The subject which I submit for your consideration this afternoon is the influence of numbers in music, as in the various combinations of consonances and dissonances which we hear every day, and to show how these are explained by the fundamental laws of the science.

The title of my paper, ‘The Formation of a National Musical Library,’ may be open to some misconception, and I should like therefore to premise that it does not simply mean a library of national music, though that certainly should form a very important and indispensable section of any national library. The subject proposed for consideration is one which must assuredly deeply interest all musicians, amateur and professional, and the theme is capable of so much expansion that I could, without difficulty, engage your attention during the whole of the time allotted for our meeting; but I shall be brief, in the hope that my few remarks may induce some considerable discussion, leading, perhaps, to practical action.

This paper is addressed to teachers, rather than to artists. In it I present to you a summary of Lussy's Treatise on Musical Expression—a work published in Paris in 1874, and now in its second edition. I know nothing of the author beyond his own statement, that for twenty years he has been a professor of the pianoforte in Paris. His work is dedicated to M. Gevaert, principal of the Brussels Conservatoire, ‘who,’ says the author, ‘when illustrious theorists and composers declared that a treatise on expression was impossible, encouraged me to proceed and gave me valuable advice.’ Musical people all shake their heads at the notion of reducing to rule such an intangible thing as expression. As well, they will say, might we show a person how to love, as how to impart feeling to what he plays. Of course there is much truth in this, but let us try for the moment to allay our prejudices, and hear what M. Lussy has to say.

The title of my paper seems to forbid any tedious method of bringing its subject before the Musical Association.

It would be incongruous, in the advocate of greater expedition in writing music, to weary you by any unnecessary beating about the bush in explaining the proposed method of attaining it.

The investigations of the late Sir Charles “Wheatstone on the subject of the powers of resonance of different masses of air enclosed in chambers of certain definite simple forms, were brought before us by Professor Adams in 1876, and it appeared to me that it might be a matter of interest to this Association to enter briefly upon the consideration of the resonance of brass wind instruments as illustrating Wheatstone's laws. There is very commonly a vagueness used in the description of such instruments which I submit is misleading; they being usually considered to be cones, or cones combined with cylindrical tubing, neither of which descriptions properly applies. And farther, they are commonly considered to be of necessity in tune, that is, in just intonation, having the vibrational numbers of the notes that may be produced from them without altering their length, in the proportion of the numbers, 1, 2, 3, &c. As so great an authority as Prof. Helmholtz writes (‘Sensations of Tone,’ pp. 511, 641): ‘Horns and trumpets have already naturally just intonation,’ and ‘brass instruments naturally play in just intonation, and can only be forced to the tempered system by being blown out of tune,’ it seemed to me worth attention that this must be taken only as being particularly, and not generally true: that is, that though the ideal brass instrument has such characteristics, this ideal is not necessarily attained to in practice. The relative and absolute numbers of vibrations of the first eight tones required on a brass instrument, taking the 4 feet C of 128 vib.

The Chairman said, Mr. Bullen, who had intended to read a paper that evening, was through serious illness unable to come, and therefore the proceedings would commence with a discussion on the paper read last month by Mr. Blaikley. He would first ask Mr. Blaikley to give a résumé of the substance of his paper.

If an apology be necessary for bringing before a learned society like the Musical Association the details connected with teaching, it is, I think, found in the supreme importance, both from an artistic and professional standpoint, of a sound basis of musical education.

If there is anything in this world so perfect as to be beyond improvement, our established notation can scarcely lay claim to such an exalted position, to judge by the many attempts that have been made from time to time to improve or supersede it.

I think it advisable first of all, to explain a little more fully the title announced in, the Syllabus for this evening's paper, viz. ‘A Practical Method for Beading Harmony.’ The title originally sent was, ‘A Practical Method for Reading Harmony, adapted to performers on the organ or pianoforte, and distinct from the composer's manner of analysis.’ I was kindly recommended to leave something to be explained, rather than adopt a title too long to be well remembered.

It is one of the great advantages of a body established upon such a basis as that upon which the Musical Association was set on foot, that it affords an opportunity for all those who have anything to contribute to the great art work in which we are so deeply interested to cast their mite into the common treasury of plans and practices, and even if they cannot hope to add largely to the learning or the science of the Association, they can still give of their best with the conviction that it will at least meet with a kind and appreciative hearing.