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The Music of Hindostan c9.s2: Modern Carnatic Scale

The Music of Hindostan c9.s2

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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.

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It remains to bring these different scale formations into relation with acoustical fact, on the one hand, and with musical fact on the other.

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When primitive man—and he is to be heard in London streets as well as in Otahiti or in the glacial epoch—begins to articulate his upward whoop or downward wail, he uses his ‘musical ear’. It is this ear which is in a low state of development when he ‘loses his key’ or ‘sings out of tune’. What is it, then, to sing in tune? It is to be able to hear, *with* a given note, certain other notes which are present in it at various pitches and intensities. ‘The’ note is known as the ‘fundamental’, and the ‘other’ notes as ‘upper partials’: the latter diminish in intensity as they rise in pitch. Intensity of sound has not yet been measured, and the amount of average diminution is not known. The following series omits octaves (as mere replicas), and hints at the average diminution by time-values:

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Ex. 189.

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The 2nd, 4th, 6th, 8th, 10th upper partials are omitted as duplicates. The B is ⅙ tone flat, the F is ¼ tone sharp on notes of the same name which are derived from lower partials, and which therefore in certain connexions have precedence. Human powers of hearing vary a good deal, and still more the power of defining and naming what is heard; so that individuals and tribes may be classified according as their powers extend to the 3rd, 5th, or even 7th upper partial; there is no certain record of powers that have exceeded that. These upper partials are present on all sound-producers; poorest on the tuning fork and flute, richest in the human voice. But they are present in different intensities,¹ and this fact gives its ‘character’ to each sound-producer.

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¹ The 2nd partial is prominent in the flute, the 3rd in the clarinet, the 3rd and 5th in the human voice, the 7th in bells, the 11th in the trumpet. Pianoforte makers cause the hammer to strike the string at a place which eliminates the 7th, which is not wanted.

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But, secondly, it seems to be a law of music (not of acoustics) that no tonal fact can be realized at all without its entering at once into all the relationships of which it is capable; and we must now consider this series in another way:

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Ex. 190.

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Each partial forms with its neighbour in the series an interval represented by a ‘super-particular’² fraction, and these intervals are the ultimate facts of music. They immediately combine to form new intervals as quotients: thus, 2/1 ÷ 3/2 = 4/3, that is, the power of hearing the Octave and Fifth carries with it the power to hear the Fourth as well. Further, 3/2 ÷ 4/3 = 9/8; that is, the hearing of the Fourth and Fifth involves the appreciation of the major Tone. This means that in order to discriminate the major Tone it is not necessary to have an ear fine enough to hear the 8th and 9th partials, which also give it (because they are partials of the 2nd and 3rd partials), but it can be apprehended directly as the ‘difference’ (strictly, quotient of) an Octave and two Fifths.

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² Of the form (a+1)/a.

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The power of hearing up to the 3rd partial provides a scheme of notes which is known as ‘quintal’ harmony; and since this is infinite, it would be possible to plot a scale in this harmony alone of twenty-two or any other desired number of degrees in the octave. But the relationships would begin soon, after the first half-dozen or so, to be remote and practically unintelligible. For instance, the obvious relationship of C to B♭ is that B♭ is a minor Third (316 cents) from G, and G is a Fifth (702) from C; total 1018. It is possible in quintal harmony also to reach B♭ from C, but only by calculating upwards in major Tones (5 × 204 = 1020), and this process confuses the ear. It does not matter that 1020 is not the same as 1018; for the difference is only 1/56 of a semitone, and it requires a good ear to distinguish even tenths of Semitones in an interval which, like C–B♭, is derived, and not a matter of immediate perception like, for instance, C–G, or C–E. What matters is that the ear cannot make so elaborate a calculation as five successive major Tones—as, indeed, Aristoxenus, quoted above, suggested.

