شکل‌گیری فضا در اثر پیوند مفهومی «موسیقی – ریاضی» و معماری (مطالعه‌ی موردی: جلوخان و آسمانهِ گنبدخانهِ مسجدِ شیخ‌لطف‌الله اصفهان)

In traditional architecture, the adherence of architects to the rules and proportions in numbers, geometry and music is present in designing and shaping many public monuments, and mathematical proportions, artistic ratios, or musical proportions are used in geometry of these buildings. Extracting and matching mathematical rules and proportions and examining them in the architecture of the traditional buildings are among complex issues which are well-worth for further analysis. The present article is aimed at finding the link between «architecture and music», «architecture and mathematics» and «music and mathematics» and determining the boundaries and mutual points of these sciences. The objective was to reorganize geometric pattern in Jelokhan of Sheikh Lotfollah Mosque in city of Isfahan and the linkage of its Asemaneh of the dome with music. This is a theoretical research and its theoretical basis is carried out with a historical interpretation method. Logical reasoning has been used in investigating Jelokhan and Asemaneh of Sheikh Lotfollah Mosque in Isfahan. In order to fulfill the purpose of the sudy, the relations between «architecture and music» and «architecture and mathematics» were analyzed in the form of a concept as «music-math» in architecture for adaptation. In examining the relationship between architecture and music, the researchers faced many stances. For instance, some authors believed that architecture is an expression of music in its further development or in its evolution, while some others indicated that architecture is the frozen music in space. Thus, to understand the relationship between music and architecture, you need to understand the language of both along with finding their mutual ties. Therefore, in extracting common principles and characteristics that include criteria, similarities and symmetries while keeping in the mind the relative importance of measuring the relationship between architecture and music, we analyzed it in terms of rhythm, equilibrium, balance, symmetry, high and low points, decoration and beauty of decorations, color, hearing sensation, pleasure, and quantitative role of numbers. In examining the relationship between architecture and mathematics, math is also considered as the purest type of thought and one of the main causes of human closeness to God. That is probably why most traditional architects bring math ideas into architectural designs so as to verify their beliefs about the Creator and the natural world around us. Mathematical expressions in architecture can be expressed numerically, symbolically, philosophically, creatively, conceptually through numerical ratios. Finally, in explaining the concept of «music-math» in architecture, we need to determine the extent to which musical and mathematical uses of architecture are parallel, shared, and reciprocal. In scrutinizing the proportions between architecture and music, architecture and mathematics, principles and common standards such as equilibrium, balance and symmetry, decorations and proportions, hearing sensation, numerical philosophy, numerical proportions, graphic geometry and numerical relations were obtained. In order to elucidate the theoretical findings of the research which are explained by the relation among the concepts of music, mathematics and architecture, we focused on Jelokhan and Asemaneh of Sheikh Lotfollah Mosque in Isfahan. The discovery of a hidden geometry in the depth of Jelokhan combined with Iranian Dastgahi music and mathematics along with finding a harmonic pattern in abstract patterns of the dome of Asemaneh coincided with changes in the frequency of the notes reflects its architect›s adherence to the principles of music and math in the architecture of this mosque. The proportions and rules contained in the musical, architectural, and mathematical Jelokhan of the mosque were analyzed through the fact that most geometric points of Jelokhan from the beginning to the end, the main lines, the lines of symmetry, the vaults, the lines of the Mogharnas, and many of the details of the mosque›s Jelokhan were built based on a pattern which is formed in a modular compendium of mathematics and music using the similarity of the Shur-e Sol Dastgah. Besides, the beautiful harmony of this Iranian Dastgah is seen in Jelokhan of the mosque and the walls of the Naghsh-e Jahan Square. In addition, the harmony of this Dastgah is present in heavenly decoration of mosque’s Asemaneh; decorations that, similar to orthogonal mathematical models are aggregated or opened. These harmonic decorations are a certificate of fine and delicate musical notes or an increase in the frequency of notes in Shur Dastgah.