873 



CHORD. 



CHORD. 



874 



Angle. Chord. 



41 . . 3502 



42 . . 3584 



3665 

 3746 

 3287 

 3907 

 3987 

 4067 



43 

 44 

 45 

 46 

 47 

 48 



49 . . 4147 



50 . . 4226 



51 . 



52 . 



53 . 



54 . 



55 . 



56 . 



57 . 



58 . 



59 . 



60 . 



61 . 



62 , 



63 , 



64 , 

 65 

 66 

 67 

 68 

 69 

 70 



71 

 72 

 7S 

 74 

 75 



4305 

 4384 

 4462 

 4540 

 4617 

 4695 

 4772 

 4848 

 4924 

 5000 



, 5075 

 , 5150 

 . 5225 

 . 5299 

 . 5373 

 , 5446 

 , 5519 

 . 5592 

 . 5664 

 . 5736 



. 5807 

 . 5878 

 . 5948 

 . 6018 

 . 6088 



Angle. 



76 . 



77 . 



78 . 



79 . 



80 . 



81 . 



82 . 



83 . 



84 . 



85 . 



86 . 



87 . 



88 . 



89 . 



90 . 



91 . 



92 . 



93 . 



94 . 



95 . 



96 . 



97 . 



98 . 



99 . 



100 . 



101 . 



102 . 



103 . 



104 . 



105 . 



106 . 



107 . 



108 . 



109 , 



110 . 



Chord. 

 . 6157 

 . 6225 

 . 6293 

 . 6361 

 , 6428 



. 6494 

 , 6561 

 . 6626 

 . 6691 

 . 6756 

 , 6820 

 . 6884 

 . 6947 

 . 7009 

 . 7071 



. 7133 

 . 7193 

 . 7254 

 . 7314 

 . 7373 

 . 7431 

 . 7490 

 . 7547 

 . 7604 

 . 7660 



. 7716 



. 7771 



. 7826 



. 7880 



. 7934 



. 7986 



. 8039 



. 8090 



. 8141 



. 8192 



Angle. 



111 . 



112 . 



113 . 



114 . 



115 . 



116 . 



118 . 



119 . 



120 . 



121 . 



122 . 



123 . 



124 . 



125 . 



126 . 



127 . 



128 . 



129 . 



130 . 



131 . 



132 . 



133 . 



134 . 



135 . 



136 . 



137 . 



138 . 



139 . 



140 . 



141 . 



142 . 



143 . 



144 . 



145 . 



Chord. 

 . 8241 

 . 8290 

 . 8339 

 . 8387 

 . 8434 

 . 8480 

 . 8526 

 . 8572 

 . 8616 

 . 8660 



. 8704 



. 8746 

 . 8788 

 . 8829 

 . 8870 

 . 8910 

 . 8949 

 . 8988 

 . 9026 

 . 9063 



. 9100 

 . 9135 

 . 9171 

 . 9205 

 . 9239 

 . 9272 

 . 9304 

 . 9336 

 . 9367 

 . 9397 



. 9426 

 . 9455 

 . 9483 

 . 9511 

 . 9537 



Angle. 



146 . 



147 . 



148 . 



149 . 



150 , 



151 . 



152 . 



153 . 



154 . 



155 . 



156 , 



157 , 



158 . 



159 , 



160 , 



161 , 



162 , 



163 . 



164 , 



165 , 



166 . 



167 . 



168 , 



169 , 



170 , 



171 



172 



173 



174 



175 



176 , 



177 



178 



179 



180 



Chord. 

 . 9563 

 . 9588 

 . 9613 

 . 9636 

 . 9G59 



. 9681 

 . 9703 

 . 9724 

 . 9744 

 . 9763 

 . 9781 

 . 9799 

 . 9816 

 . 9833 

 . 9848 



. 9863 



9877 



. 9890 



. 9903 



. 9914 



. 9925 



. 9936 



. 9945 



. 9954 



. 9962 



. 9969 

 . 9976 

 . 9981 

 . 9986 

 . 9990 

 . 9994 

 . 9997 

 . 9998 

 . 9999 

 10000 



To use this Table, roughly, take out the chord of the nearest degree, 

 multiply by the diameter, and divide by 10,000. Thus for a diameter 

 of 2 feet, and an angle of 10 (supposing decimals are to be avoided), 

 take out 872 opposite to 10, and multiply by 2, giving 1744, which 

 in inches is 20,928, which divided by 10,000, gives 2 inches, and l-10th 

 of an inch, very nearly. 



