Paul Hindemith

 

 

 

 

   

Once one has taken the step into the realm of equal temperament, one is tempted to increase the advantages it has over all other intervallic systems; unhindered access to every region of a tonality and absence of any commatic regulation. Could not the stimuili afforded by this carefree calculation be heightened if we replaced our twelve-tone division of the octave by a different number of tones? . . . .

. . . if we take a number exceeding twelve tones within the octave, we find it promising, the more so because we may get a chance to reduce the minor but ever-present toxic effect of impure intervals by diminishing the amounts of the tolerances. . . .

 

 
     
Paul Hindemith, A Composers' World, Horizons and Limitations, A Doubleday Anchor, 1961Book, p103
   

. . . our natural twelve-tone system, with its tendency towards maximum purity and its flexible commatic regulations achieved with the aid of expanded or contracted intervals readily tolerated, is doubtless the best one we can find. In its tempered form it is still close enough to nature so that its deviations are not felt as new intervals and so that it can be used together with the untempered form without causing serious disturbances.

 

 
     
Paul Hindemith, A Composers' World, Horizons and Limitations, A Doubleday Anchor, 1961Book, p105
 
       
 
                                                            
           
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