장단조혼용 기법의 재조명 : 화성분석을 위한 실제적 접근

박재성 이화여자대학교 음악연구소 2009 이화음악논집 Vol.13 No.2

“장단조혼용”(mode mixture) 기법은 조성음악의 화성 기법들 중에서 고도의 색채적인 기법일 뿐만 아니라 조성 체계의 쇠퇴를 야기시킨 직접적인 화성 기법이다. 이외에도 이 기법은 전조의 영역을 확대시킬 뿐만 아니라 오페라를 포함한 성악곡에서는 가사의 의미 전달에도 큰 역할을 한다. 장단조혼용 기법은 바하의 작품에서도 사용되었을 뿐만 아니라 바그너의 작품에서도 중요한 화성 기법이다. 이러한 점에서도 이 기법은 “화음의 사용법” 이상의 의미를 지니며, 재조명되어 화성 분석 및 화성학 강의를 위해 더욱 실용화되어야 할 것이다. 본 논문에서는 장단조혼용 기법의 심층 연구를 통하여 이 기법의 세부 분류를 시도하고, 이러한 개념을 응용한 화성분석 기법을 개발을 시도하였다. 모두 여섯 개의 장으로 구성된 본 논문은 첫 장의 서론과 마지막 장의 결론을 제외한 네 개의 장이 본론으로 되어 있다. 본론의 첫 장에서는 장단조혼용 기법의 정의와 범위가 설정되었고, 이어서 차용화음의 분류와 표기법이 제시되었다. 다음 장에서는 장단조혼용 기법이 기능별로 일곱 가지로 분류되었는데 이 장은 장단조혼용 기법을 화성분석에 직접적으로 접근시키기 위해 마련된 장이다. 본론의 마지막 장에서는 차용화음군을 다른 두 종류의 반음계적 화음, 즉 증6화음군과 나폴리6화음군과 비교하고 있다. Mode Mixture is not only a highly developed device for harmonic uses but also a harmonic technique which actually leads to the weakening of tonal system. Also this technique extends the modulatory limits and plays an important role to communicate the meaning of vocal songs including operas. The technique of mode mixture is a very important harmonic technique used in the works of J. S. Bach through Richard Wagner. Thus mode mixture has significance in more than a simple harmonic use and has to be developed practically to the lectures for harmony and harmonic analysis. The present article aims to categorize mode mixture techniques in more detail and explore devices for harmonic analysis in the viewpoint of the notion of mode mixture. The present author makes an attempt in this article at practical approach to and classification both for practice and scholarship. Harmonic analysis, in substance, does not aim at identifying chord names. It is a task to understand harmonic progressions based on the single or individual chord, and analyze their relationships between the harmonic progression and the structure of music. As is the main work for music analysis to simplify musical composition, harmonic analysis also the work to simplify the harmonic progressions of the composition. Harmonic analysis considers, in addition to the simplification to harmonic progression, harmonic connections and interrelation with melodic elements. Thus the firsst stage for harmonic analysis is, based on this notion, to prepare harmonic reduction. Most of the music examples in the present article provide harmonic reduction score for analysis. Chords by mode mixture, the borrowed chords, do not have their own chord names comparing to those of augmented chords or Neopolitan chord, although the mode mixture chords have the same level of importance with those chords. The present article provides particular chord names to the borrowed chords such as M1, M2, M3, M4, M6, M7, L. This methods makes it easier to identify the borrowed chords for practical uses in harmonic analysis.

