96 320/243 4/3 27/20 512/375 (2187/1600) 62/45 25/16 45/32 (7/5) 64/45 36/25 90/62 375/256 (19/13)

major third ditone large major third small fourth fourth large fourth small augmented fourth harmonic tritone cyclic tritone large augmented fourth

97 102 107 111 115 120 125 130 135 139 143 148 153 158 162 166

E(Ga) + ++ 1/4 L- L+ p 3/4 -

18 19 20 21 22 23 24 25 26 27 28 29 30

240 INTRODUCTION TO MUSICAL SCALES

Cyclic Scale exact savarts 171.06 176.09 181.96 187.83 193.70 199.57 204.61 210.47 216.34 222.21 227.24 with ratios C (Sa) 32/21 66 31/21 80 68 39/21 58 77 39/21 81 50 69 33/24 serial number of fifth 42nd 1st 13th 25th 37th 49th 8th 20th 32nd 44th 3rd

Harmonic Scale exact savarts 170.7 176.06 181.49 186.39 (187.88) 190.33 193.82 197.71 (199.67) 204.12 207.61 209.52 216.45 221.85 227.24 with ratios C (Sa) 40/27 31/2 243/160 192/125 (19683/12800) 31/20 25/16 128/81 (19/12) 8/5 50/31 81/50 400/243 5/3 27/16 intervals with C (Sa) small fifth 6th large fifth small diminished sixth diminished sixth diminished sixth small sixth harmonic sixth cyclic sixth

near-intervals in savarts 171 176 181 186 190 194 199 204 208 212 217 222 227 Notes 31 - + ++ 1/4 # L b 3/4 - - A (Dha) + 32 33 34 35 36 37 38 39 40 41

THE SCALE OF SOUNDS 241

233.11 238.98 244.85 250.72 255.76 261.62 267.49 273.36 278.4 284.26 290.13 296. 301.84

315/238 327/248 339/261 351/280 310/215 322/234 334/258 346/272 357/297 317/226 329/245 341/264 353/288

15th 27th 39th 51st 10th 22nd 34th 46th 5th 17th 29th 41st 53rd

232.15 (234.08) 236.09 239.58 244.99 (243.04) 249.88 255.27 258.28 262.21 (260.67) 267.62 (268.84) 273.99 278.4 (277.91) 289.31 286.79 (287.21) 290.73 295.63 301.03

128/75 31/18 125/72 225/128 16/9 9/5 29/16 40000/2187 (729/400) 50/27 (13/7) 15/8 243/128 (256/135) 48/25 60/31 (31/16) 125/64 160/81 2/1

large sixth small minor seventh minor seventh minor seventh small seventh major seventh cyclic major seventh large major seventh small octave octave

232 236 240 245 250 255 259 263 268 273 278 282 287 291 296 301

++ 1/4 # L- L+ b 3/4 - B (Nii) + 1/4 - C (Sa)

43 31 44 45 46 47 48 49 50 51 52 53 1

242 INTRODUCTION TO MUSICAL SCALES

Numbers of Vibrations.

C (Sa) = 2⁹ =512 + =512 × 81/80 =518.4 ++ =518.4 × 81/80 =524.88 1/4 =512 × 31/30 =529.06 # =512 × 25/24 =533.33 L- =512 × 256/243 =539.35 L+ =512 × 16/15 =546.13 b =512 × 27/25 =552.96 3/4 =512 × 135/124 =557.41 -- =568.88 × 80/81 =561.85 - =512 × 10/9 =568.88 D (Re) =512 × 9/8 =576 + =576 × 81/80 =583.2 ++ =583.2 × 81/80 =590.49 1/4 =512 × 93/80 =595.2 # =512 × 75/64 =600 L =512 × 32/27 =606.81 b =512 × 6/5 =614.4 3/4 =512 × 75/62 =619.35 -- =632.10 × 80/81 =624.29 - =640 × 80/81 =632.10 F (Ga) =512 × 5/4 =640 + =512 × 81/64 =648 ++ =512 × 32/25 =655.36 ¼ =512 × 31/24 =661.33 -- =512 × 135/96 =666.66 - =682.66 × 80/81 =674.23 F (Ma) =512 × 4/3 =682.66

F+ =512 × 27/20 =691.2 ++ =691.2 × 81/80 =699.84 1/4 =512 × 62/45 =705.42 # =512 × 25/18 =711.11 L- =512 × 45/32 =720 L+ =512 × 64/45 =728.17 b =512 × 36/25 =736.88 3/4 =512 × 90/62 =743.22 -- =758.52 × 80/81 =749.15 - =512 × 40/27 =758.52 G (Pa) =512 × 3/2 =768 + =512 × 243/160 =777.6 ++ =777.6 × 81/80 =787.32 ¼ =512 × 31/20 =793.6 # =512 × 25/16 =800 L =512 × 128/81 =809.09 b =512 × 8/5 =819.2 3/4 =512 × 50/31 =825.80 -- =512 × 81/50 =829.44 - =853.33 × 80/81 =842.80 A (Dha) =512 × 5/3 =853.33 + =512 × 27/16 =864 ++ =864 × 81/80 =874.76 ¼ =512 × 31/18 =882.33 # =512 × 125/72 =888.88 L- =512 × 225/128 =900 L+ =512 × 16/9 =910.22 b =512 × 9/5 =921.6

AHOBALA

"Sañgīta Parijāta" Calcutta edit., 1884 (in Sanskrit).

AL FĀRĀBĪ

"Kitâbu L-Mûsîqî Al-Kabîr" (Arabic). (French translation by d'Erlanger, Paul Geuthner, Paris, 1939).

AMIOT (le P.)

"De la musique des Chinois tant anciens que modernes," Mémoires concernant les Chinois, vol VI, 1780).

ARGOS

"Dante et l'Hermétisme" (Voile d'Isis, 1931).

ARISTOTLE

"Physics" "Politics"

AVICENNA (Abû Ali al-Husayn ibn Abd-Allâh ibn Sîna)

"Kitâbu Š-Šifâ" (Arabic). (French translation by d'Erlanger, Paul Geuthner, Paris, 1935).

AVITUS

"Notes sur le Yî King" (Voile d'Isis, 1931).

BASU (Śivendranāth)

"Sañgīta Praveshikā" (in English and Hindi) (Benares Hindu University, undated). "Sañgīta Samuchchaya" (in Hindi) (Bhārata Kalā Parishada, Benares, 1924).

BHARATA

"Nātya śastra" (in Sanskrit) (Vidya Vilas Press, Benares, 1929).

BHATKHANDE (Pandit Viṣṇu Nārāyan)

"Hindusthani Sañgīta Paddhati" (in Hindi) (Bombay 1937).

BIOT (Édouard)

"Le Tchéou li ou rites des Tchéou" traduit pour la première fois du Chinois, (3 vol. Paris, 1851).

BOETHIUS

"De Musica" (in Latin)

BOSANQUET (R. H. M.)

"On the Hindu Division of the Octave" (Proceedings of the Royal Society March 1877—29 December 1877, London) (Reproduced in Tagore's "Hindu Music").

1. The description of some of the works quoted is incomplete because they were not within our reach at the time of printing this book.

BOUASSE (H.) "Acoustique Générale" (Paris, Delagrave, 1926).

BOURGAULT-DUCOUDRAY (L. A.) "Etudes sur la musique ecclésiastique Grecque", Mission musicale en Grèce et en Orient, Janv. Mai 1875. (Paris, Hachette, 1877).

BRITT (Ernest) "La lyre d'Apollon" (Editions Vega, Paris, 1931). "La Synthèse de la Musique" (Editions Vega, Paris, 1938).

BURNELL (A. C.) "The Arsheya brahmana of the Sâma Veda" Sanskrit text . . . . . with an introduction and index to words. (Mangalore, 1876).

CALLIAS (Hélène de) "Magie Sonore" (Librarie Vega, Paris, 1938).

CHACORNAC (Paul) "Michel Maier" (Voile d'Isis, No. 150-151, Juin-Juillet 1932).

CHAVANNES (Edouard) "Les mémoires historiques de Se-ma Ts'ien", traduits et annotés par, (Paris, 1895).

CLEMENTS (E.) "Introduction to the study of Indian Music" (Longmans, Green and Co., 39 Paternoster Row, London 1913).

COOMARASWAMY (A. K.) "The transformation of Nature in Art" (Harvard University Press, Cambridge, Massachussetts, 1935). "Beauté, Lumière et Son" (Etudes Traditionnelles, No. 206, Février 1937). "A New approach to the Vedas" (Luzac and Co., London, 1933).

COURANT (Maurice) "Chine et Corée", Essai historique sur la musique classique des Chinois, (Encyclopédie de la Musique : Delagrave, Paris, 1922).

DANTE "Divine Comedy".

DAVID ET LUSSY "Histoire de la notation musicale depuis ses origines" (Imprimerie Nationale, Paris, 1882).

BIBLIOGRAPHY DICTIONNAIRE DU CONSERVATOIRE

DUBROCHET (H.) "Mémoires sur une nouvelle théorie de l'Harmonie" (Paris, 1840).

EMMANUEL (Maurice) "GRECE", Art Greco-Romain, (Encyclopédie de la Musique, Paris, Delagrave, 1924). "Le Tyran Ut" (unpublished).

