在蒙德里安架構下闡釋音樂和弦

本文提出用聽覺的蒙德里安架構來闡釋音樂和弦的本質。在此蒙德里安架構裡，音符被視爲聽覺的基本形式美。而音樂和弦則由同時演奏的音符組成，但此組合會受到協和音與不協和音的限制。傳統上，協和音與不協和音是透過人耳來主觀認定的。事實上，生理學裡的臨界頻寬才是這些限制的來源，而判別音樂和弦的詳細分析需要涉及複雜的計算。相對於這兩者，本文提出使用神經圖來做爲判別音樂和弦的主要分析工具。這裡分成三步驟來解釋此新的神經圖方法。首先分析不協和音、拍音與臨界頻寬的關係。特別是強調不同兩音符的臨界頻寬形成之理論基礎。其次將這些研究成果擴充至說明協和音程與不協和音程的形成原因。再客觀地判斷與找出所對應神經圖的各項特徵。最後則將這些找出來的特徵運用來判別音樂和弦，像是三和弦、複合三和弦等的分析。這些新的研究成果不只縮短了分析流程，更豐富了聽覺蒙德里安架構的內容。

關鍵字

蒙德里安架構；和弦；協和音；神經圖

並列摘要

A Mondrian framework on listening is proposed for exploring the essence of musical chords. Within this framework, notes are treated as the basic forms of beauty for listening. Also a musical chord essentially consists of a combination of simultaneous notes, but this combination is under consonance and dissonance constraints. Traditionally consonant and dissonant sounds are subjectively identified through human ears. In fact, critical bandwidth from a biological viewpoint is the main reason why the constraints come, and a detailed analysis of identifying musical chord needs complicated computations. Instead of both approaches, neurogram is used as a main analytical tool in this paper for identifying musical chords. Three stages are involved for explaining the new neurogram approach. First, the relationship among dissonances, beats, and critical bandwidths is analyzed. Especially the theoretical foundation of critical bandwidth formation between two different notes is emphasized. Second the research results are naturally extended to the consonant and dissonant intervals. Then the characteristic features of the corresponding neurograms are identified and extracted objectively. Third the extracted features of neurograms are applied for identifying musical chords such as triads, doubling triads, etc. This new research results not only shorten the analytical process but also enrich the Mondrian framework on listening.