The Music of Hindostan c9: Chapter IV. The Scale

The Music of Hindostan c9

Language: English

c9.s1 List of Sanskrit Authorities — 77 parts
c9.s2 Modern Carnatic Scale — 107 parts

Chapter IV. The Scale

c9.2

You can work it out by Fractions or by simple Rule of Three,
But the way of Tweedledum is not the way of Tweedledee.
*The Jungle Book.*

THE subject now to be discussed is complex. To do justice to the problems which it involves would require a large book; all that is attempted here is to state them, and to give a possible reading of the available data.

c9.4

Scales are a tabulation of the facts of song. In a country of the size of India these facts are very various, and that there should be one parent scale is hardly to be expected. From the facts given in Chapter I for the south, and in Chapter II for the east of that country, we should perhaps draw the following conclusions:

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(1) that the compass increases with the state of civilization;

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(2) that there are two broad tendencies in scale-building: to step melodically to the ‘next door’ note, and to leap harmonically to one which is not ‘next door’;

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(3) that the ‘steps’ are of various sizes, viz. anything up to, not as a rule beyond, a whole tone—although the means of defining the exact intervals was not at hand;

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(4) that the ‘leap’ from a given note is to a note which is consonant to it—for instance, an upward leap through F would generally be to A if the preceding note was E, to Ab if the preceding note was Eb;

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(5) that the ‘steps’ seem to prevail in the south, the ‘leaps’ in the east;

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(6) that whether ‘step’ or ‘leap’ is in use, the melody pivots on two notes which are a Fourth apart, much more rarely a Fifth.

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It may be observed in passing that this distinction between step and leap, between a ‘melodic’ and ‘harmonic’ scale, lies at the bottom of all music. It appears in our music in the form of ‘passing’ and ‘substantive’ notes; in two successive chords¹ the constituent notes of the second of them can be, and can only be, justified as melodic steps or as harmonic leaps from those of the first, however much the current conception of what is melody and what is harmony may grow. But, just as in our music the two ideas were held apart to some extent and ticketed as Counterpoint and Thoroughbass respectively, but afterwards fused in Harmony, so,
(7) together with the ‘melodic’ and ‘harmonic’ scales, we find everywhere in India the ‘complete’ scale—a scale, that is, which extends beyond the small gamut of adjacent notes, or which fills up the gaps left by the sparse notes.

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¹ Chords are compressed arpeggios, and arpeggios are, or may be, skeleton scales.

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No melodies have been noted in India until quite modern times, so that we have no direct means of determining what those songs were of which the scales were later tabulations. But we may perhaps take remoteness of local origin to be an efficient substitute for antiquity of record; and these seven ‘conclusions’ may therefore not be without value as a guide to the constitution of the early forms of scale. At any rate no reading of the theory would be satisfactory if it did serious violence to the practice.

c9.14

Another guide is to be found in the tunings of local instruments. These are, if we can interpret them, a record of the essential notes of the melodies of the district to which the instrument belongs. Essential, because other subsidiary notes are got, or are always there to be got, by special fingerings and by varying pressure of lip or finger. We will examine some of these Ludwig Riemann¹ has given, from observations made on Indian stringed and wind instruments, with the help of an *Appunn's Tonmesser*—scales correct to an eighth of a tone. His results for stringed instruments may be neglected because the frets undoubtedly shift by lapse of time, by handling, and by the shaking of the journey, and also because such instruments as those of the *vīṇā* aud *satār* tribes, from which his examples are mainly taken, belong to civilized, i. e. modern, music. There is more help to be got from the wind instruments, because niceties of intonation obtained by fingering and overblowing belong rather to a fully developed art, whereas these rustic flutes would tend to be pierced in accordance with the accepted local scale, so as to save trouble in performance.

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¹ *Über eigentümliche bei Natur- und orientalischen Kulturvölkern vorkommende Tonreihen.* Essen, 1889, pp. 3, 27-30.

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The following table divides the Semitone into four parts. It will be useful to remember that the Tone² is here 8 of such parts, the minor Third 12, the major Third 16, the Fourth 20, the Tritone 24, the Fifth 28, and the Octave 48 :

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² The true relations of major Tone, minor Tone, and Semitone would be best expressed (in single figure integers) as 9, 8, and 5.

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*Flute scales.*

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| Approxi- | 0 8 16 20 28 36 44 48 | Riemann's | Name and |
| mate | | numbering | origin of |
| European | 8 8 4 8 8 8 4 | | instrument. |
| Just scale. | C D E F G A B C | | |
| | | | |
| | 1. | 2 5 3 5 5 | 77*a* | Flute, Lahore. |
| | 2. | 4 3 5 8 | 74 | Flute, Lahore. |
| Fourth. | 3. | 4 6 4 6 6 | 77*b* | Flute, Lahore. |
| | 4. | 6 6 4 4 7 | 78*a* | Flute, Lahore. |
| | 5. | 4 4 3 4 8 8 | 76 | Oboe, Ceylon. |
| | 6. | 4 4 4 6 4 | 75 | Double flute, |
| | | | | Ludhiāna. |
| | 7. | 4 4 4 5 6 | 66 | Flute, Jaipur. |
| | 8. | 13 6 8 10 9 4 | 81 | Reed flute, |
| | | Fourth Tritone | | South India. |
| | | | | |
| Tritone. | 9. | 6 8 10 | 67*b* | Bansri flute, |
| | | | | Mathura. |
| | 10. | 13 8 9 15 | 80 | Flute, Kandha. |
| | | Fourth | | |
| | | | | |
| | 11. | 8 7 8 8 | 67*a* | Bansri flute, |
| | | | | Mathura. |
| | 12. | 10 1 7 8 | 76*b* | Bansri flute, |
| | | | | Ludhiāna. |
| | 13. | 1 9 8 10 12 10 4 | 95 | Bansri flute, |
| Fifth. | | | | Sovala. |
| | 14. | 6 8 6 8 | 76*a* | Bansri flute, |
| | | | | Ludhiāna. |
| | 15. | 8 8 8 4 8½ (A) 8 | 65 | Flute, East |
| | | | | Bengal. |
| | 16. | 8 8 8 4 10 8 10 | 73 | Thumri double |
| Fourth | | | | flute, Lahore. |
| and | 17. | 8 8 4 8 8 (A) 8 10 | 70*b* | |
| Fifth. | | | | Nai flutes, |
| | 18. | 8 4 8 8 8 (A) 8 9 | 70*a* | Kashmir. |

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We have no hint as to which note is to be regarded as the tonic, though it would be a reasonable guess to consider the lowest note to be so as a rule, because the large majority of Indian melodies are authentic, not plagal. Ignoring any suggestion of that sort, the arrangement adopted here is to group together those scales which respectively make (1) the Fourth, (2) the Tritone, (3) the Fifth, or (4) the Fourth and the Fifth, their basis, placing between the groups those which show approximations to these intervals. Where there might be doubt as to which interval was intended, a slur, or if an approximation a dotted slur, has been added.

