chinese musical system psychological aspects

7/27/2019 Chinese Musical System Psychological Aspects

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Philosophical Review

On Some Psychological Aspects of the Chinese Musical SystemAuthor(s): Benjamin Ives GilmanSource: The Philosophical Review, Vol. 1, No. 1 (Jan., 1892), pp. 54-78Published by: Duke University Presson behalf of Philosophical ReviewStable URL: http://www.jstor.org/stable/2175529.

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ON SOME PSYCHOLOGICAL ASPECTS OF THECHINESE MUSICAL SYSTEM.

SINCE the publication in I862 of Helmholtz's renownedLelre von den Tonernpfindungenthe investigation of thepsychology of tone has been actively pursued by students of the

science of mind. The effort made by Helmholtz to interpretthe achievements of the constructive genius of modern Europewith the material of tone by a reference to the dealings there-with of other races and ages has in particular given a greatimpulse to the collection of accurate data in regard to non-European music and their psychological study.1

The present paper aims to contribute to this branch ofresearch a discussion of the musical system of China, basedupon observations of performances by native musicians. Thesemusical ideas and musical products it is our purpose to examine,not from the artistic, but the psychological point of view. Weshall consider them as illustrations of the movements of thehuman mind in hearing, imagining, and reflecting upon tonesand their combination, as material for a comparative psychologyof that element of our sensations of sound which is known asthe quality of pitch.

1 Among many recent students of the psychology of tone may be mentioned inEngland, Messrs. Gurney and Sully; in France, R. Koenig; in Germany, Pro-fessors Preyer, Mach, Lipps, and especially C. Stumpf of Munich, of whoseimposing Tonpsychologie wo volumes only have as yet appeared. The studies ofnon-European scales by the late A. J. Ellis, those of Professor Land of Leyden inArabian and Javese music, those of T. Baker in the music of the North AmericanIndians, are specimens of the contributions of the last decade to our knowledge ofprimitive musical usages. We may hope for much light from inquiries of the latterkind upon the problem of the origin of music; an interest in which has recentlybeen reawakened by an essay contributed to Mind (October, I890), by Mr.Herbert Spencer.54

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CHINESE MUSICAL SYSTEM. 55The specimens of Chinese music to whose interpretation in

the light of their theory this paper is devoted have been studiedin phonographic reproduction. Through the kindness of Dr.Frederick Starr of New York, who was acquainted with severalof the Chinamen living at the time in the city, I obtained theopportunity on the 17th of March last to bring a phonograph tothe quarters of one of them in Mott Street; and with Dr. Starr'sassistance to take inscriptions of several melodies played by twoperformers. A few days later Dr. Starr invited some of thesame Chinamen to meet us at his rooms, where again with hisaid I took inscriptions of several more melodies played by twoother performers. The following table gives a list of the songsthus obtained:

NAME. PLAYER. NAME. PLAYER.

SAY-QUAW-CHUNG HUNG-YU. LONG-HOW-SA . . . . JU-MOY.HAN-KANG . . JU-MOY. HOP-WONG-HIN. . . . itMONG-LUT-LAO SAN-FA-TIU . . . . . AdYEN-JEE-QUAW-CHANG SAI-TON . . . . . .GIE-WONG . . . . . SONG-TING-LONG . . . {CKWAN-MOK . . . . .LO-TING-NYANG.do . YING-PARK. MAN-NEN-F6N . Unknown.SO-YFN . . . . . . JU-MOY. LONG-HOW-SAI.

All of them excepting the last two were played upon theSamien (Samin, Sam-jin, San-hien, San-hsien), a long-neckedguitar having three strings of which the two upper were tuneda fifth and an octave above the lowest. Man-nen-fan and Long-how-sa were played upon a small horn called the Gie-erh.2 Themusic accompanying this paper consists of four of these melo-dies represented as exactly as is possible in our European nota-tion, which is here intended to signify the ordinary temperedinterval order of equal semitones embodied on our keyed in-struments, the black keys being indicated by sharps.3 It is

1 Different airs.2 J. A. Van Aalst (Chinese Music, Shanghai, I884) describes (p. 72) an instru-ment very similarto the Gie-erh under the name of Kuant-zu.3 An interval may be roughly defined as the difference in pitch between two



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56 THE PHILOSOPHICAL REVIEW. [VOL. I.probable that the absolute pitch as here expressed does notvary from that of the performances by more than a fractionof a tone. A line drawn above a note signifies that the soundis between that written and the note a semitone higher. Inorder to avoid the multiplication of bars and an appearance ofregularity in the sequence of stronger notes which does notalways characterize this music, emphasis has in all cases beendenoted by accents. The sharps apply only to the notes againstwhich they are written.

