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

by Benjamin Ives Gilman

ON SOME PSYCHOLOGICAL ASPECTS OF THE CHINESE MUSICAL SYSTEM.

I.

SINCE the publication in 1862 of Helmholtz's renowned ''Lehre von den Tonempfindungen'' the investigation of the psychology of tone has been actively pursued by students of the science of mind. The effort made by Helmholtz to interpret the achievements of the constructive genius of modern Europe with the material of tone by a reference to the dealings therewith of other races and ages has in particular given a great impulse 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 of research a discussion of the musical system of China, based upon observations of performances by native musicians. These musical ideas and musical products it is our purpose to examine, not from the artistic, but the psychological point of view. We shall consider them as illustrations of the movements of the human mind in hearing, imagining, and reflecting upon tones and their combination, as material for a comparative psychology of that element of our sensations of sound which is known as the quality of pitch.

The specimens of Chinese music to whose interpretation in the light of their theory this paper is devoted have been studied in phonographic reproduction. Through the kindness of Dr. Frederick Starr of New York, who was acquainted with several of the Chinamen living at the time in the city, I obtained the opportunity on the 17th of March last to bring a phonograph to the quarters of one of them in Mott Street; and with Dr. Starr's assistance to take inscriptions of several melodies played by two performers. A few days later Dr. Starr invited some of the same Chinamen to meet us at his rooms, where again with his aid I took inscriptions of several more melodies played by two other performers. The following table gives a list of the songs thus obtained:

	Name	Player
	Say-Quaw-Chung	Hung-Yu.
	Han-Kang	Ju-Moy.
	Mong-Lut-Lao	”
	Yen-Jee-Quaw-Chang	”
	Gie-Wong	”
	Kwan-Mōk	”
	Lo-Ting-Nyang	”
	⁠do	Ying-Park.
	So-Yūn	Ju-Moy.
	Long-How-Sa[2]	Ju-Moy.
	Hop-Wong-Hin	”
	San-Fa-Tiu	”
	Sai-Tōn	”
	Song-Ting-Long	”
	Man-Nen-Fōn	Unknown.
	Long-How-Sa[2]	”

All of them excepting the last two were played upon the Samien (Samin, Sam-jin, San-hien, San-hsien), a long-necked guitar having three strings of which the two upper were tuned a fifth and an octave above the lowest. Man-nen-fon and Long-how-sa were played upon a small horn called the Gie-erh^[3]. The music accompanying this paper consists of four of these melodies represented as exactly as is possible in our European notation, which is here intended to signify the ordinary tempered interval order of equal semitones embodied on our keyed instruments, the black keys being indicated by sharps^[4]. It is probable that the absolute pitch as here expressed does not vary from that of the performances by more than a fraction of a tone. A line drawn above a note signifies that the sound is between that written and the note a semitone higher. In order to avoid the multiplication of bars and an appearance of regularity in the sequence of stronger notes which does not always characterize this music, emphasis has in all cases been denoted by accents. The sharps apply only to the notes against which they are written.

Our present knowledge of Chinese music is very largely a knowledge of its theory, which seems to have assumed a very elaborate and exact form from even the most remote times.^[5] Kiesewetter warns us, however, against mistaking such information about the musical theories of a people for knowledge of the state of the art itself among them. " I have long felt," he writes,^[6] "that the practical music of many Asiatic peoples, ancient and modern, must have been and must be a totally different thing from the metaphysical or mathematical music of their philosophers, which as pure speculation must always have held itself apart from practice. We have erred in reasoning from the writings of theorists among these peoples to the nature of their art itself." In large measure, doubtless, this tendency among students of the ethnology of music to forget that the books of theorists may not reflect the methods of performers is the result of the extreme difficulty of investigating the actual products among other races of an art essentially evanescent as music is. The cases are rare in which they come to the hearing of trained musicians; we can infer for the most part only their scale structure from instrumental forms: and their record in notation is in general both imperfect and scanty. The invention of the phonograph bids fair to render the practice of music among non-European peoples as accessible to study as their ideas about the act have hitherto been. Whenever a phonographic cylinder can be exposed to a musical performance a close copy of the original texture of tone is fixed in a form which admits of subsequent examination of the most careful kind whenever and wherever desired.^[7] 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 on this work at Columbia College. An account of the method employed and of a set of experiments made to determine its accuracy and that of the phonograph will form the subject of an appendix to this paper. (See next number of the Review.)^[8]