ENCYCLOPEDIE DE LA MUSIQUE et DICTIONNAIRE DU CONSERVATOIRE (Fondé par Albert Lavignac, Paris, Delagrave, 1922). Première Partie, Histoire de la Musique, I, Antiquité Moyen-âge : Egypte, Assyrie-Chaldée, Syriens, Perses, Hittites, Phrygiens, Hébreux, Chine-Corée, Japon, Inde, Grèce, Moyen-âge, Italie, Allemagne, France, Belgique et Hollande, Angleterre, Espagne, Portugal, Russie, Finlande et Scandinavie, Autriche-Hongrie, Tziganes, Arabes, Turquie, Perse, Thibet, Ethiopie, Birmanie-Cambodge-Laos-Siam, Annam-Tonkin-Cochinchine, Insulinde, Madagascar, Canaries, Amérique, Indiens Peaux-Rouges. Deuxième partie : Technique, Pédagogie et Esthétique.

ERLANGER (Baron Rodolphe d') "La Musique Arabe", 3 vol. (Librairie Paul Geuthner, Paris, 1930).

ETUDES TRADITIONNELLES, year 1936 to 1941, (Chacornac, 11 quai St. Michel, Paris).

FABRE d'OLIVET "La musique expliquée comme Science et comme Art" (Edit. Jean Pienasseau, Paris, 1928).

FETIS (F. J.) "Histoire générale de la Musique" (Published 1869).

FIROZE FRAMJEE (Pandit) "Theory and practice of Indian Music" (in English, Poona, 1938).

FOX STRANGWAYS (A. H.) "The Music of Hindosthan" (Clarendon Press, Oxford, 1914).

GASTOUÉ (Amédée) "La Musique Byzantine et le chant des Eglises d'Orient" (Encyclopédie de la Musique, Paris, Delagrave, 1924).

250 INTRODUCTION TO MUSICAL SCALES

GEVAERT "L'Histoire et la Théorie de la Musique dans l'Antiquité" (2 vol., Gand, 1875-1881). "Problèmes Musicaux d'Aristote" (1903). "Mélopée antique". GHYKA (Matila C.) "Esthétique des proportions dans la Nature et dans les Arts" (Paris, Gallimard, 1927). "Le nombre d'Or" (Paris, Gallimard, 1931). GROSSET (Joanny) "Inde, Histoire de la Musique depuis l'origine jusqu' à nos jours" (Encyclopédie de la Musique, Paris, Delagrave, 1924). "Contribution à l'étude de la Musique Hindou" (Paris, Leroux, 1888). "Bhâratîya-Nâtya-Çâstram. Traité de Bharata sur le Théâtre" texte Sanscrit, édition critique . . . ., (Paris, Leroux, 1888). GOUNOD (Charles) (Ménestrel, of the 22nd february, 1882). GUÉNON (René) "L'Esotérisme de Dante" (Editions Traditionnelles, 11 quai Saint Michel, 2e edit. Paris, 1939). "Le Roi du Monde" (Editions Traditionnelles, 11 quai Saint Michel, 2e edit. Paris, 1939). "Le Symbolisme de la Croix" (Editions Vega, 43 rue Madame, Paris, 1931). "Remarques sur la notation mathématique" (Etudes Traditionnelles, No. 205-206-207, Janvier, Février. Mars, 1937). "Les Arts et leur conception traditionnelle" (Voile d'Isis, No. 184, Avril, 1935). "Quelques aspects du Symbolisme du Poisson" (Etudes Traditionnelles, No. 104, Février, 1936). "La Langue des Oiseaux" (Voile d'Isis, No. 143, Novembre, 1931). "Orient et Occident"

(Editions Didier et Richard, 56 Rue Mazarine, Paris, 1930). HARIHARĀ NANDA SARASAWATI (Swāmī) "Śabda and Artha" (in Hindi) (Siddhant 1-43, Benares, 1941).

HELMOLTZ (Blaserna and) "Le son et la Musique", HELMOLTZ (H.) "Théorie physiologique de la Musique", fondée sur l'étude des sensations auditives. (Trad. de l'Allemand par G. Guéroult, Paris, V. Masson, 1868).

JONES (Sir William) "On the musical modes of the Hindus" (Asiatic Researches, vol. III p. 55, Calcutta, 1792). (reproduced in Tagore's Hindu Music).

KRISHNA RAO (H. P.) "The Psychology of music" (Bangalore, 1923).

KSHEMARĀJA "Commentaries on Shiva Sûtra Vimarshini" (Sanskrit Kashmir series, Vol. I Srinagar, 1911,) (French transl. André Préau, Voile d'Isis, No. 188-189, Aout-Septembre, 1935).

LALOY (Louis) "Aristoxène de Tarente et la Musique de l'Antiquité" (Paris, 1904).

LANGEL (A.) "La voix, l'oreille et la musique" (Bibliothèque de philosophie contemporaine, Paris, Germer-Bailliere, 1887).

LEBASQUAIS (Elie) "Tradition Hellénique et Art Grec" (Voile d'Isis No. 192, Décembre, 1935).

LEVI (Sylvain) "Le Théatre Indien" (Paris, Bouillon, 1890). Article "Inde" in the "Grande Encyclopédie".

LEVIS (J. H.) "Chinese musical Art" (Henri Vetch, Peiping, 1936).

MANSFIELD (O. A.) "The Student's harmony" (Theodore Presser Co., 1712 Chestnut street, Philadelphia London, Weekes and Co., 1896).

MENGEL (G. de) (Voile d'Isis, 1929, p. 494). NĀRADA "Nārada Śikṣa" (in Sanskrit) (Benares Sanskrit series, Benares, 1893).

OUSELEY (Sir W.) "An essay on the music of Hindustan" (Oriental collections, illustrating the history, antiquity, literature, etc. of Asia ; London 1797-1800) (reprinted in Tagore's Hindu Music).

PLATO "Timaeos",

"The Republic".

PLUTARQUE "Isis et Osiris" (traduction Mario Meunier) (L'Artisan du livre, 2 rue Fleurus, Paris, 1924).

POPLEY (H. A.) "The Music of India" (Associated Press, 5 Russell street, Calcutta. J. Curwen and sons Ltd, London, 1921).

PRÉAU (André) "Le secret des Mantras", commentaires sur le Shiva Sûtra Vimarsinî (de Kshemarāja) (Voile d'Isis, No. 188-189, Août-Septembre, 1935).

"Lie Tseu" (Voile d'Isis, No. 152-153, Août-Septembre, 1932).

"La Fleur d'Or" (Voile d'Isis, 1931).

QUINTILIANUS (Aristides) "De Musica" (in Latin) (Meibom).

RĀMĀMĀTYA "Svaramela Kalānidhi" (in Sanskrit) (edition and translation by M. S. Ramaswami Aiyar, Anna malai University, 1932).

RAOUF YEKTA BEY "La Musique Turque" (Encyclopédie de la musique, Paris, Delagrave, 1922).

RIVAUD (Albert) Notice et traduction du "Timée" (Platon, oeuvres completes, Société d'éditions 'Les Belles Lettres', 95 boulevard Raspail, Paris, 1925).

ROUANET (Jules) "La Musique Arabe" (Encyclopédie de la Musique, Paris, Delagrave, 1922).

ROUSSEAU (J. J.) "Dictionnaire de la Musique".

ROY (Hemendra Lal) "Problems of Hindustani Music" (Bhārati Bhāvan, Calcutta, 1937).

SERAPHIN LECOUVREUR (Le P.) "Li Ki ou Mémoires sur les bienséances", texte Chinois avec une double traduction (2 vol., Ho Kien Fou, 1906).

BIBLIOGRAPHY

'Le Cheu King", texte Chinois avec une double traduction en Latin et en Français. (Ho Kien Fou, 1896).

"Chou King", texte Chinois avec une double traduction (Ho Kien Fou, 1897).

SAFIYU-D-DIN AL-URMAWI "As Šarafiyyah" and "Kitāb Al-Adwār" (French translation by d'Erlanger, Paris, Paul Geuthner, 1938).

ŠĀRNGADEVA "Sangīta Ratnākara", with commentary of Kallinātha (in Sanskrit).

(Ānandāshram edition, Poona, 1897).

SOMANĀTHA "Rāga Vibodha" (in Sanskrit) (Lahore, 1901).

TAGORE (Sourindro Mohun) "Hindu Music", reprinted from the 'Hindoo patriot' September 7, 1874. (Calcutta, 1874).

"Hindu Music from various authors" (Calcutta 1875. 2e edit, Calcutta, 1882).

VISNU DIGAMBAR (Paṇḍit) "Rāga Praveśa" (in Hindi) (Bombay, 1921).

VOILE D'ISIS (Le) years 1929 to 1935, (Chacornac, 11 quai St. Michel, Paris).

VULLIAUD (Paul) "La Tradition Pythagorienne" (Voile d'Isis No. 170-171, Feb. March, 1934).

WEBER (A.) "Indische Lit. Geschichte" "Indische Studien"

"The History of Indian Literature", translated from the 2nd German edition by John Mann and Theodor Zachariae, with the sanction of the Author. (London, Trübner and Co., 1882).

WIDOR (Ch. M.) "Initiation Musicale" (Librairie Hachette, Paris, 1923).

WILLARD "Of Harmony and Melody" (Reproduced in Tagore's Hindu Music).

WOODROFFE (Sir John) "The Garland of Letters" (Varnamālā) Studies in the Mantra Shāstra. (Ganesh and Co., Madras. Luzac and Co., London, 1922).