로마숫자를 통한 화성분석의 효용성을 위한 제언

송무경 한양대학교 음악연구소 2012 音樂論壇 Vol.28 No.-

The present research begins by examining the harmonic analysis by Roman numerals, which has been settled down as a most rudimentary way of music analysis in the undergraduate curriculum, and furthermore explores diverse ways of increasing its analytic validity by modifying and supplementing its concepts and notations. In spite of its crucial role, the Roman numeral analysis has been regarded merely as a labeling tool in its initial stage of analysis, not a systematized theory that has logical assumptions and hypotheses. The goal of this article is to propose a systematic and comprehensive method of tonal music analysis by taking useful concepts of the Schenkerian theory and applying them to the Roman numeral analysis. For this task, I will review undergraduate textbooks dealing with harmony and analysis and then explore what subsidiary symbols other than Roman numerals the authors of the textbooks devise and introduce in order to supplement the Roman numeral analysis. Second, I will first explore possible ways of carrying out the layered analysis using Roman numerals by referring to Neumeyer and Tepping’s didactic tutorial of the Schenkerian theory. Finally,I will assess validity of the methodology by contemplating an ultimate goal of harmonic analysis, in which prototypical structural harmonic progressions based on the cadential axiom and its elaboration and expansion are revealed in the analytic practice. 본 논문은 로마숫자를 통한 조성음악 분석의 효율적인 방법론을 제안을 목표로하는 실용적 성격의 글이다. 필자는 국내외에서 최근 10여년 이상 꾸준히 사용되어 왔던 화성법 및 분석 교재들을 비판적으로 검토하고 로마숫자가 단순한 명명방법이 아닌 보다 체계적인 분석 방법론으로 자리매김할 수 있는 방안을 모색하였다. 이를 위해 필자는 샤흐터(Carl Schachter)와 앨드웰(Edward Aldwell),Harmony and Voice Leading, 코스카(Stefan Kostka)와 페인(Dorothy Payne),Tonal Harmony with an Introduction to Twentieth-Century Music, 골딘(Robert Gauldin), Harmonic Practice in Tonal Music, 백병동 『화성학』, 김홍인 『화성』,허영한·한미숙 『조성음악의 화성진행』, 송무경 『연주자를 위한 조성음악분석』에서 전제하고 있는 기본화음(3화음, 7화음), 로마숫자 표기법, 그리고 통사론에대한 취급 방법 등에 대해 살펴보고 비교하였으며, 로마숫자를 보완하는 기호들을 검토하고 그 의미에 대해 고찰하였다. 또한 각 교재들이 제시하는 장점을 취하여 실제 분석에 적용함으로써 분석적 가능성을 탐구하였다.

Complex harmonic modal analysis of rotor systems

한동주 대한기계학회 2015 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.29 No.7

Complex harmonic analysis for rotor systems has been proposed from the strict complex modal analysis based upon Floquet theory. Inthis process the harmonic balance method is adopted, effectively associated with conventional eigenvalue analysis. Also, the harmoniccoefficients equivalent to dFRFs in harmonic mode has been derived in practice. The modes are classified from identifying the modalcharacteristics, and the adaptation of harmonic balance method has been proven by comparing the results of the stability analyses fromFloque theory and the eigen analysis. The modal features of each critical speed are depicted in quantitatively and qualitatively by showingthat the strengths of each component of the harmonic coefficients are estimated from the order of magnitude analysis according totheir harmonic patterns. This effectiveness has been verified by comparing with the numerical solutions.