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The ear, therefore, takes by preference the intervals derived from the 5th partial, the major Third, which form ‘tertian’ harmony. As ‘quintal’ harmony was derived from the Octave and Fifth, so tertian harmony is derived from the Octave, Fifth, and Third; and ‘septimal’ harmony, if it is ever used, is derived from these three and the 7th partial. In tertian harmony the series is again infinite, as indeed any of these series must be, since no basic interval is an exact power (or root) of another basic interval. But since there are three basic intervals instead of, as before, two, it is found by experience that a larger number of derived intervals, about eight, are easily intelligible in tertian harmony. We have no experience of septimal harmony, and it is impossible to say what intervals the ear would here accept. And this is important. With the acoustical material available, many and diverse scales might be constructed, and they would all look equally well—or ill—on paper. Whether Indians have modified the ancient Hindu theory of strictly quintal and tertian intervals by the introduction (due, Mr. Clements suggests, to Mohammedan influence) of septimal intervals, can only be established on evidence. If any people hears septimal intervals, the Indians and Greeks, with the fine ear which practised and the fine discrimination which recorded the niceties of the *genera* and the *grāmas*, would have been among the first to do it; but to establish the fact it requires, in the complete absence in their theoretical works of any hint that they did so, a broader basis of observation than is provided by the performance of a single singer.

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With regard to the transilient scales, I received from the melodies sung in them a strong impression that they were in just intonation—that a major and minor Tone made a major Third, that the Sixth was just and not sharp. There is no reason, however, why tertian intervals (which this implies) should not have been accepted in pentatonic scales later, and yet the origin of these have lain originally in pure quintal harmony. An argument may be found to support this.

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Quintal pentatonic scales are based on a series of five Fifths—say, C–G–D–A–E. Reducing these within the limits of an Octave, and relating them to a common tonic, we get the following scheme for the five pentatonics:

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| CENTS. | RATIOS. | { | Scale on ‘white’ notes, as from | | | | |
| | | C | G | D | A | E |
| C | 1200 | 2 | C | C | C | C | C |
| b | | | | | b | b | b |
| Bb | 996 | 16 : 9 | ... | ... | Bb | Bb | Bb |
| # | | | # | # | | | |
| A | 906 | 27 : 16 | A | A | ... | ... | ... |
| b | | | | | | | b |
| Ab | 792 | 128 : 81 | ... | ... | ... | ... | Ab |
| G | 702 | 3 : 2 | G | G | G | G | ... |
| F | 498 | 4 : 3 | ... | F | F | F | F |
| # | | | # | | | | |
| E | 408 | 81 : 64 | E | ... | ... | ... | ... |
| b | | | | | | b | b |
| Eb | 294 | 32 : 27 | ... | ... | ... | Eb | Eb |
| D | 204 | 9 : 8 | D | D | D | ... | ... |
| C | 0 | 1 | C | C | C | C | C |

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The worst scales—the least euphonious, those which involve the more abstruse fractions—are those of C and E; that of D is the best. This D scale

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Ex. 191.

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is the type, which goes under the name of Sārang, of a favourite form of pentatonic Rāg. We saw also (p. 70) that there was a decided preference in the Garhwālī songs for the A scale:

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Ex. 192.

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though not to the exclusion of the C and E scales.¹

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¹ In the Journal of the English Folksong Society (vol. xvi), Miss Gilchrist records her belief that the typical Scotch pentatonic is the G scale. A cursory glance at the first hundred or so in Petri’s collection suggests that the Irish favourites are the G and A scales. (A song may be in a pentatonic scale although more than five distinct notes are touched in it, if it has only five substantive notes and the other one or two are used as passing notes.)

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But the D and A scales (and G) are the best of the five only if the intervals are taken as strictly quintal; if tertian intervals are substituted, i. e. if ‘merging’ takes place, the five scales are equally ‘good’. If, therefore, these particular scales are found to be the favourites in a country, it is an argument that all the pentatonics were in that country taken as strictly quintal, at any rate originally, though tertian intervals may have crept in later.

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The śruti enters into music as one of three definite intervals. Just as there are three diatonic intervals (svaras), so there are three enharmonic intervals (śrutis). The diatonic intervals we have seen to be Major Tone, 9/8, 4 śrutis Minor Tone, 10/9, 3 śrutis Semitone, 16/15, 2 śrutis and the enharmonic intervals are such intervals as correspond to a difference of one between the śrutis of the svaras (or are the various quotients of the fractions which answer to those svaras). The numbers 4, 3, and 2 may be handled in three ways so as to produce a difference of one; thus:

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(a) 4 - 3 = 1 śruti 9/8 · 9/10 = 81/80 = 22 cents. This is the ‘indicative’ śruti, the ‘Comma of Didymus’.

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(b) 3 - 2 = 1 śruti 10/9 · 15/16 = 25/24 = 70 cents (strictly, 70·6). This is the ‘small semitone’.

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(c) 3 + 2 - 4 = 1 śruti 10/9 · 16/15 · 8/9 = 256/243 = 90 cents. This is the ‘Pythagorean Limma’.

