As in adding sharps to the clef, we follow a series of ascending fifths or descending fourths, and as the sharp is always to be put in the same place of the scale, it is plain that the notes to be sharpened will be found by the same rule, that is, by counting five degrees upward, or four down ward, from the last added sharp; therefore they will observe the following order, F*, C*, G*, D*, A*, E*. After the same manner, as in adding flats at the clef, we follow the inverse order, that is, a series of fourths upward, or fifths downward, the order of flattened notes will be fottnd to be Bb, Eb, Ab, Gb, cb.
87. It may now be natural to ask, where these sounds are to be found in keyed instruments; for it is evident we have now a much greater number of notes, than there are finger keys in any octave of the instrument. We have already noticed the two short finger-keys, F*, C*, and the two short finger-keys Bb, E b. Now if we go a step farther in the addition of sharps and flats, we shall find that the next sharp and the next flat meet on the same finger-key. For in the scale of A we must have G* a semitone below A ; and in the scale.of Eb we must have A b, also a semitone below A. On keyed instruments in general, there is but one sound to answer for both. It is proper here to apprise the reader, that this is a great hnperfection; and on instruments which are callable of being played perfectly in tune, the dif ference between these two sounds is very considerable. To give the reader some idea, in passing, of this :natter, which will be fully explained in the sequel, let the major third, CE, be tuned quite exact, and another third, EG*, be also tuned quite exact, then the G* will be quite true as major seventh to A, the major sixth in the scale of C. Again, if Ab be tuned a major third below C, it will then be true as fourth in the scale of E b, the minor third to C. If now thesP two sounds, G* and Ab be compared, they will be found to dif fer very sensibly. The difference is about the fourth part of a tone, and it is called the enharmonic fourth of a tone, or the enharmonic diesis. From this the reader will be sensi ble, that keyed instruments, in general,are not tuned to the most perfect intervals; but this matter we must not enter on at present. In the mean time we see that each of the black finger-keys, and even some of the long finger-keys, have two names, and answer for two sounds; thus D* and Eb belong to the same finger-key, as do also A* and BO ; and in the scale of F* we have E* semitone sharper than E, which therefore comes to be the same finger-key with F. So also following the additional flats after A b , we have Db and C*, Gb and F*, Cb and B. And when we come to the last of each series here set down, viz. F* with six sharps at the clef, and GO with six flats, the two scales are exactly the same throughout ; insomuch, as far as regards keyed instru ments, that it is a matter of indifference in which wav the music for that scale be written. But the reader will easily see that
it is of much importance to preserve the distinction between A* and Bb &c. even in composing for keyed instruments. Inextricable confusion would indeed result from a contrary practice. These remarks are the more necessary, that some persons, deceived by the identity of the sounds on keyed instruments, have concluded that there is no such distinction among musical sounds; and it is sometimes very difficult to make them comprehend that there is such a thing. We shall afterwards find that even these sharps and flats are not suf ficient for all the purposes of the musician, insomuch that double flats and sharps frequently occur, thus denoted b b and x . So x put before the note F*, sigmifies that it is to be taken a semitone still higher, which on keyed instruments is the saine with G. b b set before Bb , makes it a semitone lower, played by the ting-er-key of A.
8S. That we may give the whole doctrine of the flats and sharps to be placed at the clef at once, we must now make the reader acquainted with another scale of musical sounds, called the minor diatonic scale. If in the natural scale, (that is, the scale of C) we take an octave of notes from A up wards, we. find a scale of a very different character from tltat of C. If this scale be played descendin, v:e find it not only very agreeable, but also that we come to a satis factory conclusion on By comparing the descent through the fifth from E to A, with the descent through the fifth from G to C, we shall he sensible of a very different effect. The former is a wailing plaintive song, and the latter more cheerful, and we may say more bold and masculine. This difference arises not from the pitch of the two songs, but from the nature of the last thirds of either descent; from C to A being a minnr third, and from E to C being a major third. If the reader wish to compare these two songs at the same pitch, he has only to play C natural and alternately, descendin,g from E: but Ile will find the transition from the one to the other, especially from the series with minor third to that with major third, more harsh than in the former conliarison. It is from these thirds principally that the two scales are named, and that music drawn from the one or other is said to be in the major or minor mode. But the minor sixth A is also an important interval in this scale, and comributes to its peculiar effect, of which the reader may easily satisfy himself by comparing the descent through an octave from d to D, with that from to A, or by playing in descending through the octave of A, while the other notes remain as in the natural scale.