The Philosophical Review/Volume 1/The Chinese Musical System - Part 2

by Benjamin Ives Gilman

ON SOME PSYCHOLOGICAL ASPECTS OF THE CHINESE MUSICAL SYSTEM.

II.

ACCORDING to Chinese tradition, the progression of fifths, which was the origin of their scale, was carried on by its inventors, Ling-lun and the Emperor Hoang-ti, until it yielded a system of twelve notes separated by hemitones, like the duodecimal chromatic scale of European music. This is the system of the twelve Lu, which according to Chinese ideas is the foundation of the whole art of tone, and which they recognize not only in theory, but in some of their instrumental forms.^[1]

Let us suppose the derivation of pipes one from another by the two-thirds measurement, which gives first the five and then the seven step scale, to be continued until twelve pipes are formed, the derivatives being doubled as before whenever necessary to keep the whole series of sounds within an octave. The theoretical result of this process would be the following interval order:

1st8th3d10th5th12th7th2d9th4th11th6th
(cents) $\cdot$ 114 $\cdot$ 90 $\cdot$ 114 $\cdot$ 90 $\cdot$ 114 $\cdot$ 90 $\cdot$ 90 $\cdot$ 114 $\cdot$ 90 $\cdot$ 114 $\cdot$ 90 $\cdot$

consisting of Pythagorean semitones alternating with an interval almost exactly the size of the diatonic semitone, 16/15 (= 112 cents); the compass of the whole twelve notes being a Pythagorean semitone less than an octave. The sounds of twelve pipes obtained one from another by this extension of the fifth progression constitute what is known in Chinese theory as the system of the twelve Lu. The hemitones of the order are regarded as equal, and it is held to include all the possible distinctions of pitch within an octave, deriving this reputation doubtless from the circumstance that to Chinese ears it appears as the limit of the derivation by fifths.^[2] For were a thirteenth pipe constructed, its note would fall theoretically 24 cents, or the eighth of a tone above the octave of the initial note; and practically, it may be presumed, would be considered by a primitive instrument maker to be that octave. The powers of the process to engender a series of notes within an octave would therefore, we may suppose, be held to have exhausted themselves in the sequence of twelve just given.^[3] To these the Chinese give the following names in the order of the series of fifths: (1) Huang-chung, (2) Lin-chung, (3) Tai-tsu, (4) Nan-lu, (5) Ku-hsi, (6) Ying-chung, (7) Jui-pin, (8) Ta-lu, (9) I-tse, (10) Chia-chung, (11) Wu-i, (12) Chung-lu. Arranged in order of pitch upwards within the octave the sequence becomes: Huang-chung, Ta-lu, Tai-tsu, Chia-chung, Ku-hsi, Chung-lu, Jui-pin, Lin-chung, I-tse, Nan-lu, Wu-i, and Ying-chung.

But it was not alone the method of deriving these twelve sounds, the interval order which they should embody, which was fixed by their inventors. Their absolute pitch was determined also by the choice of a standard intonation for Huang-chung, the note of generation. This Ling-lun made by one account to coincide with the murmur of the spring whose bamboos furnished the first Lu, and which proved to be the source of the Hoang-ho river. Under successive dynasties various prescriptions of the most elaborate and exact character as to the size and make of the Huang-chung pipe have been applied in the settlement by law of this corner-stone of the Chinese musical system. The pitch now recognized in China as the standard for Huang-chung is given by van Aalst (p. 13) as a close approximation to the present d' of the European scale.

To the primitive system of the Lu were eventually added another at the octave above and another at the octave below, but the compass of this scale being greater than that of the voice, Prince Tsai-yu (1596) reduced it from thirty-six to twenty-four Lu by admitting only the lower six of the upper Lu and the upper six of the lower Lu.^[4] This restriction gives a scale having a compass of one semitone less than two octaves, from the sixth semitone below the primitive Huang-chung to the fifth semitone above its higher octave, the pitches of the whole system of twenty-four Lu being approximately those given in the accompanying scheme:

^[5]

From the table on page 63 it appears that the Samien songs of our collection cover a compass of pitch identical with this to within a semitone, their highest note being g' and their lowest g instead of g#. The songs of the horn-player also are included within the same range.^[6]

That this coincidence is the result of a conformity in this music to the prescriptions of Chinese theory is rendered probable by the fact that the notes most frequently used in both horn and Samien songs are those which fall within the primitive system of the Lu, from d' to c''#. As in the theory so in the practice of Chinese music so far as the evidence of our collection of songs goes, this octave takes the position of first importance.

We have seen that the Chinese regard their scales as results of the same process of the derivation of pipes which, carried as far as primitive workmen can, produces the system of the Lu. In this account of the origin of their five and seven step octaves, the Chinese base them upon an achievement of theoretical grasp and practical skill which must certainly be assigned to a much later date than the appearance of scales in their music. Moreover, the choice of five or seven steps is still unexplained, for the fifth progression affords scales of any number up to twelve. Evidently the opposite derivation is the true one. Just as the Pythagorean use of the progression of fifths did not create, but was the result of the Greek scale of his time, so in China the same progression became the foundation of theory through the fact that by its use an accurately determinate form could be given to the scale of five alternate approximate tones and thirds (and perhaps of seven approximate tones) which was already in use among them.^[7] For these ancient octave forms themselves another origin must be sought: we may, perhaps, surmise that they are what may be called the natural precipitates of all simpler melody. That these natural interval orders can be formed by a progression of fifths is a wonderful fact: wonderful, too, it must have been to these primitive theorists to see the generative powers of the fifth progression exhaust themselves in the formation of an interval order of twelve equal semitones. In their eyes the fifth progression became the natural foundation of all music. From it their scales came to be regarded as derived, and, to its limit, the system of the twelve Lu, an origin not alone mathematical was ascribed; they were obtained by Hoang-ti from the mysterious symbols of the Emperor Fu-hsi (B.C. 2852), and were heard by Ling-lun in the songs of birds and the voices of a remote race of men.^[8]

Since in ancient Chinese theory the scale was determined by the first seven members of the same progression which carried through twelve terms gave the system of the Lu, each of the first seven Lu became intimately associated in their music with the note of the scale produced by the same number of fifths. These associations are exhibited in the following schemes of the fifth progression, first as a continuous sequence and then brought within the octave:^[9]