INDEX

A

Abbaside Khaliphs

166

Abū Āli al-Husayn ibn' Abd-Allāh

ibn Sīnā, see : Avicenna.

acoustic, definition of the division

of śrutis, 123 ; — intervals, 24,

46, 197 ; — laws,

25, 92, 104,

176 ; — musical theory, grounds

of the Eastern , 137 ; — principles, 21 ; — ratios, 229 ; —

reality, 22, 74, 137, 204 ; — system,

196

adhibhautika (terrestrial),

111

adhidaivata (angelic, celestial),

111

adhyātma, or adhyātmika, (meta-physical),

111

Agni (fire, fire deity),

144, 146

ahamkāra (notion of individual ego),

127

AHOBALA,

130, 143, 146, 149 ;

system of —,

147

air, opaque to sounds, motionless,

106; — vibration, 105, 106

Ākāśa (ether), 7, 64 ; see also : ether

AKBAR, Emperor,

10

al-FĀRĀBĪ,

46, 126, 128, 161,

171, 179

ALPHONSO X the Wise, 208

altered notes,

143

ambitus (double octave),

133

AMIOT, the P.,

75

AMPION,

11

analogies of expression (Jātis).

140

animals' names attributed to the

notes, 144

Antiphonary,

209

anudātta (not raised) notes,

109,

146, 147, 152

anuvādī (assonant), 149

apotome (2187/2048),

78, 8c, 117,

123, 136, 164, 181, 197, 230,

245 ; complement of the —,

244

Arab, division into seventeen

sounds,

126, 128, 246 ; — divisions of intervals into halves,

179 ; — music,

133, 145, 160,

162 ; — scales,

168 ; — system

of modal music,

26, 230 ; — terms, 171 ; — theories, 46, 136,

230

Arabs, 109, 122, 124, 126, 129,

139, 150, 160, 161, 162, 166,

1. Figures in italics refer to important definitions.

256

INTRODUCTION TO MUSICAL SCALES

170, 182, 183 ; basic division

two, 12, 62, 66, 69, 75 ; — used by the —, 124 ;

ARCHYTAS,

178, 186

ARGOS,

13

arithmetic mean (4/3),

164, 165

ARISTIDES QUINTILIAN,

47, 166, 177

Aristotelian, body of harmony,

50, 109, 167 (see also : harmony, body of, ) ; — physics, 125

ARISTOTLE,

109, 148, 157, 167, 218

ARISTOXENES,

135, 196; scale of —, 47

āroha (ascending scale),

148

arpeggio,

102

artha (significance), esoteric,

9

ascending, part of day and night

(male) 150 ; — scale, 29, 30, 110, 174, 176, 244 ; — scale (āroha), 148 ; — series, 29, 67, 233

assonant (anuvādī),

149

astrological correspondences,

68

Asuras (genii),

147

aśvakrāntā mūrchhanā,

119, 211

ati-komal (flat by two intervals),

42

atisavāra (extreme note) B (Ni),

110, 147

A.U.M., the monosyllable,

8

authentic modes in Gregorian music,

192, 210-212

autumn,

71, 87, 89, 91 .

auxiliary, degrees or sounds, the

tonic, 110

avaraha (descending scale),

148

AVICENNA,

136, 162, 171, 208

AVITUS,

58

āyata (abundant) jāti,

140-142

B

Bacchus,

148

BALZAC, H. de,

227

Barbarian ( = Phrygian ) harmonies,

167

basic, note, perfect relation with a,

41 ; — sound, 23, 196

beats (variations of intensity),

45, 219, 221

BEETHOVEN, L. von,

27, 83

BERLIOZ, Hector,

152

Bhairavī, mode of E (Ga),

114, 189, 211 ; — = Dorian mode, 195 ; — ṭhāṭ (modal scale), 114. 143, 165

BHARATA,

101, 112, 116, 122, 146 ; scale of —, 116; system of —, 147

Bilāval, rāga (the Hindu major mode),

114, 118, 215 ; — mode of C (Sa) 195 ; — ṭhāṭ (modal scale), 114, 143, 165

bindu,

7

birthplace of the notes,

146

BLASERNA,

220

BOETIUS, 162, 178, 179, 197, 208, 210 BOSANQUET, R. H, 124 BOURGAULT-DUCOUDRAY, 26 Brahmā (the creator, in the Hindu trinity), 101, 144, 146 Brahman (the first undifferentiated Principle), 8, 128 Brāhmaṇa (a member of the priest caste), 143, 146, 147 brass instruments, 31 BRIT'T, E , 137, 217, 218 buddhi (intellect), 127 Byzantine, chant, 27 ; — ison ; — modes, 209 ; — music, 26, 27 ; — peoples, 139, 160 cantores of the primitive Christian church, 194 castes, the four, 64 ; — of the notes, 144, 146 CHAVANNES, M., 73 'cello, 90 Celtic modes, 22 cents, 40 CHACORNAC, Paul, 11 Chaldea, 216 Chaldeans, 13 Chaldeo-Assyrians, 70 chataka (a mythical bird), 146, 147 chaturtha (the fourth note) = C (Sa), 110, 146 33

INDEX 257

CHÉNG, crown prince, 63 CHÉNG HYUÂN, 68 CHEÛ, the dynasty of the , 63 Cheu kwân, the, 56 CHEÛ KYÛ (544-520 B.C. c.), 63 Cheu lû, 89 chhandah (harmony), 9 chhandovatî śruti, 131, 14:, 141 ; — = the measuring sound, 27 CHHÊN CHÓNG-JÛ, the scholar, 72 Chhāyānaṭa (a Hindu mode), 193 CHI, Prince of ( 522 B.C.), 63 chi (fifth. = G (Pa)), 17, 74, 82, 89, 91 ; modified — (pyén chi= myeú), 75, 79, 91 ; sharp — Âb (Dha b), 80 chY-shî, the seven beginnings, 62, 63, 87 Chîn, the land of, 66 Chinese, division of the octave, 90, 124 ; — great year (yuên), 68 ; — music, 30, 32, 55-94, 124, 152, 160 ; — musical system, 30, 57, 62, 93, 160, 231 ; — numbers to represent the notes, 74 chông-lyù (lyû XII), the eleventh fifth F+ (Ma+), 79, 86, 87, 220 chông (bell), 86 CHOPIN, F., 5, 83, 221 chord, of the first harmonics, 47 ; fundamental of a — , 27 ; meaning of a — , 5, 26, 101, 203, 204

258 INTRODUCTION TO MUSICAL SCALES

chords, 31, 32, 99, 103, 104, 196, 203, 216-218, 221, 222; consonant -, 203, 221; structure of -, 104, 130, 203 chromatic, division, equalized, 70; - division of the octave, 180; - genus, 167, 170, 171, 180-185, 207; - of the musicians, 182; - of the physicists, 181; - scale, harmonic form of the, 121; - scale, mode corresponding to the, 184; - series, 88; softened -, 182, 183; strong -, 182, 183; temperate -, 223; vulgar -, 181-183; weak -, 182, 183

CLEMENTS, E, 135 colour, black (north), green (east), red (south), white (west) and yellow (centre) emperors, see: emperors; black -, 60, 90, 91, 144, 147; blue -, 90, 91; gold -, 144; green -, 146; jasmine -, 144; lotus -, 144, 146; orange -, 146; red -, pale, 60; reddish-yellow -, 144; variegated -, 144; white -, 60, 90, 91; white jasmine -, 147; yellow -, 60, 83, 86, 90, 91, 144, 147 colours, of the notes, 89, 90, 91, 144, 146, 147; relations of -, 26; the seven - of the spectrum, 13, 62, 107

comma, 14, 15, 176; - diesis (81/80 = 5.4 savarts), 40-43, 111-113, 122, 124, 135, 154, 229, 231, 234, 237, 243; double -(46/45 = 10 sav.), 175, 178, 243; - = interval, 11; interval of one -, 90, 92; Pythagorean -(319/219 = 5.88 sav.), 67, 72, 77, 112, 124, 229, 233, 234, 237, 243

CONFUCIUS (KONG-TSE), 6, 14, 60, 85 consonance, 24, 123, 164; - of fifths, 170, 185; fundamental -, 172

COOMARASWAMY, A. K., 15, 111 correspondences, between the aspects of manifestation, 6, 61, 143; - between sounds and the aspects of the universe, 11; - of the notes, 91, 143, 144; - of the notes, emotional, 103, 129, 216; psychological -, 129 cosmic, circles, the twenty-one, 125; - condition of a certain period, 195; - correspondences, 103; - cycles and the tonic, 113; - data, actual, 165; - laws, 48; - limits, transgression of, 56; - medium, limitless, 106; - order, 16; - period, note adapted to the, 30; - spheres, 12

cosmogonic principles, the two, 61 cosmogony, 58

INDEX 259

cosmological, significance of numbers, 74 ; - theory, 7

counter-point, 205, 207

COURANT, Maurice, 17, 25, 53, 64, 220

creation, process of the world's, 58; laws of -, 100

cycle, 14, 29, 50, 220 ; annual -, 87, 152 ; cosmic development of the -, 195 ; deterioration of the -, 126 ; - of equinoxial precession, 68 ; - of fifths, 29, 55-94, 112, 152, 215 ; - of fifths, graphic representation of the, 76 ; numbers of each -, 68 ; numerical -, 65 ; - of 45,524, of 25,920 solar years, of 666, 68

cyclic, divisions into twelve, 71 ; - intervals, 230 ; - scale, 234, 237-241 ; - system, 29, 55, 152, 160, 196, 203, 236 ; - system, the fourth in the, 236 ; - system of the Pythagoreans, 185

cymbals, 29

D

DAMO, 16

DANTE, 3, 6, 12, 13, 125, 209

DAVID and LUSSY, 93

day, cycle of, 29 ; divisions of the -, 149, 150 ; - and night, conjunction of, 151 ; note adapted to the -, 30

dayāvatī śruti, 130, 131, 140, 141

degree, second ascending -, 64 ; seventh -, 64 ; sixth -, 67 ; - of the scale, 12, 17, 63, 67, 72, 74 ; - of the scale, correspondences of the, 91 ; - of the scale, the seven, 62, 63

