244 THE NATURE OF MUSIC 



perception, the first builders of chords worked induc- 

 tively and were not troubled by laws of acoustics. 

 Moritz Hauptmann* tells us that treatises on harmony 

 usually open with a learned chapter on acoustics the 

 half-truths in which have little if any influence on the 

 chapters that follow. The truth is that the com- 

 monly adopted rules for building chords were formu- 

 lated in accordance with the dictates of harmonic 

 feeling and perception. The rules are: for building 

 triads, superadd third and fifth to root; for seventh- 

 chords, superadd seventh to triad; for ninth-chords, 

 superadd seventh and ninth to triad. The validity of 

 these rules as applied to simple chords has been con- 

 firmed by the three -tone, four -tone and five -tone 

 threads of original harmony in one voice. This prin- 

 ciple of chord-building by superadding third upon 

 third has been extended beyond the ninth to the 

 eleventh and thirteenth. The resultant chords, all of 

 which are compound, are known as chords of the 

 eleventh and thirteenth. The above rules apply ex- 

 clusively to simple chords. Their application to 

 chords in general is a purely arbitrary procedure and 

 has caused much gratuitous confusion in heads and 

 books. For when our intellectual or conceptual re- 

 port on a specific chord in a specific relation does not 

 agree with and is in truth utterly refuted by our con- 

 crete perception of that chord's harmonic report, how 

 can we help feeling confused! Theories that present 

 such conceptions are certainly false. Viewed in the 

 abstract a chord is musically dead; we have done 

 with it when we describe its structure and classify it. 

 Viewed in the concrete a chord is alive, each of its 



