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more or less complicated variations were executed between one verse and another, or even between the parts of a verse. With them music was an auxiliary art, intended to increase, by ideal. izing it, the effect of words.

The development of their music must be regarded only from this point of view, and in this respect it must be admitted that they arrived at a considerable degree of perfection, notwithstanding the truly primitive form under which it appears at the present time. It was, in fact, a sort of lofty declamation, with more variable rhythm and more frequent and more pronounced modulation than ordinary declamation. This music was much enjoyed by the Greeks, and when it is considered that the Greeks were the most artistic and most creative nation that has ever existed, it becomes necessary to look with care for the refinements which their music must, and in fact does, contain.

The Greek musical scale was developed by successive fifths. Raising a note to its fifth signifies multiplying its number of vibrations per second by . This principle was rigorously maintained by the Greeks; rigorously because the fourth, of which they made use from the very beginning, is only the fifth below the fundamental note raised an octave. To make the tracing out of these musical ideas clearer, recourse will be had to our modern nomenclature, making the supposition that our scale, which will be studied later on in its details, is already known to the reader; calling the fundamental note c, and the successive notes of our scale, d, e, f, g, a, b, c, with the terms sharps and flats for the intermediate notes, as is done in our modern music. In this scale the first note, the c, represents the fundamental note, the others are successively the second, the third, the fourth, the fifth, the sixth, the seventh, and the octave, according to the position which they occupy in the musical scale.

If the c be taken as a point of departure, its fifth is g, and its fifth below is f. If this last note be raised an octave so as to bring it nearer to the other notes, and if the octave of c be also added, the following four notes are obtained:

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These four notes, according to an ancient tradition, constituted the celebrated lyre of Orpheus. Musically speaking, it is certainly very poor, but the observation is interesting that it contains the most important musical intervals of declamation. In fact, when an interrogation is made, the voice rises a fourth. To emphasize a word, it rises another tone, and goes to the fifth. In ending a story, it falls a fifth, etc. Thus it may be understood that Orpheus's lyre, notwithstanding its poverty, was well suited to a sort of musical declamation.

Progress by fifths up and down can be further continued. The fifth of g is d, and if it be lowered an octave its musical ratio will be g. The fifth below f is b flat, whence its musical ratio when raised an octave is 16. We have then the following scale:

c, d, f, g, b flat, c, whose intervals are,

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which is nothing more than a succession of fifths, all transposed into the same octave in the following way:

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This is the ancient Scotch and Chinese scale, in which an enormous number of popular songs are written, especially those of Scotland and Ireland, which all have a peculiar and special coloring.

But the scale can be continued further by successive fifths. Omitting, as the Greeks did, the fifth below b flat, and adding instead three successive fifths upward, we shall have a as the fifth of d, and e as the fifth of a; and finally b as the fifth of e.

The ratios of these notes, when brought into the same octave, will be.

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The first and the second of the last three fifths mentioned above, the a and the e, were introduced by Terpandro; the last, the h, by Pythagoras, whence the Greek scale still bears the name of the Pythagorean scale. It is formed, as has been seen, by successive fifths — that is to say, with the fundamental idea of simple ratios.

But it is necessary to observe that the execution of this idea is not entirely happy. It is true that the law of formation is very simple, but the individual notes have, nevertheless, an origin very distant from the fundamental note. The mode of formation of the scale was well suited for tuning the strings of the lyre, and this seems to have been one of the principal motives for adopting this mode of formation; but the interval between any two notes of the scale is anything but simple. It may thus be seen further that some of the notes bear extremely complex ratios to the fundamental note.

This is especially the case with the three notes last introduced into the scale, – that is to say, those corresponding to our a, e, and b, — which no longer bear simple ratios to the fundamental note, being expressed by the fractions {, 81, 145.

The last would not be a matter of much importance. The b can only be considered as a passing note, which by its open dissonance leads up to the c, or other consonant note. Its being more or less dissonant does no harm, and may in certain cases be pleasing. But that the third and sixth bear complex ratios is a grave defect, and this is probably the principal reason why the Greek music did not develop harmony. The Pythagorean third and sixth are decidedly dissonant, and with the fourth and fifth alone no development of harmony is possible, the more so that the interval between the fourth and fifth is rather small, and therefore dissonant.

