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SIR, There is not, perhaps, any branch of the Musical Science more necessary to a composer than Modulation. It may be said to be the key which opens to the admiring ear all the treasures of harmony. A knowledge of it imparts a clear insight into the harmonious beauties of great masters, whilst a deficiency in this essential branch is likely to render abortive the exertions of the greatest genius, either in composition or extempore performance. Rameau, who, if I mistake not, was the first to systematize harmony, considers modulation to be the manner of removing from one key to another, and in this sense, I believe it is generally understood in the musical world. The above, as well as many succeeding authors of great eininence, having so largely treated on this subject, I propose chiefly to direct the attention of the reader to such points as I do not recollect to have met with in other authors, or which are but slightly commented on.

I shall first consider the order of relation in the minor key. The nearest relations to the key note, according to Mr. Kollmann in his Essay on Musical Harmony, chap. 10, are first, its 5th minor, second-, ly its 4th minor, thirdly its 3d major, fourthly its minor 7th major, fifthly its minor 6th major; and according to Rousseau, as quoted, by Kollmann, 1, the 5th major; 2, the 3d major; 3, the 4th minor;, 4, the minor 6th major; 5, the minor 7th major. But the transitions are not the same as in the major key, owing to the minor keys requiring a major 7th in ascending; for if we proceed from a minor key to its 5th, the ear expects a major third ; and if we ascend from a key note to its fourth, the key note seems to require a major third. The most natural transitions therefore seem to me to be, from a key note to its third and to its sixth; for as those are not the progressions of a chord of the seventh, no deficiency is felt, and although I presume to differ from the above writers on this point, it is simply with regard to transition, for if the dominant of the new key is introduced, it of course removes all objections.

Although the transition from a minor key to its minor sixtlı major is very larmonious, yet from the sixth to the key is not equally so,

which may be thus accounted for. The key being minor, the ear does not demand any particular progression, whereas, in passing from the sixth to the key note, the car seems to require the chord of the sixth or fb rather than the common chord.

None of these difficulties occur in passing from a minor key to its third major, or vice versa, for, first, (as it has been already remarked) the ear expects no particular progression from a minor chord, and secondly, the key note of the minor key forms no part of the common chord of its third major.

When a major common chord is used, it may be considered and treated as a key note, a fifth or a fourth, it being particularly proper to those intervals on aocount of their commanding the cadences. This rule, however, does not apply in natural modulation, where an. accidental major chord is felt as the dominant of the new key. A minor chord can be but a key note or fourth, because the fifth of the key, as such, always carries a major chord.—(see page 141 of this work.) The minor chord, however, is often used as a leading chord to a dominant, and the imperfect chord is seldom used in any other capacity. The proper use of the inversions of these chords is naturally deduced from the above observations. The inversion of chords answers three purposes. Ist. It prevents that monotonous effect which a constant succession of fundamental chords would necessarily produce. 2d. It softens certain progressions, which would sound somewhat hard in their fundamental state, particularly when the inversion causes the bass to move by gradation. Sd. It renders a bass much more melodious.

The resolution of discords seems to me to have been too much limited by Rameau and other writers, as the ear appears satisfied, if the discord is followed by a concord. Suppose the discord to be C D, the C may descend to B, or the D ascend to E. This latter resolution takes place in Rameau's chord of the sub-dominant, which I wish to extend to all other discords. Rameau's sub-dominant, however, is limited to rising a fifth, which appears unnecessary. I will therefore notice some progressions of the chord of the seventh, which vary from those usually taught: such as, G7 A6-G7 A G7 A*. As in these three examples the bass has ascended to resolve the discord, I leave it to the judgment of the composer, : whether the bass note may not be doubled in the octave, that while one part rises to the resolution of the discord, the other may take a

fundamental progression. Thus G7 F-G7 D-G7 D*. This second resolution will of course add to the number of chords that interrupt the cadence. By inversion, these progressions are as follows: B; C.-B5 A6-BĚ A :-B; A*_D4CA-D; D}-Dş Dos &c. &c. On the same principle Ci may be followed by C4, or by B7-C9 by B'}, &c. and I wish to be understood, that a concord resulting from any of these resolutions may be treated as if no discord had appeared; thus, By, CD5x, G. But if discord follows discord, the proper progression must be attended to. Having submitted these observations on the treatment of discords to two gentlemen well versed in the science of music, their approbation has induced me to submit them also to the candour of the profession; not that I wish to encourage the immoderate use of discords, but with a view of introducing such a variety of harmonious combinations as to supersede the necessity of too frequent a use of the chord of the diminished seventh ; for though Mr. Kollmann, in his rondo on that chord, has shewn its immediate progression to all the twelve major and minor keys; yet as some of those progressions are harsh, composers have selected the most harmonious of them for general use, which begin now to be distinguished, not only by the scientific, but by the musical ear; and as the progressions are generally the same, a continuation of them would be likely to descend from elegance to insipidity. It follows, therefore, that as concords are not limited in their progression, and as they leave the ear in a pleasing uncertainty, every variety of effect, from the most sublime to the most airy, may be produced by the use of them sparingly interspersed with discords, particularly by admitting the two-fold resolution of the latter. This kind of resolution may be applied even to the chord of the diminished seventh, as may be seen by the following example in C minor modulating into Bb minor. B7, C., Db, Bb, Fb, Fş, Bb. I need not give any further examples, as they will naturally follow from what has been said above.