The fixation of a definite interval-order which shall serve as the scale of their performances is the starting-point of Chinese musical theory. All the different pitches which are used in a given piece of music, taken together embody a certain set of intervals arranged in a certain order from low to high. The fact of scale in music is the fact that in general in the music of one age and race different pieces embody in this way the same order of intervals, or one or other of a few different orders. Scales are the generic interval-orders of compositions. According to the prescriptions of Chinese theory all their music embodies one interval-order or scale, which may be varied by the omission of one or both of two subsidiary notes. This scale consists of notes repeated in octaves. A note and its octave are called by the same name in China, and are apparently looked upon as essentially the same thing.^[9] Evidence of this identification of octaves in the Chinese mind is given in the song, Yen-jee-quaw-chang, where among the slight variations of the second performance in one place the melody follows its previous course for several notes at an octave below the original pitch. Five primary intervals span an octave in the Chinese scale, the two intermediate notes which are used in a subsidiary way increasing this number to seven. These pentatonic and heptatonic octave divisions originated according to Chinese accounts through the employment of a continued progression upward in pitch by the interval of the fifth.^[10] We are here reminded of the Pythagorean derivation of the diatonic interval order of the Greeks in like manner from a progression of fifths; but if Chinese sources are to be trusted, its application in their music antedates the Pythagorean discovery by a score of centuries.^[11] The musical theory of the Greeks had its origin in the division of a string; that of China, in the measurement of pipes. The vibration ratio of the fundamental tones of two pipes will, other things being equal, be very nearly if not exactly the inverse of the ratio of their lengths. Thus a pipe giving a tone an octave above another like one (vibration ratio 2/1) will be of half its length; a pipe giving a tone a fifth above another (vibration ratio 3/2) will be of two-thirds its length. This connection between the simplest ratios and striking facts of pitch-relation seems from time immemorial to have been employed in giving a philosophical basis to the Chinese musical system. Père Amiot quotes (p. 117) a speculation about the foundations of music written by Hoai-nan-tsee, King of Hoainan (B.C. 105), which begins as follows: "The principle of all science is unity. Unity as single cannot produce anything, but it engenders everything, insomuch as it includes within itself the two principles of which the harmony and the union produce everything. It is in this sense that one can say, unity engenders duality, duality triplicity; and from triplicity all things are engendered."^[12]

According to these principles, a pipe whose note is at the interval of the fifth (3/2) above that of another, will be a natural derivative from it, since the proportion of the two (1 : 2/3) embodies the fundamental ideas, unity, duality, and triplicity. The continued application of this proportion gives, as a natural progression of notes, those corresponding, through the sizes of their sources, to the numerical series

1⁠2/3⁠(2/3)²⁠(2/3)³, etc.

Let us suppose such a progression by upward fifths to be carried on until a series of five notes be formed, the pipes being doubled, that is, the lower octave of a note being taken, whenever necessary to keep the compass of the series within an octave. The following interval-order would be the theoretical result, the initial note occupying the lower extreme:

⁠⁠1st⁠3d⁠5th⁠2d⁠4th
(cents)⁠$\cdot$ 204 $\cdot$ 204 $\cdot$ 294 $\cdot$ 204 $\cdot$

Of these two intervals, the smaller is that called in European music the major tone (9/8); and the larger is an interval (3/22/7) closely approximating to a minor third (316 cents). The primary scale of Chinese theory consists of notes at these intervals repeated in octaves above and below. This extension introduces no new interval into the order, the compass of the above four being just 294 cents less than an octave. The complete order consists, therefore, of approximate minor thirds, alternating first with one and then with two tones. To these five notes and their octave repetitions were given the following names: the note from which the order can be derived by a progression of fifths, that one, namely, which lies below the sequence of two tones was called Koung; the note between the two tones was called Chang; that above them, Kio; the note below the isolated tone was called Tche; that above it, Yu. Were the fifth progression carried on two steps further, still keeping it within the octave, two more major tones would be introduced, giving the following order:

1st⁠3d⁠5th⁠7th⁠2d⁠4th⁠6th
(—294—)
$\cdot$ 204 $\cdot$ 204 $\cdot$ 204 $\cdot$ 90 $\cdot$ 204 $\cdot$ 204 $\cdot$
K⁠Ch⁠Ki⁠⁠T⁠Y

The two new notes divide the two thirds of the scale in the same way: a new interval of 90 cents, which is that called in European music a Pythagorean semitone (2/25/46/3), appearing between one of the new notes and Tche, and the other and the higher octave of Koung. These two are the subsidiary notes of the Chinese scale, and were called the two "pien," the name signifying literally "changing into."^[13] That next below Tche was called " pien-Tche," and that next below Koung, "pien-Koung." The whole series was called the "seven principles" (Tsi-Ché). This is the identical determination of the intervals of a seven-step octave scale, which, given in the theory of Pythagoras, remained the foundation of the European musical system for two thousand years thereafter, and was definitely relinquished only during the sixteenth century. The Tsi-Ché of China and the diatonic scale of classical and mediæval Europe may be alike defined as an order of intervals in which a (Pythagorean) semitone alternates first with two and then with three major tones.^[14]

While in China music has been founded in the main upon the simpler scale of five steps, evidence of the antiquity of the "pien" is not wanting. In answer to theorists who regarded them as an innovation, Prince Tsai-yu (1596) declares that one only needs to read the works of Confucius (among many others) to see that the "seven principles" have been recognized in China from the remotest times: it is only the half learned, he says, who deny this. (Amiot, p. 161.) All seven are certainly fully 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 pien are used much less often than the others, yet to omit them would in all cases materially alter the character of the music. In this point our songs contradict Van Aalst's statement (p. 16) that the Chinese of the present, while theoretically admitting seven sounds, practically never use but five to the octave.^[15]

In determining the scales actually embodied in the songs of the present collection, the successive pitches of which each melody consisted were determined as closely as possible by a method to be detailed in the appendix. They proved in all of the songs excepting the horn melody Long-how-sa to gather themselves into groups generally covering a compass of not over an eighth of a tone. The centre of gravity of each group was taken for the indicated note, and the order of intervals separating the indicated notes became the scale of the song. The table on the following page presents the result of this calculation in cents for all of the Samien songs. The scale of the horn 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 of the thirteen, occasional use was made of a note between e’ and g’, and of another between b’ and d’’. The other notes were all repetitions of these seven in the lower or the higher octave.

CHINESE NOTES.