The Pythagorean scale held almost exclusive sway in Greece. However, in the last centuries before the Christian era,- that is to say, during the period of Greek decline in politics and art, many attempts at modifying it are found. Thus, for example, they divided the interval between the notes corresponding to our c and d into two parts, introducing a note in the middle. At last they went so far as again to divide these intervals in two, thus introducing the quarter tone, which we look upon as discordant. Others again introduced various intervals, founded for the most part rather on theoretical speculations than on artistic sentiment.

All these attempts have left no trace behind them, and there. fore are of no importance. But the Pythagorean scale passed from Greece to Italy, where it held sovereign sway up to the sixteenth century, at which epoch began its slow and successive transformation into our two musical scales.

It ought to be added that the Greeks, in order to increase the musical resources of their scale, also formed from it several different scales, which are distinguished from the first only by the point of departure.

The law of formation was very simple; in fact, suppose the scale written as follows:

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Any note whatever may be taken as a starting point, and the scale may be written, for example, thus:

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It is evident that seven scales in all can be formed in this way, which were not all used by the Greeks at different epochs, but which were all possible. A musical piece, founded on one or other of them, must evidently have had a distinctive character; and it is in this respect, in the blending of shades, that Greek melody must be considered as richer than ours, which is subject to far more rigid rules.

The different Greek scales underwent much disturbance in Italy. Ambrose, Bishop of Milan, and later, Pope Gregory the Great, had the merit of re-establishing the first four; and the second, the rest of the Greek scales. Thus ecclesiastical music (the Ambrosian and Gregorian chants) acquired a clearer and more elevated character. It was a recitative on a long-sustained or short note, according to the words that accompanied it, music for a single voice, which is still partially retained, and which may be said to differ from the Greek music only by the purpose for which it is intended.

In the tenth and eleventh centuries an attempt was begun, especially in Flanders, at polyphonic music, – that is to say, at music for several voices. It consisted in combining two different melodies, so as not to produce discord. This sort of music also advanced rapidly in Italy. In the time of Guido d' Arezzo, the celebrated inventor of musical notation, such pieces were composed, in which frequent use was made of successive fifths — a thing most displeasing to the ear, and which we now look upon as a serious mistake in music. By the impulse of Josquino and Orlando Tasso, the last and perhaps the most important composer of that school, polyphonic music was developed in a surprising manner. Three, four, and more melodies were combined in a most complicated fashion, in which the art of combination had a much more considerable part than artistic inspiration - mere tours de force without any musical worth! Such music was especially cultivated by church singers, to whom was thus given a means of displaying their own ability. The voices were interwoven in a thousand ways, and the only restraint on the composer was not to produce unpleasant discords. Luther's great Reformation put an end to this fictitious and artificial style of music. Protestantism, rising into importance at that time, made it a necessity that church singing should be executed by the congregation, and not by a special class of singers. The music was therefore obliged to be simplified to put it within the power of all. The ground was already prepared for this. The Troubadours, Minstrels, and Minnesänger had developed primitive and simple melody, whence sprang madrigals and popular songs. And thus for polyphonic music another form was substituted, in which the different voices sustain each other.

Harmony, properly so called, arose from these simple and sustained chords, and from the easy movement of the different voice parts.

The shock of the German movement was felt even in Italy, where musical reform was initiated in a truly genial way by Palestrina, partly, indeed, to follow the deliberations of the Council of Trent. Palestrina abandoned the artificial method in use up to that time, and laid the most stress on simplicity and deeply artistic inspiration. His compositions (“Crux fidelis,” “Improperia,” “Missa papæ Marcelli,” etc.) are, and always will be, a model of that style.

But so radical a transformation could not be brought about by one individual, nor in a short time. The Pythagorean scale, which was in general use at the time, was opposed to a true development of harmony, and the more so when the execution of the music was intrusted to human voices in which every discord becomes doubly perceptible. True harmony could only be

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