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We must not argue from these eighteen scales to any preference for a particular size of interval, for neither do we know how representative this list, a mere handful of the flutes of India, may be, nor can we hope to base anything upon the sporadic list of ‘origins’. But a given scale tends to consist, on the whole, of one size of interval, showing that there was an average feeling, varying of course locally, of the sort of distance it was to the ‘next door’ note. We see, however, that in no scale is this distance uniform. The scale is conceived ‘diatonically’, that is to say, mixing up large and small intervals. This throws light incidentally on a statement of Aristoxenus that ‘it is impossible to hear three next door notes in succession’.¹

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¹ His name for them is ‘passage-note’ (diesis). Gevaert (*Musique de l’Antiquité*, vol. i, p. 285) thinks that there is a tinge of exaggeration in this statement; but it is possible to believe that Aristoxenus meant what he said. He always subscribes to the musical not the acoustical view, and his words must be taken to mean not that the mind cannot think these intervals in the abstract, but that the voice will not sing them in the concrete; that they are what we should call ‘unvocal’. This may be observed whenever a village choir wrestles with three or four semitones in succession.

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The interest of this table centres in the basic intervals (Fourth, Fifth, &c.) and the way they are filled up. So far as this small list may be considered to be representative, we find in it the largest group based on the Fourth, the next largest on the Fourth and Fifth together. This corroborates the conclusions from the Folksongs given above. But more interesting is the appearance of the Tritone as a base, and of the various approximations to it. There was a fairly large number of songs which employed this interval in Chapters I and II; so that it must be taken as an important factor of scale.

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Also, in no case (until the last four examples, where the scale is thoroughly established) is the basic interval filled in in exactly the same way. There are signs, indeed (especially in Nos. 1, 3, 4, 7, 8, 9, and 12), that the process was to supplement a chosen melodic interval by a residue. In No. 1, for instance, the general scheme involves large semitones (5, 5, 5). But the tetrachord begins with a quarter-tone (2), and to this there is a residue in a larger quarter-tone (3).

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There are also signs of a practice which is familiar to us,¹ of sharpening the higher intervals. In No. 7 the semitones get larger as they ascend; in No. 13 the tones. In Nos. 8 and 13 the octave is sharp; in Nos. 16, 17, 18 the eighth note is considerably sharp on the octave. In No. 10 the octave is the first harmonic. In no other case is the octave true. This shows that the octave was not considered a basic interval in the sense in which the Fourth, Tritone, and Fifth were; and this again accords with what we find in the songs.

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¹ Pianoforte tuners have found by experience that the English public likes to have the upper octaves tuned sharp, as being more brilliant. The rise in pitch since Handel's time is said to be due to the desire to secure greater brilliance by tuning brass instruments sharper than normal.

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There is no accounting for this Tritone: it must be accepted as a fact.² It may have been arrived at by a series of Tones, as Nos. 9–12 would seem to suggest; or it may be the result of a shift of tonic—e. g. B–E becoming C–F, with a resultant interval B–F—in support of which view some arguments will be adduced later. But in any case it is a fundamental fact of Indian music. The Carnatic system classifies the *Rāgams* into those which employ the Fourth and those which employ the Tritone as basic interval (*Śuddhamadhyama* and *Pratimadhyama*), and it will be seen that the same principle underlies the *Rāgs* of Hindostan. It might be supposed that F♯ (in C–F♯ G) was felt as a leading note to G merely, were it not that it is used in many *Rāgs* with obvious pleasure in descent also; and we must conclude that Indians value the Tritone for its own sake.

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² Cp. the *Kanwar*'s tuning on p. 31, and the progression of the bass in Debussy and Stravinsky.

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We turn now to the theory. There are in all about three dozen Sanskrit musical works which may be dated with varying degrees of confidence; they are, with the exception of half a dozen (marked with an asterisk), as yet unpublished, and the MSS. are scattered about in various Indian and a few European libraries. A list, extracted from Aufrecht’s and other catalogues, is here given, in case it should be of use to future students of the subject:

List of Sanskrit Authorities

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These catalogues contain references also to thirty-eight more of which the author and the locale of the MS., but not the date, is known; fourteen of which the author only is known; and seventeen of which the locale of the MS. only is known. Total 103. The twenty-eighth adhyāya of Bharata which is concerned with music (the subject of the work being the drama) has been translated into French by Jean Grosset. Mr. Clements’s *Introduction to the Study of Indian Music*, 1913, gives extracts from Bharata and Śārṅgadeva.

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The *Rāgavibodha* of Somanātha is in course of translation in the *Indian Musical Journal*, Mysore.

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It will not be possible to speak with confidence about Indian theory until all the important books have been adequately translated. What is here said is taken from Grosset's translation of Bharata.

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We begin with the explanation of a few technical terms.

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*Grāma*, lit. ‘village’, as opposed to jungle (*araṇya*), means a civilized as opposed to an unsophisticated scale.¹ The name has been applied specifically only to three scales—the *Sa-grāma*, our major with a sharpened Sixth, the *Ma-grāma*, our major C-c, but intended presumably to be used as an F-f scale with a sharpened Sixth, and the *Ga-grāma*, possibly intermediate between these two, long obsolete.

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¹ The usual explanation is that the notes are arranged in a scale as mankind are in a village, which gives rather a poor sense.

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*Thāṭ*, lit. ‘array’, is used in Hindostan for the setting of the frets of a string instrument (especially the *satār* or *surbahar*) for the purpose of playing in a given mode. But, as one setting will do for several modes, *Thāṭ*, which takes the name of one typical mode—e.g. *Bhairavī Thāṭ*, or *Kāfī Thāṭ*—has a classifying sense. The South Indian term for this classificatory sense is *Melakarta*, lit. ‘group maker’, because it groups together several *Rāgams*; though it does not seem to be applied to ‘setting’, and, indeed, I never met with a *Satār* in the south.

