Preface

Reason and Experience

Whatever progress Music may have made up to our own time, it seems that the mind has grown less curious to penetrate its true principles in proportion as the ear has become sensible to the marvellous effects of this Art; so much so that one may say reason has lost its rights there, while experience has acquired a certain authority.

The writings that remain to us from the Ancients show us plainly enough that reason alone provided them with the means of discovering the greater part of the properties of Music. Yet although experience still leads us to approve most of the rules they have given us, we today neglect all the advantages that reason could supply in favour of a merely practical experience.

If experience can alert us to the different properties of Music, it is not in itself capable of making us discover the principle of those properties with all the precision that belongs to reason. The consequences one draws from it are often false, or at the least leave us in a certain doubt that it falls to reason alone to dispel. For example: how could we prove that our Music is more perfect than that of the Ancients, when it no longer appears susceptible to the same effects that they attributed to it? Would it be by saying that the more familiar things become, the less they occasion surprise, and that the admiration into which they can throw us at their discovery degenerates insensibly as we grow accustomed to them, and turns at last into a simple amusement? That would be at most to suppose equality, not superiority. But if by the exposition of an evident principle, from which one may afterwards draw just and certain consequences, one can show that our Music is at its last degree of perfection, and that it falls well short of the Ancients having attained this perfection — (one may see on this subject Chapter XXI of the Second Book) — one will then know for certain what to think; one will feel the force of the preceding reflection far better; and knowing by this means the limits of the Art, one will give oneself to it more willingly. Persons of superior taste and genius in this kind will no longer fear lacking the necessary knowledge to succeed in it. And in a word, the lights of reason, dispelling in this way the doubts into which experience can plunge us at every moment, will be sure guarantors of the success one may promise oneself in this Art.

If the Modern Musicians (that is, since Zarlino*) had applied themselves, as the Ancients did, to rendering account of what they practise, they would have put an end to many prejudices that are not to their advantage, and this would have even brought them back from certain errors of which they are still full and which they have great difficulty freeing themselves: Experience is too favourable to them, it seduces them; and in some manner, since it is itself the cause of the little care they take to instruct themselves thoroughly in the beauties it reveals to them each day, their knowledge is proper only to themselves — they do not have the gift of communicating it. And since they are not aware of this, they are often more astonished at what one does not hear from them than at what they do not make themselves understood. This reproach is a little sharp, I admit; but I report it such as I perhaps still deserve it myself, despite all that I have been able to do to protect myself from it. Be that as it may, I should always wish it had produced upon them the effect it has produced upon me. And it is principally also to revive this noble emulation that once reigned, that I have ventured to make public my new researches, in an Art to which I endeavour to give all the simplicity that is natural to it, so that the mind may conceive its properties as easily as the ear perceives them.

Mathematics as the Foundation of Harmony

A single man is not capable of exhausting a matter as profound as this one; it is almost impossible that he should not always overlook something, despite all his care. But at the least the new discoveries he may add to what has already appeared on the same subject are so many cleared paths for those who can go further.

Music is a science that ought to have certain rules; these rules ought to be drawn from an evident principle, and this principle can scarcely be known to us without the help of Mathematics. Although I might have acquired in Music, through having practised it for a sufficiently long period of time, whatever experience could give me, it was nonetheless only through the help of Mathematics that my ideas became disentangled, and that the light which succeeded a certain obscurity of which I was not previously aware came to me. Without knowing how to distinguish principle from rule, the principle itself offered itself to me with as much simplicity as evidence; the consequences it then furnished me made known in those consequences so many rules which ought consequently to relate to this principle — the true sense of these rules, their just application, their relation to one another, the most simple always serving as introduction to the less simple, and so by degrees — finally the choice of terms: all this, I say, that I was ignorant of before, developed itself in my mind with such clarity and precision that I could not prevent myself from agreeing (as someone told me one day when I was applauding the perfection of our modern Music) that the knowledge of Musicians of this century falls short of the beauty of their Compositions. It is therefore not enough to feel the effects of a Science or an Art; one must conceive them in such a way that one can render them intelligible. And it is to this that I have applied myself principally in the body of this Work, which I have distributed into four Books.

