arising from the subdivision of a tube, gives a Major Third much flatter than equal temperament, and a Fifth much sharper than the meantone system. [See Node; and Partial Tones.] There is necessarily a great deal of false harmony whenever the brass is prominently heard in tempered music. Again, the tuning of the string-quartet is accomplished by just Fifths (C—G—D—A—E), but as these instruments have free intonation, they can execute tempered intervals when supported by the pianoforte or organ. In the absence of such an accompaniment, both violinists and singers seem unable to produce equally tempered scales or chords. This is precisely what might have been expected on theoretic grounds, as the consonant relations of the different notes being partially lost through temperament, the altered intervals would naturally be difficult to seize and render. Fortunately, we have positive facts to prove the truth of this deduction. The subject has been recently investigated by two French savans, MM. Cornu and Mercadier.[1] Their experiments were made with three professional players, M. Léonard the Belgian violinist, M. Seligmann, violoncellist, and M. Ferrand, violinist of the Opéra Comique, besides amateur players and singers. The results showed that a wide distinction must be drawn between the intervals employed in unaccompanied melody, and those employed in harmony. In solo performances, continual variety of intonation was observed; the same pitch was seldom repeated, and even the Octave and the Fifth were sometimes sharpened or flattened. So far as any regularity could be traced, the intervals aimed at appeared to be those known as Pythagorean, of which the only consonant ones are the Octave, Fifth, and Fourth. The Pythagorean Major Third is obtained by four just Fifths up, and is consequently so sharp as to amount to a dissonance. In melody, a scale tuned in this manner is found to be not unpleasant, but it is impossible in harmony. This fact also was verified by Cornu and Mercadier, who report that, in two-part harmony, the players with whom they experimented invariably produced the intervals of just intonation. The Thirds and Sixths gave no beats, and the Minor Seventh on the Dominant was always taken in its smoothest form, namely the Harmonic Seventh. 'I have myself observed,' says Helmholtz, 'that singers accustomed to a pianoforte accompaniment, when they sang a simple melody to my justly intoned harmonium, sang natural Thirds and Sixths, not tempered, nor yet Pythagorean. I accompanied the commencement of the melody, and then paused while the singer gave the Third or Sixth of the key. After he had given it, I touched on the instrument the natural, or the Pythagorean, or the tempered interval. The first was always in unison with the singer, the others gave shrill beats.'2[2]
Since, then, players on bowed instruments as well as singers have a strong natural tendency towards just intervals in harmony, it is not clear why their instruction should be based on equal temperament, as has been the practice in recent times. This method is criticised by Helmholtz in the following words:—'The modern school of violin-playing, since the time of Spohr, aims especially at producing equally tempered intonation.… The sole exception which they allow is for double-stop passages, in which the notes have to be somewhat differently stopped from what they are when played alone. But this exception is decisive. In double-stop passages the individual player feels himself responsible for the harmoniousness of the interval, and it lies completely within his power to make it good or bad.… But it is clear that if individual players feel themselves obliged to distinguish the different values of the notes in the different consonances, there is no reason why the bad Thirds of the Pythagorean series of Fifths should be retained in quartet-playing. Chords of several parts, executed by a quartet, often sound very ill, even when each one of the performers is an excellent solo player; and, on the other hand, when quartets are played by finely cultivated artists, it is impossible to detect any false consonances. To my mind the only assignable reason for these results, is that practised violinists with a delicate sense of harmony, know how to stop the tones they want to hear, and hence do not submit to the rules of an imperfect school.'
Helmholtz found, by experiments with Herr Joachim, that this distinguished violinist in playing the unaccompanied scale, took the just and not the tempered intervals. He further observes that, 'if the best players, who are thoroughly acquainted with what they are playing, are able to overcome the defects of their school and of the tempered system, it would certainly wonderfully smooth the path of performers of the second order, in their attempts to attain a perfect ensemble, if they had been accustomed from the first to play scales by natural intervals.'
The same considerations apply to vocal music. 'In singing, the pitch can be made most easily and perfectly to follow the wishes of a fine musical ear. Hence all music began with singing, and singing will always remain the true and natural school of all music.… But where are our singers to learn just intonation, and make their ears sensitive for perfect chords? They are from the first taught to sing to the equally tempered pianoforte.… Correct intonation in singing is so far above all others the first condition of beauty, that a song when sung in correct intonation even by a weak and unpractised voice always sounds agreeable, whereas the richest and most practised voice offends the hearer when it sings false or sharpens.… The instruction of our present singers by means of tempered instruments is unsatisfactory, but those who possess good musical talents are ultimately able by their own practice to strike out the right path for themselves, and overcome the error of their original instruction.… Sustained tones are preferable as an accompaniment, because the singer himself can immediately hear the beats between