Our present knowledge of Chinese music is very largely anotes. It is found that when the differencein pitch between the components of anytwo pairs of notes is the same, the ratio between the numbers of vibrationsper sec-ond producing the two notes of one pair is the same as that between the numbersproducing the two notes of the other. To each interval, in other words, correspondsa certain ratio between the rapiditiesof vibration of the two sources of sound pro-ducing the notes entering into it. In our modern keyed instrumentsthe distance inpitch or interval between any pair of adjacent notes is the same as that between anyother pair, and is called a semitone. This equalization of the interval betweenadjacent notes is what is known as equal Temperament. Any two keys betweenwhich eleven others are included give the interval called the octave, conspicuous forthe likeness in sound between the notes concerned. A tempered semitone is there-fore an interval one-twelfth the size of the octave. Mr. Ellis has proposed to expressdifferenceof pitch in terms of the hundredth partof a tempered semitone; that is, thetwelve-hundredthpart of an octave. This unit, called by him the cent, we shall findit convenient to use in our discussion. The compass in cents of the intervals prin-cipally used in music, in their perfect form and as they are approximatelygiven ontempered instruments,is as follows True. Tempered.Semitone ratio16 112 i0OMinor one . 10? I82 200-9Majorone . 204 200

6Minor third .i . 3i6 300Major third . 386 400Fourth . . 498 500Fifth. 3 702 700Minor ixth . 8 814 8ooMajorsixth . . 884 900Major eventh. 1 io88 1100Octave 2 1200 1200

In the text we shall use the common symbolism of accented and unaccentedletters for the sequence of notes on a keyed instrument. The letters ec c/ d/ . .bindicate the middle octave, whose notation reaches from the first ledger line belowthe treble stave to the third line from the top of it; the pitch here meant by c' beingproduced by 268 vibrations per second. The next lower octave is written withoutaccents, and the next higher is doubly accented.



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No. I.] CHINESE MUSICAL SYSTEM. 57knowledge of its theory, which seems to have assumed a veryelaborate and exact form from even the most remote times.1Kiesewetter warns us, however, against mistaking such informa-tion about the musical theories of a people for knowledge of thestate of the art itself among them. I have long felt, he writes,2

that the practical music of many Asiatic peoples, ancient andmodern, must have been and must be a totally different thingfrom the metaphysical or mathematical music of their philoso-phers, which as pure speculation must always have held itselfapart from practice. We have erred in reasoning from thewritings of theorists among these peoples to the nature of theirart itself. In large measure, doubtless, this tendency amongstudents of the ethnology of music to forget that the books oftheorists may not reflect the methods of performers is theresult of the extreme difficulty of investigating the actual prod-ucts among other races of an art essentially evanescent asmusic is. The cases are rare in which they come to the hearingof trained musicians; we can infer for the most part only theirscale structure from instrumental forms: and their record innotation is in general both imperfect and scanty. The inventionof the phonograph bids fair to render the practice of musicamong non-European peoples as accessible to study as theirideas about the act have hitherto been. Whenever a phono-graphic cylinder can be exposed to a musical performance aclose copy of the original texture of tone is fixed in a form whichadmits of subsequent examination of the most careful kindwhenever and wherever desired.3

1 The principal sources of information in regard to Chinese music are the work ofPere Amiot, which forms vol. vi of Memoires concernant l'histoire, les sciences, etc.,des Chinois, par les Missionaires de Pekin, Paris, 1780; and the recent essay of J. A.Van Aalst already referredto.2 Ueber die Musik der neueren Griechen,p. 32, quoted in Ambros, Geschichte derMusik, i862, vol. i, p. 56.3 The need for an instrument of this description in the study of music was ex-pressed thirty years ago by Moritz Hauptmann (Briefe an Hauser, Leipzig, i871, Bd.ii, p. I50). Would that we could make musical photographs which should pre-serve our present art for the future: and would that we had them from the past.Then we should know, among other things, something about Greek music, which weare now acquaintedwith only through the entirelyunmusicalphilologists; i.e. are notacquaintedwith at all.



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58 TILE PHILOSOPHICAL REVIEW. VOL. I.Such a detailed examination of the Chinese performances of

our collection forms the foundation of the present discussion.I have to thank President Low for the permission to carry onthis work at Columbia College. An account of the methodemployed and of a set of experiments made to determine itsaccuracy and that of the phonograph will form the subject ofan appendix to this paper. (See next number of the REVIEW.)'

