ence the law that a sensation from an unfatigued sense organ, with no unpleasant associations, is naturally agreeable. A more complicated problem is presented by the pleasantness or unpleasantness of tone-combinations, simultaneous and successive. All theories of consonance make some attempt to refer the cause of the agreeableness or disagreeableness that is produced when two tones are sounded together to laws that transcend the field of music and are based on human nature as a whole; but some theories must travel a long and weary road of speculation before the connection is establisht. For example, Stumpf finds that consonant tone intervals are those in which the two tones sound most like one-those which have what he calls the greatest fusion degree. In the dissonant intervals of the second and the seventh it is apparent to the ear that there are two distinct tones. In the supremely consonant interval of the octave, on the other hand, the two tones blend almost indistinguishably, and the intervals of the fifth and major third make an impression of greater singleness and simplicity than do the second and seventh. But there is no obvious reason why simplicity of impression should be more agreeable than a reasonable degree of complexity. We do not enjoy a solo more than a duet. It is only dissonant complexity that is disagreeable, which leaves the question where it was before. Much theorizing, into which we have not time to follow him, is needed to enable Stumpf to bring the pleasantness of consonance into relation with any other esthetic principle. A similar criticism may be made of another famous theory, that suggested by Lipps. As you all know, the vibration rates of the air waves that produce the tones used in the musical scale stand in certain fixt ratios to one another. If the vibration rate of the first tone in the octave be regarded as 1, that of the octave above will be 2. The ratio of the rate of a tone to that of the fifth tone above it is 2 to 3; that of a tone to the major third above it is 4 to 5; that of a tone to the fourth above it is 4 to 3. Thus the pleasant or consonant tone-combinations are those whose vibration rates stand in simple ratios. On the other hand, the tones which are unpleasant when sounded together have their vibration rates in complex ratios; the minor second has the ratio 16 to 15; the major second the ratio 9 to 8; the seventh, the ratio 15 to 8. Lipps says that a tone-combination is pleasanter the simpler the ratio of the vibration rates of the tones combined. But how can this be when people who are perfectly ignorant of the simplicity or complexity of these ratios still find fourths agreeable and sevenths disagreeable? It is a matter, Lipps says, of unconscious rhythm. If two vibrations, falling on the ear, have frequencies that are in a simple ratio, such as 1 to 2, every second nervous impulse will coincide; if the ratio is complex, like 8 to 15, there will be a perfectly irregular and unrhythmic excitation. Altho we are not conscious of this rhythm as such, yet Lipps seems to think we can explain it as we explain our enjoyment of the consciously experienst rhythm of a drum. Certainly this is a far-fetcht and unattractive hypothesis.

One hesitates to simplify where such authorities as Stumpf and Lipps have found it impossible to do so, yet I cannot refrain from hoping that in place of fusion degree or unconscious rhythm some of the principles which we have already mentioned may be found sufficient to explain the pleasantness or unpleasantness of tone-combinations. One of these principles is that we like what we are used to, so long as its familiarity is not so great as to pass over into fatigue. We are all thoroly used to the intervals which have the highest degree of consonance, namely, the octave, the fifth, and the major third, not because they are used in music, but because nature constantly provides them for us as partial tones. The first overtone is the octave, the second overtone is the fifth, the third overtone is the second octave, the fourth overtone is the major third. To these tone-combinations our ears are forst to respond in the great majority of cases where tones are heard. The cross-principle, that we grow fatigued with the too familiar, will explain a whole series of phenomena in the range of musical appreciation, from the fact that most people find the octave and fifth insipid compared with the fourth, to the fact that some people find Haydn insipid compared to Richard Strauss.

