Having established, we trust, in the most ample and substantial manner, that there are only seven sounds in music, we will now show the relation between them mutually, remarking, that, of course, every part of the scale must be affected in a similar manner as the octave we shall treat of, and which, for the sake of con venience, we shall select from the treble stave, adding the tenor note C.
Example 2, represents what is called the extent of an octave ; it is in the tre ble cleft, as may be seen by the prefixed figure. The lowest note is C, the sound is D, the third is E, the fourth is F, the fifth is G, the sixth is A, the seventh is B, and the eighth is C ; forming a replicate of the first note C. Each of the above notes is designated according to the manner in which musicians compute them, always reckoning the first note 1, the next to it a second, and so on throughout: thus E is the third to C, and G is third to E, or fifth to C ; always counting from, and in eluding the lowest note. In the above example all the notes are what is termed natural, 1:1; because no sharp, 0, or flat, 17, is necessary, to give them that relative distance which naturally prevails in the disposition of the eight preceding notes of an octave. This, only hap pens when C, 0, is the first, and its oc tave the last note of the succession, and results purely from the above cause. This we shall explain. The notes do not all stand at equal distances mutually. The first interval, from C to D, is a whore tone, the second from D to E, is likewise a whole tone ; from E to F, is only a simi tone (or half a tone ;) from F to GI is a whole tone; from G to A, is a whole tone ; from A to B is a whole tone ; and from B to C, is only a semi-tone.
The above are the distances at which nature has placed the notes composing an octave in the major key, of which, as well as the minor key, we shall treat amply.
If the notes, as thus arranged, be play ed on an instrument, or be sung by a well tuned voice, they will be found to follow in a most pleasing manner. The smaller intervals, as they are called, between the third E, and the fourth F ; and between the seventh B, and the octave C ; form the succession into two distinct periods, of which the former raises the expecta tion, while the latter satisfies it. We could not stop at F without disappoint ment ; we should feel the want of some termination ; whereas, at C, that termina tion is given ; and we feel convinced that we have arrived at a conclusion.
Such is the case in every octave of which the key-note leads, and its eighth is the final ; and so invariable is the succes sion of intervals we naturally expect to find in the major key, that every devia tion therefrom distracts our attention, and sets the ear in search of that conclu sion at which it never arrives. To prove
this, let the lowest C, in the second exam ple, be done away, and D be substituted above the upper C, as in Example 3: play all the notes natural, and the succession will not prove either pleasing or conclu sive f because the order of the intervals is perverted. For, instead of the two first intervals being whole tones, the second (between E and F) is but a semitone ; and in lieu of a whole tone between B, the sixth, and C, the seventh of the scale, there is but a semi-tone ; and instead of a semi-tone between the seventh, C, and the eighth, D, there is a whole tone., Now, to remedy this, the third must be made to approach the fourth, and the se venth to approach the eighth : this is done by making them, i. e. F and C, both sharp ; so that the distances between them and their next superior notes, should be reduced half a tone each; which halves of tones are thus added to the notes respectively below F and C ; and the whole octave is duly regulated ; the proper intervals being established: this is called "giving a sharp third and seventh :" whereby a major key is indi cated. The minor key has two variable notes; namely, its sixth and its seventh. In ascending, they are invariably played sharp, the same as in the major key (or rather mode); but, in descending, they are played flat. Thus, in Example 4th, we take the key of C minor, which re quires a flat third, a flat Sixth, and a flat seventh. To effect this change, which gives a peculiar plaintive expression to the music, we are obliged to adjoin three flats ( 5); namely, an F. flat, to make the third so ; an A flat, to depress the sixth ; and a B flat, to reduce the seventh to a full semi-tone below the eighth. See ex ample 4. The practical ear at once dis tinguishes the minor from the major mode : they may always be ascertained by counting the semi-tones included in the third : if the mode be major, there will be found five semi-tones; but if it be minor, only four. See Example 5th, where there are five, consequently the mode is major: in example 6th, which has three fiats prefixed, there are only four; therefore the mode is minor. The following table of flats and sharps is of the utmost importance to be thoroughly understood.