This appears to me to the clearest and most intelligible method of explaintng the resolution of discords, it being quite unnecessary to consider them in a double point of view, which Rameau, by his subdominant, and other writers by various theories, have done: and I believe, that in the most complex organ points, concords will be found to follow discords, either against the bass or amongst the parts, in such a manner, as that the holding bass is related to the whole.

Although in removing from one key to another, the new key may be announced by one of the inversions of its dominant, yet the threefold use that may be made of the common chord, as I have already explained, must be of great utility in uniting the different keys, and rendering the modulation casy, natural, and flowing. The common chord is, indeed, thus treated by all good composers, but I do not recollect having met with this explanation of it. In further illustration of this, C, with its common chord major, may be considered as a key note, or as a fourth to G or fifth to F, after which any progression may be taken that belongs to those scales. E with a chord of the sixth may be indifferently used, as a third to C, a sixth to G, or a seventh to F. As F, the fourth in the key of C, frequently carries a chord of the sixth, it may in that case be considered as belonging to the scale of C, or as a third to D minor, or as the descending minor sixth of A minor, where D, the fundamental note, hecomes a fourth.

When D in the key of C carries a chord of the sixth, it may be indifferently used as a second of C or the fourth of a minor. In the first case, it is derived from an incomplete chord of the seventh to G, and in the second, from the imperfect chord of B. The first inversion of the above three chords thus explained will enable the reader to pursue their second at his leisure.

It has been a received rule, that any two common chords may follow each other, which contain a note common to both ; but this rule appears to be of less use in natural than abrupt modulation : for in passing from a major chord to its third, the ear rather expects a chord of the sixth orb than its minor chord : whereas passing from the major chord to its second above with a minor one, seems more agreeable on account of its being one of the progressions of the interrupted cadence. The common chord on the fourth of the key sometimes succeeds that on the fifth, which is rendered agreeable by the expectation of the imperfect cadence or one of its inversions. Now in these two progressions, the succeeding chords have not a note in common to unite them. Again, if the second of two chords ascending diatonically should be major, when a minor chord was expected it is rendered agreeable by being felt as the dominant of a new key. But in abrupt modulation, as from C to F minor, from C to Ab major, from C to Eb major, from C to A major, from C to E major, the note in common is of considerable importance, as it not only sanctions the transition, but may serve as a direction to the

position of the chords; for when, to produce particular effects, such transitions are used, the note that unites the two chords should generally be laid uppermost, in order to render them harmonious. That from C to F minor, indeed, seems exempted from this rule, since C with its major third is its dominant. The first order from C to Ab appears to be C in its first position, Ab in its second, the second C in its third position, Ab in its first. I imagine no composer would use C in its first and Ab in its third position. The first order from C to Eb major may be C in its third, Eb in its second position, the second C in its first, Eb in its third position. With respect to the transitions from C to A major, or from C to E major, it seems better to avoid the third uppermost in the succeeding chord, as that would characterise it as a dominant. This observation, however, does not apply to Ab or Eb, as the notes to which they would be dominants, are too remote from the key of C.

Although there is a note in common to C major and G minor, and to C minor and F major, thosc progressions seem somewhat hard; for in the first case the E natural has the effect of a major 6th to G, which ought to ascend; and in the second the A natural, being the major sixth of C minor, seems to forbid the adoption of F as a key hote.

There is also a note in common to C minor and A minor, and to C minor and E minor, but the second of each of those chords seems too remote to be used in succession.

A fine effect and an agrecable surprise to the ear may be produced, by using in the major key the interrupted cadence, properly belonging to the minor previous to a perfect cadence, being made as in the following example in the key of C:-F3, G43, Ab, G4, G

C. I shall conclude my present remarks by observing, that though the rules of harmony constitute what is particularly taught in modulation, yet if the modulator would entertain himself and his hearers, he must assiduously cultivate melody which ought to be supported and enriched, but not obscured by modulation.

J. TAYLOR. 58, Pottergate-street, Norwich,

March 8, 1819.

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