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*Mūrchana* (Sanskrit), *murchhana* (Hindostani), from a root *mūrch*, ‘to increase’, means primarily the ‘swelling of sound’ and seems to have been applied originally to high and low pitch and to have meant the rise and fall of the voice in song. Then it came to have the technical sense of (1) a rise and fall from and to a particular note of a specific scale, and in this sense is accurately translated by ‘mode’. (It may be worth mentioning that the *mūrchanas* are always given as a descending series.) But since the note on which they started was the most important and was generally ornamented with a grace note, *murchhana* has come to mean (2) grace note as applied to a particular *Rāg*. When grace is otherwise applied, i. e. not to single out the predominant note of a *Rāg*, it has either the general name *Gamak* or the particular names *Miṇḍ* or *Ghasīt*. These are treated of in a later chapter. In the old sense of the word the ‘mode’ consisted of seven notes, i. e. two tetrachords, so that mūrchana may (3) be held also to translate the Greek *harmoniā* (heptachord).

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*Rāga*, from a root *rañj*, ‘to be dyed, to glow’, means ‘colour’; hence colour of mind, i. e. emotion. Its European analogue will therefore be whatever gives colour to a piece of music; and since this may be according to circumstances melody, harmony, counterpoint, or instrumentation, but most of all harmony, we have no real equivalent for a word which applies technically only to melody. *Rāga* is connected with *Rakti*, ‘affection’. *Rāga* is Sanskrit, and is used in this book when the general sense is intended; *Rāg* is North Indian, and *Rāgam* South Indian. The same is the case for *Tāla*, *Tāl*, and *Tālam* (time). Its usual translation is ‘melody-type’, or ‘melody-mould’, or even ‘tune’. If it must be translated, perhaps ‘Mood’ would convey as much as is compressible into one word. Its definition is rather long, and will not mean much until the chapter on *Rāga* has been read:—An arbitrary series of notes characterized as far as possible as individuals, by proximity to or remoteness from the note which marks the tessitura, by a special order in which they are usually taken, by the frequency or the reverse with which they occur, by grace or the absence of it, and by relation to a tonic usually reinforced by a drone. Although Indians never confuse the masculine *Rāg* with the feminine *Rāgiṇī*¹ the attributes of these are indistinguishable.

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¹ ‘*Rāg*’ means strictly one of the Six Original *Rāgs*; all others are considered to be descendants of these, and are called *Rāgiṇīs*.

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*Saptaka*, a ‘set of seven’, takes the place of our word ‘octave’; the *saptaka* contains seven *svaras*, i. e. not notes, but intervals between them; and all Indian notations assume three *saptakas*, a higher (*tāra*), middle (*madhya*), and lower (*mandra*), arrived at as the average compass of the human voice (in their art songs).

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*Svara*, from root *svṛ*, ‘hear’, is also a degree of the scale, or a diatonic note. It may be natural (*śuddha*) or chromatic (*vikṛta*). ‘Natural’ means not a ‘white’ note, but ‘proper to the scale’, whatever the scale may be. *Vikṛta* notes are sharp (*tīvra*) or flat (*komala*), very sharp (*atitīvra*) or very flat (*atikomala*). F is the only note which is sharpened, and it has three degrees of sharpness—F♯ (*ma tīvra*), F♯♯ (*ma tīvratar*), F♯♯♯ (*ma tīvratam*)² F being rarely used the names are more often moved on one place, so that F♯ is *ma tīvra* and F♯♯ *ma tīvratar*. Three degrees of flattening are sometimes wanted for D, E, A, B: D♭ is *Ri atikomal*, D♭ is *Ri komal*, and D is sometimes called *Ri madhya* (middle).¹ *Tīvra* and *komal* are, literally, ‘strong’ and ‘tender’. Divine attributes are assigned to all the *svaras*. Their full names are—C, *śadja*; D, *ṛṣabha*; E, *gāndhāra*; F, *madhyama*; G, *pañcama*; A, *dhaivata*; B, *niṣāda*; and their abbreviations *Sa, Ri, Ga, Ma, Pa, Dha, Ni*. In South India D♭, D, D♯ are called *Ra, Ri, Ru* (as the Tonic Sol-fa system names them *Ra, Ray,* and *Re*) and the others analogously. In old music the *svara* names the interval; when it names the note it names the note above the interval; thus, *Ga* means the interval E–F, and in old books the note F, in modern parlance the note E.

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² -tar and -tam are the Greek -teros and the Latin -timus (e.g. finitimus, optimus, &c.).

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¹ ‘Intermediate’ between *Ri śuddha* and *Ri komal*, D and D♭.

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*Śruti*, from root *śru*, ‘hear’, is the (smallest) ‘audible sound’. Like the *svara* it names both the interval and the note. The twenty-two *śrutis* have special names, and specific attributions of divine qualities lie no doubt concealed in these. The first of them, i. e. C–D♭, is called *Tīvra* (sharp); the other names are obscure.

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*Vādī, samvādī, anuvādī, vivādī* (translated ‘sonant’, ‘consonant’, ‘assonant’, ‘dissonant’) are survivals of a theory of consonance (*samvāditva*) now forgotten. *Samvādī* definitely means the consonance of Fourth or Fifth, as we should say ‘Perfect consonance’. *Vādī* is the note to which it is so related. *Vivādī* is applied by Bharata to the Semitone. He speaks (verse 24) of notes being *vivādī* to one another when they are at the distance of twenty *śrutis*. This is the same thing as two *śrutis* (22–20), which reading actually appears in another manuscript. *Anuvādī* is the name for ‘all other relations which are not *vādī, samvādī,* and *vivādī*’. These three relationships belong to the tetrachord, and presumably *anuvādī* does too. Current tradition makes *anuvādī* the major Third. But Bharata says ‘all other’ (*śeṣa*), as if more than one relationship was *anuvādī*. If it is possible to suppose that in the term *anuvādī* he included the major and minor Tone (which together make up the major Third) all the determining elements of Bharata’s scale (see below) would be accounted for.

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In discussing the scale (*grāma*) the first difficulty which confronts us lies in the double meaning of *svara*, ‘note’ and ‘interval’.¹ Does the *Sa-grāma*, for instance, begin with the Sa-interval, or on the S-note? In the former case it will begin on what we should call C (the Indian N), in the latter on our D (the Indian S). Bharata gives some colour to the latter view in verse 25, where he says the arrangement of the *śrutis* in the *Sa-grāma* is 3, 2, 4, 4, 3, 2—i. e. that they begin with the *svara* Ri, which is of three *śrutis*, and therefore on the S-note (our D).

