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in his soul, and without which he can never reach the summit of his art. The plurality of intelligent people who believe in a future life will probably agree that our main purpose during the short stay on this planet should be to develop the soul and prepare it for a higher existence. From this view it becomes a religious duty, which the disciple of music owes to his own being, to cultivate principally that kind of music which has the most ennobling influence.

Even from a practical point of view, the would-be artist must take this high stand, if he expects to succeed in becoming a great artist, which is the goal for which all earnest students should strive, although perhaps one alone out of a million may reach it. Yet even those who fall short of it are equally benefited, since they acquire greater excellence than if they had taken a lower aim. A singer without an idea, and without love for his art-one whose all-absorbing thought is to make the greatest possible amount of money out of his voice—may become a clever artificer and a good artisan, but nothing more. He may attain a certain financial success by catering to the tastes of the vulgar; but even in this respect he cannot compete with the truly great vocalist who can earn more money in a few nights than the former can in a year. I earnestly warn the professional musician and singer against this tendency to regard his art chiefly as a means of money-making—a marketable merchandise; for in all my experience I have never known an instance of this that has not proved disastrous. The tendency prevails much more in America than in Europe. Among all the professional singers that I taught there, I remember from my personal experience very few who lacked love and enthusiasm for their art; but here, alas! it is too often the case that the money question takes precedence in the student's mind.

I have often observed, to my sorrow, that a pupil with great natural ability has shown antagonism and made no progress when classical songs were given him to study. Upon asking the reason for this indifference, the answer has invariably been: "These songs will never take, so why should I waste my time learning them? I want something 'catchy,' to make a 'hit;'

nothing else pays." Nine times in ten, desire of immediate gain will so blind the student that he cannot see the necessity of improving his taste, and after pleading with him in vain I find it useless to insist. It goes without saying that such a man can never become an artist, even if his voice is glorious and his ear perfect. It must, however, not be understood that I condemn the study of light music altogether. The ideal performer should be able to execute all grades of music equally well; and this he can only achieve by practising them all. What I mean is that he should give most of his time and thought to classical music, and that his taste should run in that direction. Neither do I condemn a moderate desire for money. It is an excellent thing as long as we look upon it as a means to some end; but it becomes a curse the moment we regard it as an end and love it for its own sake. It is easy to see that the all-absorbing greed of money can only develop low cunning, and will gradually stifle all those fine and exalted sentiments which constitute the very soul of music.

Are my ideas of music too exalted? Do I exact too much from those who profess it? For the benefit of any who are inclined to think so, I will give some extracts from Rev. Dr. T. Munger's highly interesting lecture, "Music and Faith;" for it must be admitted that, if a lover of music has such sublime conception and such high appreciation of it, so much at least should also be expected from one of its professors:

"Music viewed mathematically is not so very abstruse. It is largely a matter of air vibrations and rhythm, or times. These vibrations, when properly used, carry us into the spiritual world; for music is a purely spiritual thing, having the air vibrations for its body. The best theory of creation is that there is a spiritual world out of which all things proceed and to which all things return. If we ask why, we ask the unanswerable question. Personal existence is an ever unknown mystery. But it is the constant and unceasing endeavor of all human beings to come out of the limited, finite existence and realize the spiritual existence and world. And one of the broadest avenues to the realization of this spiritual world is music. It is as though a door had been left open by which men might pass in. Schopenhauer was the first of the great philosophers that have given music its true place. He says that, ⚫ were we able to give a thoroughly satisfactory theory of music, we could VOL. II.-19

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give a thoroughly satisfactory theory of the world.' We might reverse this and say that, could we give a thoroughly satisfactory theory of the world, we could perfectly and fully explain music. Music should ever be accompanied by severer studies. For the reason that we enjoy music, we are shown that we share in the universal harmony of creation. The world itself is embodied music. It is a type and expression of the eternal music and symmetry of things. . . . So music is the closest and truest expression of the spiritual. It lifts and elevates men's thoughts and brings them into closer relations with the spiritual, toward which the human heart ever yearns."

