1864.] 



m Instruments with Fixed Tones. 



97 



CE Gy c feb ffi ox AtC^E, ac e, the chords are here termed synonymous. 

 If the interval of the major third is contained by the same tones, as C E 

 ace; or '\E\> G t-Sb, c they are termed relative. If two chords, 



major or minor, have the fifth tone of the one the same as the first tone of 

 the other, ^.bFAC.CEG; f-\a\> c, c-\e\>g\ fU\> c, C E G ; F AC.c^^ 

 they are here termed dominative. If a chain of three such dominative chords 

 be formed (asFAC,CEG, GBD, or /fab c, cfeb ^, ^ t^b d, the mmor 

 and major chords being interchanged at pleasure), the first is called the 

 subdominant, the second the tonic, and the third the dominant. Three such 

 chords contain seven tones, and if such octaves of these tones are taken 

 that all seven tones may lie within the compass of one octave they form a 

 scale, of which 24 varieties can be formed by varying the major and minor 

 chords, and beginning with the first of any one of the three chords. 

 These scales include all the old ecclesiastical modes and several others. If 

 all three chords are major and the scale begins on the first of the tonic 

 chord, the result is the inajor scale, C, D, E, F, G, A, B, c. If all three 

 chords are minor and the scale begins on the first of the tonic chord, the 

 result is the minor descending scale, c^, t^^^> t«b, g,f, feb, d, c. If the 

 first and second are minor, and the third major, or if the first and third are 

 major and the second minor, we have the two usual ascending minor scales, 

 c, d, td?,/, g, t«b, h, or c, d, feb,/, g^ a, h, c^. Three major chords 

 may therefore be considered to represent a major scale, but both major and 

 minor chords are necessary for the various minor scales. If to each of 

 three dominative major chords we form the relative and synonymous minor 

 chords, the synonymous and relative majors of these, and the relative 

 minor of this synonymous major, we shall have a group of 9 major and 

 9 minor chords, which I shall call the key of the first of the tonic chord. 

 Thus the following is the 



KeyofC. 



Eelative Ma. 

 (of Syn. Mi.). 



Synonymous 

 Minor. 



Primary 

 MAJOE. 



Eelative 

 Minor. 



Synon. Ma. 

 (of Eel. Mi.). 



(Sub-) Eela- 

 tive Minor. 



tAb C tEb 



tEb atBb 



tBb D tF 



ftabc 

 cteb g 

 gtbbd 



F A C 

 C E a 

 a B D 



|df a 

 ace 

 e gb 



JD +Ffl A 

 A|CJt E 

 E+GflB 



+b Jd tffl 

 tfS a tcJf 

 icJt e igfl 



These chords contain 1 6 tones, which, when reduced to the compass of the 

 same octave, form the complex scale c, Xcj^^, ^d, d, feb, e, f, (ff), 

 g, Xff^) t^^» ^> t^^j (W* ^'j 0^ which the acute fourth (f/), and the grave 

 seventh (Xb), have been enclosed in parentheses, as being of rare occurrence. 

 From this complex scale 54 scales of 7 tones each m.ay be formed, similar 

 to the 24 scales already named. A selection of 12 tones, such as c, Jcjf, 

 d, feb, e,f, Xf% ff> f^^i t^b, b, forms the so-called chromatic scale, 

 which, however, has no proper existence except in equal temperament. 

 Now proceed to form a series of seven dominative major chords, as 



