Mathematical-Physical Properties of Musical Tone Systems By

In this article the fundamental properties of the physical-mathematical laws are studied upon which music is based. Thus this article is not a study of music as such, but a study of the properties of the component elements which are the ‘‘building blocks’ ’ of music in the hands of the composers. These ‘‘building blocks’ ’ are the musical sound frequencies – the musical tones. It is the intrinsic physical-mathematical structure of the musical tones, and the interrelationships among these tones, which is studied. The physical-mathematical properties of the tones, together with the physical-mathematical laws governing the relationships between the tones, that forms the musical tone system which is discussed in this article. The fundamental properties of musical tones (also referred to as intrinsic internal musical properties) rest upon the laws of physics and mathematics. As such, they are independent of cultural priorities regarding the perception of beauty in musical tones, even though these fundamental properties form the basis upon which the various musical systems are built. The cultural priorities find their way into music via th