1

2

3

4

5

6

7

8

9

10

11

12

H-CH

L-CH

T-T

N-L

K-S

Y-CH

J-P

T-L

I-T

C-HCH

W-I

CH-L

K

T

CH

Y

K

pK

pT

1

8

3

10

5

12

7

2

9

4

11

6

H-CH

T-L

T-T

CH-CH

K-S

CH-L

J-P

L-CH

I-T

N-L

W-I

Y-CH

K

CH

Ki

pT

T

Y

pK

From the earliest times it appears to have been admitted also that besides the primitive coincidences here indicated each one of the notes of the scale might be identified also with any one of the other eleven Lu, giving in all eighty-four correspondences (or modulations, as Amiot calls them). The correspondence of any one note of the scale with a given Lu, determining those upon which the others must at the same time fall, the number of different sets of simultaneous coincidences was twelve. But these were not viewed simply as identifications of the scale with different sets of Lu. A notion of the coincidence of its notes with the first seven added itself to all of them. This appears from the nomenclature adopted for those seven different embodiments of the scale in the Lu which were regarded as the fundamental ones. These were the cases in which the note of generation, Koung, coincided with any one of the first seven Lu, and they were named from the notes of the scale that fell upon these when Koung was at Huang-chung. Thus the identification of Koung with the Lu Huang-chung was called a modulation or intonation in Koung, its identification with the Lu Ku-hsi a modulation in Kio, since when Koung is at Huang-chung, Kio is at Ku-hsi. Although for the cases when Koung falls on one of the intermediate Lu no nomenclature referring to the primal form of coincidence seems to have been used, they must nevertheless have been conceived as intermediate modulations, and it is for this reason perhaps that we hear less of them.

Thus with the idea of each of the twelve possible embodiments of the scale in the Lu became combined the notion of another, in notes bearing definite relations of pitch (which might be unison) to those of the first. Now this conception of the relation in pitch between two embodiments of the same scale is exactly what is known in European music as a Key. The various possible identifications of the scale with different selections of Lu came therefore through the mingling with them all of the notion of one primal scheme of coincidence, to be so many keys. Had an association between the scale and the first seven Lu not been formed in the Chinese mind, had the various embodiments of the scale in sets of Lu been conceived each for itself, their music would have possessed what might be called a system of transposition, but not a system of keys. To the conception of Key the idea of the definite reference of one set of pitches embodying a scale to another is essential.

A relation emerges whenever we regard any two things from the point of view of either. The two relations of fatherhood and sonship appear in considering the same two beings according as we regard one with reference to the other or the second with reference to the first. The embodiment of the scale from the point of view of which we consider another we shall here call the referred scale, the embodiment with regard to which we consider it the scale of reference. The relation between them may be conceived after two manners which we may call respectively individual and representative. Either we may recognize the relation subsisting between each individual note in the one embodiment and one in the other, or we may take a single note of the scale as standard of comparison and regard the interval between its two positions as the representative of the same interval between all other pairs of corresponding notes. In either case the recognition of unison (identity) as a possible form which the relations concerned may take is necessary for systematic completeness.

The nomenclature we have just described indicates that it is the latter simpler manner of regarding keys that obtained in China. The compound relation of pitch in whose recognition a Key consists was there conceived by means of that between corresponding notes of the two embodiments of the scale concerned. In naming the fundamental keys of their music, the Chinese used Koung as a note of comparison and stated the interval between its two pitches by giving the note of the scale of reference upon which the Koung of the referred scale falls.

In both of the two theories of music which have in succession developed themselves upon European soil, that of the later Greeks and that of modern times, the element of key has a conspicuous place. In the former the representative conception of key, which had been developed in China, received another embodiment; and this still persists in the music of modern Europe. But as we shall see, the origin of the modern system of modulation in the conception of small displacements in pitch in the notes of a diatonic order has given it a character fundamentally individual.

That the practical limit of the fifth progression is an octave of twelve approximate hemitones was known to the Greek theorist, Aristoxenus (fourth century B.C.); and like the Chinese the later Greeks laid down as the entire system of distinctions of pitch to be recognized in their music, a series of twelve notes separated by hemitones and repeated in the octave above and the octave below.^[10]

Again as in China, the notes of the diatonic scale were associated primarily with certain of the elements of this order, and with the same elements as in the system of the Lu, Fa (= Koung), being identified with the lowest pitch of the whole three-octave interval order. Exactly as in China, again, the Greeks permitted all possible relative positions of the scale and the duodecimal octave; and since the same conception of their primary relation (Fa = lowest note of the octave) that persisted in China formed a part also of the Greek theory, their transpositions of the scale came to be united likewise into a duodecimal system of keys. To this striking list of theoretical similarities must be added a no less striking difference between Greek and Chinese nomenclature. Although the keys to be named were identical, the intervals involved between corresponding notes being those of unison or of one, two, etc., up to eleven hemitones, yet the method of naming them was, in a manner, opposite in the two systems. The Chinese proceeded by designating the note of the scale of reference upon which, or (hypothetically) the notes upon the semitone between which, a certain note (Koung) of the referred scale should fall. The nomenclature of the Greeks was derived from that of their ancient Schemata, or, as we should now call them, modes. These were the different sequences of tones and hemitones between octaves of each different note of the scale. Giving to the notes of the diatonic order their modern names, between octave repetitions of Do the following sequence of tones and hemitones is included: T T H T T T H; between octave repetitions of Sol, the following: T T H T T H T. The first was called by the Greeks the Lydian scheme, the second the Hypo-Phrygian: and other like names were given to the others. Since their keys involved an interval of pitch of a certain number of hemitones between two embodiments of the scale, the note Fa of the scale of reference fell in each either upon some note of the referred scale, or halfway between two. In the former case the key was given the old name of the scheme or mode bounded by that note; in the latter case the name of the mode bounded by the next note below the intermediate pitch with which Fa coincided, a variation in the name distinguishing this key from the one in which Fa actually coincided with this note. The keys of the former class correspond with those in the Chinese system in which Koung in the referred scale falls on one of the first seven Lu; and those of the latter class to its coincidences with the intermediate members of the series. Just as in Chinese music the seven modulations in the first seven Lu — that is, in the notes of the primal scale — have been recognized from antiquity, according to Prince Tsai-yu, as the fundamental ones; so in Greece the keys in which Fa in the scale of reference coincided with the outlines of the seven ancient modes in the referred scale were the earlier and principal ones, and those in which it fell between them, keys of later growth. As in the Chinese, so in this nomenclature, regard was had to the coincidences of a certain note in one of the two related scales with various notes of the other, and the same note (Fa, Koung), was used as the note of comparison in both systems; but while in China the name came from that note of the scale of reference with which the Koung of the referred scale coincided (modulations in Chang, pien-Tche, etc.), in Greece the name came from the mode upon whose boundary note in the referred scale the Fa of the scale of reference fell (Dorian, Lydian, etc., Tonos or Tropos).