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This general conformity with the theoretical seven-step order is accompanied by divergencies of detail which are not without marked effect on the music. In the first place, as our table shows at once, the position of the two pien is different from that assigned to them in theory. As the sixth and seventh numbers of the progression of fifths, the two pien are in the theoretical scale, each placed 90 cents below the next higher note. In these scales the interval between the upper pien-Tche (the lower is omitted in all the songs) and the note above is never less than 185 cents, while that separating it from the note below, which is theoretically 204 cents, is never greater than 125 cents. The intention of these performers is evidently to lower pien-Tche from its theoretical position through a semitone. According to Van Aalst this habitude is at present general in China; and dates from the invasion of that country in the fourteenth century by the Mongols, whose scale was identical with that of the Chinese, with the exception of this semitone's difference in the position of pien-Tche. Although the note was preserved in the scale at both positions for a time by the decree of Kubla Khan, the theoretical pitch was finally given up.^[16] It is a striking fact that in the history of the same theoretical scale among the Greeks there arose likewise an alternative usage involving the difference of a semitone in one of its steps, and that the note affected was the same in Greece as in China. This was the note since called Si in the diatonic scale, and its differing pitch was the basis of the distinction between the disjoined and conjoined tetrachords of Greek theory.^[17] The double intonation continued during the middle ages, and was the germ from which has grown the whole system of modern modulation. While it is open to us to suppose that the appearance of the same phenomenon in Chinese musical history is due to the influence of Western civilization, we are not told that the Mongols brought the varying usage with them, but that it arose when their scale met that of China. Perhaps both the theory of conjoined and disjoined tetrachords and the story of the Mongol scale are equally unreal hypotheses invented to explain the expedients by which the Greeks and the Chinese met each in their own way a practical difficulty arising in diatonic music. The notion of the diatonic order as a product of the fifth progression involves the conception of Fa as the generating note, the origin of the others. If we assume that this position of prominence in the minds of theorists gave the note a like importance in the ears of listeners to music, the supposition is natural that the inharmonious interval Fa-Si (an augmented fourth or tritonus) would be noticed as a blemish in the scale. The pitch a hemitone below Si makes with Fa the conspicuously harmonious interval of the pefect fourth, and this we may suppose would tend to be used with it. That Si was displaced in the Chinese scale and retained at both intonations in Greece may be regarded as due to the fact that in the Chinese scale it was one of the pien, a note whose exact pitch was of subsidiary importance, while in the fully developed heptatonic octave of the Greeks it stood on an equal footing with the other notes and tended to maintain its individuality.

The irregularity in the position of pien-Koung in our melodies is of a different kind. While in theory it should be 90 cents below Koung (as the Mi of the European scale remained always a semitone below Fa), it is placed by our performers from no to 190 cents below, the interval in most cases being not under 125 nor over 175 cents. The result is the division of the minor third Yu-Koung into two intervals approximating to equality. The authorities on Chinese music make no mention of this intermediate intonation of pien-Koung. In the songs given in notation by Barrow and Van Aalst the note has the normal diatonic position a semitone below Koung. In the two scales obtained by Mr. Ellis it appears that while pien-Tche is flatted in both, pien-Koung is flatted in one and sharped in the other. It is sharped in all of the scales of instruments 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 used pien-Koung; but it recurs and with the intermediate intonation in the two melodies of the horn-player, hereafter to be referred to. Furthermore, in giving the notation of two melodies, while the pien do not occur in either, Van Aalst remarks upon a quarter-tone deviation of the notes in performance from their theoretical intonation similar to that exemplified in the intermediate pitch of pien-Koung.

Examples of the equal division of the minor thirds of a scale are not wanting in other musical systems, and the explanation which Mr. Ellis has offered for these may prove to be the true one in this Chinese case. Celtic music, which is often compared with that of China on account of its pentatonic basis, would have another striking characteristic in common with our melodies were it played upon the Highland bagpipe with equally divided minor thirds whose scale is given by Mr. Ellis. The same writer reports also a modern Arabian scale which is practically identical with this. A minor third divided into two approximately equal parts is also found in the tetrachord called the equal diatonic, and ascribed to the Alexandrian musician Ptolemy (200 B.C.). The intervals of this order are 12/11, 11/10, 10/9, or 151, 165, and 182 cents; and they can be produced in a string by stopping it at a quarter of its length and at one-third and two-thirds of this quarter. Mr. Ellis regards this process of the tri-section of the quarter of a string as the ultimate source of all these equal divisions of the third. The intermediate pien-Koung of our scales may according to this have a mechanical and not a musical origin. Another hypothesis will, we shall find, suggest itself in the course of our examination of the Chinese system of modulation.

The non-diatonic intervals which result from the intermediate pien-Koung are the most striking feature of these Samien songs. The note is most commonly reached from or left for those immediately adjacent above and below, separated from it by about 150 cents, or three-quarters of a tone; the interval Tche—pien-Koung, or pien-Koung—Chang (350 cents), occurs nearly as often; and the progressions Kio—pien-Koung (350 cents) and pien-Tche—pien-Koung (650 cents) each occur once. To our ears trained in the diatonic scale all of these intervals have a very strange and half-barbaric sound; but the quality is most marked in that of about 350 cents, an interval between a minor and a major third (316-386 cents). This intermediate third neither charms the ear like the major nor touches the heart like minor, but stands between them with a character of gravity, "like middle life between youth and old age," to use the expression of a friend who has listened to this music.^[18]

