目錄 第一章音樂基礎(chǔ)知識............................................1 x1.1 聲音...................................................1 x1.2 樂音體系................................................6 x1.3 唱名...................................................11 x1.4 音樂的坐標系||五線譜....................................13 x1.5 音程...................................................16 x1.6 協(xié)和音程與不協(xié)和音程.....................................20 第二章弦的振動................................................24 x2.1 一維振動方程............................................24 x2.2 一維振動方程的解.........................................25 x2.3 振動模態(tài)與泛音...........................................27 x2.4 達朗貝爾行波解...........................................29 x2.5 傅里葉級數(shù)與撥弦振動.....................................31 第三章樂律||樂音體系的生成...................................38 x3.1 三分損益法..............................................38 x3.2 畢達哥拉斯五度相生律.....................................41 x3.3 純律與中庸律............................................44 x3.4 平均律..................................................49 x3.5 音分...................................................54 x3.6 連分數(shù)..................................................56 第四章調(diào)式、音階與和弦.........................................61 x4.1 調(diào)式與音階..............................................61 x4.2 和弦...................................................65 x4.3 調(diào)式中的和弦............................................68 第五章音樂與對稱..............................................76 x5.1 等價關(guān)系與音類...........................................76 x5.2 旋律的移調(diào)變換...........................................81 viii 目錄 x5.3 旋律的逆行與倒影.........................................86 x5.4 旋律的變換群............................................89 x5.5 十二音技術(shù)..............................................95 x5.6 音列的計數(shù)..............................................101 第六章節(jié)奏...................................................109 x6.1 固定節(jié)奏型..............................................109 x6.2 節(jié)奏型的影子與輪廓.......................................113 x6.3 比約克倫德算法與歐幾里得節(jié)奏..............................116 x6.4 相移與《拍掌音樂》........................................118 第七章和弦與音網(wǎng)..............................................127 x7.1 和弦的幾何..............................................127 x7.2 音階...................................................136 x7.3 三和弦之間的變換.........................................142 x7.4 音網(wǎng)...................................................146 x7.5 新黎曼群................................................153 第八章音樂與隨機性............................................160 x8.1 音樂骰子游戲............................................160 x8.2 隨機音樂................................................166 x8.3 馬爾科夫鏈..............................................170 x8.4 有色彩的噪聲, 1=f 音樂.....................................174 附錄A 集合與映射..............................................180 附錄B 與書中內(nèi)容有關(guān)的群論知識..................................185 參考文獻.......................................................195 名詞索引.......................................................200 人名索引.......................................................206