CORNELL

CHAPTER IV(e)the duodecuple (or twelve-note) scaleBy far the most revolutionary .of all the modern traits inmusic is the complete acceptance of the equal temperamentalDivision^^^ling with all that it entails.Hitherto, notwithofthe standing the fact that the semitone is a practicalctave.Qj^^ jjQJ- g^ theoretical one, the whole system ofharmony and melody has been built largely upon the basis ofthe pure unequal tuning.Even with the equal tuning such a course is really neitherimscientific nor unnatural. Does not the mathematicianhave to be content with his unending decimal, and the trigonometristwith his unsquared circle? The acoustical discrepanciesof the " equal temperament ''are so very slightthat even Nature herself makes no bother about them. Oneonly of a hundred various experiments wiU prove this. Takethe most troublesome note of the "equal tuning" on thepianoforte. Press the middle F-sharp down silently, thenstrike a low D rather sharply, and the F-sharp will at onceautomatically respond in sympathetic vibration.The outcome of all this is the ability to hear, think, andwrite freely in either of these opposing systems, and it is a.J curiotis fact that composers who avowedly bindJ-,Use of the themselves to using one temperament entirely, areTwo constantly found thinking and writing in the other.ys ems.j^ ^^^ always been, and probably always will beso with composers and listeners alike, and the musical art isimmensely enriched thereby.To return to the scales, the reader miust carefully dis-„ . tinguish between the older " chromatic " scale and"witirthe" the " new semitonal " one. Both, of course, divideChromatic ^q octave into twelve steps, but the older view'^"'assumes that the chromatic notes are only ofsecondary importance to the diatonic ones, from which, indeed,33