The intermediate intonation of pien-Koung involves, as we have seen, a conspicuous violation of Chinese theoretical principles. Leaving now this note out of consideration, most of the intervals formed by the remainder still differ noticeably in these Samien songs from those of the prescribed Chinese scale. In the seven-step order, as given by theory, while fifths and fourths are perfectly embodied, no combinations of notes give more than an approximation to the other harmonic intervals, thirds and sixths.^[19] For this reason diatonic thirds and sixths were not admitted by early theorists among the consonances. The Venetian musician, Zarlino, the first conspicuous authority to demand the abandonment of the Pythagorean theory of the scale, speaks in his Institutioni Harmoniche (1558) of the habitude of "participatione," by which the musicians of his day found it necessary to modify the theoretical thirds and sixths in practice for the better "contentment of the ear."^[20] The European ear has never found itself contented by any Chinese performances, and Van Aalst seems to attribute this as well to the Pythagorean scale of the music as to the want of technical precision among the musicians of China.^[21] Yet in these Samien scales we are unexpectedly confronted with a deviation of practice from the theoretical intervals, similar in character to the "participatione" of the Italians. The examination of the foregoing table (leaving pien-Koung out of consideration) shows that of the combinations of notes which are perfect fifths and fourths in the theoretic scale only about a third give, in the estimated scales, intervals varying noticeably from just intonation; while of the combinations of notes which in the theoretic scale give approximate thirds and sixths only a very small fraction in the estimated scales give perceptibly worse intervals, and nearly half give intervals perceptibly better than the diatonic approximations. Taking all the combinations of notes together, which in the theoretical scale give either just or approximate harmonious intervals, in the estimated scales the aberration from perfection is not over that of the theoretical thirds and sixths in four-fifths of the cases, while in half of them it is not over half this error. In a word, cases of aberration in the practical scales from the perfection of the theoretical fourths and fifths are balanced by cases where the approximate thirds and sixths of theory have been improved upon in practice; the intervals in general showing a tendency to come closer to just intonation than do the thirds and sixths of the theoretical order. Apart from the abnormal intonation of pien-Koung the deviation of these scales from that of Chinese prescription may be regarded on the whole as an improvement upon it.

Although according to the indications of these Samien melodies, Chinese performance is not always as barbarous as is commonly asserted,^[22] it must be admitted that one, at least, of the horn-player's songs goes far to maintain the ancient reputation of the Chinese for inaccuracy of intonation. In the song Man-nen-fōn, although the groups of attempts at the same note of the scale have a wider compass than in the Samien melodies, they are still distinguishable, and taking their centres of gravity yield the following scale:

T⁠Y⁠pK⁠K⁠Ch⁠Ki⁠T⁠Y
$\cdot$ 190 $\cdot$ 155 $\cdot$ 155 $\cdot$ 200 $\cdot$ 200 $\cdot$ 300 $\cdot$200 $\cdot$
d’⁠e'⁠f’⁠g'⁠a'⁠b'⁠d"⁠e"

Here f', by its infrequency, announces itself as a pien. Koung has accordingly the customary pitch g', and the scale is of nearly the customary form.

The second horn melody, Long-how-sa, is characterized by the greatest uncertainty of intonation. The groups of attempts at the same note of the scale are here indistinguishable, and the intonations at which the performer probably aimed must be obtained by the separate examination of successive fragments of the song. The result of this analysis is the following set of notes in which d’, g'# and a’ are by their infrequency determined as pien and d'# therefore as Koung.