Again, one of the earliest theories of consonance, that of Helmholtz, correlated the disagreeableness of a dissonance, such as the second or the seventh, with the law that all rapidly intermittent stimulation is unpleasant because somehow injurious to the nervous apparatus. Dissonant intervals, he held, always involve the roughness of beats, either between the fundamental tones or their overtones, and the disagreeableness of beats is like that of a rough surface or a flickering light. One of the most recent theories— that of Krueger-seems to explain consonance as due to the absence of interference from difference tones. There is some experimental evidence against the supposition that beats are the source of dissonance, but into this we have not time to go. If all unpleasant tone-combinations are those which produce fatiguing interference phenomena, such as beats, one would have to explain the pleasantness of consonant-combinations on the same principle that makes the single tone an agreeable experience-if a single tone is pleasant, the more tones we hear simultaneously without disagreeable roughnesses due to interference the more pleasure we get.

This principle, again, may be applied to the theories which relate the agreeable character of a consonant interval to what is called tone relationship. Two tones are more nearly related the more overtones or partial tones they have in common. Since all the overtones of the upper tone in an octave are also overtones of the lower tone, the octave has the greatest degree of direct tone relationship: the upper tone of the fifth has four overtones in common with the lower tone within the compass of three octaves, while the dissonant intervals of seventh and minor second have no common overtones at all. When overtones do not coincide, we may get interference

phenomena; when they do coincide, we get more pleasantness because more tones are present.

On the whole, it seems probable that all the facts regarding the pleasantness of simultaneous tone-combinations may be derived from laws whose generality transcends the special field of music. The same may be said, I think, of the pleasantness of successive tone-combinations. There are two groups of facts which fall under this head: the facts of melody and those of rhythm. Authorities on musical esthetics tend to explain melody on the same principle that they use to explain consonance; thus Lipps applies the law of simple ratios, and Stumpf even declares that fusion occurs between one tone and the memory image of its predecessor. There is, however, the added problem as to how a melody, a series of tones, gains unity for the mind. Apparently the agreeableness of recognition applies to our satisfaction with the return to the tonic; we enjoy everywhere and always the safe return to a recognized starting-point after wanderings. Thus we enjoy the recurrence of a musical phrase in a composition as we enjoy the recurrence of a motive in a decoration; to recognize in the midst of diversity is a reassuring experience. The pleasantness of a rhythmic series of sounds, as distinct from its deeper emotional appeal, of which I shall speak presently, rests mainly on two principles: first, there is the law that we enjoy whatever suggests free and unhampered bodily movement, as we enjoy the upward sweep of the Gothic arch. Free movement, owing to the construction of the human body, is naturally rhythmic; unrhythmic movements are for the most part constrained and difficult. The second principle is that we like to have our expectations satisfied. We like not only to meet the same motive repeated in a decoration, but to have it recur at equal and symmetrical intervals, just when we expect it. A rhythmic series of sounds is one in which the accents occur just when we expect them. In an unrhythmic series, we feel precisely the same kind of irritation that we experience when someone makes a mistake in a familiar quotation. The disappointment of expectation is closely related to that primitively dangerous experience of surprise.

I think we may sum up a discussion of the sources of musical pleasure by saying that all of them are sources not peculiar to music. We enjoy music for the same reasons that we enjoy other things. There is a problem of musical enjoyment—a problem of great complexity-but there is no mystery of musical enjoyment. The case is somewhat different with regard to our second topic, of which I must speak in a very few words-the emotional appeal of music.

The uniqueness of music's appeal to the emotions is, as you all know, its power to reach them directly. It gets at them without the use of any associations derived from the individual's experience. The other arts suggest emotion to us by giving us thoughts or mental pictures which our past personal history has associated with emotions. The musician cannot sug

gest thoughts, except musical thoughts, and he cannot suggest imagery with any definiteness. In an investigation carried out by Weld, at Clark University, a piece of music of the most pronounst program type, intended to describe a hunting scene, called up in its hearers images of a circus, an auction sale, an amusement park, and a battle. Yet there is no such inconsistency in the emotions and moods awakened by music. Since, then, its emotional appeal is thus independent of association with individual experience, it must be based on racial experience.