In the representative names of keys used with its individual nomenclature, the modern world has let fall the Greek usage and taken up that of the Chinese, making changes therein which are the expression of a fundamentally different attitude of the musical consciousness toward the scale. These changes we shall find, and the fact is a most surprising one, have had a counterpart in the process which has brought the newer (or mediæval) musical system of the Chinese out of their ancient (or immemorial) theory of the art.

At the downfall of the Græco-Roman civilization, a few fragments of its theory of music were preserved for the uses of the Christian church. These were a two-octave diatonic scale beginning and ending on the note La (with its higher interval, La-Si, divided into two hemitones), and the ancient schemes or sequences of tones and hemitones between the various notes of this scale and their octaves, within one or other of which all ecclesiastical melodies were restricted.^[11]

From the beginning of the tenth century the notes of this interval order were designated by the letters of the Latin alphabet, the lowest note being called A, and the successive higher ones B, C, etc., notes at octaves receiving the same name. The intermediate note of the higher octave (corresponding to the flatted pien-Tche of the Chinese scale, and a survival, as we know, from the Greek tetrachord synnemenon) came, therefore, to fall between A and B. To designate it, B was again used, the two B's being distinguished by writing the lower one round, b (B rotundus), and the upper one square, B (B quadratus). In the development of the art during the later middle ages and in Reformation times, further notes intermediate to those of the old Greek order came into use. But the authority of classic and Catholic tradition was such that these were at first supplied by the singers without being written (Musica Ficta or Falsa); and when later it became the habitude to express them in notation, they were looked upon as derived either from the diatonic note above by a displacement like that which would produce b from B, or from the diatonic note below by a displacement which would produce B from b, and were designated by affixing to the letter denoting the diatonic step in question these two signs, b and B, which had already come to be written b and #.

The key system of modern European music rose out of this conception of the displacement of notes of the diatonic order. Since each one of the new notes introduced into the previous scale A to G was looked upon and named as a derivative from one of its notes, each of the new embodiments of the diatonic order which it became possible to form with their aid carried with it a reference to this fundamental series, and became therefore a key.

It proves that in the series of alternate groups of two and three tones separated by hemitones, which constitutes the diatonic scale, there is a certain note (viz. that below the group of three tones, or F), and only one, whose hemitone displacement upward will leave the order of the diatonic form; and one, and only one (viz. that above the group of three, or B), whose displacement downward will have the same result; further, that the diatonic character of the order will be left unchanged when a certain pair, a certain group of three, etc., up to a certain group of six, are all displaced upward, and when a certain other pair, group of three, etc., up to a group of six are all displaced downward; and that no other hemitone displacements will result in the diatonic order except that of all seven notes up and that of all seven notes down. The number of possible different embodiments of the diatonic scale which can be obtained from a given one by such hemitonic changes in its notes is therefore fourteen: those in which a certain one, two, etc., up to all seven of its notes, are moved upward a hemitone, or, as we say, sharped, and those in which a certain one, two, etc., up to all seven of its notes, are moved downward a hemitone, or, as we say, flatted.^[12]

The formation of keys by the unrestricted use of hemitone displacements of the notes of the ancient diatonic order A to G resulted, therefore, in a system of fourteen. To these the ancient scale itself became added as a fifteenth key, illustrating the limiting case in which the displacements were zero in number.

The nomenclature of this system of modulation is in the first place individual. We speak of the keys of one flat or five sharps, implying that the other notes of the order are neither flatted nor sharped, and thus asserting a relation of hemitone divergence in certain pairs of notes of the two embodiments and a relation of coincidence in the remainder.^[13]

The representative nomenclature of the modern key system is distinguished from that of the later Greeks and that of the ancient Chinese by the recognition of two notes as alternative standards of comparison, neither of the two being that below the three tones (Fa, Koung), which was the note used both in Greece and in China. These two notes are the note below the group of two notes (called Do or C in the mediæval scale) and the note between the upper two of the group of three (called La or A in the mediæval scale). This change is a victory of practice over theory. To the musical theorist, Fa, as the note of generation, the origin of the scale, is its limiting and ruling one. To the listener to music any note on which his mind has learned to dwell becomes beginning and end, foundation and summit, of the scale. This practical predominance of a note is in contemporary discussion called Tonality.^[14]

In the course of the development of Catholic Plain Song mediæval music-hearers acquired the habit of regarding either of the notes Do, Re, Mi, Sol, La, of the diatonic scale as the predominant one of a composition, this place being never assigned to Si, and but rarely to Fa. We have already argued in seeking to explain the flatting of pien-Tche that a feeling of the tonality of the theoretically prominent note Fa is incompatible with the maintenance of Si in its normal position. A like remark applies to Si in its turn, and to this cause is due the avoidance by the mediæval musicians of these two tonalities.^[15]

Finally, in modern times, three of the five commonly used in church music were abandoned, and musical textures fell into two grand varieties, one appealing to the listener's grasp of the note Do, and the other to his grasp of the note La as the important one of the diatonic order. The former is called the major, the latter the minor mode. All of the fifteen keys may occur in either mode. In the representative nomenclature of the one the key is named from the note of the scale of reference (or the displacement of one of its notes) with which the Do of the referred scale coincides; in that of the other, from the note with which La coincides. We speak therefore of a composition as in the key of F or F# major, meaning that the notes which it uses form a diatonic scale whose Do (or note below the group of two tones) is the note F or its displacement F#; or as in the key of F or F# minor, meaning that in the embodiment of the scale in notes partly chromatic in which it is written, this note F or its displacement F# takes the place of La (or note between the upper two of the group of three tones).

