CHI TIẾT NGHIÊN CỨU …
Tiêu đề
Counting melodies: Recursion through music for a liberal arts audience
Tác giả
Ludwick K.
Năm xuất bản
2015
Source title
PRIMUS
Số trích dẫn
0
DOI
10.1080/10511970.2015.1122689
Liên kết
Tóm tắt
In the study of music from a mathematical perspective, several types of counting problems naturally arise. For example, how many different rhythms of a specified length (in beats) can be written if we restrict ourselves to only quarter notes (one beat) and half notes (two beats)? What if we allow whole notes, dotted half notes, etc.? Or, what if we allow each note to be selected from some specified set of tones (e.g., C, C#, D, etc.)? In my course on music and mathematics for the liberal arts, I use these questions as a method of introducing students to the concept of recursion, as it turns out that such questions lead naturally to sequences (indexed based on the length of the rhythms or melodies being considered) defined by recurrence relations, such as the Fibonacci sequence. © Taylor & Francis Group, LLC.
Từ khóa
Counting; Fibonacci sequence; Liberal arts mathematics; Mathematics and the arts; Music and mathematics; Recursion
Tài liệu tham khảo
Harkleroad L., The Math Behind the Music, (2006); Singh P., The so-called Fibonacci numbers in ancient and medieval India, Historia Mathematics, 12, 3, pp. 229-244, (1985)
Nơi xuất bản
Taylor and Francis Inc.
Hình thức xuất bản
Article
Open Access
Nguồn
Scopus