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Allen Forie 1973年发表的《非调性音乐的结构》一书,是音级集合理论体系成熟的标志。十多年来,在现代音乐中,无论是在音级组合及其关系的定量描述方面,还是在音乐文献的分析方面,该体系一直扮演着十分重要的角色。作为标记系统数量化和分析技术标准化的理论体系,它的发展方兴未艾。本文便是这一理论体系发展的继续。作者认为,在非调性音乐中,对集合类型之间关系的描述或解释,不应停留在相似性测度系统和集合复合形系统的水平上,而应继续进行更深入的研究,以抽象出具有共同子集特性的集合类型。他在论文中,把调查研究限定于音程级的极大值相似性范围之内:从ic极大值点出发,将其汇集成极大值点组;通过把ic向量转换成mm向量,以表明与每一极大值点成比例的ic涵量;最后,根据七个特定的mm向量模式来限定集合的较大家族,即区域。作者指出,在非调性音乐中,区域的分析可以通过较为直接而明确的方式表明结构的更高层次和细节。就我国的实际情况来看,除少数专家和学者之外,人们对音级集合理论体系在西方的发展状况及目前所达到的研究水平,仍较为陌生。因而,在运方面做一些介绍工作似乎是非常必要的。译者认为,对于此类在某种意义上标志着西方现代音乐研究水平的理论体系的深入了解和借鉴,对我国现阶段现代音乐理论研究走向规范化和定量化,有着十分重要的方法论意义。
Allen Forie’s 1973 book, “The Structure of Non-toned Musical Notes,” is a hallmark of the sounding class theory. For more than a decade, in modern music, the system has always played an important role both in the quantitative description of sound-level combinations and their relationships, and in the analysis of musical literature. As a theoretical system for the quantification and analysis of the marking system, its development is in the ascendant. This article is the continuation of the development of this theoretical system. The author believes that in the non-tonal music, the description of the relationship between the type of collection or explanation should not stay in the similarity measure system and set complex system level, but should continue to conduct more in-depth study to abstract out Collection types with common subset properties. In his dissertation, he confined the investigation to the range-of-range maximum similarity: starting from the point of maximum ic, it was assembled into a set of maximum points; by converting the ic vector into mm vector, Indicating the amount of ic content that is proportional to each maximum point; and finally, the larger family of the set, the region, is defined based on seven specific mm vector patterns. The author points out that in non-tonal music, the analysis of the area can indicate a higher level and detail of the structure in a more direct and definite way. Judging from the actual situation in our country, with the exception of a few experts and scholars, people are still unfamiliar with the development of the sound level theory system in the West and the level of research currently achieved. Therefore, it seems necessary to do some introductory work on the transport side. The translator believes that it is very important methodological significance for us to further understand and learn from such a theoretical system that in some sense marks the research level of modern western music and to standardize and quantify the study of modern music theory in our country at this stage.