This concentration of modern music upon two varieties of texture, major and minor, has been interpreted as a result of the substitution, at the time of the Reformation, of a music of Chords (Harmony) for the music of simultaneous melody (Polyphony) which had grown up in mediæval Europe.^[16] The musical products of the Chinese consist entirely, according to our present information, either of pure melody, or of melody carried in octaves, notes at the fifth or fourth being occasionally added. No music of chords appears to exist among them, nor even a music of different simultaneous melodies. Nevertheless, what information we possess about later Chinese musical theory gives reason to believe that the Chinese recognize either of two notes as the fundamental one in their diatonic scale; that these two are Do and La; and that in theory, therefore, music in China exhibits the same division into a major and a minor system which it appears to have reached in Europe only after a long course of development into an entirely different form from that of the Chinese art. If we adopt the hypothesis that this dual structure was transmitted to China from Europe, it must, if we trust their accounts, have been assumed by European music at a time long anterior to the rise of the harmonic style. Whether original or acquired, therefore, the existence of this characteristic in Chinese musical theory gives reason for the belief that other causes beside their harmonic capacity may be operative in directing the growth of diatonic music into two forms, major and minor.

During the middle ages a new set of names was given to the notes of the Chinese scale, according to Van Aalst in the fourteenth century and by the Mongols. Among them was one which Amiot writes Kong, Van Aalst giving the same spelling Kung to both this name and the ancient one called by Amiot Koung. The new name Kong was applied to the note anciently called Yu, three hemitones below Koung. Of the habitude of the flatted pien-Tche, which Van Aalst tells us was also derived from the Mongols, and has since become general in China, Amiot says nothing. We have ourselves found it in all the records of Chinese scales (Barrow, Van Aalst, Ellis, and our own songs) in which we have been able to establish the identity of the notes at all. Making this change in the position of pien-Tche, the scale appears with its mediæval and ancient names as follows:

Mediæval: HoSseYChang TcheKongFanHo
$\cdot$ (T) $\cdot$ (T) $\cdot$ (H) $\cdot$ (T) $\cdot$ (T) $\cdot$ (T) $\cdot$ (H) $\cdot$
Ancient: Koung Chang KiopTcheTcheYupKg Koung

Through this change, the scale still remaining diatonic, Koung is no longer the note below the group of three, but that below the group of two tones, and Kong is not, as Yu was, the note intermediate to the group of two, but that between the upper two of the group of three. In a word, Koung has become Do, and Kong has become La: the ancient nomenclature marks out the European major; the mediæval, the European minor, mode.

The similarity in their Chinese names renders it antecedently probable that the two notes Do and La have in later times shared between them the position of theoretical primacy anciently possessed by Fa alone. While on this point Amiot is again silent, Van Aalst prints in Chinese characters (with a translation) the flute part of a Spring Hymn to Confucius, together with a heading which it seems hardly possible to doubt determines the key of the piece by naming the note of the scale of reference on which the Kong (formerly Yu) and not the Ho (formerly Koung) of the referred scale falls. The conclusion of the heading runs in Van Aalst' s translation: "When employing Chih (Tche) to intone a tune we must exclude, leave aside the notes Kung (Yu) and Yi (Kio). Forming the key of Chih (Tche), using Kong (Yu) as the note of comparison, this proves to be the case: but not so when Ho (Koung) is used for the keynote, as the following schemes show:

		Kong as keynote:	K $\cdot$ CH $\cdot$ Ki $\cdot$ $\cdot$ T $\cdot$ Y $\cdot$ $\cdot$ K
			CH $\cdot$ Ki $\cdot$ $\cdot$ T $\cdot$ Y $\cdot$ $\cdot$ K $\cdot$ CH
		Koung as keynote:	K $\cdot$ CH $\cdot$ Ki $\cdot$ $\cdot$ T $\cdot$ Y $\cdot$ K
			$\cdot$ $\cdot$ T $\cdot$ Y $\cdot$ $\cdot$ K $\cdot$ CH $\cdot$ K

We may accordingly interpret this heading as indicating the use of Kong instead of Koung as keynote. That Koung continues to exercise this function is expressly stated by Van Aalst, who gives an instance of its employment in the music of the Stone-chime in the same hymn to Confucius. We may therefore conclude that the dual system of major keys, or keys of Do (Koung, C) and minor keys, or keys of La (Kong, A) that is now exemplified in European music, is a fact also of present Chinese theory.

But further, the remainder of the heading of the Spring Hymn contributes evidence showing that beside using Do and La as alternative notes of comparison or keynotes, the Chinese make them the bases of alternative systems of modulation, in one of which the Koung of the scale of reference and in the other its Kong (or Yu) coincides in pitch with the primal Lu, Huang-chung. The indication is contained in the words with which the heading begins, — "Chia-chung acting as Koung." For Chia-chung, being the fourth Lu, if Koung coincide with it, Yu comes to fall upon Huang-chung. The key of Tche, which the heading goes on to specify, is then a key referring to a primitive scale in which not Koung but Kong coincides with the primal Lu. If this surmise is correct, the Chinese system of modulation has a complication not existing in our own, and which may be expressed in European terms by the supposition that our musical notation should represent alternative intonations a minor third apart, so that the same pitch could be called either A or C. The relation of pitch between scales embodying the same key in the two systems is that between the scales of reference themselves, and is expressed in the following scheme:

Mediæval: Y pK K CH Ki pT T Y
Ancient: K CH Ki pT T Y pK K

It is such a relation between two Koungs that is illustrated in the transposition from Man-nen-fon to Long-how-sa; and we may infer that in the scales of these two compositions we have the same key given in each of the two systems of modulation, the ancient or major system of Koung, and the mediæval or minor system of Kong.^[17] If we assume that the chromatic note in the scale of the Gie-erh and the Kuantzu was introduced to make this transposition possible, the construction of these two instruments becomes evidence that the distinction of major and minor in Chinese music is not a matter of pure theory, but a factor in existing musical practice.

