. MUSIC. 



-iiltn of previous uxporimenta by a third, and 

 . by an eighth, * mi.! h. -re \%;n : 

 VH. * * The attempt (boyond theso throo 

 ion of tint "Canon" in other wonU, at tho 

 i; into tho lengths which produoo tho sounds 

 tlmt mnl>- u\-.'. :< in a Binglo key wan a failuro." 



'l'hi> < \i> [inn -nt of modern philosophers have been rewarded 



with tli.- <lixcovory that a inuxical Hiring divided in tho pro- 



(.M , . u underneath will produoo tho notes of tho soalo as 



there described. Let it bo noticed that th figure 1 stands for 



>lo length of the string, whether a foot, a yard, or any 



other measure, and whatever wound (in pitch) it gives that 



Bound beintf taken for tho key note DOH. It may also bo 



mentioned that tho samo numbers denote tho comparative 



lengths of organ pipes capable of sounding tho corresponding 



notes. 



i 



A 



Perhaps these proportions will bo bettor understood by tho 

 annexed diagram. A single string thus stretched and used 

 for these experiments is called a monochord. If the student 

 is of a mechanical turn, lot him make ono and verify tho 

 measurements hero given. Lot him suspend a board 

 of four or fivo feet in length against a wall. To tho 

 upper part of this board fasten tho end of a piano- 

 forte-wire or other musical string which is of tho 

 same thickness throughout. Let tho wire pass down 

 the face of tho board, over a firm wooden bridge, 

 an inch or so high, and closo to tho top, and over a 

 movable bridge at tho bottom ; and lot it be kept 

 stretched by a heavy weight. Set your movable 

 bridge (which tho weight will keep in its place) at 

 tho bottom, marking tho spot, and take tho sound of 

 tho whole string, by tho help of a fiddle bow, for 

 your DOH, or key-note. Then (having properly 

 measured and marked tho board) move tho bridge 

 to the other divisions, sounding each note as before. 

 It may bo well to mention that Colonel Thompson 

 maintains, and with good show of reason, what he 

 calls the " duplicity" of BAY and TE. They are 

 sometimes sounded by good singers and violin- 

 DOH< players a very small degreo lower than their usual 

 position given above. Theso experiments will fix 

 in your mind a clear notion of tho scale. 



It will be well for you to understand the con- 

 nection between these musical notes and the vibra- 

 tions of tho sonorous body which produces them 

 SOH whether that body be tho string of a violin, the air 

 in an organ pipe, a small plato of glass or metal, or 

 tho "chorda) vocales" the vocal chords of that 



} FAH wonderful littio box instrument, called the " larynx," 



which you can feel in your own throat. Sounds 

 produced by irregular vibrations are not musical. 

 They form the " roar, rattle, hiss, buzz, crash," or 

 some other noiso. But sounds produced by equal 

 and regular vibrations aro musical. " That musical 

 notes are produced by a rapid succession of aerial 

 impulses at equal intervals, is very clearly illus- 

 trated by an instrument called the syren, tho in- 



: DOH vention of Cagniard do la Tour. A blast of air is 



forced through a narrow aperture in a pipe ; and a 

 flat circular disk, perforated near its circumference 

 with a number of small holes equidistant, and in a 

 circle concentric with tho disk, is so applied to tho 

 pipe, that tho blast is interrupted by it, excepting 

 when ono of tho holes in tho disk is opposite to that of the pipe ; 

 and when tho former is mado to revolve rapidly, tho resulting 

 aerial impulses cause a series of isochronous vibrations that pro- 

 duce a musical note, and tho corresponding number of its 

 vibrations can very easily bo computed, from knowing tho 

 number of holes and of revolutions of tho plate. The results 

 obtained by this instrument agree exactly with those found by 

 other methods." The more rapid tho vibrations of tho sonorous 

 body, tho more " acute " (shriller, or higher) the note produced. 



A MONO- 

 CHOKD. 