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¹ Bharata speaks of two *svaras* (notes) being *samvādi* when they are nine *śrutis* (a Fourth) or thirteen *śrutis* (a Fifth) apart. Again, he speaks of Sa (one of the *svaras*) as ‘of’ four *śrutis*, meaning the interval from the note N to the note S. [Sa is hereinafter used for the interval, S for the note.]

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But if we reflect that the scale is always spoken of as a ‘set of seven’ (sc. intervals), whereas it consists actually of eight notes, that these seven are always given as beginning with Sa, and that a scale so taken (from N-note or Sa-interval) satisfies the demands of the practice (in Chapters I and II), we shall not be disposed to attach too much importance to this *obiter dictum* of verse 25, even supposing that were the only way in which it could be interpreted. We assume, therefore, that the *Sa-grāma* begins with the Sa-interval, on the N-note (our C).

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But there is a second difficulty, which Mr. Clements’s recent book raises. Was the *grāma* a scale beginning on a definite note at all, or was it not rather a gamut, a continuous series, which might be started at any point, but which differed from some other *grāma* by having one place where the series diverged? But there is the difficulty of the names. Why were they called *Sa-grāma*, *Ma-grāma*, unless they had some obvious connexion with Sa and Ma? And what could that connexion be except that they began there? The distinction between *grāma* (scale) and *mūrchana* (mode) may well be, essentially, that between *genos* and *harmoniā* (scale and mode), only that the Indian *grāma* did not and the Greek *genos* did not begin on a particular note.

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In assigning the *śrutis* thus, for the *Sa-grāma*, Sa Ri Ga Ma Pa Dha Ni 4 3 2 4 4 3 2

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Indian theory is indicating the relative sizes of the major Tone (4), the minor Tone (3), and the Semitone (2) with accuracy sufficient for its purpose. Complete accuracy would demand 4·08, 3·64, and 2.24 respectively.¹ The *Ma-grāma* is formed from this by the interchange of the *śruti*-values of Pa and Dha; ‘Dha takes one *śruti* from Pa’—thus:

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¹ That the numbers 4, 3, and 2 do represent these intervals is usually taken for granted. It appears to depend ultimately on the current tradition that *anuvādi* means the major Third; that is to say, that early theory recognized the major Third and not the Ditone, i. e. the major and minor Tone and not two major Tones.

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*Ma-grāma* Sa Ri Ga Ma Pa Dha Ni 4 3 2 4 3 4 2

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But the *Ma-grāma* is so called, we must think, because it begins on the note Ma. Hence the scale intended is:

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Ma Pa Dha Ni Sa Ri Ga 4 3 4 2 4 3 2

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But there is a third scale, the *Ga-grāma*, which is not mentioned by Bharata. It is said by Śārṅgadeva to have ‘retired to Indraloka’ (heaven). In spite of this, however, he knows how it was formed.

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When (*a*) Ga takes one *śruti* from Ri and one from Ma, (*b*) Dha takes one *śruti* from Pa, (*c*) Ni takes one *śruti* from Dha and one from Sa, then this arrangement is what Nārada taught us as the *Ga-grāma*.

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The process is as follows:

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Sa Ri Ga Ma Pa Dha Ni *Sa-grāma* 4 3 2 4 4 3 2 (*a*) 4 2 4 3 4 3 2 (*b*) 4 2 4 3 3 4 2 (*c*) 3 2 4 3 3 3 4 *Ga-grāma* beginning on Ga } 4 3 3 3 4 3 2

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The three *grāmas*, put for comparison together, are:

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*Sa-grāma* 4 3 2 4 4 3 2 *Ga-grāma* 4 3 3 3 4 3 2 *Ma-grāma* 4 3 4 2 4 3 2

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and the notes of which these are composed may be represented by:

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*Sa-grāma* C D E F G A# B C *Ga-grāma* C D E F G A# B C *Ma-grāma* C D E F# G A# B C

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In favour of this explanation, which is in principle that adopted in Mr. Clements's book, it may be said (1) that the *Ga-grāma* is thus made a true *grāma* and differs from the *Ma-grāma* (as that did from the *Sa-grāma*) by the alteration of one *śruti* only; and (2) the difference between the three *grāmas* lies in the treatment of the F, and this is just the difference we were led to expect by the Folk-songs, and still more by the flute tunings.

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Against it, however, it must be said (1) that this explanation is based on a solitary passage of a thirteenth-century writer, and that the scheme of the other two *grāmas*, given in full by a writer of the fifth century A.D., the principle of which can be traced to the fifth century B.C., makes no mention of a third *grāma*; and (2) it is difficult to imagine so much prestige¹ as belongs to the *gāndhāra* scale attaching to a series of notes which makes the principal interval (the Fourth) break the law of consonance by consisting of ten *śrutis* instead of nine. The *Ga-grāma* must, one would think, have been some series of notes which is as fundamental a part of Indian music as the other two *grāmas* are.

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¹ The *Harivaṃśa* (fourth century A.D.) speaks with enthusiasm of music composed in the *āgāndhāragrāmarāga*, ‘the scale which comes down to *gāndhāra*,’ i.e. which, if taken upwards, begins on *Ga*. The *Mahābhārata* speaks of ‘the sweet *Gāndhāra*’, and this implies a mode or scale, since no note is sweeter than another until it has a context.

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But the directions of the *Ratnākara* may be taken in another way. The *Ga-grāma* may be intended there to be derived not from the *Sa-grāma*, but from the *Ma-grāma*. Thus:

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| *Ma-grāma* | 4 | 3 | 2 | 4 | 3 | 4 | 2 |
| (*a*) | 4 | 2 | 4 | 3 | 3 | 4 | 2 |
| (*b*) | 4 | 2 | 4 | 3 | 2 | 5 | 2 |
| (*c*) | 3 | 2 | 4 | 3 | 2 | 4 | 4 |

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This is the scale A B C D E F G A, which is open also to the objection of having the Fifth A-E consisting of twelve instead of thirteen *śrutis*. But in an early, i.e. a vocal, scale the Fifth is not nearly so important as the Fourth; and that is perfect (3 + 2 + 4 = 9). We notice also that, though derived here from the *Ma-grāma*, it is a mode of the *Sa-grāma* (and not a distinct *grāma*), and with that we leave it for further discussion in Chapter X.

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The A♯ of the *Sa-grāma* and *Ma-grāma* differed from A by the Comma of Didymus ((Major Tone)/(Minor Tone) = 81/80 = 22 Cents). Bharata calls this comma the ‘indicative’ (*pramāṇa śruti*). He uses it for the tuning of the *vīṇā*.