조류 조화상수의 월변동성 완화 방법 고찰

변도성 한국해양과학기술원 2011 Ocean and Polar Research Vol.33 No.3

This is a preliminary study of the feasibility of obtaining reliable tidal current harmonic constants, using one month of current observations, to verify the accuracy of a tidal model. An inference method is commonly used to separate out the tidal harmonic constituents when the available data spans less than a synodic period. In contrast to tidal constituents, studies of the separation of tidal-current harmonics are rare, basically due to a dearth of the long-term observation data needed for such experiments. We conducted concurrent and monthly harmonic analyses for tidal current velocities and heights, using 2 years (2006 and 2007) of current and sea-level records obtained from the Tidal Current Signal Station located in the narrow waterway in front of Incheon Lock, Korea. Firstly, the l-year harmonic analyses showed that, with the exception of M2 and S2 semidiurnal constituents, the major constituents were different for the tidal currents and heights. K1, for instance, was found to be the 4th major tidal constituent but not an important tidal current constituent. Secondly, we examined monthly variation in the amplitudes and phase-lags of the S2 and K1 current-velocity and tide constituents over a 23-month period. The resultant patterns of variation in the amplitudes and phase-lags of the S2 tidal currents and tides were similar, exhibiting a sine curve form with a 6-month period. Similarly, variation in the K1 tidal constant and tidal current-velocity phase lags showed a sine curve pattern with a 6-month period. However, that of the K1 tidal current-velocity amplitude showed a somewhat irregular sine curve pattern. Lastly, we investigated and tested the inference methods available for separating the K2 and S2 current-velocity constituents via monthly harmonic analysis. We compared the effects of reduction in monthly variability in tidal harmonic constants of the S2 currentvelocity constituent using three different inference methods and that of Schureman (1976). Specifically, to separate out the two constituents (S2 and K2), we used three different inference parameter (i.e. amplitude ratio and phase-lag diggerence) values derived from the 1-year harmonic analyses of current-velocities and tidal heights at (near) the short-term observation station and from tidal potential (TP), together with Schureman's (1976) inference (SI). Results from these four different methods reveal that TP and SI are satisfactorily applicable where results of long-term harmonic analysis are not available. We also discussed how to further reduce the monthly variability in S2 tidal current-velocity constants.

Analysis on Harmonic Loss of IPMSM for the Variable DC-link Voltage through the FEM-Control Coupled Analysis

Park, Hyun Soo,Jeung, Tae Chul,Lee, Jae Kwang,Lee, Byoung Kuk The Korean Institute of Electrical Engineers 2017 Journal of Electrical Engineering & Technology Vol.12 No.1

This paper describes the loss analysis based on load conditions of the air conditioning compressor motors using variable dc-link voltage. The losses of PMSM (Permanent Magnet Synchronous Motor) should be analyzed by the PWM (Pulse Width Modulation) output of inverter. The harmonic loss by the PWM cannot consider that using the current source analysis of the inverter. In addition, when the voltage of dc-link is variable with the condition of variable speed and load conditions in motor, the losses of motor are also changeable, however it is hard to analyze those losses by only electromagnetic finite element method (FEM). Therefore, this paper proposes the analysis method considering the carrier frequency of the inverter and the varying state of the dc-link voltage through the FEM-control coupled analysis. Using proposed analysis method, additional core loss and eddy current loss of permanent magnet caused by PWM could be analyzed. Finally, the validity of the proposed analysis method is verified through the comparison the result of coupled analysis with experiment.

Analysis on Harmonic Loss of IPMSM for the Variable DC-link Voltage through the FEM-Control Coupled Analysis

Hyun Soo Park,Tae Chul Jeung,Jae Kwang Lee,Byoung Kuk Lee 대한전기학회 2017 Journal of Electrical Engineering & Technology Vol.12 No.1

This paper describes the loss analysis based on load conditions of the air conditioning compressor motors using variable dc-link voltage. The losses of PMSM (Permanent Magnet Synchronous Motor) should be analyzed by the PWM (Pulse Width Modulation) output of inverter. The harmonic loss by the PWM cannot consider that using the current source analysis of the inverter. In addition, when the voltage of dc-link is variable with the condition of variable speed and load conditions in motor, the losses of motor are also changeable, however it is hard to analyze those losses by only electromagnetic finite element method (FEM). Therefore, this paper proposes the analysis method considering the carrier frequency of the inverter and the varying state of the dc-link voltage through the FEM-control coupled analysis. Using proposed analysis method, additional core loss and eddy current loss of permanent magnet caused by PWM could be analyzed. Finally, the validity of the proposed analysis method is verified through the comparison the result of coupled analysis with experiment.