Let us suppose a flute or horn incorporating within a range of ten or twelve notes one of the keys of the mediæval system; for example, Koung = g, as is common in our songs. If it were desired to perform in the same key in the ancient system the notes which it would be of principal importance to add would be g# and c#, as is shown in the following scheme:

Mediæval: T Y pK K CH Ki pT T Y pK K
d' e' f# g' (g'#) a' b' c" (c"#) d" e" f"# g"
Ancient: pK K CH Ki pT T Y pK K CH

The result of leaving pien-Koung to be produced by the harder blowing of the former Tche would be to make it a note intermediate between Yu and Koung; and this supposition may take its place beside Mr. Ellis's mechanical theory of the three-quarter tones as another possible hypothesis of the origin of this peculiarity of the Chinese scale. The intermediate intonation of pien-Koung is on this view, like the rest of the Chinese musical system, the outgrowth of performance not on stringed instruments, but on pipes; and performance, moreover, principally pentatonic, since it is the subsidiary importance of pien-Koung that renders unnecessary its presentation in the ancient key by a special note. The pitch of the note is regarded on this hypothesis as a mark left on the Chinese scale by the duality of key structure which we have reason to suspect is fundamental in Chinese music.^[18]

Since c# represents a pentatonic note in the one scale, and C only a pien in the other, a natural simplification of the scale of the instrument would be the sacrifice of c. With this change the scale supposed is that of the Kuantzu, excepting that by a further and less defensible simplification, f#, upon which pien-Koung falls in the mediaeval scale, is abandoned in the lower octave, and Chang of the ancient scale left to be represented by g. To judge from the notes used in Man-nen-fon and Long-how-sa, other devices have been employed in adapting the Gie-erh to give a key in both systems. The note g# has been added, but not c#, the ancient Yu being produced by the harder blowing of c. The mediaeval pien-Koung has apparently been made an intermediate note (f̄) perhaps after the analogy of the resultant pien-Koung of the ancient scale. This equalization of the (mediæval) intervals Yu-pien-Koung and pien-Koung, — Koung has apparently misled our performer into playing the ancient Kio as g instead of using g#, the extra note provided for the purpose, the latter becoming then an alternative pien-Tche. He has endeavored, moreover, to enlarge the (ancient) intervals, K-CH-Ki by depressing e (Koung) to d̄# and f̄ (Chang) to f. The note d then becomes the customary intermediate pien-Koung without alteration. The curious scale of Long-how-sa thus appears as an unskilful use of not altogether perfect devices incorporated on the Gie-erh for the performance of a given key in both the systems of Chinese modulation.^[19]

A further inquiry remains to be made regarding the Chinese system of modulation. In European music the keynote is also a Tonic: besides its position of primacy as note of comparison in the determination of keys, the Do or La of the scale is apt to appear in a melody at the first accented beat, and with special frequency thereafter: its upper fifth (or dominant) is apt to be used at points of rest in the music, and the note itself at the close.^[20]

To the question whether Chinese music exhibits this characteristic of tonic structure the answer suggested by a first glance at our collection of songs is a negative one. There is no note which is unequivocally defined as the axis of the music in any of them. An impression of want of unity, doubtless in part due to this cause, seems in general to be produced by Chinese music. Barrow calls their melody "an aggregation of harsh sounds," and Ambros speaks of it as "well-nigh devoid of sense and connection." Yet a closer examination of our songs brings to light a tendency to the embodiment of a certain form of less pronounced tonic structure. In most of them the note of the scale on which the composition ends has also been somewhat more frequent than the others during its course. Moreover, in these cases it is either the note a fifth above, or the note a fifth below, the supposed tonic (its dominant or sub-dominant), which is apt to be the next most prominent note. The songs showing this quasi-tonality are given in the following list, together with the note acting as tonic in each:

	Say-quaw-chung	Tche (d')	Long-how-sa (Samien)	Yu (e')
	Han-Kang	“	Hop-wong-hin	Kio (b')
	Gie-wong	“	San-fa-tiu	Tche (d')
	Kwan-mōk	“	Song-ting-long	Koung (g')
	Lo-ting-nyang	Chang (a')	Sai-tōn	Tche (d')

All the notes of the scale excepting the pien being represented here, and Tche (which in these songs has the pitch d' of the primal Lu, Huang-chung) more often than the others, the inference suggests itself that it may rather be to this absolute pitch d' than to any particular pentatonic note that the Chinese tend to attribute tonic functions. The two pien, which are always subsidiary, are the notes called Fa and Si in the European scale. It was these two notes, it will be remembered, that were excluded from the position of predominant note in the music of mediæval Europe, and as far as our songs are evidence, exactly the same degree of freedom of tonic choice exists in Chinese musical practice.

In the course of the present study we have had occasion to note an unexpected number of points of contact between the European and the Chinese musical systems. The fixation of a seven-step scale by the progression of fifths, and its extension to form a duodecimal octave, have been recognized as independent achievements of the Chinese since the work of Père Amiot. We have found further in the philosophical interpretation of this process in ancient China a suggestion of ideas current in our own time and race; and in the Chinese resolution of the problem of a music upon this foundation, several striking likenesses to that reached by the European musical consciousness. A device of detail like the Guidonian hand, proves to have its counterpart in China: perhaps also the "participatione" of the mediæval Italians. The same step (La-Si, Kio-pien-Tche) of the identical diatonic scale of Europe and China came to be equally divided in the two systems by a note which in China finally took the place of the next higher, while in Europe the two remained to form the germ of the modern chromatic scale. The transposing scales of ancient Greece seem to have been based originally upon an interval order identical with the ancient three-octave extension of the Lu, and to have constituted a system of primary and secondary keys like that of China, the nomenclature of the two being in a manner opposite. The Chinese method of naming is adopted in the key system of modern Europe, although the different origin of the latter results also in another which we have called individual. The distinction fundamental in European music since the Reformation, of a major and a minor scale, seems to have been incorporated in Chinese theory during mediæval times. We have seen reason to suspect, on the other hand, an extension of this distinction to the absolute pitch of the scale of reference such as has no counterpart in European music. Finally, our songs indicate that Chinese compositions may sometimes be conceived as written in the Tonic style, and that the same tonalities are recognized therein as obtained in European music of the middle ages.

Although the music we have been studying is that of a third of the population of the globe, it is still in great measure unknown to the rest of the world. The conclusions in regard to the Chinese system of keys which we have here based on the few data accessible to the Occidental student, are to be regarded not as established results, but as suggestions for further inquiry.

