نگاهی به مفهوم تئوریک "جموع ناقصه"در رسالات موسیقایی مکتب منتظمیه

Ambits of tones (as one of the most important elements of mode structure) in Old Iranian music have multiple kinds and definitions. Middle Eastern Musicologists have always tried to explain and devise tones ambits, because ambits of tones and structure of mode are irrefrangible. Generally purpose of division of ambits to their components is explanation of melodic modules and their combination. Some musicologists explain more clearly relationship between these two elements: ambit of tones and mod. Jam’, Jens, Bahr, ZolArba’, Zol Khams ZolKol, ZolkoleMarrateinetc, are some melodic modules in musical treaties of Islamic realm. Defining the function of tone structure, special melodic demeanors, and some other musical elements, make it possible to convert a melodic module (such as mentioned melodic modules) into a sonic-musical atmosphere with definite aesthetic effects. This article studies some of these concepts and ideas and their implication in old and contemporary music of Iran. Despite the importance of tetrachords and pentachords as a most fundamental melodic module in Middle Eastern music, the smaller cells than tetra chord and larger cells thanpentachordcan also be used. In contemporary music in Iran, there are some melodic modules which have 3, 6 or 7 tones. Different treaties have diverse information about their modal futures. In systematist treaties, the term that includes all of these cells (trichord, tetrachord, pentachord, ZolKoletc) are JAM’. Jam’ is one of the most significant melodic modules in old treatises of Middle Eastern music. After some theoretical changes, this concept had been particularly closest word to Mode in systematist school and music section of DorratolTaj (one important book of mentioned musical school). Research problem of this article is “what is the relationship between jam’ and theoretical concept of Mode?” Qotboddin e Shirazi defined “PARDE” as a melodic module with practical potential. After that he distributed treats of “PARDE” to concept of jam’. This is a useful step to reach to an exact definition of Jam’. Qotboddin e Shirazi believed that a melodic module needs at least 3 notes. Study of modal units in contemporary practice of Iranian music justifies their hypothesis. Surely some melodic modules needs rather than three notes for transmission of modality. This comparative method can lead contemporary music in Iran (Dastgahi music) to be theorized base on its traits. At the end, it indicates thatJamis closest concept to theoretical idea of Mode and Modal Module among definitions of systematist At first, the article studies definitions of main treaties of systematist school and its Persian branch. In addition, it focuses on differences between definition of Jam’ and “Jomou e Naghese”, in this school and scholastic school (chief school before systematist). Furthermore, it tries to find implications of Jam’ in practice of contemporary Iranian music. As a result, this research includes a comparative study between definitions in old treaties and sonic objectivity of Dastgahi music. Comparative study can assess accuracy of our understanding aboutjam’.