In a footnote to Blaserna's “Theory of Sound in relation to Music” (p. 94), it is stated that Euler was acquainted with the importance of the numbers 2, 3, and 5, and that he “established upon them a rule for the development of our musical system.” To understand this statement it is necessary to know that a musical note is an effect of regular vibrations of a sounding body—that is to say, of vibrations occupying equal intervals of time; and that two notes cannot be consonant unless the proportion subsisting between their two rates of vibration is simple. These things being understood, it may be shown that the importance of the numbers 2, 3, and 5, employed for the purpose of expressing the ratios of vibration rates, cannot be overestimated. When the intervals between musical notes are expressed by the ratios of the vibration rates of the notes, these three numbers alone, with their squares, cubes, and other powers, and numbers arising from their intermultiplication, are capable of expressing the ratios of consonant notes; and not only so, but they alone are capable of expressing the ratios of all notes belonging to the same scale, and of all notes belonging to all scales into which it is possible to pass from the original scale by modulation.

Though not one of that class of musicians about whom the public talks with feverish excitement, and though his ways and words were not the object of journalistic curiosity, Frederick Arthur Gore Ouseley was a man of wide influence, and one whose character and labours deserve careful study. He was distinctively a representative man, and in furthering the objects he had in view in life he was uniformly consistent, as indeed every man must be who conscientiously draws up a scheme of work founded on a sense of duty, and turns neither to the right nor left while pursuing it. Whether he chose the best scheme of life or not, we shall by-and-bye try to discover; but the simplicity of his mind, the purity of his motives, the calm persistence with which he aimed at his object, and his immense self-sacrifice in securing it, seem to point more to the chivalrous knight of a bygone age than to the modern worldly artist, who rapidly faces about this way or that way, but who, somehow or other, is always found treading the path which leads to the best market for his wares.

When it was intimated to me that I might be invited to read a paper at one of the meetings of the Musical Association, I hesitated for a moment, should the invitation come, feeling doubtful whether it was in my power to say anything that would not be as well, or better, said by any one of its members.

Ladies and Gentlemen,—I feel that by way of preface I must ask your pardon for venturing to intrude upon your notice a paper very hastily composed, scrappily written, and to a great extent carelessly put together. I must tell you that when the idea of this paper first suggested itself to me I hoped that I should be able to devote much time and study to the consideration of so vast and absorbing a subject, but since then circumstances have materially altered, and I have been obliged to give my whole time to other matters more especially connected with my work as a clergyman which previously had not been thrown in my way. But is not this the way with so many matters in this hurrying, driving, bustling, brain-wearing age in which we live; we propose to ourselves great things, but how many attain to them ? I at least so far as this paper is concerned must in dust and ashes sit with covered head and say “Peccavi, I have sinned.” And then again, why should I speak to you about Richard Wagner ? I never knew the man, I only saw him once; I have never been to that musical Mecca, Bayreuth; I have never seen any of his operas performed in his native land; and I have not exhaustively studied his life, works, or character. Well, I suppose there are two reasons to account for this whimsical caprice in my selection of a subject : first, a blind following of the spirit of the age, a spirit which prompts people to talk a great deal about what they know very little of; and secondly, an earnest desire on my part to ascertain the attitude of members of this Association towards so great a genius as Wagner, and to elicit a genuine expression of opinion as to the future prospects of what has been not inaptly, though I will not say prophetically termed “The music of the future.” If this paper only arouses and awakens an interesting discussion amongst the members here present, my object will have been more than fulfilled, and we shall all leave this room with the very candid opinion that the second half-hour has been far more entertaining and useful than the first one. Such sentences may suggest to wily-minded individuals that I am what is called “fishing for compliments,” but I assure you I am not; I am convinced within myself that I am speaking solid and indisputable truth.

The history of the flat, sharp, and natural is not a dull record, but a tale full of stirring incidents. If my narrative does not succeed in engaging your interest, in stimulating your curiosity, and in now and then sending a thrill of excitement through you, I have failed to do justice to the noble subject of my choice. These remarks may lead you to suppose that I am going to speak of the human flats, sharps, and naturals of our profession. This, too, is, if not a noble, certainly an interesting subject; but it is not the one of which I intend to treat on this occasion. My subject is the origin, rise, and vicissitudes of the musical signs that raise and lower natural notes and restore raised and lowered notes to their natural state. No doubt most people would suspect such a history to be dull; but nothing is dull if only we go deep enough into it. The subject in question is certainly not an exception to this rule, which could be confirmed by the study of hundreds of the apparently dry details of our notation. It is with these details as with the humble constituents of society; with the flat, sharp, and natural as with those lowly neighbours of ours whose lives seem to us an unbroken level desert. How great is always our astonishment when chance allows us to get a glimpse of what is hidden behind the plain, prosaic exteriors, and we discover loves and hates, hopes and disappointments, joys and sorrows, aspirations, successes, and failures—in short, at least as much romance as in the lives of the great and mighty. Well, let us try to get a glimpse of what is hidden behind the plain exteriors of the humble friends now under consideration.

The Assistant Secretary.—In the discussion on Mr. Niecks's paper read in March, on “The Sharp, Flat, and Natural,” reference was made to the absence of a single sign to indicate a double flat, such as is used in the case of a double sharp. I have been asked to bring under the notice of the members of this Association two signs with that object, which have been invented by Mr. Ross, of Messrs. Novello's printing establishment, through whose hands our “Proceedings” pass when in course of publication. A very great deal of music being now printed from type, it is found that the double sign at present in use occupies so much space as to interfere with the symmetrical appearance of the music when thus set up, and Mr. Ross was therefore led to devise some sign which should obviate this disadvantage. The two signs which he has produced achieve this object, and in presenting them to you for your opinion, Mr. Ross hopes that approval from distinguished authority may lead to the general adoption of one or other of them. It is, of course, desirable that any new sign, in order to gain ready acceptance, should present to the eye some resemblance to the present double flat, and thus suggest that the note must be lowered from its normal position. It will be noticed that both signs fulfil this requirement The following passages show first of all the present double sign and then the two signs invented by Mr. Ross.

It is perhaps a rather startling question to put to the learned and accomplished members of such an Association as this—What is sound ? All your lives long you have doubtless held very firm and clear convictions on the subject of Sound; and have trustingly accepted the theory which has obtained, one may almost say, since the time of Pythagoras, and which has, in our day, been fostered by all the great acousticians, and dogmatically taught by Professors Tyndall, in England, Helmholtz, in Germany, and Mayer, in America.

In venturing to read this paper, I have not undertaken the work with the view of giving instruction, but rather of eliciting information from those who are better able than myself to teach.

It is the fashion now-a-days amongst the members of that class of society to whom the term of musical amateur belongs to express the greatest admiration for the folk-songs and melodies of the people. Unlike many of their tastes, this is one which, if rightly used, is worthy of great commendation, for nowhere can the characteristics and feelings of a nation be better read and understood than in the songs of their people. It is in their music that their real selves stand revealed, and it is in music that their inmost thoughts and feelings are expressed.