In connection with the quotation from Schopenhauer, I would also quote Pythagoras, who said that "numbers rule the universe." These assertions are very suggestive, and worthy of contemplation. Probably Schopenhauer had the latter in his mind when he pronounced the former; for there can be no doubt that numbers rule music, and this is the point where both of these conceptions meet.

The standard A, after which a piano is pitched, has 435 vibrations per second; the octave above, 870, and all the intervening tones have likewise their exact number of vibrations. A chord consists of a certain number of tones; a measure consists of a certain number of chords and tones, and of a certain number of beats or pulses; a melody and a modulation consist of a certain number of measures, and a symphony consists of a certain number of melodies and modulations, repeated a certain number of times through a certain number of keys. Other things being equal, the more mathematically exact are these numbers the more perfect the music. A composition should measure a definite number of beats or pulses during a definite period of time. Failing in this, the tempo will be wrong and the music will lose its character and beauty. Each tone in a harmony must have an exact number of vibrations, and between each interval must be an exact numerical proportion. If one or more

of these tones either increase or decrease the number of vibrations, while the rest remain unchanged, there will be discord;

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The ear is not able to detect a very slight discord, which is fortunate; for otherwise we could never enjoy listening to a piano or to an orchestra. In reality, sharps are higher than flats, but on a piano there is no difference between them; consequently they are all a little out of tune. Most orchestra instruments become

and if they all change, but keep the right proportion, there will be perfect harmony, but the pitch will either rise or fall.

Aside from this mathematical exactness of number, which is necessary to produce right pitch and rhythm, perfect geometric symmetry is necessary to produce beauty of tone. It seems that nature never produces anything without clothing it in beauty. How often I have watched her draw ice-crystals on a window-pane with such rapidity and exquisite symmetry that it was hard to realize that they were not traced by an invisible hand. Who has not admired the delicate beauty of snow-crystals? This law of beauty and symmetry, which seems to be omnipresent, causes resonating bodies to vibrate in figures not unlike these snow-stars. Such sound figures can, among other ways, be made visible by causing a metal disc, covered with dry sand, to emit a tone. The parts of the disc which vibrate will then throw off the sand, and the clearer the tone the more regular and distinct will be the figures. A piece of music executed with ideal exactness would contain a definite number of vibrations, sound figures, and rhythmical pulses-not one more or less. To execute music, or even anything else, with such ideal exactness, is, of course, far beyond human power; but if we analyze the cosmical harmony, we shall find this ideal exactness realized. We shall also find that, like music, everything can be expressed in numbers; in other words, can be mathematically understood.

The real purpose, therefore, not only of music but of all art, is to open our hearts and our eyes to all that is noble, and beautiful, and true.

somewhat out of tune during performance on account of their being handled, change of temperature, etc.




[Translated from the German by the author.]

A UNIVERSITY system should embody all sciences, the leading divisions being represented in the faculties. A perfect system, therefore, should be the basis of universities and of their scientific organization. Many systems of science have been constructed, especially by philosophers; but, as a rule, they have included the theoretical and omitted the technical. My system, so far as I know, is the only one which embodies both qualifications, and which shows at the same time the proper relations of each to the other.

The theoretical sciences-asking the fundamental question, What is the essence of everything existing ?-must form the basis of the technical sciences. The latter ask, How can we act methodically upon material things in order to produce values? Before acting, knowledge of the essence of the things upon which we wish to act is necessary, or at least desirable and useful. Therefore, we should study first the theory, and afterward the technics based upon it.

In the history of sciences we find that the theoretical and technical branches have grown contemporaneously. Unscientific practices have necessarily preceded all sciences, and it has been from these practices that the two great scientific divisions have been developed. The human race existed on the earth thousands of years before the sciences of anatomy and surgery were known; but with the development of these sciences the cause of learning was promoted. The aim of theoretical science

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