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Take two *vīṇās*, he says, alike in all respects, and tune them both in the *Sa-grāma*. On one of them diminish Pa [i.e. lower the note P so as to form our A♯ instead of A♯] by this *pramāṇa śruti*, but in such a way that the Pa of the *Sa-grāma* can be put back again. This is the diminution of one *śruti*. By a second diminution Ga [on one *vīṇā*] becomes Ri [on the other], and, similarly, Ni becomes Dha. [The second *śruti*, then, is the difference between the *pramāṇa śruti* and the Semitone, and the *śrutis* were therefore not equal in size.] By a third diminution D and R of one *vīṇā* coincide with P and S of the other; and by a fourth diminution P, M, and S coincide with M, G, and N. This scheme shows the twenty-two *śrutis* of the two *grāmas*.

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The only thing this establishes is that the *śrutis* were not equal in size. They are of three sizes: (1) the difference between the major and minor Tone, the *pramāṇa śruti*, twenty-two Cents; (2) the difference between the minor Tone and the Semitone, seventy Cents; and (3) the difference between the Semitone and the *pramāṇa śruti*, ninety Cents. He does not tell us in what order these diminutions are to be made; and if we took him literally, and made them successively downwards from each note we should get quite a wrong idea of his scale.

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What that scale is we discover from his account of the *jātis*. There are seven modes (*mūrchanā*) of each of the two *grāmas*, i.e. fourteen in all; but only seven of these fourteen are in practical use under the name of *jātis*, species. In the following table each mode is given as from a common tonic. The constituent units of the *Sa-grāma* (4 3 2 4 4 3 2) are successively added, and each *mūrchanā* begins on a different one of these notes. The same is done for the *Ma-grāma*, giving another set of seven *mūrchanas*, each of which differs in one note, and only one, from some mode of the *Sa-grāma*.

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| Mūrchanā. | | | | | | | | | | | | | Jāti. |
| Abhirudgatā | D mode | 0 | ... | 3 | ... | 5 | ... | 9 | ... | 13 | ... | 16 | ... | 18 | ... | 22 | Arṣabhī. |
| Aśvakrāntā | E mode | 0 | ... | 2 | ... | ... | ... | 6 | ... | 10 | ... | ... | ... | 15 | ... | ... | ... | 19 | ... | 22 | |
| Matsarīkṛta | F mode | 0 | ... | ... | ... | 4 | ... | ... | ... | 8 | ... | 11 | ... | ... | ... | 17 | ... | ... | ... | 22 | |
| Śuddhaṣaḍjā | G mode | 0 | ... | ... | ... | 4 | ... | 7 | ... | 9 | ... | ... | ... | 13 | ... | 16 | ... | 18 | ... | 22 | |
| Uttarāyatā | A mode | 0 | ... | 3 | ... | 5 | ... | ... | ... | 9 | ... | ... | ... | 12 | ... | 14 | ... | ... | ... | 22 | Dhaivatī. |
| Rajanī | m ode | 0 | ... | 2 | ... | ... | ... | 6 | ... | ... | ... | 9 | ... | ... | ... | ... | ... | 19 | ... | 22 | Niṣādīnī. |
| Uttaramaṇdrā | (C mode) | 0 | ... | ... | ... | 4 | ... | ... | ... | 7 | ... | 9 | ... | 13 | ... | 17 | ... | 20 | ... | 22 | Ṣaḍjī. |
| | Sa-grāma | C | Db | D | Eb | E | F | F# | G | Ab | A | Bb | B | C | | | | | | | |
| Śuddha-madhyamā | Ma-grāma, i (C mode) | 0 | ... | ... | ... | 4 | ... | 7 | ... | 9 | ... | ... | ... | 13 | ... | 16 | ... | 20 | ... | 22 | |
| Kalopannatā | D mode | 0 | ... | 3 | ... | 5 | ... | ... | ... | 9 | ... | 12 | ... | ... | ... | 16 | ... | 18 | ... | 22 | |
| Harinaśvā | E mode | 0 | ... | 2 | ... | ... | ... | 6 | ... | ... | ... | 9 | ... | 13 | ... | 15 | ... | 19 | ... | 22 | Gāndhārī. |
| Sauvirī | F mode | 0 | ... | ... | ... | 4 | ... | 7 | ... | 9 | ... | 11 | ... | 13 | ... | 17 | ... | 20 | ... | 22 | Madhyamā. |
| Hṛsyakā | (Ma-grāma, ii) G mode | 0 | ... | 3 | ... | 4 | ... | 7 | ... | 9 | ... | 10 | ... | 13 | ... | 15 | ... | 16 | ... | 18 | ... | 22 | Pañcamī. |
| Pauravī | A mode | 0 | ... | ... | ... | 4 | ... | 6 | ... | ... | ... | ... | ... | 13 | ... | 15 | ... | 19 | ... | 22 | |
| Margī | B mode | 0 | ... | 2 | ... | ... | ... | 6 | ... | 9 | ... | 11 | ... | ... | ... | ... | ... | 18 | ... | 22 | |

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We will now digress for a moment to record an important date in this connexion.

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The scheme as a whole is much earlier than Bharata. The theory of consonance (*samvāditva*), or at least the terminology which that theory uses (*samvādī, anuvādī, vivādī*), is alluded to in the *Mahābhārata* (14, 14, 19). The date of the *Mahābhārata* is generally considered to be 400 B. C.–200 A. D., and the fourteenth is a late book. The author gives as the ‘ten elements of sound’ the seven notes of the scale (Sa, Ri, Ga, &c.), and three others, *iṣṭa*, *aniṣṭa*, and *saṃhata* (lit. ‘agreeable’, ‘disagreeable’, and ‘struck together’). These last are described as ‘classificatory’ (*pravibhāgavān*); and it is tempting, therefore, to see in them the terms ‘assonant’, ‘dissonant’, and ‘consonant’ with which we are familiar.

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But a much more important passage is to be found in the *Ṛkprātiśākhya*, which is probably not later than 400 B. C. It is there said that there are twenty-one notes in all, seven for each voice register (*sthāna*)—the lower (*mandra*), the middle (*madhya*), and the upper (*uttama*).¹ These seven notes (of the octave, or of course twenty-one of the three octaves of the gamut) are described as twins (*yama*). ‘Each twin is separated from its fellow by such a small distinction that from one point of view the difference is hardly perceptible; yet, from another, the two are distinct things.’ The metaphor of ‘twins’ describes so accurately the pairs of scales we have been discussing, which are identical in six notes and differ in the seventh by an almost imperceptible interval, and puts the finger so unerringly upon the salient point of the system, that there can be little doubt as to the reference. This highly elaborate system may, then, be dated back beyond the time of Aristoxenus, to the fifth century B. C., and, like his, points to a long antecedent period of development.²

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¹ The modern name for the upper register is *tāra*.

