This book introduces polytempic polymicrotonality as a new musical aesthetic. It proposes music with more than one microtonal tuning system and discusses examples from the literature to give an historic framework showing that this tendency has been present throughout human musical history. Polytempo is a tool for which polymicrotonal structures can function in relief from its background, and it acts as a frame, or ground structure, that is multidimensional, akin to the advancement of perspective in Renaissance art. The book has historic significance as it is the only book of its category, or genre, in music that features polymicrotonality in music composition or production. It displays examples of music literature for musical precedence in this area, focusing on Charles Ives's Universe Symphony, unfinished since 1925.