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'dissonance in the case of tones produced by instruments with fixed notes, such as the piano. To execute music in all recognized keys on the same instrument with a given tuning would require an impracticably great number of tones in each octave, if all the intervals were to be produced with exactness. To meet this difficulty, the system of equal temperament divides the octave into twelve equal intervals, each therefore represented by the ratio of frequencies expressed by 2 (1.05946 approximately) which is the number which taken as a factor twelve times gives two, the ratio denoting the octave. The result is to confuse approximately equal intervals, making no distinction for example between C-D#, an augmented second, and C-Eb, a minor third; also, to slightly falsify all of the intervals of the scale except the octave, but fortunately by less than one per cent. in every case. Plainly, however, this inaccuracy affects the frequency of beats, and therefore modifies the degree of consonance in the approximated intervals.

It would be unjust to the tempered scale to speak of it merely as an expedient to meet an instrumental difficulty, and as involving tonal disadvantages, without giving it due credit for introducing a certain freedom in modulation. Thus, to mention one illustration only, the musician knows that the chord of the diminished seventh in a given minor key will enharmonically do duty in three others, thus closely relating the four keys and their related keys.

Musically, the effect of a given dissonant combination of tones depends vitally upon the chords that precede and follow it, upon the preparation and resolution. But this, of the first importance artistically and esthetically, is a matter hardly within the scope of the present discussion.

Having now spoken briefly of intervals that are recognized and used in music, it will perhaps be appropriate to close with a word concerning some possible but unused intervals. If we arrange a table as follows, showing all ratios between 1 and 2 represented by whole numbers with denominators from 1 to 8 we have

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5/5 6/5 (7/5) 8/5 9/5 10/5

6/6 (7/6) 8/6 9/6 10/6 (11/6) 12/6

7/7 (8/7) (9/7) (10/7) (11/7) (12/7) (13/7) 14/7

8/8 9/8 10/8 (11/8) 12/8 (13/8) (14/8) 15/8 16/8

With the exception of those bracketed, the intervals represented by these simple numbers are all found in the major and minor scales, and it is noteworthy that the more consonant intervals are represented by the simpler numbers, though it would be a mistake to suppose that the ear has a direct appreciation of this numerical simplicity.

The bracketed ratios are the unused intervals, unused in the sense that the musical scales, including the chromatic, do not contain them. But examination will show that they differ by almost or quite inappreciable amounts from well known intervals, and are undoubtedly often produced unintentionally, and thus actually used in practice though not in theory. They occur, moreover, among the overtones in complex sounds.

I can produce for you the interval 7/4 which lies between the augmented sixth and the minor seventh; the interval 7/5 which is slightly greater than an augmented fourth, and the interval 7/6 which is a little narrower than an augmented second. A trial will show that to the modern ear these examples of unused intervals are not unendurably dissonant.

LITERATURE IN TIME OF WAR

BY PERCY V. D. SHELLY

Assistant Professor of English

The war is barely ended, and yet, though at present we are greatly taken up with the problems of peace, we are already to some extent beginning to see the gigantic struggle for what it was. In a measure we are coming to grasp it as a whole, to understand better the number and nature of the forces that were in conflict, and to identify more clearly the factors that determined the outcome. Especially, as we look back upon it in a somewhat truer perspective, we are becoming more aware of its enormous complexity. In the earlier days we indulged in a good many loose generalizations, and made facile formulas that disposed of the whole thing in a single antithesis or summed it up in a slogan for billboard or poster. At one time we were told that it was a war of machinery, and that that side would win which had the greatest and best machines. For a while we were in danger of accepting this view of the matter. Politicians saw in the struggle only a conflict between two political systems-autocracy and democracy. Economists reduced it to a simple contest for colonies and world-trade. To the food experts, winning the war was a problem in proteins and fats. System-mongers thought of it as a race in efficiency, and saw the fate of the world hanging upon the Allies' genius for card filing. Each of these partial truths had its day and no doubt served its purpose. But now that we have had time to examine them, we perceive their inadequacy. We are less sure of explanations so simple, and today we are impressed most of all, perhaps, by the vast number and often the extreme subtlety of the forces that have been at work.

In particular we are coming to a better understanding of the powerful spiritual influences which played so great a part in winning the war. Our interest in the more obvious physical forces at work often obscured the fact that these were largely

dependent upon purely spiritual conditions. True, we always kept in mind the men behind the machines and realized that the machine without the man is useless. But often we have thought of the strength of our men in terms only of bone and muscle, and have ascribed their excellent morale to good food and warm clothing. We have sometimes lost sight of the fact that the man is but as strong as the spirit within him. Morale is essentially a condition of mind,-of the mind of men in action and of the nation at home. If the Allies in part won through the possession of superior material resources, even more did they win through the superiority of their ideas, of their will and faith, through all those things that sustain and quicken the spirit and keep the mind cheerful and healthy even in the most desperate passes. One of the most striking features of this war was the unprecedented number and variety of the influences that helped to sustain the spirit of the nations through four years of the worst suffering known to humanity. Many of these influences were obvious, some exalted. The church, the press, the school and university-these we all think of as having helped greatly.

But there were other less obvious and less hallowed institutions that did their share too. For example, the theatres and moving pictures. Must we not recognize in them-in their recreational even more than their publicity and advertising features a force that did much to lighten our minds and keep bright the spirit within us? Charlie Chaplin, I imagine, did more toward winning the war by playing the fool on the 'screen than he did going about in right-sized shoes and proper hat campaigning for liberty loans. Study the files of the British comic papers from 1914 to 1918. The student of national psychology is bound to see in them not only a phase of British strength but a support to British morale. A nation that could joke so much and so well in such times of stress was a long way from going under and must still have had an enormous moral reserve to draw upon. Again, take the mere presence of a venerable figure or the mere power of a name. Clemenceau! Can you doubt that in France the sight of the "Old Tiger"

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