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² See Weber's *Indische Studien*, the eighth volume of the *Beiträge für die Kunde des indischen Altertums*, pp. 262 and 271.

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It appears from the table of *mūrchanas* that all the twenty-two *śrutis* except the first and twenty-first are accounted for. These two are inserted, by analogy, in the next diagram in square brackets as consonant notes from the eighth and tenth *śrutis* respectively. If we take account of the *jātis* only, we find that these two, the eighth and the tenth, are not in use; they are accordingly placed in round brackets. No. 11 is arrived at in two ways, with different results.

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In the following diagram column I gives the constituent elements of each note in terms of the major Tone (a = 9/8), the minor Tone (b = 10/9), and the Semitone (c = 16/15). Columns IV and V give the representative fractions, distributed into ‘quintal’ (those derived from the Fifth (3/2) alone), and ‘tertian’ (those derived jointly from the Fifth and the Third (5/4)). Column II gives the equivalent of these in cents,¹ and Column III their differences (or, speaking

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¹ Cents are a set of slightly modified logarithms of fractional ratios between 1 and 2, and represent musical intervals within the compass of an octave (2/1) correct to the hundredth part of a semitone. The system is explained in Appendix XX of the second edition of Ellis’s Translation of Helmholtz’s *Sensations of Tone*. (This appendix is not in the first edition.)

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For the following statement of the theory, and of practical rules for finding cents, the writer is indebted to the kindness of Mr. T. B. W. Spencer, of Wellington College:

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The number of cents corresponding to any musical interval must satisfy two conditions, namely, that the addition and subtraction of cents should correspond to the product and quotient of the intervals they represent; and also that 1200 cents should correspond to the interval 2/1, that is the interval between a note and its octave.

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The first condition is satisfied by representing any interval by its logarithm to any base; the second, by multiplying these logarithms by some factor.

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Using common logarithms, the logarithm of 2/1 is .3010300. As the number of cents corresponding to this interval is 1200, the factor that the logarithms must be multiplied by is 1200/.3010300 that is by 3986.

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The rule, then, to find the number of cents corresponding to any interval is as follows: Find the common logarithm of the ratio, and multiply the result by 3986.

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Example. If the ratio is 9/8, the logarithm of 9/8 is .0511525. Multiply this by 3986, and the result is 204 to the nearest whole number.

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The above is the only accurate rule, but as it is intelligible only to those who are acquainted with logarithms, we proceed to obtain a rule for calculating cents by means of elementary arithmetic.

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The common logarithm of any fraction (m/n) is given by the formula log m/n = 2 × .43429 (m-n)/(m+n) + ⅓ ( (m-n)/(m+n) )³ + ⅕ ( (m-n)/(m+n) )⁵ +

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which is proved in every book on Higher Algebra. The number of cents is 3986 times this expression, that is, number of cents corresponding to m/n is 3986 × 2 × .43429 (m-n)/(m+n) + ⅓ ( (m-n)/(m+n) )³ + ⅕ ( (m-n)/(m+n) )⁵ + that is, 3462 × (m-n)/(m+n) + 1154 × ( (m-n)/(m+n) )³ + 692 ( (m-n)/(m+n) )⁵ + in ratios, their quotients). Columns VI and VII are adjustments proposed by Mr. Clements on the strength of observations taken by Mr. Deval of Poona on a dichord: his two tertian intervals are a Fourth apart, and his two septimal, a Fifth. [Septimal intervals are derived from the septimal seventh; 7/4 = 969 cents.]

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If we take m/n less than 4/3, (m-n)/(m+n) is less than 1/7 and 692 ((m-n)/(m+n))⁵ is less than · 04; therefore this term and all those after it may be neglected. Also 1154 × ((m-n)/(m+n))³ is less than 1154 × 1/(7³), that is, less than 3·4; hence to the nearest whole number this term is either 0, 1, 2, or 3.

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It is therefore simpler to calculate the number of cents, corresponding to m/n, from the formula 3462 × (m-n)/(m+n), and add 1, 2, or 3 as required.

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No simple rule can be given which will always give the correct result. The following, although slightly more complicated than that given by Ellis in his article on ‘The musical scales of various nations’ in the *Journal of the Society of Arts* for March 27, 1885, has the advantage of being more accurate.

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(a) If the ratio is less than 4/3, multiply 3462 by the difference of the numerator and denominator, and divide by their sum, obtaining the quotient to the nearest whole number. If this quotient is over 262 add 1, ,, 378 ,, 2, ,, 448 ,, 3.

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(b) If the ratio is greater than 4/3 and less than 3/2, multiply the larger number by 3 and the smaller by 4 and proceed as before, and finally add 498 to the result.

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(c) If the ratio exceeds 3/2, multiply the larger number by 2 and the smaller by 3 and proceed as in (a), and add 702 to the result.

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Examples:
(a) The ratio is 10/9. Multiply 3462 by 1 and divide by 19. Result, 182.
(b) The ratio is 45/32. Multiply 45 by 3 and 32 by 4, giving 135/128, difference 7, sum 263. Then (3462 × 7)/263 = 92. Add 498 and the result (in cents) is 590.

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(c) The ratio is 7/4. Multiply 7 by 2 and 4 by 3, giving 14/12, i.e. 7/6. Then 3462/13 = 266. Since 266 is more than 262, add 1 as well as 702. The result is 266 + 1 + 702 = 969, the cents required.

