IN .Ml 





degrees ; therefore, the three interior angled of any of the fire 

 equal and equiangular triangles, of which the pentagon in Fig 



made up, are together equal to 180 degrees. Now the 

 angle at the apex, r, of any of these angles was shown to be 

 equal to 72 degrees, therefore the angles at the base are together 

 (1)11111 to 180 72 degrees, or 108 degrees. Bat as the triangles 

 which compose the pentagon are isosceles triangles, the angles 



>>ase are equal to each other, and each of them contains 

 108 -r- 2, or 54 degrees. Any angle of the polygon, which u, of 



. composed of two of these equal angles, contains 108 

 degrees. The following is a table of regular polygons, from the 

 triangle or trigon of three sides and angles to the polygon 

 of twenty sides and angles, with the numerical value of the 

 angle of each polygon in degrees, minutes, seconds, and fractional 

 parts of a second ; and the numerical values of the angles at 

 the apex and base of the triangles into which each polygon may 

 be divided by drawing straight lines from its salient angles to 

 its centre. 



TABLE OF REGULAR POLYGONS. 



LESSONS IN MUSIC. IX. 



CHARACTER AND EFFECT OF PRINCIPAL NOTES. 



Don (being the " governing " note) gives a sense of POWER 

 to the hearer, and of SECURITY to the singer in a greater 

 degree than any other. The singer feels it to be the note to 

 which he can, from any point, most easily return. It is more 

 easy to perceive musical effects, than to find words that will 

 sufficiently represent them ; but if the names must be given, 

 this note should be called (in reference to its effect in a slow 

 movement) THE STRONG OTjirm NOTE. 



Sou has a similar effect to DOH, but is not equal to it in 

 power. It may be distinguished (when sung slowly) as THE 

 GRAND or clear NOTE. 



ME has a somewhat graver and softer effect than Son. It 

 may be denominated (especially in slow movements), THE 

 STEADY or calm NOTE. 



When DOH, ME, and SOH predominate in a tune, they con- 

 tribute to its general character : if the movement be a quick 

 one, great BOLDNESS and DECISION ; and if the movement be a 

 elow one, they give it DIGNIFIED SOLEMNITY. Of course, the 

 power of any particular note to give a character to the tune in 

 which it occurs, will depend on the frequency and the emphasis 

 with which it is used, and will be modified, also, by the kind of 

 " measure " and the rythniical arrangement in which it occurs. 

 In studying the following examples, let the pupil always strike 

 or sing the chord of the key-note, and part, at least, of the 

 scale before ho begins to sing the phrase ; for our assertions in 

 reference to the mental effects of notes are not true, unless the 

 car is first filled with " a sense " of the scale in which they 

 occur. 



For " dignified solemnity," notice the power of EOH, ME, and 

 EOH in the following opening phrases from Handel. You will 

 remark how, in each case, the great artist takes advantage of 

 the' e bold and grand notes to bring out, by contrast, a very 



marked effect on some of tho other notes, as with KAT oa the 

 word " fair," and with r AH on the word " Ibdecmer ; " bfjt 

 of these notes we shall speak afterwards. Yon will also notice 

 how the "triple time" (trinary measure), in the second ex- 

 ample, allows increased emphasis and power to the great notes 

 which so folly express the grand and sore confidence of faith. 



Ki.v K. 





To illustrate the peculiar effect of ME, when song slowly 

 full of SERENE REPOSE it might be enough to refer to the 

 calm and restful effect of the best known of all chant*, of 

 which the churches will never weary Tallis's Gregorian Chant. 



KETF. 



r :d 



sha-ll 



not 



But another striking illustration occurs to us. A minister had 

 heard, and had been greatly moved by Mendelssohn's song 

 " Oh ! rest in the Lord." He preached on the text, and thought 

 much of that repose which comes, not with weariness or sleep, 

 but with living blessedness. Some time after, thinking on the 

 power of the notes of the scale, it occurred to him that Mendels- 

 sohn must surely have expressed the idea of rest in God, chiefly 

 by means of the third note of the scale, Ml, which we hare 

 called the note of serene repose. " If by any other note," he 

 said to himself, "that peculiar effect was produced on my 

 mind so strongly, then the theory about mental effects must fall 

 to the ground." He at once analysed the song, and found 

 that the very first emphatic note was that which he had ex- 

 pected that the power of this note was brought out, by placing 

 it in ever- varying but most effective positions ; and that, even 

 when the key changes, the ear is surprised and pleased by the 

 recurrence again of this same third note in the new scale. 

 Among other studies in this delightful song, it was pleasant to 

 notice the change in the manner in which the word " Lord " 

 is expressed in the hitter part of the song. At first, it is 

 uttered with the firm and sure confidence of the note DOH ; bat, 

 when that spirit of confidence has risen to a somewhat tri- 

 umphant feeling, then it must use the "clear" and "grand" 

 note sou. 



KEY C. 



