April 2014
Beginner to intermediate
830 pages
15h 21m
Chinese
Content preview from Mathematica 錦囊妙計
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394
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第九章
討論說明
計算 ADSR 的 4 個區域的調變函數並不如你想像中這麼困難。直線方程式為
y
= m
x
+ b，
其中 m 為斜率、b 為 y 截距。若斜率為 -2 且
y
截距為 4，則方程式為
y
= -2
x
+ 4。
若你正在尋找 ADSR 調變的第二區域（衰退區域）調變函數，你只需將原函數之
x
取
代為 (
x
- 位移 ) 向右進行位移即可。一般而言，此函數可以寫成
y
= m (
x
- 位移 ) + y 初
始截距，以本範例而言，向右移動 2 格，可得到新函數為
y
= -2 (
x
- 2) + 4 或簡化為
y
=
-2
x
+ 8，然而此新函數的斜率不變，而截距變為 8。396
ch09.indd 394 2014/4/7 下午 12:33:18
9.15 探索音階與樂器調音原理 （Alternate Tunings）
|
395
9.15 探索音階與樂器調音原理
（Alternate Tunings）
問題點
你想進一步了解音階的劃分以及樂器調音的原理。397
解決方案
當代西方音樂使用 12 平均律劃分音階，但從大自然振動物理的角度而言，這其實是折
衷方案，至少這並非 3000 年前古希臘人理想中的完美語言。古希臘人（或更早的巴比
倫人）注意到，當兩物體的振動頻率為簡單整數比
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