The fixation of a definite interval-order which shall serve asthe scale of their performances is the starting-point of Chinesemusical theory. All the different pitches which are used in agiven piece of music, taken together embody a certain set ofintervals arranged in a certain order from low to high. Thefact of scale in music is the fact that in general in the music ofone age and race different pieces embody in this way the sameorder of intervals, or one or other of a few different orders.Scales are the generic interval-orders of compositions. Accord-ing to the prescriptions of Chinese theory all their musicembodies one interval-order or scale, which may be varied bythe omission of one or both of two subsidiary notes. Thisscale consists of notes repeated in octaves. A note and itsoctave are called by the same name in China, and are apparentlylooked upon as essentially the same thing.2 Evidence of thisidentification of octaves in the Chinese mind is given in thesong, Yen-jee-quaw-chang, where among the slight variationsof the second performance in one place the melody follows itsprevious course for several notes at an octave below the originalpitch. Five primary intervals span an octave in the Chinesescale, the two intermediate notes which are used in a subsid-iary way increasing this number to seven. These pentatonicand heptatonic octave divisions originated according to Chinese

1 Chinese musical practice has been hitherto very little studied. Pere Amiot givesin European notation a part of a temple hymn. Pere du Halde in A Description ofthe Empire of China, London, I79I (translation), vol. ii, p. 125, gives the notes offive songs. John Barrow, in Travels in China, 2 ed., London, i8o6, pp. 316-322,gives the notes of ten songs, and p. 8i, a boatman's chorus exhibiting a rudimentarycanonic imitation. Van Aalst gives nine pieces, expressly stating, p. 22, that they canonly be approximately rendered in European notation. None of these songs areincluded in our collection.2 Van Aalst, p. i8.



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No. i.] CHINESE MUSICAL SYSTEM. 59accounts through the employment of a continued progressionupward in pitch by the interval of the fifth.' We are herereminded of the Pythagorean derivation of the diatonic intervalorder of the Greeks in like manner from a progression of fifths;but if Chinese sources are to be trusted, its application in theirmusic antedates the Pythagorean discovery by a score ofcenturies.2 The musical theory of the Greeks had its origin inthe division of a string; that of China, in the measurementof pipes. The vibration ratio of the fundamental tones of twopipes will, other things being equal, be very nearly if notexactly the inverse of the ratio of their lengths. Thus a pipegiving a tone an octave above another like one (vibrationratio -1) will be of half its length; a pipe giving a tone afifth above another (vibration ratio 4) will be of two-thirds itslength. This connection between the simplest ratios and strik-ing facts of pitch-relation seems from time immemorial to havebeen employed in giving a philosophical basis to the Chinesemusical system. PWre Amiot quotes (p. I17) a speculationabout the foundations of music written by Hoai-nan-tsee, Kingof Hoainan (B.C. io5), which begins as follows: The principleof all science is unity. Unity as single cannot produce any-thing, but it engenders everything, insomuch as it includeswithin itself the two principles of which the harmony and theunion produce everything. It is in this sense that one cansay, unity engenders duality, duality triplicity; and from tri-plicity all things are engendered. 3

According to these principles, a pipe whose note is at theinterval of the fifth (2) above that of another, will be a natural

1 Amiot, p. ii2; Van Aalst, p. 14.2 Van Aalst, p. 7. The Emperor Huangti (B.C. 2697) and his minister Ling-lun

are by one account credited with the invention of the fifth progression.3 We find similar ideas made the foundation of musical theory in Europe two mil-lenniums later in the Harmonik und Metrik of Moritz Hauptmann (2d ed., Leipzig,1873, p. 8). Rightness- that is, reasonableness of musical structure has for itslaw of formation unity with the negation of it and the resolution of this contradiction:an original unity which passes through a state of inner contrarietyto become a unityrestored. This process must continually repeat itself, either upon original unity orupon the result of a previous process. So the unity of a single note becomes in itsrestoration the triad, the unity of the triad becomes in its restoration the scale(since the scale may be viewed as a chain of three triads).