Deities of the notes, 144, 146

demiurge, 163

descending, interval, 179 ; - part of day and night (female), 150 ; - scale, 29, 30, 110, 148, 166, 174, 176, 184, 244 ; - series, 67, 233

deśī (regional), music (= gāna), 100, 152 ; - rāgas, 111

devas (angels) or devatās, 9, 143, 146, 147 ; - deities of the notes, 146

Dhaivata (deceitful), the sixth degree of the Hindu scale, 108-110

dhvani (sound), 102, 106, 107

dhikr, 9

diabolus in musica (tritone), 151

diapason, Hindu usual, 197 ; - = octave, 11 ; pitch of the -, 72, 113, 145 ; rise in the -, 73 ; Western modern -, 75, 145, 197

diapente, = fifth, 11

diatonic, 188, 204, 206 ; - division of the scale, 169, 181 ; - genus, 167, 170, 171, 185-191, 198, 207 ; - half-tone, 41, 43, 45 ; - of the physicists, 166 ; - scale, 6, 28,

41, 112-115, 117, 217; - scale = grāma, 169; - scale, modern, 143, 234 ; - scale, unlimited, 113 ; - series, 111, 113; - sounds, the seven, 207, 212, 213 ; vocal -, 169; vulgar -, 169 DIDYMUS, divisions of, 178, 179, 182-184 diesis, 154, 170, 172, 178, 180, 186 ; comma -, 229, 231, 234, 237, 243 ; division into twenty-four -, 177, 180, 181 ; - = śrutis, 180 dimensions, the three, 65; the third -, 65, 125 dīpak rāga (mode of fire), 10 dīptā jāti (shining, illustrious), 140-142 directions of space, 12, 64, 85, 86, 91 disjunct, perfect group, 168 ; - tetrachord, 167, 168 disjunctions in the harmonic scale, 153, 154 disjunctive of the central sound, 168 dissonant, ratios, 48, 196, 221, 236 ; - = vivādi, 149 dithyramb, 148 ditone (third of the scale of fifths = two major tones = 81/64), 11, 41, 78, 91, 13c, 170, 172, 239 ; - = E + (Ga +), 9c ; see : kyō division, of the day, 150; equaliz-

ed - of time, space and sound, 70 ; - of the first order, 123 ; - of the second order, of the third order, of the fourth order, etc., 124 ; - of the octave, 11, 41, 123, 125, 134, 181, 245, 246 ; - of the octave, chromatic, 180 ; - of the octave, harmonic, 153 ; - of the octave into seven sounds, 181 ; - of the octave into twelve, cyclic, 12, 13, 71 ; - of the octave into twelve half-tones, 70, 71, 181 ; - of the octave into seventeen intervals, 17, 124, 125, 126, 128, 137, 181, 246 ; - of the octave into twenty-two intervals (śrutis), 122, 124, 125, 133, 136, 181, 245 ; - of the octave into twenty-four (diesis), 177, 180, 181 ; - of the octave into fifty-three intervals, 41, 45, 46, 68, 112, 124, 152, 229, 234, 236, 245, 246 ; - of the octave into sixty intervals, 11, 12, 25, 72, 229, 246 ; - of the octave into sixty-six intervals, 229 ; - of the octave into three hundred and fifty-eight intervals, 124 ;

• of the octave, Western, 136; - of the scale of sounds, 41, 107, 116, 151; - of sound, 63, 103-105, 107, 108; - , articulate, 108; - , equal (temperate), 70, 134, 179, 182, 184; - of the tone, 175 dodecagon, star, 71 dodecahedron, 13 Dodekachordon (1517), by Glareanus, 215 dominant, note (vadi), 148, 149, 162, 178, 210; pseudo -, 111, 190 Dorian, first, 188, 189, 190, 192, 211, 212; first - (= Sa grama), 111; - harmonies, 167, 185, 187, 189; hyper -, 198; hyper - tone, 197; hypo - (= Eolian), 192; hypo - tone, 188, 190, 192, 193, 198; - mode, 111, 148, 166, 174, 185, 187, 196, 208; - mode (= Bhairavi), 114, 195; - modes, the two, 74; second -, 188, 189; second - (Ma grama), 111; - tone, 197 Doristi, Greek, 28, 208, 209 DUBROCHET, H., 32 Durga raga (a Hindu mode), 181 dvitiya (second), second degree of the ancient Hindu scale, 110, 146 dwipa (continents), the seven, 62, 144, 146

ear, judgment of the, 10, 34; limits of discrimination of the -, 24; sensitiveness of the Earth, 11, 14; the element -, 83, 85, 86, 88, 91, 105; Heaven and -, 64, 74; - influx, 57, 83; - (khwen), 59, 60; - manifested in sounds, 72; number of the - "5", 89 Eastern, modes, 223; - music, 27, 32, 94, 174; - musical theory, 137 Egypt, 64, 159, 171, 185, 216 Egyptian, doctrine, 10; - music, 159 elements, the five, 12, 64, 231; - corresponding to the degrees of the scale, 91; influence upon the -, 61; theory of the -, 104 EMMANUEL, Maurice, 27, 137, 170, 172-174, 194, 216 emperors, 84, 85, 91; black (North), green (East), red (South), white (West) and yellow (Centre), celestial -, 61, 85, 86, 87 enharmonic, 30, 171, 185, 204, 213; - division of the octave, 133, 175, 180; - genus, 167, 170, 171, 172-177, 178, 181, 207; - interpretation of the notes, 177; - notations, 169; - scale, 121, 122, 137, 169; vocal -, 173

Eolian, mode, 190, 192; - mode = Yavanpārī Toḍi, 189; - tone, 68, 236; 52nd -, fifths above 197, 198; - tone, hyper, 197, 198; - tone, hypo, 198 equinoxial precession, 68 ERATOSTHENES, 182-184 ERLANGER, Baron R.d', 128, 135, 136, 139, 160, 167, 171, 179 ether (ākāśa), 7, 64, 105-107, 232; sound, quality of -, 105; vibration of -, 106 EUCLID, 117 evocation, phenomenon of musical, 6, 9, 10, 24, 49, 143, 205

262 INTRODUCTION TO MUSICAL SCALES fifths, consonance of, 170, 185; cycle of -, 33, 55-94; cycle of -, graphic representation of the, 76; female -, 71, 73, 76; modal -, 111, 189-194; numbers representative of the -, 76, 234; numbers of the -, serial, 237-241; scale of -, 11, 46, 68, 69, 72, 73, 77, 104, 213, 229-232, 234; series of -, 25, 67, 70, 76, 233; spiral of -, 14, 15, 65, 69; succession of -, order in the, 77; tuning by means of -, 169; four -, the first, 74; five -, difference of, 244; five -, the first, 62, 72; twelve - and seven octaves, 71; twelve -, cycle of, 14, 71; twelve-, intervals of the first, 75; twelve -, successive series of, 67; fifty-three -, periods of, 68; sixty -, the first, 72, 76 figured bass, 45 fire, deity (Vahni), 144, 146; - element, 72, 89, 91, 105; - līt, 59, 60; - luminary, 150, 151; mode of - (Dīpak rāga). 10; numbers of -, 89

F FABRE d'OLIVET, 1c, 13, 30, 33, 75, 205, 207, 210, 212 FETIS, F. J., 93 fifth, ascending (= lower generation), 73; - conflict with octave, 25; - degree, G (Pa), 103, 143; flattened -, 30; large -, 80, 240; modifications of the -, 128, 133, 177; - note (Pañchama), 63, 108-110, 116, 147; - note (pañ-chéan), 63; passive character of the -, 73; small -, 80, 240; - as subsidiary tonic, 232; 1st - (lýū II), 75; 4th -, intervals beyond the, 233; 5th successive -, 67, 232, 233, 244; 6th -, 73, 233, 236; 12th -, 68,