The Four Books of This Treatise

The First contains an abridgement of the relation of Sounds, Consonances, Dissonances, and Chords in general. The principle of Harmony is discovered in a single Sound, and its most essential properties are explained there. One sees, for example, how by its first division this single Sound engenders another which is its Octave, and which seems to make but one with it; how it next appropriates this Octave to form all the Chords; that all these Chords are composed only of this principle, of its Third, its Fifth, and its Seventh; and that it is the force of the Octave from which arises all the diversity of which these Chords are susceptible. One finds there still several other properties, less interesting, it is true, for practice, but necessary nonetheless to lead us there — all of it demonstrated in a sufficiently simple manner.

The Second Book concerns equally Theory and Practice. The principle is there represented in that Part of Music called the Bass, to which one adds the epithet Fundamental. All its properties, and those of the Intervals, Chords, and Modes that depend from it alone, are explained there. One speaks also of all that can serve to render a Music perfect in execution. One recalls for this purpose, where appropriate, the reasons of the preceding Book, experience, and the authority of the best Authors in this kind, without sparing them however, when they have been able to err; for in novelties one endeavours to satisfy the learned by reason; those who defer only to their ear, by experience; and those who have too much condescension for the rules of their Masters, by discovering the errors those rules may contain. Finally, one takes care to prepare the Reader to receive without constraint the rules that are prescribed there, and that are found deduced in order and at greater length in the following Books.

The Third Book contains a particular Method for learning Composition in a very short time. The proof of this has already been made — but since one is seldom persuaded in such a case except by one’s own experience, I shall keep silence on this matter, and shall content myself with urging those to whom this Method is unfamiliar to see the fruits that can be drawn from it before disputing it. He who wishes to learn troubles himself little about the manner in which he is taught, provided he succeeds.

No rules have yet been seen for teaching Composition at the degree of perfection where it stands today; there is not even a single capable man in this kind who does not sincerely confess that he owes almost all his knowledge to his experience alone; and when he wishes to convey it to others, he finds himself often constrained to add to his lessons that Proverb familiar to Musicians: Cætera docebit usus. It is true that there are certain perfections that depend on genius and taste, to which experience is even more advantageous than science itself. But this does not prevent a perfect knowledge from always having to enlighten us, lest this experience deceive us — when it comes to knowing how to apply to their true principle the novelties it could make us produce. Besides, this perfect knowledge serves to bring into operation genius and taste, which without it often become useless talents. It is for this reason that I believed I ought to seek the means of procuring more easily and more promptly this perfection, which one has been able to attain only through simple practical experience — by first giving a reasoned, precise, and distinct understanding of all of Harmony, through the sole exposition of three Intervals, from which are formed two principal Chords, and the whole Progression of the Fundamental Bass, which at the same time determines that of the other Parts. So that this single understanding, which can be acquired at the first reading of this Book, determines everything else, as it is easy to make clear.

The Fourth Book contains the Rules of Accompaniment, both for the Harpsichord and for the Organ; where the position of the hand, the arrangement of the fingers, and all that can serve to acquire the practice as promptly as possible, are deduced.

The substance of these rules can equally serve for Instruments on which one accompanies in more or less the same manner as on the Harpsichord.

These last two Books have much in common; that is why they will be equally useful to those who wish to apply themselves only to the practice of Composition, or to that of Accompaniment. And one will not do badly to consult the Second Book, if one wishes to be ignorant of nothing — supposing that I have forgotten nothing. For I do not doubt that one could still improve upon me, despite the care I have taken to omit nothing, as my long discourses and my repetitions prove well enough. A defect that comes as much from my attention to rendering things clear and intelligible as from the weakness of my genius. As for what concerns the First Book, it is, in some fashion, useless for practice, and one will make such use of it as shall be thought fit — having placed it at the head of this Treatise only as proof of all that it contains concerning Harmony.

Since it was not possible for me, to satisfy the requirements of my employment, to see this Work through the press myself, I was obliged to reread it with fresh attention, and I found that I ought to make some changes and certain necessary corrections, which will be found at the end in a Supplement. I have placed at the beginning two Tables: one of the Contents of this Treatise; the other containing an Explanation of Terms, whose understanding is necessary to serve as Introduction to this entire Work, which I dedicate to the Public.

The citations of Zarlino in his Institutions Harmoniques are from the Venice edition of the year 1573.