Mario Pizarro

The Piagui Musical Scale: Perfecting Harmony Mario Pizarro

TheTempered scale proposed in 1482 as a practical solution to discords was onlyintroduced and applied 240 years later by J. S. Bach. Since then, this scalehas ruled the tone frequencies in all variety of chords.¿ Due to its simple conception, small imperfectionsin harmony are unavoidable. Nowa new musical scale is proposed, and this book details the new concepts andfeatures and their application in the manufacture of musical instruments, tointroduce the new sounds in harmony to the world market. TheNatural Set of forty-seven elements was the beginning of the research.¿ The M comma, the smallest consonance that canbe distinguished by the ear, together with J and U, allowed the attainment ofthe Natural Progression of Musical Cells, while its 624 elements led to thediscovery of K and P semitone factors to establish the Piaguioctave. The proper sequence of eight K and four P replace the twelve T factorsof the Tempered intonation. Theorigins of K and P are the ten tone frequencies found in the Pythagoras and Aristoxenus heptatonic scales. Piaguiand Tempered chord wave peaks of basic twenty-four triads are drawn by computerto demonstrate the true concords and discords respectively.