Until the discovery of the non-Euclidean geometries (Lobatchewsky, 1826 and 1829; J. Bolyai, 1832; B. Riemann, 1854), geometry was universally considered as being exclusively the science of existent space. (See section VI. _Non-Euclidean Geometry_.) In respect to the science, as thus conceived, two controversies may be noticed. First, there is the controversy respecting the absolute and relational theories of space. According to the absolute theory, which is the traditional view (held explicitly by Newton), space has an existence, in some sense whatever it may be, independent of the bodies which it contains. The bodies occupy space, and it is not intrinsically unmeaning to say that any definite body occupies _this_ part of space, and not _that_ part of space, without reference to other bodies occupying space. According to the relational theory of space, of which the chief exponent was Leibnitz,[19] space is nothing but a certain assemblage of the relations between the various particular bodies in space. The idea of space with no bodies in it is absurd. Accordingly there can be no meaning in saying that a body is _here_ and not _there_, apart from a reference to the other bodies in the universe. Thus, on this theory, absolute motion is intrinsically unmeaning. It is admitted on all hands that in practice only relative motion is directly measurable. Newton, however, maintains in the _Principia_ (scholium to the 8th definition) that it is indirectly measurable by means of the effects of "centrifugal force" as it occurs in the phenomena of rotation. This irrelevance of absolute motion (if there be such a thing) to science has led to the general adoption of the relational theory by modern men of science. But no decisive argument for either view has at present been elaborated.[20] Kant's view of space as being a form of perception at first sight appears to cut across this controversy. But he, saturated as he was with the spirit of the Newtonian physics, must (at least in both editions of the _Critique_) be classed with the upholders of the absolute theory. The form of perception has a type of existence proper to itself independently of the particular bodies which it contains. For example he writes:[21] "Space does not represent any quality of objects by themselves, or objects in their relation to one another, i.e. space does not represent any determination which is inherent in the objects themselves, and would remain, even if all subjective conditions of intuition were removed." Entry: VII
Lest the passage above quoted from Berlioz should be suspected of bias or irrelevance, we cite a few phrases from Cherubini's _Treatise on Counterpoint and Fugue_, of which, though the letter-press is by his favourite pupil, Halévy, the musical examples and doctrine are beyond suspicion his own. Concerning the 16th-century idiom, incorrectly but generally known as the "changing note" (an idiom which to any musical scholar is as natural as "attraction of the relative" is to a Greek scholar), Cherubini remarks, "No tradition gives us any reason why the classics thus faultily deviated from the rule." Again, he discusses the use of "suspensions" in a series of chords which without them would contain consecutive fifths, and after making all the observations necessary for the rational conclusion that the question whether the fifths are successfully disguised or not depends upon the beauty and force of the suspensions, he merely remarks that "The opinion of the classics appears to me erroneous, notwithstanding that custom has sanctioned it, for, on the principle that the discord is a mere suspension of the chord, it should not affect the nature of the chord. But since the classics have pronounced judgment we must of course submit." In the whole treatise not one example is given from Palestrina or any other master who handled as a living language what are now the forms of contrapuntal discipline. As a dead language Cherubini brought counterpoint up to date by abandoning the church modes; but in true severity of principle, as in educational stimulus, his treatise shows a deplorable falling off from the standard set a hundred years before in Fux's _Gradus ad Panassum_ with its delightful dialogues between master and pupil and its continual appeal to artistic experience. Whatever may have been Cherubini's success in imparting facility and certainty to his light-hearted pupils who established 19th-century French opera as a refuge from the terrors of serious art, there can be no doubt that his career as a teacher did more harm than good. In it the punishment drill of an incompetent schoolmaster was invested with the authority of a great composer, and by it the false antithesis between the "classical" and the "romantic" was erected into a barrier which many critics still find an insuperable obstacle to the understanding of the classical spirit. And yet as a composer Cherubini was no pseudo-classic but a really great artist, whose purity of style, except at rare moments, just failed to express the ideals he never lost sight of, because in his love of those ideals there was top much fear. Entry: CHERUBINI
EPISODE, an incident occurring in the history of a nation, an institution or an individual, especially with the significance of being an interruption of an ordered course of events, an irrelevance. The word is derived from a word ([Greek: epeisodos]) with a technical meaning in the ancient Greek tragedy. It is defined by Aristotle (_Poetics_, 12) as [Greek: meros holon tragôdias to metaxy holôn chorikôn melôn], all the scenes, that is, which fall between the choric songs. [Greek: eisodos], or entrance, is generally applied to the entrance of the chorus, but the reference may be to that of the actors at the close of the choric songs. In the early Greek tragedy the parts which were spoken by the actors were considered of subsidiary importance to those sung by the chorus, and it is from this aspect that the meaning of the word, as something which breaks off the course of events, is derived (see A.E. Haigh, _The Tragic Drama of the Greeks_, 1896, at p. 353). Entry: EPISODE
Brahms has often been called the last of the great classical masters, in a sense wider than that of his place in the long line of the great composers of Germany. Though only the most superficial observers could deny him the possession of qualities which distinguish the masters of the romantic school, it is as a classicist that he must be ranked among modern musicians. From the beginning of his career until its close, his ideas were clothed by preference in the forms which had sufficed for Beethoven, and the instances in which he departed from structural precedent are so rare that they might be disregarded, were they not of such high value that they must be considered as the signs of a logical development of musical form, and not as indicating a spirit of rebellion against existing modes of structure. His practice, more frequent in later than in earlier life, of welding together the "working-out" and the "recapitulation" sections of his movements in a closer union than any of his predecessors had attempted, is an innovation which cannot fail to have important results in the future; and if the skill of younger writers is not adequate to such a display of ingenuity as occurs in the finale of the fourth symphony, where the "passacaglia" form has been used with an effect that is almost bewildering to the ordinary listener, that at least stands as a monument of inventiveness finely subordinated to the emotional and intellectual purport of the thoughts expressed. His themes are always noble, and even from the point of view of emotional appeal their deep intensity of expression is of a kind which grows upon all who have once been awakened to their beauty, or have been at the pains to grasp the composer's characteristics of utterance. His vocal music, whether for one voice or many, is remarkable for its fidelity to natural inflection and accentuation of the words, and for its perfect reflection of the poet's mood. His songs, vocal quartets and choral works abound in passages that prove him a master of effects of sound; and throughout his chamber music, in his treatment of the piano, of the strings, or of the solo wind instruments he employs, there are numberless examples which sufficiently show the irrelevance of a charge sometimes brought against his music, that it is deficient in a sense of what is called "tone-colour." It is perfectly true that the mere acoustic effect of a passage was of far less importance to him than its inherent beauty, poetic import, or logical fitness in a definite scheme of development; and that often in his orchestral music the casual hearer receives an impression of complexity rather than of clearness, and is apt to imagine that the "thickness" of instrumentation is the result of clumsiness or carelessness. Such instances as the introduction to the finale of the first symphony, the close of the first movement of the second, what may be called the epilogue of the third, or the whole of the variations on a theme of Haydn, are not only marvels of delicate workmanship in regard to structure, but are instinct with the sense of the peculiar beauty and characteristics of each instrument. The "Academic Festival" overture proves Brahms a master of musical humour, in his treatment of the student songs which serve as its themes; and the companion piece, the "Tragic" overture, reaches a height of sublimity which is in no way lessened because no particular tragedy has ever been named in conjunction with the work. Entry: BRAHMS