Note O — Front matter

“The equal temperament of 12 degrees, which was discussed theoretically as early as about 1500, but not established as a principle until shortly before 1700 (by Andreas Werkmeister), divides the octave into twelve equal portions (semitones, hence ‘twelve-semitone system’) through which mean values are obtained; no interval is perfectly pure, but all are fairly serviceable.” (Riemann, “Musik-Lexikon.”) Thus, through Andreas Werkmeister, this master-workman in art, we have gained the “twelve-semitone” system with intervals which are all impure, but fairly serviceable. But what is “pure,” and what “impure”? We hear a piano “gone out of tune,” and whose intervals may thus have become “pure, but unserviceable,” and it sounds impure to us. The diplomatic “Twelve-semitone system” is an invention mothered by necessity; yet none the less do we sedulously guard its imperfections.