Harmonic Analysis

Abstract: This chapter investigates the issue of the role of the computer,in musical analysis. Starting with a survey of the main approaches in computer analysis, we focus on the particular problem of Jazz chord sequences harmonic analysis. We propose a theory of chord sequence analysis, based on an explicit conceptual hierarchy of analysis objects. We discuss the implementation,of the theory

The regional and interanual variability of daily extreme temperature frequencies in Argentina from 1959 to 1998 was analysed. Maximum and minimum daily temperature series from more than 60 weather stations of all the country were used for this purpose. A quality control of the data was previously done. The results pointed out an important diminution of cold minimum temperature frequencies

The dynamic characteristics of an edge-emitting laser under large-signal modulation are analyzed in the frequency domain using a harmonic balance method on device level. The simulations reveal the nonlinearities of the carrier dynamics in the quantum well region which strongly influence the optical power in the higher harmonics.

The rapid increase in the size of databases required to store power quality monitoring data has demanded new techniques for analysing and understanding the data. One suggested technique to assist in analysis is data mining. Data mining is a process that uses a variety of data analysis tools to identify hidden patterns and relationships within large samples of data. This paper presents several data mining tools and techniques that are applicable to power quality data analysis to enable efficient reporting of disturbance indices and identify network problems through pattern recognition. This paper also presents results of data mining techniques applied to power quality data from an MV electrical distribution system to identify disturbance patterns.

By means of the model results, important harmonic constants of the tidal heights and currents, as well as the form factor, were computed. These results have revealed that there is a phase delay and an increase in amplitude of the major constituents as the tide ...

A new dynamic harmonic estimator is presented as an extension of the fast Fourier transform (FFT), which assumes a fluctuating complex envelope at each harmonic. This estimator is able to estimate harmonics that are time varying inside the obser- vation window. The extension receives the name "Taylor-Fourier transform (TFT)" since it is based on the McLaurin series expan- sion of

This paper presents the design and analysis of a parallel connected inverter configuration of. The configuration consists of parallel connected three-phase dc/ac inverter. Series resistors added to the inverter output to maintain same current in each inverter of the two parallel inverters, and to reduce the circulating current in the parallel inverters to the minimum. High frequency third harmonic injection PWM (THIPWM) employed to reduce the total harmonic distortion and to make maximum use of the voltage source. DSP was used to generate the THIPWM and the control algorithm for the converter. Selected experimental results have been shown to validate the proposed system.

Within the past decade, music-theoretical analysis of popular music has become increasingly common. Nonetheless, until quite recently the purview of such research has been relatively limited, focusing mainly on classic and art rock from the 1960s and 70s. While these repertoires have provided fertile ground for analytical exploration, several more recent genres and styles raise interesting structural, semiotic, and aesthetic questions that also merit study. One of the most distinctive types of contemporary popular music is electronic dance music, a broad category that includes styles such as techno, house, drum-n-bass, and trance. Electronic dance music differs from both rock and art music in a number of ways, all of which suggest avenues for productive theoretical investigation. While many genres of popular music are distinguished from each other on the basis of "surface" differences such as instrumentation or lyrical content, electronic dance music presents a distinctive overall formal structure in addition to its characteristic instrumentation. It also differs from most other types of Western music in its rejection of harmony as a primary musical parameter. Its use of pitch is typically restricted, with the majority of musical development taking place instead in the realms of rhythm, meter, texture, and timbre. Consequently, these areas should be principal concerns for the analyst wishing to pursue a close examination of musical sound in this repertoire. Rhythm provides an ideal starting point, as it seems to be the element to which listeners and fans of EDM relate most directly. This connection is most immediately apparent on the dance floor, where audiences physically enact the rhythms of the music. Written discussions of electronic dance music also tend to highlight its rhythmic qualities-references to its "unrelenting rhythm," "pulsing dance rhythms," and "irresistible tribal rhythm" are common (and fans often refer to the music simply as "beats" (as in, "let's go to the club and hear some beats"). Yet EDM poses a challenge to the analyst, for it differs in many ways from the repertoires that current music-theoretical models of rhythm and meter were developed to address. Transcription can give the impression that it is less complex rhythmically than these other bodies of music: although it typically consists of many different textural layers, each of which has a different rhythmic pattern, these patterns can appear quite simple when considered individually, and they repeat for long periods of time without changing. The

T I. INTRODUCTION HIS paper deals with some mathematical aspects of the discrete Fourier transform (DFT), studied with linear algebra and matrix theory methods. The vast majority of papers on the DFT have concerned computational issues, most notably the extensive literature ...