Resonance Characteristics Analysis of Grid-connected Inverter Systems based on Sensitivity Theory

Jian Wu,Wanqin Han,Tao Chen,Jiaqi Zhao,Binbin Li,Dianguo Xu 전력전자학회 2018 JOURNAL OF POWER ELECTRONICS Vol.18 No.3

Harmonic resonance exists in grid-connected inverter systems. In order to determine the network components that contribute to harmonic resonance and the composition of the resonant circuit, sensitivity theory is applied to the resonance characteristic analysis. Based on the modal analysis, the theory of sensitivity is applied to derive a formula for determining the sensitivities of each network component parameter under a resonance circumstance that reflects the participation of the network component. The solving formula is derived for both parallel harmonic resonance and series harmonic resonance. This formula is adopted to a 4-node grid-connected test system. The analysis results reveal that for a certain frequency, the participation of parallel resonance and series resonance are not the same. Finally, experimental results demonstrate that the solving formula for sensitivity is feasible for grid-connected systems.

Analysis on Harmonic Loss of IPMSM for the Variable DC-link Voltage through the FEM-Control Coupled Analysis

박현수,정태철,이재광,이병국 대한전기학회 2017 Journal of Electrical Engineering & Technology Vol.12 No.1

This paper describes the loss analysis based on load conditions of the air conditioning compressor motors using variable dc-link voltage. The losses of PMSM (Permanent Magnet Synchronous Motor) should be analyzed by the PWM (Pulse Width Modulation) output of inverter. The harmonic loss by the PWM cannot consider that using the current source analysis of the inverter. In addition, when the voltage of dc-link is variable with the condition of variable speed and load conditions in motor, the losses of motor are also changeable, however it is hard to analyze those losses by only electromagnetic finite element method (FEM). Therefore, this paper proposes the analysis method considering the carrier frequency of the inverter and the varying state of the dc-link voltage through the FEM-control coupled analysis. Using proposed analysis method, additional core loss and eddy current loss of permanent magnet caused by PWM could be analyzed. Finally, the validity of the proposed analysis method is verified through the comparison the result of coupled analysis with experiment.

An Analysis Method of Harmonic Transfer Characteristics From AC-side to DC -side of Modular Multilevel Converter

Pengfan Xu,Yue Wang,Taiyuan Yin,Shiyuan Yin,Zhang Wang,Kai Li 전력전자학회 2019 ICPE(ISPE)논문집 Vol.2019 No.5

With the development of new energy sources, more and more isolated islands are interconnected to grid through MMC. However, isolated islands systems are easily influenced by harmonic disturbances. The analytical analysis of the harmonic transfer characteristics between AC/DC side of the Modular Multilevel Converter (MMC) is of great significance for understanding the harmonic issues and stability analysis. In this paper, the quantitative analysis method of the harmonics on the DC-side excited by the AC-side harmonics of MMC is presented in this paper. First, the influence of harmonics on MMC electric system and control system is analyzed. Second, the equivalent MMC harmonic transfer model is established based on the average switching function. Finally, the analytical expression of DC-side harmonic transferred from AC-side is derived. A 232-level simulation model was built in MATLAB/Simulink. The accuracy and validity of the proposed analytical expression were verified by comparing the simulation results with the analytical results.

리저버 탱크의 Die Turning Injection 적용을 위한 Multi-field CAE 해석

이성희,Lee, Sung-Hee 한국금형공학회 2021 한국금형공학회지 Vol.15 No.1

In this study, die turning injection(DTI) mold design for manufacturing reservoir fluid tanks used for cooling in-vehicle batteries, inverters, and motors was conducted based on multi-field CAE. Part design, performance evaluation, and mold design of the reservoir fluid tank was performed. The frequency response characteristics through modal and harmonic response analysis to satisfy the automotive performance test items for the designed part were examined. Analysis of re-melting characteristics and structural analysis of the driving part for designing the rotating die of the DTI mold were performed. Part design was possible when the natural frequency performance value of 32Hz or higher was satisfied through finite element analysis, and the temperature distribution and deformation characteristics of the part after injection molding were found through the first injection molding analysis. In addition, it can be seen that the temperature change of the primary part greatly influences the re-melting characteristics during the secondary injection. The minimum force for driving the turning die of the designed mold was calculated through structural analysis. Hydraulic system design was possible. Finally, a precise and efficient DTI mold design for the reservoir fluid tank was possible through presented multi-field CAE process.