APPENDIX. — ON THE PHONOGRAPHIC STUDY OF MUSICAL PERFORMANCE.

The reproduction of sound is effected in the phonograph by contact between a needle fixed in a diaphragm and a wax cylinder on which an inscription has previously been made by another needle. Raising a lever raises the needle off the wax, and the arm bearing the diaphragm being movable, another contact may be made at any desired point on the cylinder. This makes it possible either to begin or to interrupt a phonographic reproduction at any instant of the flow of sound reproduced. Should we wish to grasp better what we have just heard, raising the lever while we move back the arm repeats it at once; should we wish to compare it with sound from another source, simply raising the lever silences the instrument. The phonograph used in this investigation was one of those run by electrical power, the rapidity of revolution of the cylinder being regulated by a screw increasing or decreasing the strength of the current entering the motor. The movement of this screw raises or lowers the pitch of the music reproduced by the phonograph at the same time that it quickens or slackens its time. In practice, the adjustment of the screw proves to be a very delicate means of temporarily tuning a phonograph note to any desired pitch within a considerable compass.

It is evident that if the sounds obtained from the phonograph can be relied upon as an accurate reproduction of those to which it has been exposed, the instrument is an invaluable apparatus for the investigation of primitive music. The phonograph brings vanished tones to actual hearing again just as photographs and casts bring visibly and tangibly before us the looks and shapes of things far away. By its aid the investigator can examine the sounds themselves of which a primitive musical performance has consisted, and in his study, at his leisure; he is no longer restricted to inferring the practice of the art more or less doubtfully from documentary evidence or from instrumental forms: he is no longer even dependent on his observations of such primitive performances as he may have been fortunate enough to hear, or on his memory of them. The phonograph places the music itself permanently at his command. Its reproductions may be indefinitely repeated; many parts of these inscriptions have in our examination been traversed perhaps a score of times; but notwithstanding these repetitions it has been impossible to detect the least deterioration in the reproduction. Whatever the life of a phonograph cylinder may be, it is far longer than suffices for the most careful examination of the inscribed sound. Moreover, as we have seen, the music preserved by the phonograph can be interrupted at any point. Both of these essentials of a stricter study are impossible in the case of actual playing or singing by primitive musicians. Our Chinamen, although no troublesome demands were made upon them, already began to grow restive during the second interview.

It cannot be claimed that the performance of the phonograph in its existing state leaves nothing to be desired. A harsh, scraping noise, very perceptible, although not loud enough to obscure the inscribed sound, is, as far as my experience goes, the constant accompaniment of a phonographic reproduction; and noises of other kinds occasionally make themselves heard.

Nor is the reproduction of musical tone in the phonograph by any means a perfect one. Beauty of timbre is very largely lost therein. This is, perhaps, in part due to the rapid quavering to which a phonograph note seems always subject, and which is very likely both a very small and quick waxing and waning of intensity and a very minute wavering in pitch, the latter being the result of the former. Although for this reason a phonograph note is never critically agreeable, yet tone-color of marked character remains readily recognizable therein. In this respect the phonographic cylinder outdoes the photographic plate which has never been able as yet to reproduce visual color at all, but at most only the distribution of light in the subject.

But these impurities of tone seriously detract from only the aesthetic, and not the scientific, value of a phonographic reproduction. It remains to ask whether the phonograph accurately reproduces the sequence of pitch in a music. If it does this, it will also reproduce its scheme of time, the other fundamental element in musical texture. Evidently in this respect the accuracy of the instrument is considerable: else the vocal selections, cornet solos, brass band pieces, etc., etc., which we hear to our greater or less satisfaction in phonographic exhibitions, would be beyond its powers. In order to determine this point more exactly, a test was made with the specially tuned harmonium invented by the late A. J. Ellis, and known to the readers of his translation of Helmholtz's Sensations of Tone as the Harmonical. One of the intervals embodied between adjacent notes of this instrument is that called the Syntonic Comma, 8/81/0, a difference of pitch of only 22 cents, less than a quarter of a tempered semitone. The Harmonical was set against the table on which the phonograph was placed, in such a manner that it could be played upon with the right hand while the left managed the phonograph. The latter instrument being adjusted to run so that the needle took about two minutes to traverse the cylinder, an inscription covering nearly the whole of it was taken of a single note of the Harmonical, alternated with various others and held at each recurrence during several seconds. In the reproduction this repeated note was tuned by a careful adjustment of the screw so that it fell between those notes of the Harmonical which are 22 cents apart, and, as far as could be judged, was as much above one as below the other. In the majority of several trials on different days, it preserved this intermediate position at each recurrence not only to the end of the cylinder, but to the end of several successive reproductions of the melody. At no time did it move in the course of one reproduction far enough from this intermediate position to be identified in pitch with either of the neighboring Harmonical notes: although on two occasions it seemed to run through this interval of about the eighteenth of a tone in the course of three continuous repetitions of the reproduction. The result of this test indicates that under favorable conditions the phonograph run by electric power at a medium rate can reproduce a sequence of pitch which covers the cylinder, correctly to within an almost imperceptible fraction of a tone.

The songs of our collection have been written down a few notes at a time by ear, with an occasional reference to one of Messrs. Mason and Hamlin's smaller harmoniums, to one of whose notes one of the prominent notes of the song was first approximately tuned, and which was set like the Harmonical within reach of the right hand. In the critical examination it was endeavored to make and keep the tuning of this note accurate; for such a study as has been made of these reproductions takes a much longer time than that during which the above test indicates the phonograph maintains its pitch accurately. Nevertheless, having carefully tuned a prominent note of the song to one of the harmonium notes at the beginning of the examination, in several cases where the reference back to this note was omitted, the two proved indistinguishable at the end perhaps of half an hour, and only in two or three cases was there doubt thrown on the work by a noticeable alteration of the phonograph pitch. It is still to be recommended that in such examinations the note tuned to the harmonium should be revisited every few minutes, to be sure that no aberration has taken place. The phonograph being accurately tuned, the pitch of each successive note of the song which exhibited that quality distinctly was then determined by cutting off the sound from the instrument the instant that note had been struck, and immediately comparing it with notes of the harmonium. In most cases, divergencies from any harmonium semitone came to light; the proportion of these divergencies from the nearest semitones above and below was then sought to be estimated as nearly as might be by repeated trials.

