方整性结构内的非方整性划分——约翰·凯奇《金属第一结构》中节奏动机的组织原则(下)

Unequal Divisions in the Integrality of Square Root: The Organizational Principles of Rhythmic Motives in First Construction (in Metal) by John Cage

凯奇早期代表作、仅使用金属打击乐器的《第一结构》(1939),受勋伯格传授的维也纳乐派逻辑性结构思维和动机展开性变奏的影响,在整体和乐句结构层面上运用他自己发明的、按4:3:2:3:4比例划分的"宏观-微观"的节奏结构体系;而对节奏动机的组织则是基于方整性结构框架内非方整性划分的原则,采用二分与三分节奏时值结合、全音符的奇数划分、对称性的节奏音值排列、节奏动机间解构与重组关系四种方式设计动机,运用动机的不定次反复、动机交替的横向对称性连接和纵向对位性叠置、动机陈述跨越与不跨越乐句和音色分层的手法组织动机[本文(上)发表于《黄钟》2011年第一期]。

In his early significant percussion work First Construction（in Metal） composed in 1939,John Cage employs his invented organizational system called macro-micro rhythmic structure based on proportion 4：3：2：3：4 for its overall and phrase structures,while designs rhythmic motives through duple and triple combined,odd-number or symmetrical value divisions and de-and re-construction,and organizes rhythmic motives via the devices of infinitive-time repetition,symmetrical arrangement,rhythmic counterpoint,phrase boundary crossing,and timbral differentiation under the principles of unequal divisions in the integrality of square root.