CDEFGABC as 24, 27, 30, 32, 36, 40, 45, 48 These are the degrees of the diatonic scale, which are indicated by the white keys of the pianoforte, as in the figure represented below.
• The interval CD is commonly called a second; CE, a third; OF, a fourth; CG, a fifth: CA, a sixth; and CB, a seventh; CC being, as already seen, an eighth or octave—names corresponding to the position of the notes on the key-board or in the diatonic scale, hut having no relation to the proper proportional numbers already given. The intervals of the third, fifth, and sixth (counting from the key-note), owing to the more intimate liar 1/1011iC relation of the notes between which they lie, afford more satisfaction to the car than the others, or are, as it is called, the most perfectly consonant intervals. Intervals may be counted from any note as well as the tonic. DF is called a third as well as CE, although these intervals mire unequal. We may have intervals beyond the octave; they are, however, substantially but repetitions of those below, CD, a ninth, being also a sec mid. and so on.
It is often desirable in the course of a musical composition to change the.key-note, which involves the formation of a diatonic scale on some other note than C, in which case we are said to modulate from one key into another. As the intervals CD, DE, EP', etc., arc by no means•all equal, the notes which we have already got will not do for a scale founded ou any other tonic than C. The ratios of the intervals in the diatonic scale, expressed in numbers by logarithms, are: At first sight it would appear that in keyed instruments there must be a separate row of keys for each tonic, but practically this is found not to be necessary. If D instead of C be taken as key-note, E, 0, and A are some approach to the correct second, fourth, and fifth, hut F and C are greatly too low in pitch for x proper third and seventh. With some notes taken as keynote, the correspondence is greater, with others it is less. The difficulty is overcome by a system of compromises called temperament (q.v.). 'Roughly
speaking, we have in the diatonic scale an alternation of two long intervals, a short interval, three long intervals, and a short interval.
long intervals 51 and 46 are styled tones, and the oynhea. half f in the middle of each tone, dividing the seven inter VMS into twelve, would make it immaterial whets the 0 D B a A B C scale a the began. e re me Aremedy actually m adopted inonostthiiscesyus, a silents. and the inaccuracy produced by this congas).
— — min is not sufficiently great to offend byear. The interposed notes, indicated by the black keys of the pianoforte (see fig.), complete what is called the chromatic scale, consisting of twelve intervals approximately equal.
The notes of music are represented in ordinary notation on a series of five parallel lines, called the staff. On these lines, and in the four spaces between them, marks are placed indicating the notes, which are counted upwards, beginning with the lowest line. Every line or space is called a degree, the staff consisting of nine degrees.
.... ss2_ =--ss- _ --- .so ___ -ella When more than nine notes are required, the spaces below and, above the staff are used, and the scale is extended by means of short added lines, called leper lines. The pitch of the notes on the scale is determined by a figure called a clef (clads, a key), placed at the beginning of the staff on a particular note, from which all the others are counted. The clefs most in use are the bass, tenor, and treble clefs, represented on the notes F, C, and G respectively (see CLEF'). The treble and bass clefs only are used in music for keyed instruments, and when a staff is required for each hand they are joined together by a brace, the upper staff for the right hand, the lower for the left. The ascending scale in these clefs is as follows: