Those who examine the subject fairly will be compelled to take the position held by Galin, Cheve and their school, that a new method of writing music is imperatively needed, because that now in use lacks the essential elements of a scientific system: it is neither simple, clear nor concise. There are certain elementary principles which must be observed in the exposition of any science, and especially in that of music, which is addressed to all classes of intelligence. Among these principles are the following, as stated by M. Cheve: _1st_. Every idea should be presented to the mind by a clear and precise symbol. _2d_. The same idea should always be presented by the same sign: the same sign should always represent the same idea. _3d_. Elementary textbooks or methods should never present two difficulties to the mind at the same time; and such textbooks or methods should be an assemblage of means adapted to aid ordinary intelligences to gain the object proposed. _4th_. The memory should never be drawn upon except where reasoning is impossible. Let us test the exposition of the ordinary musical notation, and also that of the school of Galin, by these principles and compare the results. _First_. Is every idea presented by a clear and precise symbol? In the ordinary method, certainly not. The musical sounds or notes are represented by elliptical curves with or without stems; by spots or dots with plain stems, or with stems having from one to four appendages, or with these appendages united, forming bars across the stems. These curves and dots are placed on the five parallel lines of a staff, as it is called, or between the lines of this staff, or on or between added or "ledger" lines above and below the staff. Certainly, these cannot be called precise symbols, especially when we reflect that _any one of them placed upon any given line or space may represent successively do, re, mi, fa, sol, la, si_, or the flats or sharps of these notes. The notes, indeed, have no names, being all alike for the various notes; but names are given to the lines and spaces of the staff; and, alas! the names of these lines and spaces change continually with the change of key or pitch. For example: if we commence a scale with C, our _do_ will be on the first added line below the staff, and its octave, _do_, on the third space counting from the lowest. If we commence a scale with G, our _do_ will be on the second line from the bottom, and the octave on the first space above the staff; and so on for all the other scales except those which commence a semitone below or above. For example: the scales of the key of G and of G flat would be placed exactly the same upon the staff, though the signature of G would be one sharp upon the staff at the beginning, and that of G flat would be six flats. The same may be said of the keys of D and D flat, F and F sharp, etc.