Achorripsis를 중심으로 한 Xenakis의 추계학적 음악 연구 = A Study of Xenakis's Stochastic Music : focused on Achorripsis

국문 초록 (Abstract)

본 논문은 작곡가이자 건축가인 이안니스 크세나키스가 독자적으로 구축한 추계학적 음악을 작품Achorripsis를 중심으로 연구하였다.
크세나키스는 이 작품의 길이를 일정한 28개의 시간 단위로 구성하였으며, 각각의 시간 단위 안에서 악기의 음색적 특징에 따라 서로 다른 7개의 음색층을 배치하였다. 또한, 각 시간 단위 안에서 평균적으로 발생한 소리의 빈도를 밀도의 개념으로 취급하여 이를 다섯 가지 밀도(Zero sound event, Single sound event, Double sound event, Triple sound event, Quadruple sound event)로 구분하였다. 각각의 시간 단위는 7개의 음색층 중 아무런 음색을 가지지 않거나 하나 혹은 복수의 음색을 가질 수 있는데, 이 때에 선택된 개별의 음색층은 또다시 어떠한 밀도를 가질지 정할 수 있다. 이에 대한 모든 결정은 확률에 관련한 수학 공식인 푸아송 분포의 계산을 통하여 이루어졌다.
본 연구는 이 곡의 핵심을 이루는 매트릭스M의 생성 과정을 살펴보고 이를 통한 결과물인 악보를 그 과정과 면밀히 비교하였다. 매트릭스M의 생성 과정은 엄격히 추계적인 방법을 따르고 있지만, 작품의 실제 예를 악보와 함께 구체적으로 비교해보면 매트릭스M안에서 결정된 사항이 완벽히 지켜지고 있지는 않다는 것을 알 수 있다. 그 이유는 작품을 만드는 과정 자체에 작곡가의 자유 의지가 존재하며 이는 예술가적인 영감에 의한 것이라고 해석된다.

다국어 초록 (Multilingual Abstract)

This thesis was to investigate stochastic music by focusing on the piece Achorripsis, which was independently established by composer and architect Iannis Xenakis.
Xenakis formulated this piece with 28 fixed time units, placing seven different layers of sound within each unit according to the instrument’s distinct timbres. In addition, the frequency of sounds within each time unit was regarded as density and classified into five categories (i.e., zero, single, double, triple, and quadruple events). Each time unit may have no sound(no timbres) or multiple timbres within the seven layers, and each selected layer may determine its own density. Such decisions were all made through the mathematical formula of the Poisson distribution which is related to probability.
This study examined the process of forming Matrix M, the core of the piece. The outcome of the process was compared with the score. The formation of Matrix M strictly adheres to stochastic methods. However, we can observe by comparing the details of Matrix M within the score as a whole that this was not followed for the entirety of the composition. The interpretation is that the reason lies in the fact that the composer’s free will is also a key piece of the process when forming a musical piece and the process results are the outcome of artistic inspiration.

목차 (Table of Contents)

• 차 례
• 국문요지 ······················································································ viii
• 제1장 서론 ····················································································· 1
• 제1절 연구 목적 ··········································································· 3
• 제 2절 연구 방법 ·········································································· 5
• 제 2장 본론 ··················································································· 7
• 제1절 크세나키스의 생애와 음악····················································· 7
• 1-1생애······················································································ 8
• 1-2 작곡 기법 ··········································································· 11
• 제 2절 Achorripsis 분석 ····························································· 12
• 2-1 매트릭스M ········································································ 13
• 2-2 푸아송 분포 ········································································· 15
• 0. 28개 세로열에서의 소리 사건의 빈도 분배에 관한 논의 ············· 25
• 1. 28개 세로열에 대한 Single events 의 계산 ······························· 27
• 2. 28개 세로열에 대한 Zero events 의 계산 ································· 29
• 3. 28개 세로열에 대한 Double events의 계산 ····························· 31
• 4. 28개 세로열에 대한 Triple events 의 계산 ······························· 31
• 5. 28개 세로열에 대한 Quadruple events 의 계산 ·························· 32
• 6. 7개 가로행에 대한 Zero events 의 계산··································· 36
• 7. 7개 가로행에 대한Single events 의 계산································· 38
• 8. 7개 가로행에 대한Double events 의 계산································ 39
• 9. 7개 가로행에 대한Triple events 의 계산 ································ 40
• 10. 7개 가로행에 대한Quadruple events 의 계산···························· 41
• 2-3 밀도 ··················································································· 47
• 2-4 악보 분석 ············································································ 53
• 1. 셀1 ··············································································· 66
• 2. 셀8 ··············································································· 68
• 3. 셀10 ············································································ 69
• 4. 셀21 ············································································ 75
• 5. 셀25 ············································································ 78
• 제 3장 결론··················································································84
• 참고문헌 ···················································································· 86
• Appendix ··················································································· 88
• 작품 목록 ··················································································· 88
• 주요 저서 ·················································································· 92
• Abstract ····················································································· 93