Rousseau attempted to find a theoretic base for this symbolic establishment of the relational quality of tones, and he dimly guessed that the order of the harmonics or upper tones of a given tonic would furnish a principle for forming the familiar major scale,[329] but his knowledge of the order was faulty.  He was perhaps groping after the idea by which Professor Helmholtz has accounted for the various mental effects of the several intervals in a key—­namely, the degree of natural affinity, measured by means of the upper tones, existing between the given tone and its tonic.  Apart from this, however, the practical value of his ideas in instruction in singing is clearly shown by the circumstance that at any given time many thousands of young children are now being taught to read melody in the Sol-Fa notation in a few weeks.  This shows how right Rousseau was in continually declaring the ease of hitting a particular tone, when the relative position of the tone in respect to the key-note is clearly manifested.  A singer in trying to hit the tone is compelled to measure the interval between it and the preceding tone, and the simplest and easiest mode of doing this is to associate every tone with the tonics, thus constituting it a term of a relation with this fundamental tone.

Rousseau made a mistake when he supposed that his ideas were just as applicable to instrumental as they were to vocal music.  The requirements of the singer are not those of the player.  To a performer on the piano, who has to light rapidly and simultaneously on a number of tones, or to a violinist who has to leap through several octaves with great rapidity, the most urgent need is that of a definite and fixed mark, by which the absolute pitch of each successive tone may be at once recognised.  Neither of these has any time to think about the melodious relation of the tones; it is quite as much as they can do to find their place on the key-board or the string.  Rousseau’s scheme, or any similar one, fails to supply the clear and obvious index to pitch supplied by the old system.  Old Rameau pointed this out to Rousseau when the scheme was laid before him, and Rousseau admitted that the objection was decisive,[330] though his admission was not practically deterrent.

His device for expressing change of octave by means of points would render the rapid seizing of a particular tone by the performer still more difficult, and it is strange that he should have preferred this to the other plan suggested, of indicating height of octave by visible place above or below a horizontal line.  Again, his attempt to simplify the many varieties of musical time by reducing them all to the two modes of double and triple time, though laudable enough, yet implies an imperfect recognition of the full meaning of time, by omitting all reference to the distribution of accent and to the average time value of the tones in a particular movement.

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