〈楊輝三角/Pascal’s Triangle Music〉 

〈楊輝三角/Pascal’s Triangle Music〉 (純音樂/Instrumental )

Music Poetic HK Op.20 與文同樂作品第二十號

Composed and Arranged by CK Kwan, based on the number patterns in Pascal’s Triangle (aka Yang Hui’s Triangle)

曲/編: 紀幾何 (根據楊輝三角的型態進行創作及編碼)

Pascal's triangle is a triangular array of the binomial coefficients which has interesting mathematical pattern. It is called “Yang Hui's triangle” in China as the triangle appeared in a book written by mathematician Yang Hui if 1261. In Western world, the pattern was described by French Mathematician Blaise Pascal in his book Traité du triangle arithmétique published in 1653. 

楊輝三角是二項式係數的一種表達方式，形似三角形，當中包括了不少有趣的數學性質。在中國，此三角形首現於南宋楊輝的《詳解九章算術》(1261)，而在西方，則由數學家布萊士·帕斯卡發現，並於著作著作Traité du triangle arithmétique 中發表 (1655)。

The music “Pascal’s Triangle” was composed using the patterns in Pascal’s Triangle. The work is influenced by Neu!, Cluster and Kraftwerk (in Autobann era). The encoding algorithm is as follows:

與文同樂作品〈楊輝三角/Pascal’s Triangle〉Op.20根據楊輝三角內的數字關係進行創作，作品採用了近似德國樂隊Neu!、Cluster 及Kraftwerk (Autobann 年代) 的風格。〈楊輝三角/Pascal’s Triangle〉的編碼方式如下: 

A. 編碼Encoding: 

1=d, 2=r, 3=m, …, 8=d’, 9=r’ etc. 

B. 主旋律 Main Melody ( 根據楊輝三角Based on Pascal’s Triangle)

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

(升八度One Octave up）

1

1 1

1 2 1

重覆Repeat

C. 低音線Bassline (根據楊輝三角Follows Pascal’s Triangle)

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1

1 1

1 2 1

1 3 3 1