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| Constituents. | Cents. | Differences. | Quintal. | Fractional ratios. Tertian. | Cents. | Adjustments. Ratios. | |
| | I. | II. | III. | IV. | V. | VI. | VII. |
| Ni. | 22. 3a+2b+2c . | 1200 | [ 90 / 22 ] | 2 | 2 | ... | ... | C |
| | 21. [Samvādi to No. 8] | [1110] | | | [243:128] | 1108 | 256:135 (tertian) | B |
| Dha. | 20. 3a+2b+c | 1088 | 70 | ... | 15:8 | ... | ... | B |
| | 19. 3a+b+2c | 1018 | | ... | 9:5 | ... | ... | Bb |
| | 18. 2a+2b+2c | 996 | 22 | 16:9 | ... | ... | ... | b |
| | | | | | | | | Bb |
| | 17. 3a+b+c | 906 | 90 | 27:16 | ... | ... | ... | A |
| | 16. 2a+2b+c | 884 | 22 | ... | 5:3 | ... | ... | A |
| | 15. 2a+b+2c | 814 | 70 | ... | 8:5 | ... | ... | Ab |
| Pa. | 14. a+2b+2c | 792 | 22 | 128:81 | ... | 787 | 63:40 (septimal) | b |
| | | | | | | | | Ab |
| | 13. 2a+b+c | 702 | 90 | 3:2 | ... | ... | ... | G |
| | 12. a+2b+c | 680 | 22 | ... | 40:27 | ... | ... | F |
| Ma. | 11. a+b+2c | 610 | 70 | ... | 64:45 | 610 | 64:45 (tertian) | F |
| | 2a+b | 590 | 20 | ... | 45:32 | | | |
| | 10. (2a+c) | (520) | 70 | ... | (27:20) | ... | ... | F |
| | 9. a+b+c | 498 | 22 | 4:3 | ... | ... | ... | F |
| Ga. | 8. (2a) | (408) | 90 | (81:64) | ... | ... | ... | E |
| | 7. a+b | 386 | 22 | ... | 5:4 | ... | ... | E |
| Ri. | 6. a+c | 316 | 70 | ... | 6:5 | ... | ... | Eb |
| | 5. b+c | 294 | 22 | 32:27 | ... | ... | ... | b |
| | 4. a | 204 | 90 | 9:8 | ... | ... | ... | Eb |
| Sa. | 3. b | 182 | 22 | ... | 10:9 | ... | ... | D |
| | 2. c | 112 | 70 | ... | 16:15 | ... | ... | Db |
| | 1. [Samvādi to No. 10] | [22] | [ 90 / 22 ] | ... | [81:80] | 85 | 21:20 (septimal) | b |
| N. | 0. | 0 | | 1 | 1 | ... | ... | Db |
| | | | | | | | | C |

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It may be noticed that since the *Ma-grāma* (4 3 2 4 3 4 2), which is identical with our major scale, can be treated in the same way, it would have been open to Europeans to divide the octave similarly into twenty parts. Having a different object in view we have preferred to do two things. First, we have ‘merged’ nearly identical intervals; that is, we have made one note do duty for two. Thus, E♭ is 204 + 112 = 316, and D♯ is 386 − 112 = 274; and we have made 316 do duty for both notes. And secondly, since we wished to have all the relations of the successive notes of the key the same, on whatever note the key began, we have ‘tempered’; that is, we have made the major Tone, minor Tone, and Semitone expressible in terms of each other by adopting a compromise. Thus 204, 182, and 112 have been altered to 200, 200, and 100. With these particular intervals the falsity of intonation does not seriously matter; but since it involves reducing the Fifth, 702, to 700, and increasing the major Third,¹ 386, to 400, the falsity on some instruments and in certain connexions is very apparent. There are purists who regret this, and others who do not appreciate the reason for it—that we have an ample compensation in Harmony, which it alone makes possible. If India were ever to adopt Harmony it would be driven eventually to the same or a similar device; there is not, permanently, any half-way house.²

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¹ The ear perceives these relations immediately, but those of the Tone, &c., mediately.

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² See Appendix.

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Bharata’s is the North Indian theory of *grāma*, though, as we have seen, it touches the South Indian theory also in one point, the division of *Rāga* into two classes, those which have the Fourth and the Tritone respectively for basic interval. But in other points the South Indian theory diverges.

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First, the Carnatic system ‘merges’; it recognizes not twenty-two, but only sixteen nominal and twelve real sub-divisions of the scale:

Modern Carnatic Scale

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| C | | Sa (śuddha) |
| B | | Ni kākali |
| A♯ B♭ | Dha śatśruti | Ni kaiśiki |
| A B♭♭ | Dha catuḥśruti | Ni śuddha |
| A♭ | Dha śuddha | |

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G Pa (śuddha) F♯ Prati-madhyama F Śuddha-madhyama E Ga sādhāraṇa D♯ E♭ Ri śatśruti Ga antara D E♭ Ri catuḥśruti Ga śuddha D♭ Ri śuddha C Sa (śuddha)

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• N.B. Śuddha, natural, normal. Catuḥśruti, of four śrutis. Śatśruti, of six śrutis. Antara, interval. Sādhāraṇa, twilight. Prati-, mock-, counter-. Kaiśiki, hair's-breadth. Kākali, low, quiet.

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The Hindostani system ran :

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śrutis 4 5 6 7 D E♭ E♭ E 204 294 316 386

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The Carnatic system, by calling the D♯-E♭ note śatśruti¹ (6-śruti), selects the 316 rather than the 294.

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¹ The nomenclature of this scale has a long history behind it, much of which will be found in Mr. Clements's book. Some of the names are transferred from the Hindostani system, e. g. Kākali, Kaiśiki, Sādhāraṇa, Antara, where they had a precise meaning which they have here lost.

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The second point which is peculiar to the Carnatic, or Dravidian, system is the designation śuddha as here applied. It will be seen that the śuddha notes taken by themselves form the scale

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C D♭ D-F G A♭ A-C

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whereby each tetrachord is filled by two semitones and a ‘residue’. This is identical in form with the ancient Greek chromatic. Not only is this chromatic scale apparent in the nomenclature, but Rāgams in this mode (or scale) were once popular, though now somewhat neglected. In the scheme of Grāmarāgas in the Ratnākara and the Svaramela-kalānidhi (both of the sixteenth century) the first on the list, by name Mūkhārī, is in this scale, and is plentifully filled with Rāgams, showing that it was popular and was considered the natural one to put first.¹ [*Grāmarāga* is an early name for *melakarta*.] Popular favour has now, however, been transferred to another scale, *Māya-Mālavagaula*:

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¹ It is still put first in the modern system under the fancy name of *Kānakangi* (part of an elaborate *memoria technica*, see Mudaliar's *Oriental Music*, p. 17).

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C D♭-E F G A♭-B C

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It looks as if the second of these two scales had developed from the first by way of modal shift of tonic. These five notes

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[Figure: Māyamālavagaula. Ex. 183. Mūkhārī.]

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show the characteristic tetrachord of each chromatic scale. The two complete scales compare thus:

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[Figure: Authentic Māyamālavagaula. Ex. 184. Plagal Mūkhārī.]

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This would sound too ingenious to be true were it not that a strictly analogous thing has happened with Greek music. The modern form of Greek chromatic is:

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C D♭ E F G♭ A B♭²

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² See the examples in Pachtikos, *Aismata Hellenica*, Athens, 1905, passim.

