in their particular key or scale. Here
the old names were preserved as being easily sung; Rousseau selected
numbers because he supposed that they best expressed the generation of
the sounds.[328]

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.