FIROZE FRAMJEE, Paṇḍit, 118, 121, 133

flat, 45, 129, 136, 143, 151, 174, 214, 215, 222 ; double -, 137 ; - = komal, 30, 213 FŌ-HI, 57 fourth (4/3), 79, 239 ; augmented -, 73, 151, 152, 208, 233 ; augmented - = tritone, 91 ; the cyclic -, 236 ; - (chaturtha), 110, 146 ; - essential element of the modal system, 236 ; half of the interval of -, 170 ; large - (27/20, F + (Ma +)), 79, 112, 118, 239 ; large augmented --, 80, 239 ; perfect -, 73, 112 ; scale of the - (Ma grāma), see : grāma; sharpened -, 30 ; small -, 79, 239 ; small augmented -, 79, 239 ; tonic on the -, 74, 190, 194, 232 Freischutz, the, by Weber, 152 frequencies, 40 frets, movable, 244, 245 ; - of the vīṇā, 125 fundamental, degree (kūṭing), 75, 88, 91 ; - note, 22, 23, 72, 84-86, 111, 113, 114, 116, 189, 191, 203, 208 ; - of a chord, 27, 203 ; - sound, 47, 48, 65-67, 218 ; tonic on the -, 74

me (French), gamut (English), for scale, 139 gāna (= deśī) music, 100 Gāndhāra (pleasing to celestial beings), the third degree of the Hindu scale, 108-110 ; - grāma (scale of E), 111, 116 Gāndharva music (= mārga), 100, 101 Gaṇeśa, 144, 147 GASTOUÉ, Amédée, 26, 206 Gaur-sāraṅg (a Hindu mode), 193, 211 GENGHIS KHAN, 22 genus, 159, 166-172, 181, 207, 210 GEVAERT, 24, 27, 145, 173 ghaṭikā (= twenty-four minutes), 150 Gitanos, modes of the Spanish. 22 GLAREANUS, 215 glissando, 161 GLUCK, 5 GOUNOD, 24 grāma (basic scale), 37, 112-113, 116, 118, 139, 169 ; Ga -(scale of the third), 111, 116 ; Ma - (scale of the fourth), 41, 74, 111, 115, 116-118, 120, 122, 149, 189, 190-192 ; Ma - (= second tonic), 41, 74, 111, 115-119, 122, 126, 141, 188, 191, 192 ; the lost -, 126

G gama (Prākrit), gamāl ah (Arabic), gamma (Greek and Latin). gam-

great perfect system, Greek, 167, 169, 186, 187, 189, 191, 194

Greek, graphic system of the, 169; -instruments, 93; -modes, 26, 162, 169, 208, 210, 223; -modes, transcription of the, 163, 223; -music, 27, 93, 111, 133, 145, 159-198; - musicians, 26, 134, 185; - physicists, 26, 159, 160, 176, 180, 185, 186, 196, 197, 243; - physicists, measurements given by, 178; - scale, 113; - scale, unaltered, 197; - tones of transposition, 197-198 Gregorian, modes, 192, 208, 209, 210-212; - plain-chant, 149, 210 GREGORY the Great (540-604 A. D.), 209 GRIEG, E., 208 GROSSET, J., 134, 138, 139 GUÉNON, René, 7, 9, 12, 16, 57, 65, 105, 106 guṇas (the three fundamental qualities), 59 Guṇakali (a Hindu mode), 173, 175-178 GUIDO d'AREZZO, (990-1040 A. D.), 139, 206, 208

39-45, 77, 112, 174, 177, 180, 182, 183, 185, 230, 231, 237, 244, 245; minor - (25/24), 39-45, 48 77, 128, 135, 141, 142, 174, 178, 180, 182, 183, 185, 221, 231, 234, 237, 244, 245; small minor -, 186; - = two śrutis, 115, 135; temperament by -s, 135; temperate -, 40, 48, 221 HÁN, dynasty, 12; - period, 72 Hán shū, the, 63 Hân-chöng (=lîn-chöng, lyü II, G(Pa) ), 87, 88 HANUMANT'A, 147 HARIHARĀNAND SARASWATI, Swāmi, 8, 102, 107, 129 harmonic, basis of melodic music, 23; - division of the octave, 152, 153; -F1/4 and flat B, 49; - form of the chromatic scale, 121; -interval, 41, 46, 103, 175, 213, 230, 232, 237; - medium division, 164; - music, 103, 145, 163; - relation, 8, 23, 41, 69, 230, 231, 245; - scale, 112, 130, 131, 237-241; universal - scale, 232, 234; seventh -, 81, 241; - system, 31, 101, 102, 205; harmonics, 22, 23, 47, 48, 50a, 216; natural -, 56; reinforced -, 23; scale of -, 49; the series of -, 48-50, 65 harmony, 9, 23, 27, 31, 32, 101,

H half-tone, diatonic, 41, 43, 45; discontinuity at every -, 234; division of the octave into -s, 70, 181; large - (27/25), 42, 77, 174, 182, 237; major - (16/15),

203, 205, 207 ; body of -, 50, 109, 162, 167, 170, 189 ; laws of -, 7, 9, 46 ; simultaneous -, 103, 205, 219 ; - of spheres, 12, 16 ; successive -, 210 hearing, perceptions, 105 ; sensitive organ of ether, 107 Heaven, and Farth, 64, 74 ; - = khyên, 59, 60 Hebrew alphabet, 125 HELMOLTZ, 220 heptachords, 209 HERMES, 13 HEÛ-LÍ-CHĂ, 64 hexacordums, durum, molle and naturale, 139 hexagon, 71, 170 hexagrams, the sixty-four, 61 HILDEPHONSE, Bishop, 127 Hindu, division of the octave, 124, 128,-129, 137 ; - origin of the Western scale, 139 ; see also : śruti and răga HÔ CHHÊNG-THYÊN (370-447 A. D.), 220 HOLDER, 68 Hû, the bull, 64 Hu-si (Western lamentation), 86 Hārāsān tunbūr, 126, 128 hwâng-chông (lyŭ I = C (Sa) ), 74, 75, 77, 82, 83, 87, 220 HWÔ, the physician (541 B. C.), 66 Hwð (auxiliary degree, B+(Ni+) ), 75, 82 34

HYAGNIS, the Phrygian, 93 HYÂO-WÊN, the Emperor (477-499 A. D.), 61 hypo, the prefix, 192

Iasti (Ionian mode), see : Ionian Iastian, hyper, 198 ; hyper - tone, 197 ; hypo - tone, 198 idea, evocation of, 25, 48, 49 ; manifested -, 129 ; - (sphoṭa), 106, 107 image, evocation of an, 31, 48, 49 ; substance of an -, 231 Indian music, 133, 138 influx, female and male, 152 ; - of the lyŭ, 72 ; terrestrial -, 68 ; Yîn and Yâng -, 86, 87 instruments, accurate, 244 ; fixed-scale -,219 ; temperate -, 104, 130 inter-stellar absolute cold, 106 intervals, 77-82 ; approximate half of -, 179 ; female and male -, 74 ; functional difference of -, 230 ; - invented by Greek physicists, 243 ; measure of -, 39 ; melodic -, 230 ; - musically identical, 230 ; - musically utilized, 236, 245, 246 ; - of the second, third, etc., order, 124 ; - smaller than a comma, 77 ; theoretical -, 214, 243

Ionian mode (or Iasti), 191, 192, 212, 215

irka (quarter-tone), 136 ison (equal), 20, 27, 209

J

jagat (that which moves = the universe), 8

JAIMINI, 106 jamāh (Arabic for scale), 139 jāti, the five families of expression, 140, 141 ; rāga -, 142 Javanese classical music, 32 Jayajavanti (a Hindu scale), 193 jñāna indriyas (senses of perception), 127 JONES, Sir William, 33, 137 jwei-pin (lyü VII, F# (MaL+)), 79, 86, 87, 152

K

Kabbala, 125 KĀBIR, 8 Kafi (mode of D (Re), a Hindu mode), 114, 118, 193, 212 ; - that, 114 kakāli Ni (pleasing Ni, raised Ni), 109, 117, 118, 141, 147, 168 KALLINATHA, 151 KAŅĀDA, 105 karma indriyas (senses of action), the five, 127

karuṇā (compassionate), jāti, 140, 141, 147, 168 ; - rasa, see : rasa Kēn (the mountain), 59, 61 Khammaj (a Hindu modal scale), 194, 211 Khan (the water), 59, 60 Khăng hī tseú tyèn, phonetic tables of the, 64 khîn, tuning of the, 72 khwēn (Earth), 59, 60 khyèn (Heaven), 59, 60 KING, the King (544-520 B.C.), 63 KĪNG-FÂNG (45 B.C. c.), 25, 58, 84, 220 ; system of -, 76 komal (flat), 42, 45, 143 KONG-TSE (Confucius), 14, 60 ; see also : Confucius Kranfcha dwipa (a continent), 144, 147 krṣṭa (pulled, dragged) = G (Pa), 110, 147 kṣatriya (knight), 143, 146, 147

KṢEMARĀJA, 7 kṣobhini śruti, 131, 132, 140, 141, 142

kū-syèn, (lyü V, E+ (Ga+)), 74, 78, 85, 86 kūng, or kōng, (the tonic, the fundamental degree C (Sa)), 6, 16, 64, 74, 75, 77, 82, 88, 89, 91 ; modified - (pyén-kūng), 75, 82 ; sharp -, D#b (ReL+), 77 Kuvera (God of wealth), 144 kwá (trigrams), the eight, 58

Kwē yù, the, 63

kyă-chŏng, ḃ (Gab), 78, 83, 84, 86 kyēn (intermediaries), 76 kyŏ (ditone, E + (Ga+)), 16, 74, 78, 89; sharp-(F+(Ma+)), 79

L

Lakṣmī, 144 LANGEL, A., 220 lă-pă-pŭ, 64 LAVIGNIAC, Albert, 53 laws, of music, 6, 11, 27, 100; - of physics, 137, 218; physical -, 46, 48, 49, 218; - of sounds, 56, 70, 108 LEBASQUAIS, Elie, 11, 16 LEVIS, J. H., 74 LEVI, Sylvain, 99, 109 LIE TSEU, 7 light, identified with the fire element, 105 Li Ki (memorial of rites edited by Confucius), 6 limma, Pythagorean (256/243), 39-45, 123, 129, 132, 164, 197, 214, 230, 232, 237, 244, 245; -complement of the minor tone (135/128), 132, 175, 230, 232, 233, 237; division of the -, 179 lĭn-chŏng (lyŭ II, G(Pa)), 74, 80, 84, 85, 220; - = hân chŏng, 88 lĭnga, 57

