The equal-tempered scale proposed in 1482 as a practical solution to discords was only introduced and applied 240 years later by J.S.Bach. Since then, this scale has ruled the tone frequencies in all variety of chords. Due to its simple conception, small imperfections in harmony are unavoidable.
Now a new musical scale is proposed, and my book: &amp;#8220;The Piagui Musical Scale: Perfecting Harmony&amp;#8221; details the new concepts and features to tune the piano correctly and in the manufacture of musical instruments, to introduce the new sounds in harmony to the world market.
The Natural Set of forty-seven elements was the beginning of the research. The M comma, the smallest consonance that can be distinguished by the ear, together with J and U, allowed the attainment of the Natural Progression of Musical Cells, while its 624 elements led to the discovery of K and P semitone factors to establish the Piagui octave. The proper sequence of eight K and four P replace the twelve T factors of the equal-tempered intonation.
The origins of K and P are the ten tone frequencies (Hz) found in the ancient Pythagoras and Aristoxenus heptatonic scales.
Piagui and Tempered chord wave peaks of basic twenty-four triads are drawn by computer to demonstrate the true concords and discords respectively.|
Most audiences assume that the equal-tempered scale is the most suitable to adequately evaluate harmony. However, there are some that might well prefer using another musical scale that is capable of producing flawless chords.
Mathematical reasoning led to the discovery of the Piagui Musical Scale, which soves the problem of imperfect musical harmony.
All tones contained in consecutive octaves on the piano keyboard are linked by perfect fifths and perfect fourths. These remarkable results made possible the achievement of the best expressions of harmony.
Mankind has sought and achieved, over millenia, the perfection of almost all things that are linked to him. Musical harmony, with wich we have lived for many centuries, was achieved and had only a small degree of imperfection left to solve. From now on, we can say that this problem no longer exists.
You can get the free preview of my book.
Mr. Frederik Magle: I wish you merry Christmas and Happy New Year.
C. Mario Pizarro
Lima, December 17, 2005