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and the two, ancient and modern, complete scales are therefore

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[Figure: Modern Greek (plagal). Ex. 185. Ancient Greek (authentic).]

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The Carnatic scale has, then, a chromatic basis; and the Greeks held that the chromatic preceded the diatonic.³ The latter we found in Hindostan taking shape in three, according to one explanation, but at any rate in two *grāmas* which differed from each other by one *śruti*, precisely as the ‘hard’ and ‘soft’ varieties of the Greek diatonic differed by one *diesis*. Here we have analogues, therefore, for two of the Greek genera. We may even trace the third genus, the enharmonic, in *Rāgs* like *Toḍi*, *Multānī*, and others. The Greek enharmonic scale, expressed in *śrutis*, appears thus

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³ South Indians claim that the Dravidian system (that of the Carnatic) is older than the Hindostani. It may be remembered also that Tamil (the prevalent language of southern India) has the oldest datable literature of any Prakrit.

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Ex. 186.

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The scale of *Toḍi* is:

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Ex. 187.

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They meet, like the old and new South Indian chromatic scales, in two overlapping tetrachords:

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Ex. 188.

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The Greeks called the three notes which are separated by one *diesis* (*śruti*) the cluster (*pyknon*), and recognized three forms of tetrachord according as the lower note (*barypyknon*), middle note (*mesopyknon*), or upper note (*oxypyknon*)² of the cluster was made the tonic, i. e. the terminal of the tetrachord. If this ever formed a part of Indian theory, no trace of it has as yet been discovered; but the fact is here—the Greek enharmonic with the *barypyknon* and the enharmonic *Toḍi* with the *oxypyknon*. Further, *Toḍi* and its congeners are really distinct from other *Rāgs*, because, as has been seen, there is no place for them in Bharata’s *jātis*, which do not provide for the first and twenty-first *śrutis* which *Toḍi* involves. They may therefore point to a different basic principle of scale.

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² Aristoxenus did not recognize the latter two; he held that the *pyknon* must always be at the lower end of the tetrachord.

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It is not suggested that the three *genera*, to borrow the term, are confined respectively to different parts of India, although the enharmonic seems to be opposed in principle to the Carnatic system.

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¹ These notes are given for the sake of clearness one quarter tone higher than they stand in Ex. 187.

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The diatonic is ubiquitous (though the sharp Sixth is not found in the South), and the chromatic is quite as popular in the North under the name of *Bhairau* as it is in the South as *Māyamālavagaula*.

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Neither is there any suggestion that Greece borrowed from India, or vice versa; their musical systems, like their languages, were no doubt part of their common Aryan inheritance—with enough likeness and unlikeness to make the comparison convincing.

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We turn now to the other class of scale, the transilient, which proceeds by ‘leap’ to the Fourth, with a bridge note. It might seem at first glance as if these were not very different from the chromatic scales, since in both there is as a rule a leap of a minor Third. But there is a great difference in the melodies which embody them. A ‘chromatic’ melody tends to centre in the cluster of semitones, and to treat the leap as an occasional excursion. A ‘transilient’ melody moves more freely, and the leap is the most important material of the song.

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We found a hint in the Gurkha and Garhwālī songs that these transilient scales had their home in the east of India. Although they are to be found everywhere, they seem to be especial favourites in Bengal; and the Bengālī system especially insists on heptatonic (*sampūrṇa*), hexatonic (*ṣāḍava*), and pentatonic (*oḍava*) as a primary division of *Rāga*, whereas the other systems, while recognizing these, draw no special attention to them. Of these names there is something to be said about *oḍava*. It is always understood to mean ‘a set of five’; but the word is neither Sanskrit nor Prakrit. What the connexion is, if any, with *Auḍavī* (an unlocated placename) or the *Oḍras* (who inhabited Orissa = *Oḍra-desha*) or with *oḍrapushpa* (the Chinese rose) must be left to others to determine. No Indian language owns *oḍava*, and, if the name is foreign, the scale may have been imported. That it is foreign is further suggested by the form *ṣāḍava*, ‘a set of six,’ formed on analogy, for which the proper Sanskrit would have been *shashtaka*.

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Indian theory, which is nothing if not complete, has names also for scales of fewer notes. Scales of one note, which seems a little Irish, are called *Arcika* (i. e. belonging to the *Rigveda*). This is curious since the *Ṛk* was by common consent chanted to three notes. Of two notes, *Gāthika*; *Gāthas* were religious non-Vedic songs. Of three notes, *Sāmika*, belonging to the *Sāmaveda*.

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(Incidentally, the *Sāman* chant involved from five to seven notes.) Of four notes, *Svarāntara* (= hiatus); this seems to be a confession that the tabulation had broken down. Still, the list as a whole may be read to mean that a small compass connotes antiquity, as we found it connoted also remoteness of locality. No one doubts, either, that pentatonic scales precede, what indeed may be considered ‘spoiled’ forms of them, hexatonic and heptatonic. They are, logically, older because they are innocent of the Semitone, which comes into the scale only when the ear can appreciate the major Third. (Fourth/(Major Third) = Semitone). Melodies in these scales have extraordinary strength and sweetness, but not much variety.

First 143 of 215 passages. Read on

Linked texts (15)

Saṅgītaratnākara — Śārṅgadeva, Sanskrit
Nāṭyaśāstra — Bharata, Sanskrit
Svaramelakalānidhi — Rāmāmātya 1550, Sanskrit
Mahābhārata — Vyāsa, Sanskrit
Harivaṃśa — Vyāsa, Sanskrit
Ṛgvedasaṃhitā — Sanskrit
Sāmavedasaṃhitā — Sanskrit
Saṅgītopaniṣad — Sudhakalasa, Sanskrit
Saṅgītanārāyaṇa — Gajapati Vīrasrī Nārāyaṇadeva 1675, Sanskrit
Saṅgītasamayasāra — Pārśvadeva, Sanskrit
Saṅgītamakaranda — Nārada, Sanskrit
Saṅgītapārijāta — Ahobilasūri 1600, Sanskrit
Nartananirṇaya — Puṇḍarīka Viṭṭhala 1574, Sanskrit
Saṅgītadāmodara — Śubhaṅkara, Sanskrit
Rāgavibodha — Somanātha 1584, Sanskrit

The Music of Hindostan c9: Chapter IV. The Scale

Contents

Chapter IV. The Scale

List of Sanskrit Authorities

Modern Carnatic Scale

Linked texts (15)