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But these intervals as such remain theoretical. They are actually sung only as increments of other larger intervals.¹ There is no case in any Rāg where two notes are separated, for instance, by the Comma of Didymus. That interval represents the difference between the two major Sixths (A and A♯), or between the major and minor Tone (D and D♭). But both notes (A and A♯, &c.) do not appear in the same Rāg; the Rāg contains the one or the other.

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¹ ‘Heterotone’ would be a better name for śruti than the usual translation ‘microtone’.

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We may notice in passing that this principle extends to the *svaras* also. A *Rāg*, *Pilu* for instance, has an E and an E♭ with a D and a F on either side of them; but in a given passage either E or E♭ will occur, but not both as a rule. And the principle, though not so strictly carried out, may be traced with tones as well as semitones. It is not at all uncommon for a *Rāg*, especially in southern India, to omit a note in ascent, but its next door neighbour in descent. Two notes, A and B♭, being ‘in’ the scale an ascending passage will employ by preference G A–C, a descending C B♭–G; though quite possibly both notes will be used occasionally. The same thing is common enough in our own Folk-song:

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*Abroad as I was walking.*¹

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¹ From the *Journal of the Folksong Society*, vol. iii, p. 124, No. 40.

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Ex. 193.

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Here the salient notes are clearly C, F, and B♭,² and it is interesting to see how the tetrachords C–F, F–B♭ are filled. In bars 1 and 13 we have the equivalent of

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² The reader may wish to add G. But ‘modes’ are tetrachordal; the tetrachord hangs about them like the ‘shame of the swaddling-clothes’; and the tetrachords are certainly not D–G, G–C.

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Ex. 194.

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though both notes (D and E♭) are present in ascent and descent in bars 2 and 3. In bar 7 occurs

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Ex. 195.

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and in bars 9 and 11

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Ex. 196.

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In these instances a non-modal writer would be more likely to have employed

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Ex. 197.] and [Figure: Ex. 198.

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and he would probably have sharpened the F's. The principle is, then, broadly that between two salient notes modal melody tends to employ only one of two alternatives, and, for choice, that alternative which is nearest to the note which is being left, not to that which is being approached.

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It is difficult to show this convincingly with regard to the *śruti*; but it may be seen in the grace-notes which occur like ‘enclitics’ in many Indian melodies, i.e. they belong to the note which is being quitted, not to that which is being approached:

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[Figure: Ex. 199.] &c.

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They are on the principle of the violinist’s slide. In passing from C to G he does not use all the intermediate notes, but only the first few:

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Ex. 200.

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Hence comes no doubt the statement that for southern India the quarter-tones (*śruti*) are ‘confined to grace’ (Day, p. 30). But that is not the usual acceptation of the word in the South. *Śruti* there means keynote. A singer has ‘lost his *śruti*’ when he sings out of tune; the drone strings of the *vīṇā* are called the *śruti*, and so on. This is clearly a transference of meaning from ‘a nice distinction of pitch’ to ‘that which determines the pitch’.

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But in the North *śruti* has retained its original meaning, nice distinction of pitch. There, however, its nature has been sometimes misapprehended. Stress has been laid on there being twenty-two of them, and the scale has come to be regarded as an octave with twenty-two stopping places. Consequently theoretical musicians are to be found who are prepared to sing from C to C, stopping at twenty-one places on the way. We have seen that this is wrong artistically, because melodies rarely use two of these, and never three, in succession. But it is wrong scientifically also. For the *śruti* did not arise as a division, equal or unequal, of the semitone. It has no independent existence. It is only a difference between two intervals considerably larger than itself. Thus the A♯ which we reach from C through D, and the A reached through F or E differ by the interval A♯-A (27/16 × 3/5 = 81/80) the ‘Comma of Didymus’.

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Ex. 201. (Musical notation showing A♯, A, A with ratios 9/8 × 3/2 = 27/16, 4/3 × 5/4 = 5/3, 5/4 × 4/3 = 5/3)

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So also with Small Semitone. Pythagorean Limma.