I believe that this direct appeal to emotion, which constitutes, if anything does, the real mystery of music, is due to its profound and ancient social significance. Herbert Spencer, you know, found the origin of music in impassioned speech, and Stumpf derives it from signal calls. These theories tell only a part of the truth, but we cannot overlook the fact that the sense of hearing has a more direct hold than any other sense on our emotions, because it is the medium of human communication, the means by which one soul reaches another; and nothing in the world is so compelling to the emotions as the mind of another human being. Again, as you know, Wallaschek accused Spencer of leaving out of his theory the most fundamental element in music, rhythm. We must not omit rhythm in speaking of the emotional appeal of music. And the emotional power of rhythm is derived from the immense emotional power of the mob. All concerted action by a mass of individuals must be rhythmic. In the wild dances of primitive man, in which the individual merges himself in the crowd and feels his powers increast a thousand fold by the contagion of its emotions, we find the source of the magic of rhythm. The sense of hearing reaches the emotions directly because it is the medium of social intercourse; musical sound is the kind of sound that is produced under the stress of emotion; rhythmic sound means that the emotion is magnified and exalted by being shared with a whole mass of one's fellow-beings.

MECHANICAL INVENTIONS AS AN AID TO THE
TEACHING OF MUSIC

LEO RICH LEWIS, PROFESSOR OF MUSIC, TUFTS COLLEGE,
TUFTS COLLEGE, MASS.

Let me give you a few results of twenty-four years of belief in automatic instruments. Let us first observe that there are three different uses of these instruments: (1) in concert, (2) in classroom demonstration, and (3) in the "laboratory." As to the first, these instruments, in their most recent developments and in the hands of a skilled performer, can do remarkable things. Educationally, these possibilities are of importance, but not of prime importance. As to the second, they make it possible for the technically unskilled but well-informed teacher to present to a class

the representative works of all periods of the art, and, with the aid of copious existing literature concerning music, to lay a firm foundation of musical taste. But the third phase of their usefulness is, it seems to me, the most important. These instruments make it possible for the student to study music exactly as he studies biology, physics, chemistry.

But these devices are doing more than that. They are helping us to practice principles of pedagogy which are now, as it seems to me, being too much neglected. I may be in error, but, in viewing the course of things pedagogical, I seem to find that we are failing to devote our attention to the organization of the mind. We make millions of imprest minds, but few organized minds. We college people are finding it necessary to do what the secondary schools have been supposed to do in many branches; and, even at that, we are finding ourselves unable to develop a real power to "tackle" a new problem. We can blame no one, certainly no individual teacher. But, in music, I prize the automatic instrument because it can fully and definitely organize the mind as to musical art; and I confess an intense regret that it is not more generally used specifically to that end. But I must not linger on this topic. It would lead us too far afield.

But you have, in the automatic player, the means by which the pupil can clarify his own ideas. And you naturally ask, "Do you expect that we shall have player pianos in such abundance that every student shall have that opportunity?" My answer is: "Probably not every student in the school, for not every student will wish to study music; but I do believe that not until we accept the principle that only by such laboratory methods can any fruitful study of the art be attained shall we be making real progress toward a respectable minimum of attainment in the study of musicnot in the performance of music, which department is now fairly well provided for.

And let me mention one other point of the many which might be taken up if time allowed. I select this point because I have not seen it discust anywhere. As things are at present in our schools, pupils are restricted to acquaintance with music which they themselves can perform, and largely to vocal music. The great monuments of the art are never presented to them unless they live in a large city. It is as tho in the study of English no Shakespeare, no Milton, could be studied, but only the lesser masters, or passages of the great authors, "arranged for school use." What a change in this respect is bound to come when the possibilities of automatic instruments are thoroly understood by those in charge of our schools!

And yet the possibilities of the player piano are not exhausted as to showing features of interpretation, for the recording instruments can bring to us characteristic renderings by great artists; and the talking machine can be of the greatest service in presenting vocal works of all sorts. These matters claim our attention here less than others, however, because we are continually reminded of them by the manufacturers of the instruments.