[O] “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.

[P] It is termed “The Science of Harmony.”

[Q] “New Music for an Old World.” Dr. Thaddeus Cahill's Dynamophone, an extraordinary electrical invention for producing scientifically perfect music. Article in McClure's Magazine for July, 1906, by Ray Stannard Baker. Readers interested in the details of this invention are referred to the above-mentioned magazine article.

[R] As if anticipating my thoughts, M. Vincent d'Indy has just written me: “… laissant de côté les contingences et les petitesses de la vie pour regarder constamment vers un idéal qu'on ne pourra jamais atteindre, mais dont il est permis de se rapprocher.”

[S] I think I have read, somewhere, that Liszt confined his Dante Symphony to the two movements, Inferno and Purgatorio, “because our tone-speech is inadequate to express the felicities of Paradise.”