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6o THE PHILOSOPHICAL REVIEW. [VOL. I.derivative from it, since the proportion of the two (i: 2) embodiesthe fundamental ideas, unity, duality, and triplicity. The con-tinued application of this proportion gives, as a natural progres-sion of notes, those corresponding, through the sizes of theirsources, to the numerical series

I 2 (2)2 (2)33 etcLet us suppose such a progression by upward fifths to be

carried on until a series of five notes be formed, the pipesbeing doubled, that is, the lower octave of a note being taken,whenever necessary to keep the compass of the series within anoctave. The following interval-order would be the theoreticalresult, the initial note occupying the lower extreme:

Ist . 3d 5th 2d 4th(cents) * 204. 204 * 294- 204 -Of these two intervals, the smaller is that called in Europeanmusic the major tone (Q-); and the larger is an interval (37-)closely approximating to a minor third (316 cents). The pri-mary scale of Chinese theory consists of notes at these intervalsrepeated in octaves above and below. This extension introducesno new interval into the order, the compass of the above fourbeing just 294 cents less than an octave. The complete orderconsists, therefore, of approximate minor thirds, alternating firstwith one and then with two tones. To these five notes andtheir octave repetitions were given the following names: thenote from which the order can be derived by a progression offifths, that one, namely, which lies below the sequence of twotones was called Koung; the note between the two tones wascalled Chang; that above them, Kio; the note below the iso-lated tone was called Tche; that above it, Yu. Were the fifthprogression carried on two steps further, still keeping it withinthe octave, two more major tones would be introduced, givingthe following order:

ist 3d 5th 7th 2d 4th 6th(-294-)204 * 204 * 204 * 90. 204 - 204K Ch Ki T Y



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No. I.] CHINESE MUSICAL SYSTEM. 6IThe two new notes divide the two thirds of the scale in thesame way: a new interval of go cents, which is that called inEuropean music a Pythagorean semitone (-y42),ppearing be,tween one of the new notes and Tche, and the other and thehigher octave of Koung. These two are the subsidiary notesof the Chinese scale, and were called the two pien, the namesignifying literally changing into. I That next below Tchewas called pien-Tche, and that next below Koung, pien-Koung. The whole series was called the seven principles(Tsi-Che). This is the identical determination of the intervalsof a seven-step octave scale, which, given in the theory ofPythagoras, remained the foundation of the European musicalsystem for two thousand years thereafter, and was definitelyrelinquished only during the sixteenth century. The Tsi-Cheof China and the diatonic scale of classical and medievalEurope may be alike defined as an order of intervals in which a(Pythagorean) semitone alternates first with two and then withthree major tones.2

While in China music has been founded in the main uponthe simpler scale of five steps, evidence of the antiquity of thepien is not wanting. In answer to theorists who regardedthem as an innovation, Prince Tsai-yu (1596) declares that one

I Or, as Pere Amiot defines it, that which passes from the state of possibility tothat of existence. (p. 55.)2 A nomenclature whose firstemploymentis attributedto Guido d' Arezzo (eleventhcentury) is now applied in the following way to the various notes of this order: Thenpte below the group of three tones is called Fa; then follow (upward) Sol and La:Si being the name applied (from the sixteenth century) to the note above the groupof three tones; the note below the group of two is called Ut (later Do), Re beingbetween, and Mi above them. With these the names given in China to the notes ofthe same order correspond as follows:Fa Sol La Si Do Re Mi* (204) - (204) * (204) * (90) * (204) * (204) -Koung Chang Kio pien-Tche Tche Yu pien-Koung

In the development which the diatonic scale has undergone in modern times, firstinto the harmonic,and then into the tempered scale of our pianos, this symbolismhas come to have two other slightly differentmeanings, as follows:Modern diatonic: . (204) * (182) * (204) * (112) * (204) * (I82) -Fa Sol La Si Do Re MiModern tempered: * (200) * (200) * (200) * (Ioo) * (200) * (200) -



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62 THE PHILOSOPHICAL REVIEW. [VOL. I.only needs to read the works of Confucius (among many others)to see that the seven principles have been recognized inChina from the remotest times: it is only the half learned, hesays, who deny this. (Amiot, p. i6i.) All seven are certainlyfully recognized in our songs, in only two of which a pure five-step order is employed. It is true in all of them the two pienare used much less often than the others, yet to omit themwould in all cases materially alter the character of the music.In this point our songs contradict Van Aalst's statement (p. i6)that the Chinese of the present, while theoretically admittingseven sounds, practically never use but five to the octave.'

In determining the scales actually embodied in the songs ofthe present collection, the successive pitches of which eachmelody consisted were determined as closely as possible by amethod to be detailed in the appendix. They proved in all of thesongs excepting the horn melody Long-how-sa to gather them-selves into groups generally covering a compass of not overan eighth of a tone. The centre of gravity of each group wastaken for the indicated note, and the order of intervals sepa-rating the indicated notes became the scale of the song. Thetable on the following page presents the result of this calcula-tion in cents for all of the Samien songs. The scale of thehorn melodies will be given later.

In each of these songs notes approximating in pitch to d', e',g', a, and b', were the most frequent of all. In eleven out ofthe thirteen, occasional use was made of a note between e' andg', and of another between b' and d . The other notes wereall repetitions of these seven in the lower or the higher octave.

