In this and in other instances of his use of it, it occupies so exactly analogous a position to the familiar use of the seventh on the subdominant which has already been commented upon at length, that the inference is almost unavoidable that composers first used the diminished seventh as a modification of that well-known device in a minor key, by sharpening its bass note to make it approach nearer to the dominant, and also to often its quality.
[App. pp.667–8: "The inference suggested on p. 681a has been happily verified by Mr. H. E. Wooldridge, who found the two forms of the seventh on the subdominant in a succession which strongly points to their common origin, in the following passage by Stradella:—
in which the minor seventh, arrived at in the manner usual at that time, is seen at (a); and the modified seventh in which the bass is sharpened so as to produce a diminished seventh appears at (b)."]
It will be necessary at this point to turn gain for a short space to theorists, for it was in relation to the standard of harmony which characterises the end of the 17th century that Bameau's attempt was made to put the theory of music on some sort of philosophical basis. He called attention to the fact that a tone consists not only of the single note which everybody recognizes, which he calls the principal sound, but also of harmonic sounds corresponding to notes which stand at certain definite distances from this lower note, among which are the twelfth and seventeenth, corresponding to the fifth and third; that as there is a perfect correspondence between octave and octave these notes can be taken either as the major common chord in its first position, or its inversions; and that judged from this point of view the lower note is the root or fundamental note of the combination. This was the basis of his theory of harmony, and it is generally considered to have been the first explicit statement of the theory of chords in connection with roots or fundamental notes. Rameau declines to accept the minor seventh as part of the compound tone of the root, and he does not take his minor third as represented by the 19th 'upper partial,' which is very remote, but justifies the minor chord on the principle that the minor third as well as the root note generates the fifth (as both C and E♭ would generate G), and that this community between them makes them prescribed by nature. D'Alembert took the part of expositor, and also in some slight particulars of modifyer, of Rameau's principles, in his 'Elements de Musique.' It is not the place here to enter into details with respect to the particulars resulting from the theory, which was applied to explain the construction of scale, temperament, and many other subordinate matters, and to discover the proper progressions of roots, and the interconnection between chords. But a passage in D'Alembert's book deserves especial notice as illustrating modern harmonic as distinguished from the old contrapuntal ideas with respect to the nature of discords; since it shows how completely the old idea of suspensions as retardations of the parts had been lost sight of: 'En general la dissonance étant un ouvrage de l'art, surtout dans les accords qui ne sont point de dominant, tonique, ou de sous-dominant; le seul moyen d'empêcher qu'elle ne déplaise en paroissant trop etrangère à l'accord, c'est qu'elle soit, pour ainsi dire, annoncée a l'oreille en se trouvant dans l'accord précédent, et qu'elle serve par là a lier les deux accords.' The sole exception is in respect of the dominant seventh, which, apparently as a mere matter of experience, does not seem to require this preparatory announcement. Tartini published his theories about the same time as Rameau, and derived the effect of chords from the combinational tones, of which he is reputed to have been the discoverer. Helmholtz has lately shewn that neither theory is complete without the other, and that together they are not complete without the theory of beats, which really affords the distinction between consonance and dissonance; and that all of these principles taken together constitute the scientific basis of the facts of harmony. Both Rameau and Tartini were therefore working in the right direction; but for the musical world Rameau's principles were the most valuable, and the idea of systematising chords according to their roots or fundamental basses has been since generally adopted.
By the beginning of the 18th century the practice of grouping the harmonic elements of music or chords according to the keys to which they belong, which is called observing the laws of tonality, was tolerably universal. Composers had for the most part moved sufficiently far away from the influence of the old ecclesiastical system to be able to realise the first principles of the new secular school. These principles are essential to instrumental music, and it is chiefly in relation to that large department of the modern art that they must be considered. Under the conditions of modern harmony the harmonic basis of any passage is not intellectually appreciable unless the principle of the relations of the chords composing it to one another through a common tonic be observed. Thus if in the middle of a succession of chords in C a chord appears which cannot be referred to that key, the passage is inconsistent and obscure; but if this chord is followed by others which can with it be referred to a different key, modulation has been effected, and the succession is rendered intelligible by its relation to a fresh tonic in the place of C. The range of chords which were recognized as characteristic of any given key was at first very limited, and it was soon perceived that some notes of the scale served as the bass to a larger number and a more important class of them, the Dominant appearing as the most important, as the generator of the larger number of diatonic chords; and since it also contains in its compound tone the notes which are most remote from the chord of the tonic, the artistic sense of musicians led them to regard the Dominant and the Tonic as the opposite poles of the harmonic circle of the key, and no progression was sufficiently definable to stand in a position of tonal importance in a movement unless the two poles were somehow indicated. That is to say, if a movement is to be cast upon certain prominent successions of keys to which other keys are to be subsidiary, those which are to stand prominently forward must be defined by some sort of contrast based on the alternation of Tonic and Dominant harmony. It is