LINOS, 93

LISTZ, Franz, 83, 221 logarithms, 40, 76, 134 LOUIS the ninth, King, 210 LUTHER, Martin, 210 Lydian, mode, 74, 192; hyper-mode, 74, 191-193, 196, 211, 212; -tone, 197, 198; hyper-tone, 197; hypo-tone, 197, 198 LYEÛ.CHÖ (d.610), 220 LYNG-LUN, 30 lyra, 12; - of Hermes, 13; sounds of the -, 11 lyŭ, 25, 56, 72, 74, 83, 84, 86-88, 152, 179; double-(low pitch), 85; - of each month, 57, 84, 85; even and odd -, 86; half-(high pitch), 85; names of the -, 77; scale of the -, 75; the seven -, 63; the six -, 63; the sixty -, 12, 58, 72, 76, 77; - = sound pipe, rule, 76, 86; - taken as tonic, 72; the twelve -, 12, 58, 72 lyù (help, accessory), 86 lyù-chĭ-chhwĕn-tshyeŭ, 73

M

Ma, see: Madhyama; - grāma, see: grāma MABILLON, 127 macrocosm, 48

madanti śruti, 130, 132, 140, 142 Madhyama (middle sound), the fourth degree of the Hindu scale, 109, 110, 111; - grāma, see : grāma Mahābhārata, 55 manas (mind), 127 manes, 61 ; - (pitṛ), 68 . mantras, Hindu, 9 Manu smṛti, 96, 105 Manvantara, Hindu, 68 mārga (directional) - Gāndharva music, 100, 101 mārjanī sruti, 130, 140, 142 MARSYAS, 93 MARTINI, 205, 207 mathematical, half-tone, 136 ; - interval, 24, 25 MATGIOI, 60 Máyā, 8 Máyāvadins, 127 Mediaeval, music, 208 ; - tonic, 118 Megh-mallar (Hindu mode of the rains), 206 melodic, figures, 23, 148 ; - music, harmonic basis of, 23 ; - scale, simplest, 232 melody, 28, 29; significance of the -, 23, 24, 27 ; - without harmony, 27, 28 ; - without īson, 27 MENGEL, G.de, 24 MERCATOR, Nicolas, 68 mesa (middle note), 27, 74, 110, 111, 145, 167, 168, 170, 188-190, 198 ; pitch of the -, 197 metaphysical correspondences, 5-17, 207, 209 microcosm, 11, 48 mid-day, 149, 151 middle-ages, 114, 139, 141, 206, 208 MILTON, 34 Mimāṅsā, philosophical system of Jaimini, 106 mīmāṅsakas, (exponents of the Mimāṅsā), 106 Mixolydian mode, 148, 189, 190, 192 mobile sounds, 166, 170, 191 mode, 23 ; definition of -, 148, 162, 166 ; expression of a -, 28, 149 ; - in Western modern music, 222 ; mixtures of -s, 148, 210 ; power of suggestion of - s, 145 modal, definition, 166 ; - degree, 103, 143, 220 ; - division of the scale, 152, 203 ; - memory, 221 ; - music, systems of, 26, 27, 99 ; - music, universal system of, 160 ; - scale, 30, 173, 191, 197 modern, music, 104, 118, 207, 217 ; - music, modes of, 194 ; - scale, 114, 154, 168, 217 ;-scale, unaltered, 118 ; - scale, Western theoretical, 115 modulation (change of tonic), 23, 25, 29-31, 50, 84, 103, 138; 196, 203, 214, 215, 221 ; - s, series of, 229

MOHAMMAD HARID, 15 mokṣa (liberation), 100, 128 Mongolian scales, 22 months, notes adapted to the, 30 ; correspondences with the -, 71 ; cycle of twelve -, 14, 71 ; lyu of each -, 57, 84, 85 moon, 58, 61, 87 ;-luminary, 150, 151; relation of Sun and -, 71 ; sacrifices to the -, 85, 87 ; sphere of the -, 11;-(mṛgaśṛka), 144 morning modes, 149, 151, 152, 178 movement, local and of alternation in Aristotelian physics, 125 mṛduh (soft) jāti, 140, 141, 142, 144 mṛgāṅka (the moon), 144 MUHAMMAD REZZA, 215 muhurt (48 minutes), 150 mulawwanah (chromatic), 171 munis (sages), 143 mūrchhanā (modal plagal scale), 117, 118, 121, 197; the fourteen -s, 119-120 ; śuddha, śuddhaantara, śuddha-kākali, and śuddha-kākali-antara -s, 117, 118 music, action of, 14, 56 ; inaudible -, 8 ; logical basis of all -, 47 musalmān, esotericism, 9, 126 ;- world, 206 myeń (different)-pyén chī, F# (MaL+), 75, 79, 91

Nāda (vibration) cry), 7: NAIK GOPAL, 10 NAKULA, 55 name, natural, 8, 9 naming, principle of, 8 nān-lyù (lyù IV, A +(Dha+)), 74, 81, 84, 86-88 NĀRADA, 144, 146, 147 ;-śikṣā, 109, 110, 163 Naṭa (a Hindu scale), 194 National harmonies (=Dorian mode), 167, 185 Nāṭya śāstra, 110, 112, 113, 116, 122, 130 Negro, music, American, 31 ;- musicians, 206, 207 NEWTON, 5 night, modes of, 149, 150 Niṣāda (seated), the seventh degree of the Hindu scale, 108-110 notation, 21, 42, 137, 222 ;-by the initial letters of the names of the notes, 109 ; enharmonic -, 169 ; Greek alphabetic -, 139 ; Indian-, 28, 45, 167; Western-, 28, 136, 222, 223 notes, representation by their vibrations, 40 number, one, 11, 13, 65 ;-two, 12, 13, 65, 74 ;-three, 65, 74 ; three, cyclic -, 230, 231 ;-three, representative of the fifth, 234 ;-four, 64-66, 110, 232 ;-

five, 117, 230-233; intervals connected with the - five, 5, 117, 234; five, - of the elements, 58, 68; ratios in which the - five appears, 233; - five, square, 233; - seven, 125, 127, 231; - eight, nine, ten, 127; - twelve, 13; square - sixteen, 127; - seventeen, 126, 127; rectangle - eighteen, 127; - twenty-two, 125; - forty-eight, fifty-four, sixty-four, seventy-two, eighty-one, 74 numbers, additionable, 40; - corresponding to the degrees of the scale, 91; fundamental -, 11, 26, 74; prime -, 231, 232 numerical, representation of a mode, 23; - substance of intervals, 231

P Pan ( god of the universe ), 10, 13; flute of -, 13 pān-chéan ( fifth note ), 63 Panchama ( fifth degree of the Hindu scale), 63, 108, 109, 116; - = Dha ( A ), 110, 147 PĀNINI, Hindu grammarian, 106 paramesa, 168 parokṣa, 111 PATAÑJALI, Hindu grammarian, 106 peacock, cry of the, 145, 146 pentagon, 76, 116, 117 percussion instruments, 29 perfect group, 168 phonetic tables, 64 Phrygian, harmonies, 167; - mode, 93, 148, 191, 193, 210, 212; hyper - mode, 198; hypo - mode ( = Ionian ), 191, 192; - scale, 194; - tone, 189, 190, 198; hyper - tone, 197; hypo - tone, 198 Phrygio-Lydian group, 191 physicists, C ( Sa ) of the, 50; -' pitch, 242; -' scale, 47, 75, 243 piano, 104, 216, 221, 222 pitch, 129, 198; American high -, 243; correct -, 244; - of the diapason, 72, 145; difference of -, 129, 219; Hindu -, 145; - of the mesa, 197; physicists' - 242; primitive -, 145, 215; - of

O octave ( 2/1 ), 25, 40, 241; cyclic -, 82; - = diapason, 11; double - ( ambitus ), 133; small -, 82, 241; the twelve regions of the -, 13, 108, 150; twelve fifths and five - s, difference of, 71 OLYMPOS, the aulēte, 93, 173 ORPHEUS, 93 OUSELEY, Sir William, 138

the tonic ( tones ), 197 pitṛs ( ancestors ), 68, 143, 147 plagal, form of a mode, 28, 129, 195 ;– forms of the Dorian mode, modes in Gregorian music, 192 ;– scales (mūrchhanās), 117- 121 plain-chant ( Gregorian ), 149, 210; modes of –, 28, 208, 209, 210-212 planets, 57, 58, 108, 144 ; names of –, 12 ; the seven visible –, 12, 13, 125, 133 PLATO, 12, 13-14, 16, 106, 164, 204 PLOTINUS, 14, 156 PLUTARCH, 127 polyphony, 32, 55, 206 popular forms of music, 206, 208, 222 powers, of the ratio 3/2, 76 ;– of "2", 50, 231 ;– of "3", 40, 231 ; fourth –, 65 praharas ( watches ), 150 prākrit, 139 Prakṛiti, 57 prāṇas ( vital airs ), the five, 127 prathama ( first ), = Madhyama F, 109, 110, 146 pratyakṣa, 111 pre-harmonic art, 208 PREAU, André, 7 prejudice for classicism, 92 principle, first, 64, 128 ;– s Yin and