Y⁠pK⁠K⁠Ch⁠Ki⁠pT⁠pT⁠T⁠Y⁠K
150⁠150⁠150⁠200⁠100⁠100⁠200⁠150⁠300
c'⁠d'⁠d'#⁠f’⁠g'⁠g'#⁠a'⁠b'⁠c"⁠d"#

This song is the only one in our collection in which any other note than (g'#) is taken for Koung. Its scale, moreover, differs from that of the Samien melodies in several points. The intervals, Koung-Chang and Tche-Yu, are three-quarter tones instead of tones, and pien-Tche appears in both its Chinese and Mongolian positions, a semitone and a tone above Kio. The explanation of these irregularities is doubtless to be found in the construction of the Gie-erh. To perform the scale perfectly, from d'# at Koung would require several notes not included in it when taken from g’. Only one (g'#) seems to be provided on the Gie-erh, and even of this the performer does not appear to have made the best use. That the instrument gives no other notes within the compass of this song is rendered probable by the resemblance between the scale of Long-how-sa and that of the Kuant-zu, which, according to Van Aalst's description, is a horn 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"⁠d"#
Notes given by the Kuant-zu: d’ e'⁠g' g'# a' b' c"# d" e" f"# g"

We may surmise that the intention in making the Gie-erh was primarily to embody the scale at what appears from our songs to be a standard pitch, and further (by the introduction of g'#) to permit in some fashion its displacement downward through a minor third. In this case, not only the irregular formation of the scale, but also the exceptional insecurity of intonation in Long-how-sa, receives a plausible explanation. The performer may be conceived as embarrassed by the unaccustomed position of the scale upon the instrument and its resulting distortion.

The use of the scale at different pitches, of which we have here a practical example, appears to have been reduced to a definite and elaborate system in Chinese theory from time immemorial. In the study of the later development of this, a possible reason will present itself for the choice by the Chinese of the particular transposition of Koung illustrated in Man-nen-fōn and Long-how-sa for (approximate) embodiment on an instrument. We shall find in the mediæval history of Chinese music the reflection of a structural distinction which has been fundamental in the art of Europe since the Reformation, and shall be able to interpret this transposition of our songs as evidence that the distinction in question is neither a purely theoretical one nor purely a matter of history, but a fact of existing musical practice in China as in Europe.

BENJAMIN IVES GILMAN.

NEW YORK.

(To be concluded.)

YEN-JEE-QUAW-CHANG.

PLAYED TWICE IN SUCCESSION BY JUMOY ON THE SAMIEN.

LO-TING-NYANG.

PLAYED BY YING-PARK ON THE SAMIEN.

MAN-NEN-FON.

(EVERLASTING HAPPINESS.)

PLAYED UPON THE HORN, GIE-ERH.

LONG-HOW-SA.

(A BRIDAL SONG.)

PLAYED UPON THE HORN, GIE-ERH.

notes. It is found that when the difference in pitch between the components of any two pairs of notes is the same, the ratio between the numbers of vibrations per second producing the two notes of one pair is the same as that between the numbers producing the two notes of the other. To each interval, in other words, corresponds a certain ratio between the rapidities of vibration of the two sources of sound producing the notes entering into it. In our modern keyed instruments the distance in pitch or interval between any pair of adjacent notes is the same as that between any other pair, and is called a semitone. This equalization of the interval between adjacent notes is what is known as equal Temperament. Any two keys between which eleven others are included give the interval called the octave, conspicuous for the likeness in sound between the notes concerned. A tempered semitone is therefore an interval one-twelfth the size of the octave. Mr. Ellis has proposed to express difference of pitch in terms of the hundredth part of a tempered semitone; that is, the twelve-hundredth part of an octave. This unit, called by him the cent, we shall find it convenient to use in our discussion. The compass in cents of the intervals principally used in music, in their perfect form and as they are approximately given on tempered instruments, is as follows:

				True.	Tempered.
	Semitone	ratio	16/15	112	100
	Minor tone	"	10/9	182	200
	Major tone	"	9/8	204	200
	Minor third	"	6/5	316	300
	Major third	"	5/4	386	400
	Fourth	"	4/3	498	500
	Fifth	"	3/2	702	700
	Minor sixth	"	8/5	814	800
	Major sixth	"	5/3	884	900
	Major seventh	"	15/8	1088	1100
	Octave	"	2	1200	1200

In the text we shall use the common symbolism of accented and unaccented letters for the sequence of notes on a keyed instrument. The letters c' c'# d' ... b' indicate the middle octave, whose notation reaches from the first ledger line below the treble stave to the third line from the top of it; the pitch here meant by c' being produced by 268 vibrations per second. The next lower octave is written without accents, and the next higher is doubly accented.