In order to gain some idea of the correctness with which the course of pitch constituting a melody can be determined in this way from a phonographic reproduction when its notes diverge in various amounts from the notes of the instrument of comparison, use was again made of the Harmonical. This instrument contains between the notes C of the four lower octaves the following complicated scale:

INTERVALS BETWEEN SUCCESSIVE NOTES IN CENTS.
cdbdebefgabagb^[21]bbbc
l82221127011220411270854970112

An inscription was taken of forty-eight Harmonical notes in which each of those between c' and c" occurred several times. This was then carefully written down according to the above method, using the harmonium as the instrument of comparison. The initial note of the sequence, which was the harmonical d', was tuned in the reproduction to d# of the harmonium. These two sounds being about 125 cents apart in absolute pitch, the notes of the reproduced melody were by this means thrown in among the harmonium semitones in such a way that it was impossible to predict where they ought to have come, and the mind was left entirely free to determine where they did come. The different estimates in the case of recurrences of the same note (however far apart in the melody) proved in general closely similar. In nine out of the thirteen different notes used in the sequence, the various judgments fell within a twentieth of a tone (or ten cents) of one another; in the other four they fell 15, 23, 25, and 28 cents apart. Taking the centre of gravity of the various estimates as the indicated pitch for each note, the following interval order resulted:

Real: (182) (22) (112) (70) (112) (204) (112) (70) (85) (49) (70) (112)
c d^♭ d e^♭ e f g a^♭ a g^♭ b^♭ b c
Estimated: 195 25 100 94 115 173 118 85 83 58 94 98

In nine of these intervals the errors are not over 15 cents, or the fourteenth of a tone; in two they are 24 cents, or the eighth of a tone; and one reaches 31 cents, or the sixth of a tone. It may be mentioned that this Harmonical reproduction was hardly as loud and clear as those of most of the songs of our collection.

These tests of the phonograph and of the ear give a basis for considerable confidence in the novel method employed in this investigation of primitive musical performance.^[22] The phonograph seems under favorable conditions to be able to reproduce a sequence of intervals with an accuracy which may be regarded as well-nigh perfect, and which one would call truly wonderful were not all wonder in connection with this instrument. Furthermore, the result of the above experiment with the intricate interval order of the Harmonical seems to indicate that a good musical ear can by this method of estimated divergences of the phonograph notes from those of an instrument of comparison gain an idea of a course of pitch presented in phonographic reproduction which will be correct to within small fractions of a tone. We may claim, therefore, for records of primitive performance made in this way from the phonograph, an accuracy sufficient for purposes of close study, and which is much greater than could be attained without its aid. In the Lehre von den Tonenpfindungen (4th ed., p. 435) Helmholtz quotes the observation of a friend, an "ausgezeichneter Musiker," in regard to the singing of the Dervishes in Cairo. That which at first was thought to be a false intonation, he finally convinced himself was the quarter tone (about 50 cents) of the Arabian scale. Although to notice in performance a musical habitude as delicate as this would demand an acute musical sense, in the detailed study it is possible to give a phonographic reproduction it would reveal itself at once even to an observer of ordinary powers. The only references we have found by previous students to the division of a semitone in Chinese music, so conspicuous in the intermediate pien-Koung of our songs, are the incidental remarks of Van Aalst already referred to.

1. Notably the Ché (an instrument like the zither) as described by Amiot (p. 58) and the Pien-ching and Pien-chung (chimes of bells and resonant stones) as described by Van Aalst (pp. 49, 54).
2. Amiot, pp. 64, 87.
3. If we carry on the fifth progression by taking account of the small interval of 24 cents above the octave of the initial note brought in by the twelfth fifth, no further interval of different size will be introduced until the seventeenth fifth is reached, which gives a note 66 cents below the octave of the starting-point. An extension of the progression to include sixteen fifths was employed by the Arabian theorists of the fourteenth century and earlier, and gives their seventeen step octave (Helmholtz, Tonempfindungen, 4 edn., p. 458). This more complex theoretical construction was, according to Mr. Ellis (fr. of Helmholtz, p. 281), a mathematical determination of an already existing interval order. The lutist Zal-zal (ninth century) had introduced certain new notes into the scale, produced apparently by the trisection of the quarter of a string; and approximations to these were yielded, it proved, by this exclusion of the fifth progression.
4. Amiot, p. 110.
5. = 301.5 vibrations.
6. Judging from Amiot's account of the Che (p. 58), he seems to regard the full two octaves as the true compass of Chinese music. The Che, which has twenty-five strings covering, like our songs, a range of twenty-four semitones, in his opinion is "the most perfect of Chinese instruments, since it includes in itself the whole extent of their musical system."
7. In the Arabian scale just mentioned, the fifth progression is again applied to determine an interval order otherwise produced.
8. Van Aalst, p. 7. We may, perhaps, regard this account of the experiences of Ling-lun as a poetical rendering of the truth that the emanation of its higher fifth from a given note is not alone a mathematical deduction, but a fact of actual hearing whenever, by harder blowing, a pipe giving its fundamental tone (for instance c), or its first overtone (c') begins to produce instead its second overtone (g').
9. They are given in the form of circular diagrams by Amiot, Plate XVIII, Fig. 13. "Hoang-chung aided and sustained by Chung-lu and Lin-chung." Fig. 12, a "Hoang-chung aided and sustained by Ta-lu and Ying-chung."
10. This range of pitch was increased by three hemitones in the system of fifteen scales of transposition (Tonoi or Tropoi) recorded by Alypios (360 A.D.).
11. This fundamental interval order of mediæval music was at the time of Guido d' Arezzo (eleventh century) extended by the addition of a note (Sol) below the lowest La, and of notes Si, Do, Re, Mi, above the highest; giving the following sequence of tones and hemitones:

    Ancient Scale.

