Jean-Philippe Rameau · section 66 of 109

Chapter twenty-three

On passing from one key to another, which is also called modulating

1. Every note bearing a perfect chord must be regarded as a tonic. Thus we may say that in our first examples of the perfect chord, each note represents a different key. Those examples must also serve as models for the rest of this chapter, since we can move naturally from one tonic to another only by a consonant interval. After beginning a piece in a certain key, we may therefore pass to another a third, fourth, fifth, or sixth above or below it. The original tonic may thus become the mediant, dominant, fourth, or sixth note of the key we enter, and we may proceed from key to key by such connections.

2. In addition to the foregoing, the tonic of a major key may sometimes become the seventh or even the second note, but never the leading note. The tonic of a minor key may become only the second note.

The seventh just mentioned is the note a whole tone below the octave, not the note a semitone below it called the leading note, which is natural to every key.

3. When, in the middle of a piece, we wish to make the dominant of a major key into a tonic, that dominant's key should naturally be major. We may sometimes make it minor, but must use judgment. The key of a minor key's dominant, however, can only be minor.

We may transgress these rules when capable of judging what we are doing, but must always fear going astray. Even the most skilful are not free of this concern.

4. Whatever key begins the piece, it is good to remain modulating within it for at least three or four measures. We may exceed that number as much as invention and good taste suggest.

5. It is better to pass to the dominant key of the original key than to another. The original tonic then becomes the fourth note. An irregular cadence can accomplish this.

6. As soon as we change key, we must know its principal note, the tonic. Conceiving that note as ‘ut’ or ‘ré’—the tonic names of our major and minor models—immediately determines the sequence and progression of all notes within its octave and tells us which chords to employ. Sharps and flats now serve to proportion the intervals of this key to those in the model keys of C and D. If I pass from C to G major, I must sharpen F whenever it occurs in any part, making its interval correspond to that of B, the leading note in C, just as F♯ is the leading note in G. If, instead, I make G minor, I must sharpen F only when it ascends, and also flatten E when it descends. E is G's sixth note and must correspond to the sixth note in D, which takes a flat in descent. Likewise, I must flatten B to make it G's minor third, corresponding to D's third; similarly for the others.

7. The ear does not welcome a key heard too frequently. Only the original key can be tolerated from time to time. As for the others, it is not good to return immediately to one just left. For example, having begun in C, I may return to it after visiting another key. But it would not be good then to return to that other key after leaving it to resume C or to enter a third key. It is therefore better to pass to a new key, and proceed judiciously from one to another, gradually returning to keys most closely related to the original one. This allows us to finish in the original key as though we had never left it. Having passed through several other keys, we must therefore modulate within the principal key a little longer at the end than at the beginning.

8. It is better to pass from a major key to the key of its sixth note than to that of its mediant. From a minor key, however, it is better to pass to the key of its mediant than to that of its sixth note. The less good choice is not thereby forbidden. Remember that the mediant and sixth degree of a major key are reckoned major, just as they are reckoned minor in a minor key.

9. To determine whether the new key should be major or minor, observe that its tonic, third, and fifth must be formed from the notes contained in the octave of the tonic just left. Furthermore, unless the length of a piece obliges us to stray somewhat, the perfect chords of the various tonics used throughout the piece must be formed from notes within the octave of the initial key, without altering those notes by new sharps or flats. For example, if I begin in C, E, F, G, A, and sometimes D, together with their thirds and fifths, are formed from the notes belonging to the modulation of C. We thus pass freely from a major key to a minor one, or from a minor to a major, according as the thirds conform to the diatonic order of the starting key, or at least of the key being left. If I pass from C major to A, the latter will be minor, because C forms its minor third; likewise elsewhere. To apply this rule in minor keys, consider their octave modulation only in descent, when the leading note loses its sharp and becomes natural. For this reason we can do likewise in major keys by adding a flat to the leading note. When we said that a tonic could become a second degree, it was only on condition that a whole tone always separate the tonic from its second. This latter modulation was already mentioned in the second article.

10. Try to pass imperceptibly from one key to another, so that the ear scarcely notices the change. Following the order just prescribed will achieve this.

11. In passing from one key to another, the last note of the key being left must always carry a consonant chord. That note can therefore only be the tonic, its mediant, or its dominant, or sometimes its sixth note bearing a sixth chord. At first, however, concentrate only on moving from a tonic to its dominant. Once this dominant becomes a tonic, follow the routes prescribed in the next example, modulating for a few measures in the key of each note through which we lead the bass.

Example

The bass may begin with the first or second measure. Remember not to stay as long in the key of the note following the initial note as in that initial note's key, and to spend still less time in the others. Sometimes we pass through only one, two, three, or four notes of one of these later keys before moving to another. This depends more on taste than on rules.