'Hi.> following aro tho results of such experimente as those jost 

 referred to. Arithmeticians may notice that the proportion ot 



. 'diem* in inversely as the length of ike ttrinyi giv i 

 But wo hero print the fractions with a common <Mnppi" . 

 mako tho relations moro obvious. 



If our arithmetical friend will now work a few Hums in pro- 

 portion, ho will be able to show tho value of the intervals be- 

 tween tho several notes of this scale.. Thus the vibrations of 

 DOH differ from those of BAT, in being three less, and (throe 

 being one-ninth of twenty-seven) Don has therefore only eight- 

 ninths of BAY'S vibrations. The same proportion will be found 

 between FAU Son, and LAH TE. These intervals are called the 

 "great tones." Tho proportion of BAY ME, and of Son LAH is 

 nine-tenths. Those are tho " small tones." The proportion of 

 ME FAU, and of TE DOH, is fifteen-sixteenth*. These are called 

 semitones, or, more ptqpetfy, Tonules. If you calculate from the 

 length of the string given above you will find still tho same pro- 

 portions existing. 



Let our arithmetical friend reduce these "ration," or pro- 

 portions, of the three intervals in tho scale to fractions having a 

 common denominator. They will then stand thus : 



THE GREAT 

 TONE 



1280 

 1440 



THE SMALL 

 TONE 



1296 

 1440 



THE 



1350 

 1440 



Now this evidently means that the lower note of the " great 

 tone " has 1,280 vibrations, while the higher note has 1,440, and 

 (aa the lengths of string are in inverse proportion to the vibra- 

 tions) that it takes 1,440 degrees of the string, while the higher 

 takes only 1,280 such degrees. Therefore tho proportional 

 difference between them, whichsoever way you look at it, is a*t 

 hundred and sixty degrees. In tho same way you will find that 

 the difference between the two notes of this " small tono" is one 

 hundred and forty-four degrees, and that the interval of the 

 "tonnle" is ninety degrees. The degrees in each case are of 

 similar value, all measured on the same scale (common de- 

 nominator) of 1,440 degrees. We may therefore treat them as 

 belonging to ono scale, and adding three "great tones," two 

 "small tones," and two "tonules" together, we shall obtain a 

 perfectly measured scale of 948 degrees. As all these numbers, 

 however, will divide by 2, retaining, of course, tho same pro- 

 portion to one another, it is better to regard the scale as com- 

 posed of 474 degrees, containing three "great tones" of 80 

 degrees, two "small tones" of 72 degrees, and two "tonules" 

 of 45 degrees, and this is tho smallest'perfect measurement of 

 tho scale in plain figures. But if the pupil will go one step 

 further, and divide each of these intervals by nine, he will see 

 how wo obtain the proximate scale of fifty-three degrees. Tho 

 tonulo will bo exactly 5 degrees, tho small tone exactly 8 

 degrees, and tho great tono only one-ninth of a degree leas than 

 9 degrees. Adding these together, as before, you will have the 

 " Index scale," as Colonel Thompson calls it, " of fifty-three," 

 and you will see that it is throe-ninths or one-third of a degree 

 too large. We strongly advise tho pupil to construct a " mono- 

 chord," and try for himself whether this is not in truth an 

 accurate description of that scale of related notes which God has 

 mado most suitable to human ears and souls. All the books of 

 science are agreed that it is; and experience bears tho samo 

 testimony. It is the more important that you should under- 

 stand those points, because the true scale is dreadfully abused 

 by tho common keyed-instruments. Many of these aro tuned by 

 what is called "equal temperament;" that is, the scale is 

 divided into twelve equal Demi-tones, and it follows that the 

 tones are all 79 degrees (of the perfect scale of 474), while they 

 ought to be sometimes 80 and sometimes 72 degrees ! and the 

 tonules (semitones) are both 39 i instead of 45 ! ! They might as 

 well cut down tho fingers of a statue to " equal temperament ! " 

 Human ingenuity will surely deliver us soon from this mon- 

 strous distortion. Yon will understand now why it is so often 

 pleasanter to sing " without the piano." 