1 A hint as to the possible source of this discrepancy is given by S. Wells Williams,The Middle Kingdom 2 ed., 1883, ii, p. 95. There are two kinds of music,known as the Southern and the Northern, which differ n their characterand arereadilyrecognized by the people. The octave in the former seems to have had only sixnotes, and the songs of the Miaotz and rural people in that portion of China, arereferable to such a [five-step] gamut, while the eight-tone scale [seven-step] gen-erally prevails in all theatres and more cultivated circles. Further examination bycompetent observers who can jot down on such a gamut the airs they hear in variousregions of China is necessary to ascertain these interesting points. . . . One of thepieces given by Van Aalst in musical notation uses one of the pien; of Barrow'seleven songs only two neglect the pien entirely.



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No. i.] CHINVESEMUSICAL SYSTEM. 63

z Z z0 z4 N c V)

-4 0~~~~~~~~0 0~~~~~~~

0J 0N Uw %D Uw 0 0

o 0 ~ r 0 0 0 0 0 0 0 0 -

o 0 -1 u 8 toou 8. .

00 ~~~~~~~~~~ -~0 Q 0 0 .

00 0 0 0 08

40 4n 0~0 0 - 0 0 -

88L 8 '- 4004-0.H0to~~~~~~~~~~~~~~~~~~~~.t) 0~ ~~~~

0 0 0 APPROX.ts) W - - 0 W - ts) ~ ~ ~ ~ ~ PTCH



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64 THIE PHILOSOPZICAL REVIEW. [VOL. I.The foundation of the scale of these melodies is therefore thenormal Chinese interval-order of the five steps to the octave,approximate minor thirds (e-g, b-d) alternating with one (d-e)or two (g-a, a-b) approximate tones. The note g' is determinedas Koung, and the scale is generally, though not always, com-pleted to a heptatonic order by the introduction of the two pien.

This general conformity with the theoretical seven-step orderis accompanied by divergencies of detail which are not withoutmarked effect on the music. In the first place, as our tableshows at once, the position of the two pien is different fromthat assigned to them in theory. As the sixth and seventhnumbers of the progression of fifths, the two pien are in thetheoretical scale, each placed go cents below the next highernote. In these scales the interval between the upper pien-Tche (the lower is omitted in all the songs) and the note aboveis never less than I85 cents, while that separating it from thenote below, which is theoretically 204 cents, is never greaterthan I25 cents. The intention of these performers is evidentlyto lower pien-Tche from its theoretical position through a semi-tone. According to Van Aalst this habitude is at presentgeneral in China; and dates from the invasion of that countryin the fourteenth century by the Mongols, whose scale wasidentical with that of the Chinese, with the exception of thissemitone's difference in the position of pien-Tche. Althoughthe note was preserved in the scale at both positions for a timeby the decree of Kubla Khan, the theoretical pitch was finallygiven up.'

1 Van Aalst, p. I6. But one of Van Aalst's songs uses pien-Tche (as a passingnote), and it is in this case flatted. The songs noted in Barrow'stravels in Chinacirca i8oo) exhibit the flatted pien-Tche. It is impossible to determine the usagein the songs given by P. du Halde (cir-c. I 700), where the scale has variousabnormalforms. Of the three five-step scales with intermediate notes for heptatonic use ob-tained by Mr. Ellis from the playing of Chinese musicians in London, one, that ofthe YUnlo (generally out of tune according to Van Aalst), has an entirely abnormalform. The other two appear to give the flatted pien-Tche. They are as follows(tr. of Helmholtz's Sensations of Tone, 2d ed., London, i885, App. XX):

K Ch K pT T Y pK KScale of the Flute, Ti-tsu: * 178 * i6i * 109 * 214- 226- 215 * 93 -Scale of the Dulcimer,Yang-chin: * 169. 105 * 217 170 * 217 ii8 * 202 .T Y pK K Ch K pT T

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No. i.] CHIXESE MUSICAL SYSTEM. 65It is a striking fact that in the history of the same theoretical

scale among the Greeks there arose likewise an alternative usageinvolving the difference of a semitone in one of its steps, andthat the note affected was the same in Greece as in China. Thiswas the note since called Si in the diatonic scale, and its differ-ing pitch was the basis of the distinction between the disjoinedand conjoined tetrachords of Greek theory.' The double into-nation continued during the middle ages, and was the germfrom which has grown the whole system of modern modulation.While it is open to us to suppose that the appearance of thesame phenomenon in Chinese musical history is due to theinfluence of Western civilization, we are not told that the Mon-gols brought the varying usage with them, but that it arosewhen their scale met that of China. Perhaps both the theoryof conjoined and disjoined tetrachords and the story of the Mon-gol scale are equally unreal hypotheses invented to explain theexpedients by which the Greeks and the Chinese met each intheir own way a practical difficulty arising in diatonic music.The notion of the diatonic order as a product of the fifth pro-gression involves the conception of Fa as the generating note,the origin of the others. If we assume that this position of

1 Cf. Stainer and Barrett's Dictionary of Musical Terms, art. Greek Music. Thelater Greek scale had a compassof two octaves, like that of our songs; but since it wasformed theoretically of four Dorian tetrachords (a sequence of a hemitone and twotones) with two added tones, the range of the two differsas follows:pT(pT) pK pT(pT) pKK Ch Ki T Y K Ch Ki T Y KLa Si Do Re Mi Fa Sol La ()Si Do Re Mi Fa Sol La*t h t t h. t * t t *h t t *h. t t

.h* t *t tAlternative position orconjoined tetrachord.

The two middle tetrachordsmight either have a note in common (syncmmenon,conjoined) or be separated by a tone (diezcugmenon, disjoined). The comparisonof the two scales shows that in the one case the note correspondingto pien-Tche wasa semitone, and in the other a tone below the next higher note. In Chinese musicthe lower octave of pien-Tche seems also to have been lowered in pitch a semitone.This was not the case in the Greek scale. The note does not occur in our songs butis given the lower position in two (IV and VII) of Barrow'scollection.



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66 THE PHILOSOPHICAL REVIEW. [VOL. I.prominence in the minds of theorists gave the note a like impor-tance in the ears of listeners to music, the supposition is naturalthat the inharmonious interval Fa-Si (an augmented fourth ortritonus) would be noticed as a blemish in the scale. The pitcha hemitone below Si makes with Fa the conspicuously harmo-nious interval of the pefect fourth, and this we may suppose wouldtend to be used with it. That Si was displaced in the Chinesescale and retained at both intonations in Greece may be regardedas due to the fact that in the Chinese scale it was one of thepien, a note whose exact pitch was of subsidiary importance,while in the fully developed heptatonic octave of the Greeks itstood on an equal footing with the other notes and tended tomaintain its individuality.

The irregularity in the position of pien-Koung in our melodiesis of a different kind. While in theory it should be go cents belowKoung (as the Mi of the European scale remained always a semi-tone below Fa), it is placed by our performers from I IO to i90cents below, the interval in most cases being not under I25 norover I75 cents. The result is the division of the minor third Yu-Koung into two intervals approximating to equality. The authori-ties on Chinese music make no mention of this intermediate into-nation of pien-Koung. In the songs given in notation by Barrowand Van Aalst the note has the normal diatonic position a semitonebelow Koung. In the two scales obtained by Mr. Ellis it appearsthat while pien-Tche is flatted in both, pien-Koung is flatted inone and sharped in the other. It is sharped in all of the scales ofinstruments given by Van Aalst, excepting in that of the Sheng,or mouth-organ, reputed the most perfect of Chinese instruments,where it is flatted in the lower octave and sharped in the higher.Among our performers neither Hung--Yu nor Ying-Park usedpien-Koung; but it recurs and with the intermediate intonationin the two melodies of the horn-player, hereafter to be referredto. Furthermore, in giving the notation of two melodies, whilethe pien do not occur in either, Van Aalst remarks upon a quar-ter-tone deviation of the notes in performance from their theo-retical intonation similar to that exemplified in the intermediatepitch of pien-Koung.



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No. i.] CHINESE MUSICAL SYSTEM. 67Examples of the equal division of the minor thirds of a scale

are not wanting in other musical systems, and the explanationwhich Mr. Ellis has offered for these may prove to be the trueone in this Chinese case. Celtic music, which is often comparedwith that of China on account of its pentatonic basis, wouldhave another striking characteristic in common with our melo-dies were it played upon the Highland bagpipe with equallydivided minor thirds whose scale is given by Mr. Ellis. Thesame writer reports also a modern Arabian scale which is prac-tically identical with this. A minor third divided into twoapproximately equal parts is also found in the tetrachord calledthe equal diatonic, and ascribed to the Alexandrian musicianPtolemy (200 B.C.). The intervals of this order are J-2, 1{, 19,or I 5, i65, and I82 cents; and they can be produced in a stringby stopping it at a quarter of its length and at one-third andtwo-thirds of this quarter. Mr. Ellis regards this process ofthe tri-section of the quarter of a string as the ultimate sourceof all these equal divisions of the third. The intermediate pien-Koung of our scales may according to this have a mechan-ical and not a musical origin. Another hypothesis will, weshall find, suggest itself in the course of our examination of theChinese system of modulation.

