The mas­tery over the ele­ments of a com­po­si­tion, the motif, the melody, the se­quence, and the har­mony – and based on that, the in­te­grated in­stru­men­tal mas­tery over the over­tone-spec­trum of a tone – have their equiva­lent in mathe­mat­ics in the ef­fort­less mas­tery over ir­ra­tional num­bers; for in mu­sic, which is struc­tured lively, all the struc­tural ele­ments of the com­po­si­tion move in ra­tios of ir­ra­tional num­bers.

Noth­ing is fixed, and yet one feels the pres­ence of an or­ga­niz­ing knowl­edge, with­out be­ing able to grasp it at any spe­cific point.

At­tempt­ing to fathom such a lively mu­si­cal or­der through analy­sis one will be un­able to com­pre­hend it from out­side alone, be­cause due to a natu­ral edu­ca­tional mecha­nism built into such com­po­si­tions, the lis­tener at some point re­places the out­ward, re­stricted ana­lyti­cal method with his in­ner, com­pre­hen­sive, syn­the­siz­ing un­der­stand­ing, and at the depths of his per­son­al­ity he at­tains in­ner knowl­edge – the knowl­edge of his Self.

Hav­ing reached his self, sound­ing mu­sic to him is the outer means for stimu­lat­ing his hap­pi­ness at the depth of his in­ner si­lence of self-con­scious­ness in a mani­fold, crea­tive man­ner. Thus, the art of mu­sic has ac­com­plished a cen­tral task: it has in­spired the mu­sic lover to sys­tem­atic self-aware­ness, and it has an­tici­pated the bliss­ful world of ex­peri­ence as­so­ci­ated with self-aware­ness.

Glo­ri­fi­ca­tion of the in­nu­mer­able facets of self-knowl­edge is the true pur­pose of genu­ine clas­si­cal mu­sic.