Yâng, 12, 72, 73, 85 proportions, harmonic, 69, 234 ; scale of –, 73, 152, 230, 234 proslambanomenos, 167, 168 pseudo, dominant, 111, 190 ;– tonic, 111 psychological, aspect of intervals, 25 ;– correspondences, 129 ;– explanation of musical experience, 10 ;– transformations, 145 psychology, 104 PTOLÉMEUS, 178, 182-184, 204 ; scale of –, 47, 178 Puruṣa, 57 pūrvāṇga ( lower tetrachord ), 109, 151, 174 pyén chī ( modified chī =Myeú ), augmented fourth, tritone, F# ( MaL +), 75, 79, 91 pyén kūng ( modified kūng ), B+ ( Ni +), 75, 82 pyramid, the, 64 PYTHAGORAS, 10, 13, 93, 204; doctrines of –, 160 Pythagorean, see : "comma" and "limma" ;– division of the octave, 169 ;– doctrine, 128 ;– scale, 47, 165 ;– system, great perfect, 167, 169 ;– theory, 16, 110, 162, 163, 185 ;– tradition, 139 ;– great year, 68 Pythagoreans, 10, 92, 117, 125, 127, 230

272 INTRODUCTION TO MUSICAL SCALES

Q quarter-tone, 21, 42, 136, 137, 154, 170-172, 176, 177, 206, 229, 237, 243 ; Greek - ( diesis ), 134, 177 ; - irka, 136 ; temperate -, 46, 135, 179 ; three -, 42 relaxed modes, 148 religious, doctrines, 128 ; - music, 208 Rikhab, see : Rṣabha rites, 17, 61 ; purpose of -, 9 ritual music, 100 RIVAUD, A., 163, 164 rohiṇī śruti, 130, 132, 140, 142 ROUANET, J., 136 ROUSSEAU, J. J., 32, 33 Rṣabha ( a bull ), the second degree of the Hindu scale, 64, 109, 110 Rṣi ( sage, seer ), 7, 144, 146, 147 ; the seven -s, 62, 63 rūpa ( form ) of a mode, 148, 149 rythm, 9, 16, 32, 138, 149, 156 rythmic formulas, 9

R rabāb, 64 rāga ( Hindu mode ), 15, 46, 111, 117, 118, 132, 133, 138, 140, 144, 145, 148, 149, 151, 162, 210 raja ( king ), 149 rajas ( expanding tendency ), 59 RĀMA, the hero, 55 RĀMĀMĀTYA, 101, 111 RAMASWAMI AIYAR, 101 RAMEAU, 30, 205, 207 rañjanī śruti, 130, 131, 140, 141 rasa ( expression, or emotional flavour, of the notes ), the nine, 112, 130, 140-142, 144, 146, 147, 151 ratikā śruti, 130, 131, 140, 141 ratios, of harmonics, 48 ; having a distinct significance, 229 ; length -, 39, 40, 108, 244 ; numerical -, 27, 232 ; - of sounds, 48, 104, 108, 206, 221 ; temper rate -, 221 ; - adequate for the representation of the world, 12 raudrī śruti, 130, 131, 140, 141

S Sa grāma ( scale of tonic ), see : grāma Sā làng-tsī, 64 Sa-thō-eāl, 64 śabda ( sound, word ), 7, 108 Ṣadja ( born of six ), the tonic of the Hindu scale, 26, 64, 108-110 ; - grāma ( scale of C (Sa) ), 111 Ṣahū d-Dīn, 128, 167 Saint AMBROSIUS, 208 Saint AUGUSTINE, 127 Saint GREGORY, 208, 209

Saint PAUL, 210

śakti ( energy ), 8, 57

SALINAS, 205

Sāma Veda, 100, 110, 144, 145, 163; classification of the -, 109; scale of the -, 16

Śambhu ( Śiva ), 101

samskāra (impression on the mind), 101

samvādi (consonant), 149, 162, 178

sandhiprakāśa rāgas, 151

sandīpanī śruti, 130, 132, 140, 142

ŚAṄKARĀCHĀRYA, 218

Sāṅkhya, 127

Sanskrit, 63, 64, 113, 139; - alphabet, 108; - names of the śrutis, 131; - notations, 163; - treatises, 113, 133, 134, 143

saraṅgī, 64

Sarasvatī, Goddess of learning, 144, 146

ŚĀRṄGADEVA, 101, 146, 147; system of -, 131

Śarva (Śiva), 144

śāstras, 217

sattva (truth), the ascending tendency, 59

SAVART, ( 1791–1841), 40

savarts, 40, 42

scale, ancient, 154, 244; basic -, 110, 113, 177, 195, 234; - of the fourth (Ma grāma), of the third ( Ga grāma ), of the tonic ( Sa grāma ), see: grāma ; - of 35

invisible worlds, 66; - (jāmā ah), 139; - of sounds, 41, 104, 112, 229, 236;

• of five sounds ( pentatonic ), 12, 62, 64, 65, 69, 72, 74, 110, 148, 180, 246;

• of seven sounds ( heptatonic ), 12, 62, 63, 66, 181, 246;

• of eight sounds, 49;

• of nine sounds, 117, 148, 232;

• of more than nine sounds, 232;

• of seventeen sounds, 137, 246;

• of twenty-two sounds, 122, 137, 139;

• of fifty-three sounds, 229, 245, 246;

• of sixty sounds, 246;

• of sounds, unity in the structure of the, 236; - of sounds, universal, 237; - starting from A (Dha), 86; - starting from C (Sa) and D (Re), 194; theory of the -, 163; - without alterations, 114

scales, modern, 114, 115, 118, 154, 168, 217; non-diatonic -, 116; progression of -, 215; reproduction of different -, 229

SCHUMANN, 152

seasons, correspondences with the, 64, 71, 72, 91, 144

second, 128; major - (9/8, D (Re)),

49, 89-92 ; minor -, 49

sectio aurea, 117

senses, 104, 105, 107 ; - of action ( karma indriyas ) and of perception ( jñāna indriyas ), the five, 127 ; - of sight, smell, taste and touch, 105, 106

SEŪ-MÀ TSHYĒN, 53, 74

seventh, cyclic major, 82, 241 ; diminished - ( Ni komal), 131 ; harmonic -, 81, 241 ; large major -, 82, 241 ; major - (15/8), 49, 82, 241 ; minor -, 28, 81, 114, 130, 241 ; small minor -, 81, 241 ; small -, 82, 241

SEVERUS of ANTIOCH, Patriarch, 209

sháng tì, sacrifices to the, 84, 85

sharps, 42, 45, 129, 136, 143, 213-215, 222 ; double -, 137 ; enharmonic and major-enharmonic -, 42 ; - (tīvra), 29, 45, 143, 144, 151, 213

Shree (a Hindu mode), 184

Shu King, 63

sitār (Indian lute), 64, 177, 244

Śiva, 57, 144, 147

śloka, 7

solstice, summer, 85, 87, 151, 152 ; winter -, 83, 85-87

sō-tho-lī (equal sound), 64

soul, the, 11, 12, 128, 156 ; - of the world, 12, 13, 163

207, 213 ; the six secondary -s, 229 ; structure of -, 22, 48 ; substance of -, 231, 232 ; successive -s, 23, 27, sphoṭa (idea), 101, 106, 107 spiral, the, 152, 215 ; -of fifths, 14, 15, 65, 69 spirits, of the earth, 68, 69 ; heavenly -, 61, 62, 68, 89 spring, 71, 85, 87, 89, 91 square, the, 60, 64, 65, 76 Śrī (= Lakṣmī), 144 sṛṅgāra rasa, see: rasa śruti, difference of a, 236 ; -jāti, 142 ; -sādhāraṇa prākara, 133 śrutis, 112, 126, 129, 131-133, 134, 135, 141, 144, 176, 182 ; definitions of the -, 130 ; - = diesis, 180 ; Hindu division of the -, 123, 178, 184, 187, 197 ; interval of two -, 180 ; - = microtonal intervals, 113 ; - = enharmonic scale, 169 ; the twenty-two -, 13, 115, 116, 122, 124, 133, 136, 140, 154, 177, 246 sthāyi bhāva (permanent impression on the mind), 102 strings, pulling of the, 177 śuddha (unaltered), notes, 144, 214 ; -, scales, 114, 117, 118, 144 śūdra (slave), 143, 146, 147 suksma śarīra (subtle body), 127 summer, 71, 87, 89, 91 sun, 11, 60, 70, 151, 167 ; -deity,

144, 147 ; -luminary, 150 ; metaphysical -, 125 ; sacrifices at the altar of the -, 85 Surya (the Sun-god), the seven horses of, 13 svaras (notes), 37, 108, 110, 111 svarga (heaven), 128 svarita (accented), 109, 146, 147 swèn (the wind), 59, 60 syáng (diagrams), 58 syào (inferior), 86 systems, the eighty-four, 84

ta'līfiyyah (enharmonic), 171 tá lyù (lyù VIII, Č# (ReL+)), 77, 83, 86, 87 tă-pú-lă, 64 tablā (Arabic drum), 64 TAGORE, Raja S. M., 101, 108, 129 tamas (descending tendency), 59 tān-pú-lă, 64 tana (melodic figure), 148 tanmātras (principles of the elements), the five, 127 tanpurā, 64 temperament, 30, 70, 135, 136, 185, 196, 206, 214, 216, 222, 223, 243 ; equal -,25, 31, 171, 173, 199 203, 218-223 ; generalization of equal -, 204 ; -of fifty-three degrees, 68 temperate scale, 13, 22, 40, 46, 104,