An easy method of verifying the preceding table (if a doubt arise in 

 any case) is contained in the following relations, which apply according 

 as x is greater or less than 120. 



ch. of (x 120) + ch. (240 x) = ch. x. 

 ch. of (120 + x) ch. (120 x) = ch. x. 

 ch. of (180 + x) = ch. of (180 a;) 



For instance, the chord of 130 is made up of those of 10 and 110^; 

 the chord of 50 is the difference between those of 170 and 70 . 

 These will be true within a unit, if the Table be correct. 



CHORD, in music, is the harmonious combination of three or more 

 musical sounds. 



To account for the origin of chords, many theories have been pro- 

 posed, the principal whereof are, that of Rameau which D'Alembert 

 endeavoured to elucidate, and Marpurg partly built his system on 

 and those of Tartini and Kirnberger. These theories, in the main, all 

 arise out of, or finally resolve into, the natural harmonics of a dis- 

 tended string. But it will be proper here to state that Sir John 

 Herschel in his treatise on Sound, contained in the ' Encyclopedia 

 Metropolitana,' declares " the insufficiency of any attempt to establish 

 the whole theory of harmony and music on the aliquot subdivision ot 

 a musical string." Nevertheless, the facts that result from the simple 

 division of a stretched string agreeing with the natural harmonic 

 divisions of a sonorous tube the French horn, for mstenceand 

 which cannot be disputed are sufficient to prove that the foundation 

 of what is properly called harmony was not arbitrarily laid, inese 

 facts may thus be briefly stated : the whole string gives, of course, the 

 gravest, or generating, sound; four-fifths of the string give the major 

 3rd; two-thirds give the perfect 5th; and one-half gives the octave. 

 Thus is produced the perfect or common chord, or toad which, 

 together with the chord of the seventh, is the source of all other 



rei The "perfect Chord consists of any given note, together with a major 

 3rd and perfect 5th, which sounds may be represented by the letters 

 CEO or by the syllables do, mi, id. It has two inversions, or deri- 

 vatives : the first is made by taking the E (mi) as the base, producing 

 the chord of the tixth ; the second, by taking the o (sol) as the base, 

 producing the chord of the ticth and fourth. Example : 



Perfect Chord. 1st Inversion. 2nd Inversion. 



This chord is denominated the Perfect Minor Chord when its 3rd 

 is flattened; and, so altered, its inversions are affected accordingly. 

 Example : 



-f- 6 66 



The chord of the seventh called the Dominant Seventh is formed 

 by adding to the perfect chord a minor 7th, and consists of a given 

 note, together with a major 3rd, a perfect 5th, and a minor 7th. It 

 may be represented by the letters o, B, D, F, or by the syllables 

 sol, si, re, fa. This has three inversions : the first is made by taking 

 the B (si) as the base, producing the chord of the sixth and fifth ; the 

 second, by taking the D (re) as the base, producing the chord of the 

 fourth and third; the third, by taking F (fa) as the base, producing 

 the chord of the fourth and second. Example : 



Chord of 7th. 1st Inversion. 2nd Inversion. 3rd Inversion. 



P 



The Perfect Chord, and its inversions, are called consonant chords 

 all other chords, and their inversions, are called dissonant chords. 



The chord of the Imperfect, or Minor, Seventh, consists of a given 

 note, a minor 3rd, an imperfect 5th, and a 7th. Example : 



-8- 



The chord of the Diminished Seventh sometimes called the Equi- 

 vocal Chord consists of a given note, its minor 3rd, imperfect 5th, 

 and diminished 7th. Example : 



Diminished 7th. 1st Inversion. 2nd Inversion. 3rd Inversion. 



67 



4 

 63 



The chord of the Dominant Ninth consists of a given note, its major 

 3rd, 5th, 7th and 9th. Example : . 



This chord has three inversions, though they are not in very common 

 use. M. Catel gives them in the following manner : 



1st Inversion. 2nd Inversion. 3rd Inversion. 



?m 



But by far the most elegant form which the chord of the Ninth and 

 Seventh assumes is a retardation of the 8th and 6th. Example : 



3^ 



98 

 76 



The Dominant Minor Ninth consists of the same sounds as the Domi- 

 nant Ninth, but the 9th is flat. Example : 



129 

 7 