—The aim of this paper is to establish the boundedness of certain sublinear operators with rough kernel generated by Calder´on–Zygmund operators and their commutators on generalized Morrey spaces under generic size conditions which are satisfied by most of the operators in harmonic analysis. The Marcinkiewicz operator which satisfies the conditions of these theorems can be considered as an example.

The growing demand for electricity makes the power grid ever expanding day by day and more and more complex. There is a potential requirement to continuously monitor the power grid and thus making it smarter and reliable. Traditional measurement systems are getting replaced by PMUs, which enables the online monitoring of the power system. With the aid of GPS, PMUs can measure the phasor values of voltages at the bus, where it is placed and the current through the branches connected to that bus. The Current measurement enables us to estimate the voltages at the neighbouring buses. Because of this, placing PMUs at all buses for the complete monitoring of the power system is redundant. Finding the optimal locations of PMUs to make the power system completely observable is of great research interest. This paper proposes the optimal locations of PMU in Tamil Nadu state of Indian power grid using ILP. PMU placement problem has been formulated and optimization has been carried out. Results showing the various optimal locations are tabulated.

At the point of common coupling (PCC), the summation of two harmonic voltage vectors at same frequency is only certain if their amplitudes and phase angles are well known. Therefore, there are many cases where the phase angle difference between harmonic voltage vectors is unknown. In practice, for example, in calculating the steady state rating of the a.c. passive harmonic filter, arithmetic summation method is often used in determining maximal harmonic level. This summation law is very conservative as it may result in high cost of equipment ratings. Actually, a compromise should be made in taking into account the equipment safety and the risk of overrating as well as excessive costs. Based on uniform distribution of difference in phase angles, the paper provides an algorithm to calculate the probability upon which the magnitude of summation vector of two harmonic voltages may exceed a given value. On the basis of the probability and the given harmonic value, harmonic summation can be assessed. This may also result in a recommendation of another harmonic summation method for the standard IEC/TR 61000-3-6.

Musical genres are categorical labels characterizing pieces of music. Automatically classifying music into genres is gaining importance as a way to structure and organize the increasingly large numbers of music files available digitally on the web. In this work such a classification algorithm is developed and examined. The algorithm uses a vector of features based on the timbral texture of the music, and maps it into a new Euclidean space, by a non-linear method called “Diffusion Maps”, before the classification stage itself. This method allows dimensionality reduction while preserving and emphasizing the distinction between different genres. The proposed classifier classifies accurately 97% when classifying 2 musical genres, and 52% when classifying 10 musical genres. This is compared to an accuracy of 88% and 28% respectively, when classifying without the proposed mapping.

Nowadays, it is a general trend to increase the electricity production using distributed power generation systems (DPGS) based on renewable energy resources such as wind, sun or hydrogen. Jf these systems are not properly controlled, their connection to the utility network can generate problems on the grid side. Therefore, considerations about power generation, safe running and grid synchronization must be done before connecting these systems to the utility network. This paper is mainly dealing with the grid synchronization issues of distributed systems. An overview of the synchronization methods as well as their major characteristics is given. New solutions to optimize the synchronization methods when running on distorted grid conditions are discussed. Simulation and experimental results are used to evaluate the behavior of the synchronization methods under different kind of grid disturbances such as voltage dips, harmonics and notches.

This paper focuses on I2R losses under nonsinusoidal conditions, mainly in cables and transformers. For this purpose, a mathematical development that takes in account the presence of harmonic components in the I2R losses calculation will be presented, so that the effects of the harmonic distortion in the power system components and consequently the impact on the power factor can be analyzed. Based on this study, a factor that evaluates the power quality performance in low voltage networks is presented. This factor is directly associated to the economical viability, once that it points when the losses minimization is interesting according to the cost/benefit ratio.

