Relative Musical Pitch in Formal Definition

This research is dedicated to the category of relative musical pitch and its objects such as tones, intervals, interval structures, and systems. Objects of relative pitch are considered as necessarily existing in their systemic unity. The study introduces the concept of structural-pitch organization (SPO), an object that signifies the unity of objects of relative pitch. SPO is defined as an aggregate of representatives of all possible classes of objects of relative pitch, taken together with the system of relations between them. Being associated with both acoustic and psycho-physiological phenomena, the SPO and its components are abstract, mental objects. The study is devoted to the abstract-logical aspect of relative pitch, considering it is strictly distinguished from the "natural" aspect. The SPO is examined as an attribute of a special type of so-called structural-pitch thinking. The aggregate of relations between SPO objects represents the specific principles of such thinking, that is, those in which it is independent of either natural factors or other types of mental activity (types of thinking and expression). The study provides formal definitions of the SPO objects. These definitions are derived by means of set theory. The study offers a formal definition of the content of the SPO (that is, the scheme of the content of structural-pitch thinking). I demonstrate that there exists not an SPO in general, but a class of SPOs, whose representatives differ in content and characterize the pitch thinking of individuals and communities in different cultures and epochs.