The non-diatonic intervals which result from the intermediatepien-Koung are the most striking feature of these Samien songs.The note is most commonly reached from or left for thoseimmediately adjacent above and below, separated from it byabout I 50 cents, or three-quarters of a tone; the interval Tche-pien-Koung, or pien-Koung- Chang (350 cents), occurs nearly asoften; and the progressions Kio-pien-Koung (350 cents) andpien-Tche-pien-Koung (650 cents) each occur once. To ourears trained in the diatonic scale all of these intervals have avery strange and half-barbaric sound; but the quality is mostmarked in that of about .350 cents, an interval between a minorand a major third (3i6-386 cents). This intermediate thirdneither charms the ear like the major nor touches the heart likeminor, but stands between them with a character of gravity,



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68 THE PHILOSOPHICAL REVIEW. [VOL. I.like middle life between youth and old age, to use the expres-

sion of a friend who has listened to this music.1The intermediate intonation of pien-Koung involves, as wehave seen, a conspicuous violation of Chinese theoretical prin-

ciples. Leaving now this note out of consideration, most of theintervals formed by the remainder still differ noticeably in theseSamien songs from those of the prescribed Chinese scale. Inthe seven-step order, as given by theory, while fifths and fourthsare perfectly embodied, no combinations of notes give more thanan approximation to the other harmonic intervals, thirds andsixths.2 For this reason diatonic thirds and sixths were notadmitted by early theorists among the consonances. TheVenetian musician, Zarlino, the first conspicuous authority todemand the abandonment of the Pythagorean theory of thescale, speaks in his Institutioni Harmoniche (1558) of the habi-tude of participatione by which the musicians of his dayfound it necessary to modify the theoretical thirds and sixths inpractice for the better contentment of the ear. 3 The Euro-pean ear has never found itself contented by any Chinese per-formances, and Van Aalst seems to attribute this as well to thePythagorean scale of the music as to the want of technical pre-cision among the musicians of China.4 Yet in these Samienscales we are unexpectedly confronted with a deviation ofpractice from the theoretical intervals, similar in character tothe participationn of the Italians. The examination of theforegoing table (leaving pien-Koung out of consideration) showsthat of the combinations of notes which are perfect fifths and

1 In Professor J. P. N. Land's discussion of the Arabianscale (quoted by Mr. Ellis)he names the interval of about 350 cents, exemplified therein and in our songs, aneutral third. Mr. Ellis in describing the effect of a third of 355 cents reports it asso nearly a musical mean between the just majorand minor thirds that a friend, onwhose delicacy of perception he seems to have placed much reliance, was quiteunable to determine to which it most nearly approachedin character (p. 525).

K Ch K pT T Y pK K2 In the scale 204 204 204 90 204 204 90Fa Sol La Si Do Re Mi FaSol-Do = 498 c = Fourth, Do-Sol 702 c = Fifth, etc.;Fa-La = 408 c = Majorthird + 22 c, La-Fa = 792 c = Minor Sixth - 22, etc.La-Do = 294 c = Minor Third - 22 c, Do-La 906 c = Major Sixth + 22 c, etc.

3 Ha Parte, Cap. 41. 4 pp. 8, 21, 71, etc.



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No. i@] CHINESE MUSICAL SYSTEM. 69fourths in the theoretic scale only about a third give, in theestimated scales, intervals varying noticeably from just intona-tion; while of the combinations of notes which in the theoreticscale give approximate thirds and sixths only a very small frac-tion in the estimated scales give perceptibly worse intervals,and nearly half give intervals perceptibly better than thediatonic approximations. Taking all the combinations of notestogether, which in the theoretical scale give either just orapproximate harmonious intervals, in the estimated scales theaberration from perfection is not over that of the theoreticalthirds and sixths in four-fifths of the cases, while in half ofthem it is not over half this error. In a word, cases of aberra-tion in the practical scales from the perfection of the theoreticalfourths and fifths are balanced by cases where the approximatethirds and sixths of theory have been improved upon in practice;the intervals in general showing a tendency to come closer tojust intonation than do the thirds and sixths of the theoreticalorder. Apart from the abnormal intonation of pien-Koung thedeviation of these scales from that of Chinese prescription maybe regarded on the whole as an improvement upon it.