    (Sol)

    (Mi)

    $\scriptstyle \cdot$H$\scriptstyle \cdot$H$\scriptstyle \cdot$

    $\cdot$

    T

    $\cdot$

    T

    $\cdot$

    H

    $\cdot$

    T

    $\cdot$

    T

    $\cdot$

    H

    $\cdot$

    T

    $\cdot$

    T

    $\cdot$

    T

    $\cdot$

    H

    $\cdot$

    T

    $\cdot$

    T

    $\cdot$

    H

    $\cdot$

    T

    $\cdot$

    T

    $\cdot$

    T

    $\cdot$

    H

    $\cdot$

    T

    $\cdot$

    T

    $\cdot$

    
    In order to facilitate the memorizing of this scale, its twenty notes (the intermediate note being counted with Si) were associated with the tips and joints of the thumb and fingers of the left hand, proceeding downward from the tip of the thumb as Sol, and then upward on each of the fingers, the twentieth note, Mi, being conceived to float in the air, over the tip of the middle finger. This mnemonic device was called the Guidonian hand, and is mentioned here only to call attention to a like use of the joints and tips of the fingers among the Chinese, who associated the root of the ring finger with Huang-chung, that of the middle and first fingers with the second and third Lu, and successive adjacent joints and finger tips with the others, the twelfth Lu falling on the root of the little finger. (Amiot, p. 127, and Plate XVII.)

12. The only hemitone displacement upward of a single step in the interval order

    THTTHTT
    ABCDEFGA

    which will result in the same sequence of tones and hemitones is that of F. The F of the new order is the C of the original one, and its displacement creates a second derivative formed from the original by two displacements upward, F and C. The displacement upward of C is impossible without that of F if the derivative order is to remain diatonic, for it results in the separation of two hemitones by a single tone only. The F of the second derivative is the G of the original, and its displacement gives a third derivative produced from the first by three displacements, F, C, G. The displacement of G without that of C is impossible for the same reason as before. A fourth, fifth, sixth, and seventh derivatives result from the displacement respectively of D, A, E, and B, the displacement of each being impossible without that of the foregoing note of the series. All the notes of the scale have now been displaced.

    In like manner, the displacement downward of one and only one note (B) of the diatonic order results in the same sequence of tones and hemitones. The B of this first derivative is the E of the original order, the displacement of which gives a second derivative; as before, the displacement downward of E is impossible without that of B. The third to the seventh derivatives are formed by the additional displacements downward of A, D, G, C, F, respectively, that of each demanding that of the previous note of the series.

    The formation of these fourteen derivative orders is given in the following scheme:

    Upward Displacement
    (1)
    ‍
    (2)
    ‍
    (3)
    ‍
    (4)
    ‍
    (5)
    ‍
    (6)
    ‍
    (7)	B	E	A	D	G	C	F

    Downward Displacement
    (1)
    ‍
    (2)
    ‍
    (3)
    ‍
    (4)
    ‍
    (5)
    ‍
    (6)
    ‍
    (7)	F	C	G	D	A	E	B

    No other sets of displacements than the fourteen here specified will reproduce the diatonic order. For consider any such set consisting of n displacements: either it contains the nth letter from the right in one or other of these two series; in which case it will not form a diatonic order unless the other n-1 letters are those to the right of this in the series in question; or it contains one of the letters to the left of this nth letter, and, lacking this, does not therefore form a diatonic order.

    The determination of the fundamental scale as Pythagorean, Harmonic, or Tempered, gives three varieties of this system of keys into whose discussion we need not here enter.

13. The character of different keys is made by Hauptmann (Harmonik und Metrik, § 279) to depend upon these conceptions of upward and downward displacement. "Every key which in comparison with another contains notes chromatically raised will seem higher and tenser; and one which differs from another through chromatically lower notes will seem deeper, quieter, more relaxed."
14. The term used by Helmholtz (Tonempfindungen, 4th edn., p. 395), following Fétis, in the sense of a "definite reference of all the notes of the scale to a single principal and fundamental note, the Tonic."
15. The inharmonious relation of these two notes is expressed in the mediæval proverb, "Si contra Fa diabolus est in musica."
16. Helmholtz shows (Tonempfindungen, 4th edn., p. 489) that when Do and La are taken for principal notes, the diatonic order yields a greater variety of more available chords than when any other notes are chosen.
17. The key may be regarded either as that of Chang major, or as that of pien-Koung minor.
18. The habitude of the intermediate pien-Koung, although not mentioned by Van Aalst, can be inferred from a note appended to his translation of the flute part of the hymn before mentioned. It is in the minor (or Kong) key of Tche (as we have seen), the pien of the scale being omitted. From Van Aalst's note we learn that the pitch of Koung is between one and two semitones below Chang. Since, as the scheme herewith shows, the Chang of this key corresponds to Koung and its Koung to pien-Koung,

    pT $\cdot$ T $\cdot$ Y $\cdot$ pK $\cdot$ K $\cdot$ CH $\cdot$ Ki $\cdot$ pT
    T $\cdot$ Y $\cdot$ $\cdot$ $\cdot$ K $\cdot$ CH $\cdot$ Ki $\cdot$ $\cdot$ T

    this remark determines the pien-Koung of the scale of reference as at the intermediate intonation.

19. In his accounts of Chinese musical history Pere Amiot often refers to the want of comprehension in later times for former achievements of theory and practice. In Prince Tsai-yu's time (1596) the scale once heptatonic had simplified itself to five notes. One of Amiot's learned Chinese friends said of ancient music, " All our books speak of it in terms of the loftiest praise, but they teach us at the same time that we have lost much of the excellent method which our ancestors employed to bring forth their marvellous effects." From the first to the sixth century music was generally neglected in China. "At that time the discovery was made of several chimes of bells (embodying the system of the Lu), and the Emperor put them into the hands of the officers in control of the music of his palace, with orders to make use of them; but since the ancient method was forgotten, the musicians employed but seven bells in each chime, the remaining five gaining the name of mute bells" (p. 46).
20. Helmholtz (p. 410) describes the tonic demand of the European musical consciousness as follows: "that the whole mass of notes and harmonic complexes should be placed in close and distinct relationship with a freely chosen Tonic note; that the whole mass of notes in the piece should be developed out of this and be brought back again to it."
21. gb is tuned as the natural seventh (ratio 4:7) of the c below.
22. The application of the phonograph to the exacter study of music was first made, as far as I know, in my examination of Indian songs from the Zuñi pueblo, of which the results were published last May in the first volume of "A Journal of American Archæology and Ethnology." (Boston: Houghton, Mifflin & Co.)