one tending somewhere
"naturally," or by the tendency of a restored tone being destroyed by
the "capacity of a flat"? The same writer, speaking of the scale of
G flat, says it is a "remarkable feature of this scale that it is
produced upon the organ and piano by pressing the same keys which
are required to produce the scale of F sharp." This is precisely
equivalent to saying that it is a remarkable feature that the notes C,
D, E, F are produced by pressing the same keys which are required to
produce _do_, _re_, _mi_, _fa_.

One more citation from the same author. Speaking of the formation of
scales, he says: "Thus we have another perfectly natural scale by
making use of two sharps." This vicious use of the term "natural" is
deplorable, because it is apt to give the pupil the notion that some
scales are more natural than others. A certain note is called "C
natural," and it is not uncommon for learners to suppose that it is
easier or more natural to sing in that key, as it is easier on the
piano to play anything in it because only the white keys are used,
while in any other at least one black key is required. Indeed, a pupil
may study music a long time before he finds out that there is no
difference between flats and sharps, as such, and other notes--that
all notes are flats and sharps of the notes a semitone above and
below. Seeing the staff of a piece of music armed with half a dozen
sharps or flats, the first thought of the pupil is that it will be
rather hard to sing. And many really suppose that flats and sharps
in themselves are different from other notes--a little "flatter" or
"sharper" in sound perhaps--and secretly wonder why their ear cannot
detect it. Of course it may be said that there is no necessity for
pupils to have such absurd notions, but it is inevitable where the
theory of music is made so difficult for the beginner. No doubt the
ambitious and naturally studious will delve and dig among the rubbish
of imperfect textbooks, analyzing and comparing the explanations
of different teachers, until order takes the place of chaos; but
textbooks should be adapted to ordinary capacities, and thereby they
will better serve the needs of the most brilliant.

_Fourth._ The memory should never be drawn upon except where reasoning
is impossible.

In science you have general laws, and from these deduce particular
facts depending upon them, but collections of facts and phenomena
without connection you must learn by h