Although according to the indications of these Samien melo-dies, Chinese performance is not always as barbarous as is com-monly asserted,' it must be admitted that one, at least, of thehorn-player's songs goes far to maintain the ancient reputationof the Chinese for inaccuracy of intonation. In the song Man-nen-fon, although the groups of attempts at the same note ofthe scale have a wider compass than in the Samien melodies,they are still distinguishable, and taking their centres of gravityyield the following scale:

T Y pK K Ch Ki T Y. 190 *155 55 200 * 200 * 300200 .d' f' g' a' b' d eHere f', by its infrequency, announces itself as a pien. Kounghas accordingly the customary pitch g', and the scale is ofnearly the customary form.

1 Cf Ambros, Geschichte der Musik, vol. i; Van Aalst, p. 6.



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70 THE PHILOSOPHICAL REVIEW. [VOL. I.The second horn melody, Long-how-sa, is characterized by thegreatest uncertainty of intonation. The groups of attempts at

the same note of the scale are here indistinguishable, and theintonations at which the performer probably aimed must beobtained by the separate examination of successive fragmentsof the song. The result of this analysis is the following set ofnotes in which d', g': and a' are by their infrequency determinedas pien and d'l therefore as Koung.

Y pK K Ch Ki pT pT T Y K150 150 150 200 100 IOO 200 150 300c' d' d': f' g' g'9 a' b' c d :This song is the only one in our collection in which any othernote than g' is taken for Koung. Its scale, moreover, differsfrom that of the Samien melodies in several points. The inter-vals, Koung-Chang and Tche-Yu, are three-quarter tones insteadof tones, and pien-Tche appears in both its Chinese and Mongo-lian positions, a semitone and a tone above Kio. The expla-nation of these irregularities is doubtless to be found in theconstruction of the Gie-erh. To perform the scale perfectly,from d': at Koung would require several notes not included init when taken from g'. Only one (g' seems to be providedon the Gie-erh, and even of this the performer does not appearto have made the best use. That the instrument gives no othernotes within the compass of this song is rendered probable bythe resemblance between the scale of Long-how-sa and that ofthe Kuant-zu, which, according to Van Aalst's description, is ahorn very like the Gie-erh. The two scales are as follows:Notes used in Long-how-sa:c'' d' d': f' g' g' a' b'c allNotes givenbythe Kuant-zu: d' e' g' g'$ a' b' c $:d e f ': gWe may surmise that the intention in making the Gie-erh wasprimarily to embody the scale at what appears from our songsto be a standard pitch, and further (by the introduction of g':)to permit in some fashion its displacement downward through aminor third. In this case, not only the irregular formation ofthe scale, but also the exceptional insecurity of intonation inLong-how-sa, receives a plausible explanation. The performer



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No. i.] CHINESE MUSICAL SYSTEM. 71may be conceived as embarrassed by the unaccustomed positionof the scale upon the instrument and its resulting distortion.

The use of the scale at different pitches, of which we havehere a practical example, appears to have been reduced to adefinite and elaborate system in Chinese theory from time im-memorial. In the study of the later development of this, a pos-sible reason will present itself for the choice by the Chinese ofthe particular transposition of Koung illustrated in Man-nen-fon and Long-how-sa for (approximate) embodiment on aninstrument. We shall find in the medieval history of Chinesemusic the reflection of a structural distinction which has beenfundamental in the art of Europe since the Reformation, andshall be able to interpret this transposition of our songs as evi-dence that the distinction in question is neither a purely theo-retical one nor purely a matter of history, but a fact of existingmusical practice in China as in Europe.

BENJAMIN IVES GILMAN.NEW YORK.(To be concluded.)



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72 THE PHILOSOPHICAL RE VIEW. [VOL. r.YEN-JEE-QUAW-CHANG.

PLAYED TWICE IN SUCCESSION BY JUMOY ON THE SAMIEN.- 120 First time.

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No. I.] CIzAESE MUSICAL SYSTEM. 73Secondtime.t t _ ? a

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74 THE PHILOSOPHICAL REVIEW. [VOL.I.LO -TING- NYANG.

10PLAYED BY YING -PARK ON THE SAMIEN.; 120.

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No. i.] CHINESE MUSICAL SYSTEM. 75MAN-NEN-FON.

(EVERLASTING HAPPINESS.)PLAYED UPON THE HORN, GIE-ERH.

J-100 at first, later 140.

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76 THE PHILOSOPHICAL REVIEW. [VOL. I.

g _$ _ _ _ 1- _ _

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No. i.] CHINESE MUSICAL SYSTEM. 77LONG -HOW- SA.

(A BRIDAL SONG.)PLAYED UPON THE HORN, GIE-ERH.J= 110at first, later 140.

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78 THE PHILOSOPHICAL REVIEW.o _ _

a n d d -g 0-air is~~:710

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chinese musical system psychological aspects

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