S-Space College of Natural Sciences (자연과학대학) Dept. of Mathematical Sciences (수리과학부) Theses (Master's Degree_수리과학부)
Computational Analysis of Key and Harmony focusing on Bach’s Works
바흐의 작품을 중심으로 조와 화성에 대한 계산적 분석
- 자연과학대학 수리과학부
- Issue Date
- 서울대학교 대학원
- 학위논문 (석사)-- 서울대학교 대학원 : 자연과학대학 수리과학부, 2018. 2. 국웅.
- This study aimed to analyze key and harmony in music. Works by Johann Sebastian Bach are the main material of this study. Using works by Bach, the main target of analysis are three properties of keys. Major and minor is to observe differences of major keys and minor keys. Key characteristic is about characteristics of each major and minor key. Key distance is to check theoretical distance between keys.
Temperaments determine frequencies of pitches and affect harmony. Frequency ratios are the fundamental part to compute harmony in this study. The ratios were intentionally designed to analyze harmony in musical works and to check three properties of keys. Using them, vertical harmony (VH) and horizontal harmony (HH) were computed for each musical work, and their dispersion within a work was also defined and computed.
From the result of computation, this study answered three properties of keys. Major and minor was verified so that harmony in minor is 35% (47%) more intensive (more dispersed) then harmony in major. Key characteristic was too weak to be significant for both major and minor keys. Key distance was not realistic, being unsupported by computation.