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Ex. 202. (Musical notation showing ratios 5/4 ÷ 6/5 = 25/24, 16/9 ÷ 27/16 = 256/243)

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The śruti is not an independent interval, but an increment of, or a defalcation from, some larger one. We get in this a suggestion which will reconcile the North and South Indian connotations of the word. A śruti is not, as it has hitherto been understood to be, the smallest audible sound, but the accurately audible sound—that which is ‘heard’ in accurate relationship to some other. This position throws some doubt on Helmholtz’s¹ account of the Greek quarter-tone (following Plutarch²) as a division (32/31 × 31/30) of the semitone (16/15). It seems possible, at least, that as the Greek and Indian systems were alike in so many other respects, they were alike also in deriving their ‘enharmonic’ tones from a persistence in just intonation and a refusal to compromise, i. e. to temper.

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¹ Sensations of Tone, English translation, 1875, p. 407.

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² De Musica, chap. viii. He says the old players ‘took the semitone as simple (A-B♭), not a compound interval (A A♯ B♭). Later the semitone was divided.’

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It is hard for Europeans to realize the state of things here described; but we have occasional glimpses of it. The major Sixth,

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Ex. 203. (Musical notation with lyrics "Be-hold . . . your God . . .")

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for instance, tends to be sung as a larger interval (since the B is forced up by the harmony to be a major tone from A) than that in where the interval E–F# is a minor tone. The first of these is, in fact, what we have been speaking of as the interval C–A, the second the interval C–A. The distinction between these two is also made use of in Schubert's *Ganymed* for a particular effect:

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Ex. 204.

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Ganymed. SCHUBERT. Ex. 205.

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Here the harmonies of the third and fourth bars wrench the melody up a major tone,¹ whereas the scale would demand in the third bar a minor tone; so that for two bars—the words ‘strebt’s hinauf! hinauf’—the voice is travelling at a pitch a fraction higher than normal, and admirably illustrates the meaning of the text, while at ‘es schweben’ it drops back (again owing to the harmonies) to normal pitch.

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¹ C, the sixth of the scale, is normally a minor tone from B♭, the fifth. But the basses E♭ and F in the third and fourth bars are a major tone apart. And therefore the melody which they bear (the B♭ and C) must here be separated by a major tone. Similarly, in the fourth and fifth bars, where we have modulated to F minor, the F and the G (and therefore the C and the D) are a major tone apart.

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This example shows also the other two *śrutis*. The Comma of Didymus and the Pythagorean Limma are correlatives; the two together make up the diatonic semitone (22 + 90 = 112). The latter occurs, therefore, in the fifth bar of Ex. 205. The ‘small semitone’ appears also in the accompaniment of the next bar. The *locus classicus* for this interval is the Elizabethan madrigal, in which a minor Third is frequently, and with beautiful effect, substituted for a major Third, as a deliberate ‘False Relation’:

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WEELKES, 1598. Phil - lis hath sworn she loves the man,

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EX. 206.

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Phil - lis hath sworn, . . Phil - lis hath Phil - lis hath sworn Phil - lis hath sworn she loves the man, . . . . . sworn, Phil - lis hath sworn, Phil - lis hath sworn she loves the man, . . she loves the man,

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or, by the reverse process, constitutes the peculiar charm of the ‘Tierce de Picardie’.

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There are also other ‘*śrutis*’ in European employ. (1) The difference between an Octave and three major Thirds (1200 - 386

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× 3 = 42 cents). It is present wherever, for instance, G♯ is taken as A♭. A fine example of this forms the climax of the introductory bars to the second Act of the *Walküre*. (2) The difference between four minor Thirds and an Octave (316 × 4 − 1200 = 64), of which a rather wooden example is to be found leading up to an entry of the C major subject in the overture to Smetana’s *Bartered Bride*. (3) The difference between twelve Fifths and seven Octaves (702 × 12 − 1200 × 7 = 24). This occurs in a descending form in the six bars which follow Wotan’s words ‘So küsst er die Gottheit von dir’ at the end of the *Walküre*, and, ascending, in the five bars which close the first of Vaughan Williams’s *Five Mystical Songs*:

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Ex. 207.

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And the same fact is present, of course, whenever the whole tone scale is played (204 × 6 − 1200 = 24), the musical effect of which is closely comparable to that of the *Pratimadhyama* scales of India. Then there is that magnificent mounting bass which compasses a Fifth in seven semitones (112 × 7 − 702 = 82) towards the close of the Finale of Schubert’s C major Symphony; and there are no doubt instances of other such intervals. The point is that we use enharmonic intervals for precisely the same reason as the Indians—for their jubilant or pathetic effect; only we do it in a different way. Equal temperament has nothing to do with this matter—we hear the effect in the orchestra and imagine it on the piano; though it has a great deal to do with the vocalization of a melody.

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