1. Among many recent students of the psychology of tone may be mentioned in England, Messrs. Gurney and Sully; in France, R. Koenig; in Germany, Professors Preyer, Mach, Lipps, and especially C. Stumpf of Munich, of whose imposing Tonpsychologie two volumes only have as yet appeared. The studies of non-European scales by the late A. J. Ellis, those of Professor Land of Leyden in Arabian and Javese music, those of T. Baker in the music of the North American Indians, are specimens of the contributions of the last decade to our knowledge of primitive musical usages. We may hope for much light from inquiries of the latter kind upon the problem of the origin of music; an interest in which has recently been reawakened by an essay contributed to ''Mind'' (October, 1890), by Mr. Herbert Spencer.
2. Different airs.
3. J. A. Van Aalst (Chinese Music, Shanghai, 1884) describes (p. 72) an instrument very similar to the Gie-erh under the name of Kuant-zu.
4. An interval may be roughly defined as the difference in pitch between two
5. The principal sources of information in regard to Chinese music are the work of Père 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 referred to.
6. Ueber die Musik der neueren Griechen, p. 32, quoted in Ambros, Geschichte der Musik, 1862, vol. i, p. 56.
7. The need for an instrument of this description in the study of music was expressed thirty years ago by Moritz Hauptmann (Briefe an Hauser, Leipzig, 1871, Bd. ii, p. 150). "Would that we could make musical photographs which should preserve 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 we are now acquainted with only through the entirely unmusical philologists; i.e. are not acquainted with at all."
8. Chinese musical practice has been hitherto very little studied. Père Amiot gives in European notation a part of a temple hymn. Père du Halde in A Description of the Empire of China, London, 1791 (translation), vol. ii, p. 125, gives the notes of five songs. John Barrow, in Travels in China, 2 ed., London, 1806, pp. 316-322, gives the notes of ten songs, and p. 81, a boatman's chorus exhibiting a rudimentary canonic imitation. Van Aalst gives nine pieces, expressly stating, p. 22, that they can only be approximately rendered in European notation. None of these songs are included in our collection.
9. Van Aalst, p. 18.
10. Amiot, p. 112; Van Aalst, p. 14.
11. 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.
12. We find similar ideas made the foundation of musical theory in Europe two millenniums later in the Harmonik und Metrik of Moritz Hauptmann (2d ed., Leipzig, 1873, p. 8). "Rightness — that is, reasonableness — of musical structure has for its law of formation unity with the negation of it and the resolution of this contradiction: an original unity which passes through a state of inner contrariety to become a unity restored. This process must continually repeat itself, either upon original unity or upon the result of a previous process. So the unity of a single note becomes in its restoration 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).
13. Or, as Père Amiot defines it, "that which passes from the state of possibility to that of existence." (p. 55.)
14. A nomenclature whose first employment is attributed to Guido d' Arezzo (eleventh century) is now applied in the following way to the various notes of this order: The note 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 group of three tones; the note below the group of two is called Ut (later Do), Re being between, and Mi above them. With these the names given in China to the notes of the same order correspond as follows:

    Fa⁠Sol⁠La⁠Si⁠Do⁠Re⁠Mi
    $\cdot$ (204) $\cdot$ (204) $\cdot$ (204) (90) $\cdot$ (204) $\cdot$ (204) $\cdot$
    Koung⁠Chang⁠Kio⁠pien-Tche⁠Tche⁠Yu⁠pien-Koung

    In the development which the diatonic scale has undergone in modern times, first into the harmonic, and then into the tempered scale of our pianos, this symbolism has come to have two other slightly different meanings, as follows:

    Modern diatonic: $\cdot$ (204) $\cdot$ (182) $\cdot$ (204) $\cdot$ (112) $\cdot$ (204) $\cdot$ (182) $\cdot$
    Fa⁠Sol⁠La⁠Si⁠Do⁠Re⁠Mi
    Modern tempered: $\cdot$ (200) $\cdot$ (200) $\cdot$ (200) $\cdot$ (100) $\cdot$ (200) $\cdot$ (200)

15. 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 in their character and are readily recognized by the people. The octave in the former seems to have had only six notes, and the songs of the Miaotz and rural people in that portion of China, are referable to such a [five-step] gamut, while the eight-tone scale [seven-step] generally prevails in all theatres and more cultivated circles. Further examination by competent observers who can jot down on such a gamut the airs they hear in various regions of China is necessary to ascertain these interesting points. . . ." One of the pieces given by Van Aalst in musical notation uses one of the pien; of Barrow's eleven songs only two neglect the pien entirely.
16. Van Aalst, p. 16. But one of Van Aalst's songs uses pien-Tche (as a passing note), and it is in this case flatted. The songs noted in Barrow's travels in China (circ. 1800) exhibit the flatted pien-Tche. It is impossible to determine the usage in the songs given by P. du Halde (circ. 1700), where the scale has various abnormal forms. Of the three five-step scales with intermediate notes for heptatonic use obtained by Mr. Ellis from the playing of Chinese musicians in London, one, that of the Yünlo (generally out of tune according to Van Aalst), has an entirely abnormal form. The other two appear to give the flatted pien-Tche. They are as follows (tr. of Helmholtz's Sensation of Tone, 2d ed., London, 1885, App. XX): ⁠K⁠Ch⁠K⁠pT⁠T⁠Y⁠pK⁠K
    ⁠Scale of the Flute, Ti-tsu: $\cdot$ 178 $\cdot$ 161 $\cdot$ 109 $\cdot$ 214 $\cdot$ 226 $\cdot$ 215 $\cdot$ 93 $\cdot$
    ⁠Scale of the Dulcimer, Yang-chin: $\cdot$ 169 $\cdot$ 105 $\cdot$ 217 $\cdot$ 170 $\cdot$ 217 $\cdot$ 118 $\cdot$ 202 $\cdot$
    ⁠T⁠Y⁠pK⁠K⁠Ch⁠K⁠P⁠T⁠T
17. Cf. Stainer and Barrett's Dictionary of Musical Terms, art. Greek Music. The later Greek scale had a compass of two octaves, like that of our songs; but since it was formed theoretically of four Dorian tetrachords (a sequence of a hemitone and two tones) with two added tones, the range of the two differs as follows: K Ch PT(PT) pK P T(pT) P K Ki T Y K Ch Ki T Y K La 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 t - Alternative position or conjoined tetrachord. The two middle tetrachords might either have a note in common (syncmmenon, conjoined) or be separated by a tone (diezcugmenon, disjoined). The comparison of the two scales shows that in the one case the note corresponding to pien-Tche was a semitone, and in the other a tone below the next higher note. In Chinese music the 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 but is given the lower position in two (IV and VII) of Barrow's collection.
18. In Professor J. P. N. Land's discussion of the Arabian scale (quoted by Mr. Ellis) he names the interval of about 350 cents, exemplified therein and in our songs, a neutral third. Mr. Ellis in describing the effect of a third of 355 cents reports it as so nearly a musical mean between the just major and minor thirds that a friend, on whose delicacy of perception he seems to have placed much reliance, "was quite unable to determine to which it most nearly approached in character" (p. 525).
19. ⁠K⁠Ch⁠K⁠pT⁠T⁠Y⁠pK⁠K
    ⁠In the scale⁠204⁠204⁠204⁠90⁠204⁠204⁠90
    ⁠Fa⁠Sol⁠La⁠Si⁠Do⁠Re⁠Mi⁠Fa
    Sol-Do = 498 c = Fourth, Do-Sol = 702 c Fifth, etc.;
    Fa-La = 408 c = Major third + 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.
20. Ila Parte, Cap. 41.
21. pp. 8, 21, 71, etc.
22. Cf. Ambros, Geschichte der Musik, vol. i; Van Aalst, p. 6.