کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9727549 | 1480203 | 2005 | 28 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The mathematical analysis of the structure of some songs
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
فیزیک ریاضی
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
The mathematical structures of six songs were studied by treating them as complex systems. The studies were based on (i) scattering diagram, (ii) spiral structure, (iii) graph theory and animal diagrams, and (iv) entropy and organization. In (i), the fractal dimension and the radius of gyration was determined for each melody. In (ii), it was shown that the total number of notes used in a song display a spiral, which can be expressed by a mathematical equation. In (iii), the animal diagram was obtained by using the pathways between the consecutive notes of the song. A ratio defined as 'the number of edges to the total number of unit edge' for the animal diagram was used as a parameter to characterize a melody. In (iv), the entropy, the maximum entropy, and the negentropy or the organization of the songs were determined. In addition, the rate of change of organization of the songs was also determined.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica A: Statistical Mechanics and its Applications - Volume 357, Issues 3â4, 15 November 2005, Pages 565-592
Journal: Physica A: Statistical Mechanics and its Applications - Volume 357, Issues 3â4, 15 November 2005, Pages 565-592
نویسندگان
Güngör Gündüz, Ufuk Gündüz,