ABSTRACT
Paul Hindemith proposed his Acoustical Harmony Theory in The Craft of Musical Composition. Based on natural phenomena of Overtone Series and Combination Tones, the author proposed a different treatment of Harmony and Melody with the concept of dissonance fluctuation. However, some physical phenomena were wrongly applied. This paper reviews these concepts and suggests a new theory. Legname proposes a visual analysis of the interval waveform graph and the relation between its complexity and the interval level of dissonance. Then, a mathematical process leads to a substitution of consonance / dissonance polarity with a smooth-curve notion of Density Degree. Analyses of a wide range of compositions from Bach to Ligeti, reveal new perspectives and the practical application of this theory, for performers, composers and theorists.
Density Degree of Intervals and Chords Paper