T

134, 176, 219, 220, 222

large major -, 79, 239 ; small

tetrachord, 29, 30, 115, 166, 171,

major -(100/81), 78, 175, 238 ;

172, 178, 180, 181, 135; con-

minor -(6/5), 28, 78, 114, 128,

jointed -, 167, 189,193, 194, 208;

130, 170, 171, 18c-183, 231,

disjunct -, 167, 168 ; highest -,

234, 238 ; small minor -, 78,

168, 189 ; lower-(pūrvāńga),

238 ; natural -, 171, 172 ;-

109, 151, 174 ; lowest -, 167,

power, limit of the, 65, 232 ;-

190 ; medium -, 167, 168 ; prin-

of the scale of fifths (ditone),

cipal -, 168 ; upper - (utta-

91, 130 ; scale of the - (Ga

rańga), 109, 115, 151, 161

grāma), 116

tetrachords, 61, 109, 112, 121, 164,

thöng (compagnions), 76

166, 170, 175, 176, 182, 209 ;

Thracians, 93

fixed structure of the -, 50 ;

three-quarter tone, 42

frame of the -, 167

tiao (system), the five, 72

tetractys, Pythagorean, 10, 65

TIMAEUS OF LOCRES, 13

Thái-shé and Thái tsï (spirits pro-

timbre, sombre or brilliant, 129,

tectors of the state territories),

222

85

time, divisions of, 26, 70

Thaí-swëi (the spirit of. the year

tīvra (sharp), 29, 45, 143, 144, 151,

identified with the planet

213 ; - Ma (F sharp), 30, 152,

Jupiter), 84

165, 168, 197, 198, 233

thái-tsheu (lyü III, D (Re) ), 74, 78,

tivra śruti, 131, 140, 141

83, 84, 86, 87

tīvratara (sharp of two śrutis) and

THAMYRIS, 93

tīvratama (sharp of three śru-

thāt, 114, 143, 165, 166

tis), 144

Thebes, 11

tone, 46 ; - of C (Sa), 29 ; divisions

thema, 148

of the -, 134, 175, 197 ; large -,

theory of the scale, 163

78, 180, 238 ; major -, (9/8),

therapeutics, musical, 15

39, 41, 43, 44, 48, 78, 112, 122,

third, 11, 89, 92, 103, 116 ;- di-

133, 135, 136, 164, 182, 213, 238;

mension, 125 ; harmonic major

large major -(8/7), 47, 49, 186 ;

-, 231 ; harmonic minor -,

minor -, 41-44, 77, 112, 135, 136,

233 ; major -(E (Ga), 5/4), 49,

180, 182, 213, 238 ; small -, 77,

78, 130, 170, 171, 175, 234, 239 ;

238 ; six perfect and six

INDEX

imperfect -s; 70; temperate -, 230 176; three-quarter -, 237; -s of transposition, Greek, 197, 198 TONG TSHUNG-CHU (2nd cent. B. C.), 6 tonic, 25, 29, 41, 89, 110, 111, 113, 114, 116, 148, 149, 152, 167; - A (Dha), 86; - C (Sa), 16, 130, 164; constant sounding of the -, 26; - D (Re), 115; - F (Ma), 164; general -, 75, 147, 187; on the fourth, 74, 194; - on the fundamental, 74; mediaeval -, 118; modal -, 114; modern -, 188; modifications of the -, 177; pedal point ot -, 28; permanent -, 23; permutation of the -, 229; relations to a -, 26, 55, 95-154; resolution on the -, 174; scale of the -(Sa grāma), see : grāma; - yekah, 145 transcriptions of Greek modes, 163, 223 transposition, 55, 68, 72, 88, 196, 213, 216; the fifteen tones of -, 197, 198; - of melody, 166 trigrams, the eight metaphysical, 58, 59, 60, 61, 62 trihemitone, 78, 170, 181, 182, 238 tritiya (third, D (Re)), 110, 146 tritone, 67, 91, 236; -(45/32), 112, 151; - augmented fourth, 91; cyclic -, 79, 239; - diabolus in musica, 151; harmonic -, 79,

tropes, 209 troubadours, 208 TSÁI-YǓ, Prince (16th cent.), 85 TSHÁI YUÊN-TÍNG, 67 tshèn (thunder), 59, 60 TSÍN, Marquess of, (541 B. C.), 66 TSÒ (541 B.C.), 66 Tsò chwán, 63 TSǓ HYĀO-SWÊN, 56, 84 TSYĀO YÊN-CHÉU, 25, 58 t'u, 83 TǓ YEǓ (d. 812 A. D.), 86 TUMBUṚU, (a celestial singer), 144, 147; - vīṇā, 64 tunbūr, Hūrāsān's, 126, 128; tuning of the -, 177 tuning, 6, 121; - by means of fifths, 169; - for each mode. 245; - of the notes, 29, 178, 195 Turkish, theorists, 136, 230; - Empress, 206; - music, 26, 133, 135; - musicians, 177 twéi (the marsh), 59, 60 twenty-two, groups of sounds, 245; - positions of the notes, or intervals (śrutis), 13, 115, 116, 122-125, 133, 136, 140, 154, 177, 245, 246

U. udatta ( raised ) notes, 109, 146, 147, 151 unaltered (śuddha), notes, 114, 214;

• scale, 114, 117, 118, 144

242, 243; representation of

unison, 7, 32

notes by their -, 40

universe, 6-8, 11, 13, 14, 16, 48, 70; action of music on the -, 56; movement of the -, 65 ; symbol of the -, 13; - = jagat, 8; limits of the -,125

vibrato, 174

uttarāñga (upper tetrachord), 109, 115, 151, 161

vibratory, movement, 106 ;- scale, 76

vādi (that which speaks), the dominant note, 148, 149, 162, 178, 210

viṇa (Hindu lute), 121, 122, 125, 177

vaggeyakāras (composers), 100

violinists, 137, 176

Vahni (fire deity), 144, 146

Viṣṇu, 144, 147

vaiśyas (traders), 143, 146, 147

vivādi, (dissonant), 149

vak (voice), 96

Vākya pudya, 96

Veda, 7, 9; perpetuity of -, 7; Sāma -, 16, 100, 109, 110, 144, 145, 163; sounds of the -s, 96; Yajur -,109

Vedāntic doctrine, 128

Vedāntist, 101, 129,

Vedic, hymns, 9 ;- scale, 110, 163; -times, 145 ;- words, 63

Verb, 7

vibration, 7-9, 105, 107, 108 ;- of air, 105, 106 ;- of ether, 106 ; measuring of -, 39, 92; numbers of -, 39, 43, 47, 107, 108,

WAGNER, Richard, 83, 152, 221, 222

WÂNG PHŌ (959 A.D.), 84

water, element, 86, 91, 105 ;- foot, 72 ;-(khaṇḍ), 59, 60 ; numbers of -, 89

waves, sound, 22, 106

WEBER, A., 139, 152

Western, modal music, ancient, 32 ;- music, 103, 160, 176, 196, 203, 214, 216, 221 ;- music, modern, 31, 203, 206, 212, 222 ;- musical system, 22, 205, 207, 219 ;- musicians, 21, 47, 104, 151, 216, 219, 223 ;- scale, modern theoretical, 199-223;- scale, Hindu origin of the, 139 ;- scale, temperate, 134 ;- vocal technique, 174

wind, instruments, 47 ; -(swèn), 59, 60

YEKTA BEY, 21, 46, 135, 161, 176

WOODROFFE, Sir John, 8, 9

YÉN TSEÚ, 63

word, creation by the, 7-9; -(śabda), 7 ; Vedic -s, 63

Yī king, 57, 58, 62

world, representation of the, 12 ; soul of the -, 12, 13, 163 ; the three -s, 126 ; limits of the visible -, 125

Yî tsè (lyü IX, Ḃb (Dhab) ), 80, 87, 88

WÙ, King, 63

Yin, principle, 12, 55, 58, 61, 62, 72, 73, 76, 85 ; -influx, 86, 87

WÙ TĪ ( 147-87 B.C. ), 56

yīng chōng (lyü VI, B+(Ni+) ), 82, 87, 88

wû yî (lyü XI, Ḃb (Nib) ), 81, 87, 88

Yins, the, 63

yoga, 8

Y

Yǔ K'ī, 16, 30, 56, 57, 61, 88, 89

Yaman (a Hindu mode), 193, 196

yoni, 57

Yâng, principle, 12, 57, 58, 61, 62, 72, 73, 76, 83, 85, 86 ; -influx, 86, 87

yī (sixth, A+(Dha+) ), 17, 74, 81, 89, 91 ; sharp -(Ḃb (Nib) ), 81

YÂNG KYÊN ( 540 A.D. ), 73

YUDHIṢṬHIRA, 55

Yavanpurī toḍī ( Hindu mode of A (Dha)= Æolian mode ), 28, 189, 190, 211

Yuē līng, 88

year, note adapted to the, 30 ; lunar -, 14, 68 ; solar -, 14, 68

Yuên (Chinese great year), 68

yekah (Arab tonic), 145

yuên (round), 86

yuên-chōng (= kyă.chōng), lyü X Ḃb (Gab), 87

ZARLINO, 6, 204, 205, 207, 212, 213 ; scale of -,212-215, 221, 229

zig-zag, 76

zodiac, the twelve signs of the, 13, 71, 108, 133, 150

END