As was suggested in the last chapter, it becomes necessary to effect a compromise between the demands of true musical intonation and the limitations of musical instruments, in order that the performance of music may be made practicable. The equal temperament, now universally employed, has only risen to its present commanding position within the last century. It seems to have been first used by Johann Sebastian Bach. HÄndel did not know it, and it struggled throughout the whole of the eighteenth century with the mean-tone system.

Temperament systems were, however, invented and used long before this period. Pythagoras, the Greek pre-Christian philosopher, was one of the earliest experimenters along these lines. The method that he devised has come down to us, and we are thus able to see wherein lies the difference between it and the modern diatonic scale. Without going into too much detail, we may note that the Pythagorean system recognizes only two intervals; namely, the tone and semitone. The diatonic scale, as we know, has a major tone, a minor tone and a diatonic semitone. The Pythagorean scale contemplates perfect fifths and sharped thirds, and is incapable of the effects of modern harmony.

The next attempt to adapt the necessary compromise in the interests of practical music was introduced after the modern diatonic scale had become the standard method of octave-division; that is to say, some time in the fifteenth century. It has been variously called the “mean-tone,” “mesotonic” and “vulgar” temperament. In this method the tone is a mean or average between the major and minor tones of the diatonic scale. The fifths are all flattened, while the thirds are justly tuned. Such a system possesses both advantages and disadvantages. On the one hand, the nearer and more frequently used scales are purer and more agreeable; on the other hand, the remoter scales are exceedingly dissonant; so much so, in fact, that they cannot be employed with pleasure to either the performer or the hearer. So long, however, as the music is written in the commoner scales the mean-tone temperament, possessing the great advantage over other methods of having pure thirds, is far more agreeable to the ear. In fact, up till a few years ago it was not uncommon to find organs in village churches in Europe that were still tuned according to this system. The mean-tone system first made harmony, as we understand it, practicable, but as the knowledge and imagination of composers widened, the desire naturally arose to take advantage of the greater powers for harmony that could alone be afforded by the unrestricted possession of all possible scales. A substitute for the mean-tone system had, therefore, to be found, and thus arose the modern and accepted method, universally known as the Equal Temperament. By this method, which is at the present time universal, the octave is divided into thirteen equally distant semitones or half-steps. All distinctions between major and minor tones and diatonic and chromatic semitones are swept away, and it is assumed that the sound between any two sounds in the scale is equally sharp and flat respectively to the sound immediately preceding and following it.

This method, of course, implies a rearrangement of the whole scale, for it is necessary to alter the precise pitch of every sound within the compass of the octave in order that the equalization may be effected. Thus it comes about that the equally tempered scale has only one interval tuned purely. This interval naturally is the octave. All the others require to be sharped or flatted in varying degrees. Every chord, every interval, with one exception, therefore, is more or less out of tune. The effect of this system of tempering cannot very well be noted accurately upon the pianoforte, owing to the evanescence of that instrument’s tone; but the organ often shows the dissonance of certain intervals and chords in a most distressing manner. Perhaps the worst of the defects of the Equal Temperament are exhibited in the inability clearly to distinguish between true consonances and true dissonances. Where the actual distinctions between the true intervals are fused together it is impossible that there should be such distinctions between them as the true scale shows, and, consequently, we often are obliged to miss many delicate shades of comparative consonance or dissonance that would be clearly exhibited in a scale in which the intervals were represented with fidelity. We already know, however, that no such method is at present possible, and we must fain resign ourselves to the compromise that we have, and hope for better things in the future. But at the same time, the Equal Temperament possesses not a few positive virtues. As explained above, there can be no difference between the sharp of a given tempered sound and the flat of the tempered sound one whole step above the former. In other words, the sharp of C in the Equal Temperament must be the same as the flat of D, for these two sounds are assumed to be equally distant from the sound which is between them, and the three are simply part of a series of equal semitones. This being the case, the ambiguity that arises from the identity of these sounds is very often found to be invaluable for the purposes of quick and convenient modulation. There are instances in which the connecting link between two modulations would entirely be lost without the peculiar intonation that is afforded by equally tempered sounds. It seems, in short, that the equal temperament, imperfect and artificial as it is, cannot easily be replaced in the existing states of our acoustical knowledge and of the mechanical musical industries.

In order that the reader may more clearly realize the actual effects of the Equal Temperament upon musical intonation, the following table has been prepared, showing the differences of frequency between the true sounds of the just chromatic scale and the corresponding tempered sounds: (We are already familiar with the identity, in tempered intonation, of the sharps and flats of adjacent degrees of the scale.) C = 528 (Philharmonic Pitch).

It would be without the province of our immediate purpose to enter into any special discussion of the possibility of manufacturing pianofortes that shall give pure intonation, as distinguished from the tempered sounds that we have thus exhibited. We have already had occasion to mention that the Equal Temperament has become so strongly and intimately bound up with the performance of music, that the majority of musicians are probably incapable of distinguishing between the idea of pure as opposed to that of tempered musical sounds.

We have already pointed out, and reference to the various tables will confirm the assertion, that the Equal Temperament imposes excessive roughness of intonation upon very few of the musical intervals. Thus the octave is pure, the fourths and fifths nearly so, and only the seconds, thirds, sixths and sevenths are so rough as to be noticeable to other ears than those of the professional pianoforte tuner. Indeed it is very doubtful whether the musical public could ever be universally educated to the point of appreciating the differences between pure and equally-tempered fourths and fifths; while at the same time it must be remembered that the second and seventh, at least, are dissonances whether purely intoned or not.

We may properly question the actual advantage that the mechanical attainment of just pianoforte intonation would produce; we may ask ourselves what would be gained thereby for the cause of art, and the answer does not appear to be other than that any conceivable benefit must be so slight as to be practically negligible.