How does rock harmony differ from that of the common practice? As several recent writings have shown, motions between individual chords-that is, functional behaviors-are often vastly different from that of the common practice. 1 Precisely how these and other harmonic differences coalesce to form surface-level progressions that depart from common-practice conventions, however, is a question that has been approached only peripherally. 2 With an emphasis on the classic-rock canon of the late 1960s through the 1980s, this article therefore investigates rock harmony from the larger perspective of the progression in an attempt to paint a more detailed picture of rock's idiosyncratic harmonic syntax. In particular, classifying triads as Tonic, Dominant, or Subdominant based largely on the similarity of their scale-degree content, or functional "kinship," reveals three central aspects of rock progressions. 3 First, they do not constrain the functional motion of their chords. In other words, unlike the TSDT paradigm of the common practice, the kinship functions of Subdominant and Dominant both move regularly to each other and to Tonic-functioned harmonies. Thus, there is no single kinship-functional paradigm that encompasses most rock progressions; rather, two paradigms appear more than any other: the authentic and plagal (described in more detail further below). Second, rock progressions that diverge from the common practice, which feature in the vast majority of songs, do so in two ways: by the ordering of the kinship functions into a form of the plagal paradigm, and/or by secondary triads that are unusual by common-practice norms, namely subtonic and mediant triads. Third, even when there appear secondary triads that are more typical by common-practice norms, namely submediant and supertonic triads, their behavior is often in opposition to those norms. This article will examine these elements of rock harmony in two parts. The first and larger part will establish a number of definitions necessary to parse progressions by their functional kinship. These include harmonic function, tonic perception, scale-degree assemblies, progressions, and types of progressions. The second part of the article will apply these definitions to a wide range of specific examples and generalizations in order to demonstrate how progressions in rock differ from those of the common practice. 1 See Nobile 2016, Quinn and White 2015, Doll 2007, and Stephenson 2002 (ch. 5). 2 Moore 2012 (71-79) views rock progressions as strongly modal, offering a flexible system for their analysis. Moore 1992 has also catalogued an extensive list of rock progressions by prominent root motions. Everett 2009 (214-301) offers a similarly-organized, comprehensive examination of rock progressions but, to categories based on root motions, he adds others based on contrapuntal motions, minor keys, modes, and chromaticism rather than by their distance from common-practice norms. De Clercq and Temperley 2011 provide a glimpse into some of rock's common "trigrams," which are three-chord successions that may occur across any perceptual boundaries rather than progressions that have a discernible beginning and end. And Biamonte 2010 is devoted to three rock-specific categories of harmonic progression: the double-plagal progression, the Aeolian progression, and modal scales thickened by harmonization in parallel triads. See also Biamonte 2012 for an extension of some of these ideas. 3 Following Harrison 1994, I capitalize the names of kinship functions (Tonic, Dominant, Subdominant) in order to distinguish them from specific triads with the same names, which remain uncapitalized.

Background One of the most important principles of tonal theory is that of harmonic syntax. This principle contains the norms of precise logical order in the succession of harmonic functions or chords in any harmonic progression in tonal music (Riemann 1893; Caplin 1998; Schenker 1954; Cadwallader and Gagne 1998; Aldwell, Schachter, and Cadwallader 2011). Such norms are shaped and determined by the frequency of specific harmonic progressions, which generate expectations in the listener acquainted with Western Classical tonal music; if the progression of chords tonic-dominant, for instance, is more common than the progressions tonic-subdominant and tonic-submediant, every occurrence of the tonic chord will generate the expectation of dominant rather than subdominant or submediant harmony. Tonal harmonic syntax is characterised by the distinct syntactical tendencies of each chord, determined principally by fifth and ascending-step (or half-step) root progressions.

In this paper, a high efficiency C-band GaN HEMT high power amplifier with internal harmonic manipulation circuits is presented. We employed a new circuit topology for simultaneous high efficiency matching at both fundamental and 2nd-harmonic frequencies. The developed GaN HEMT amplifier has achieved over 57% drain efficiency (50% power-added-efficiency) with 100 W output power at C-band. This is the state-of-the-art efficiency of GaN HEMT high power amplifier at C-band to the best of our knowledge.

My purpose with the article is to help you to find your parameter settings and find the best way that can help you to utilize this very complex and complete indicator to prosper. See the list of its parameters below in this article. Enjoy! Starting from ZUP v 150 new addition; being able to mark Elliott waves on the chart and have an easier GUI (graphical user interface) helping users. The development of ZUP took place over a decade. There is no question about how much effort, hard work and contribution of lot of traders went into this development. Due to this, ZUP was and is one of the most popular harmonic pattern indicators.
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