THE THREE GENERA OE THE GREEKS. 215 



matic; those belonging to the first root are some chromatic and some diatonic; 

 they require no preparation and have various resolutions. The word chromatic 

 is of Greek origin, it signifies colored; a note or a chord either belongs to the key 

 of the passage that precedes it or to the key of the passage that succeeds it ; if 

 that which preceeds it and that which succeeds it be both in the same key, this 

 note, or chord, though foreign to the signature, induces no modulation, and is 

 therefore chromatic. The phenomenon that every musical sound generates 

 others, is the basis of the free or chromatic style of harmony. This phenomenon 

 is demonstrable on every string, and every pipe of length sufficient and conse- 

 quent depth of tone, for the ear to detect the more and more delicate sound of 

 its generated notes, or harmonics as they are technically called, when they suc- 

 cessively become evident to the perception. All wind instruments yield their 

 harmonics, not together indeed, but successively to the stronger pressure of the 

 player's breath, and those of the class of horns and trumpets have no other notes 

 than their harmonic sounds, and the performer has no means of varying these 

 but by the different manner in which he may direct his breath through the pipe. 



Instruments of the violin class have also their harmonics which are produced 

 by a mechanism totally different from that for intonating the consecutive notes 

 of a scale. A cathedral, being a hollow form, is an enormous pipe, and this 

 property which it possesses in common with the smallest wind instruments of 

 giving out harmonic or generated sounds, must be the reason why early musi- 

 cians, as a rule made their final closes upon a major chord, though the key of 

 their piece were minor; since the major third is one of the most prominent notes 

 of the harmonic series, so prominent indeed in buildings of great reverberation as 

 to jar against the minor third if this be long sustained. We have but to extend 

 further the inferential idea of smaller or larger vibrating media, and to follow 

 this in thought into infinity, and we may willingly acknowledge the unmeasured 

 concave of nature to be an immense musical instrument ; when the Pythagorean 

 doctrine of the music of the spheres will cease to seem a figurative image, a 

 scientific myth, and will appear to ordinary comprehension but the statement of 

 a fact, whose manifest evidence is within the reach of our senses. The whole 

 system of chromatic or generated harmony is based on the following well estab- 

 lished principles, viz : that the sounds of nearly every musical instrument with 

 which we are acquainted are not, as they are ordinarily taken to be, single tones 

 of one determinate pitch, but compound sounds containing an assemblage of such 

 tones, 



These are always members of a regular series, forming fixed intervals with 

 each other; for instance, if we take C an octave below tenor C as a generator, the 

 first overtone or harmonic audible is its octave, then the fifth above that octave, 

 then the second octave or fifteenth above the generator, then the major third or 

 two octaves and a major third above the fundamental sound, etc. This may be 

 illustrated as follows : If a stretched string fastened at both ends, be caused to 

 vibrate, communicating its vibrations to the air, the whole length of the string 

 vibrates alone only momentarily; its divisions also vibrate, which produce cer-- 



