Journal articles: 'Harmonic partials'

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Fine, Philip A., and Brian C. J. Moore. "Frequency Analysis and Musical Ability." Music Perception 11, no. 1 (1993): 39–53. http://dx.doi.org/10.2307/40285598.

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Soderquist (Psychonomic Science, 1970, 21,117–119) found that musicians were better than nonmusicians at separating out ("hearing out") partials from complex tones and proposed that this might be explained by the musicians having sharper auditory filters. In Experiment 1, the auditory filters of two groups, musicians and nonmusicians, were measured at three center frequencies by using a notched-noise masker. The filters were found not to differ in bandwidth between the two groups. However, the efficiency of the detection process after auditory filtering was significantly different between the two groups: the musicians were more efficient. In Experiment 2, the ability to hear out partials in a complex inharmonic tone was measured for the same two groups, using a tone produced by "stretching" the spacing between partials in a harmonic complex tone. Unfortunately, most of the nonmusicians were unable to perform this task. The ability of the musicians to hear out partials was not significantly correlated with the auditory filter bandwidths measured in Experiment 1. The musicians were also tested on the original harmonic complex tone (before "stretching"). For some partials, their performance was better for the inharmonic tone, reflecting the fact that the separation of the partials in frequency was greater for that tone. However, it was also found that those partials that were octaves of the fundamental in the harmonic series were identified better than corresponding partials in the inharmonic tone.

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Nicholson, Thomas, and Marc Sabat. "FAREY SEQUENCES MAP PLAYABLE NODES ON A STRING." Tempo 74, no. 291 (December 19, 2019): 86–97. http://dx.doi.org/10.1017/s0040298219001001.

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AbstractNatural harmonics, i.e. partials and their harmonic series, may be isolated on a vibrating string by lightly touching specific points along its length. In addition to the two endpoints, stationary nodes for a given partial n present themselves at n − 1 locations along the string, dividing it into n parts of equal length. It is not the case, however, that touching any one of these nodes will necessarily isolate the nth partial and its integer multiples. The subset of nodes that will activate the nth partial (termed playable nodes by the authors) may be derived by following a mathematically predictable pattern described by so-called Farey sequences. The authors derive properties of these sequences and connect them to physical phenomena. This article describes various musical applications: locating single natural harmonics, forming melodies of neighbouring harmonics, sounding multiphonic aggregates, as well as predicting the relative tuneability of just intervals.

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de Cheveigné, Alain. "Harmonic fusion and pitch shifts of mistuned partials." Journal of the Acoustical Society of America 102, no. 2 (August 1997): 1083–87. http://dx.doi.org/10.1121/1.419612.

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Tervaniemi, M., T. Ilvonen, J. Sinkkonen, A. Kujala, K. Alho, M. Huotilainen, and R. Näätänen. "Harmonic partials facilitate pitch discrimination in humans: electrophysiological and behavioral evidence." Neuroscience Letters 279, no. 1 (January 2000): 29–32. http://dx.doi.org/10.1016/s0304-3940(99)00941-6.

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Moore, Brian C. J., Brian R. Glasberg, and Robert W. Peters. "Thresholds for hearing mistuned partials as separate tones in harmonic complexes." Journal of the Acoustical Society of America 80, no. 2 (August 1986): 479–83. http://dx.doi.org/10.1121/1.394043.

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Dai, Huanping. "Harmonic pitch: Dependence on resolved partials, spectral edges, and combination tones." Hearing Research 270, no. 1-2 (December 2010): 143–50. http://dx.doi.org/10.1016/j.heares.2010.08.002.

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Brunstrom, Jeffrey M., and Brian Roberts. "Profiling the perceptual suppression of partials in periodic complex tones: Further evidence for a harmonic template." Journal of the Acoustical Society of America 104, no. 6 (December 1998): 3511–19. http://dx.doi.org/10.1121/1.423934.

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Milne, Andrew J., Robin Laney, and David B. Sharp. "Testing a spectral model of tonal affinity with microtonal melodies and inharmonic spectra." Musicae Scientiae 20, no. 4 (August 1, 2016): 465–94. http://dx.doi.org/10.1177/1029864915622682.

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Tonal affinity is the perceived goodness of fit of successive tones. It is important because a preference for certain intervals over others would likely influence preferences for, and prevalences of, “higher-order” musical structures such as scales and chord progressions. We hypothesize that two psychoacoustic (spectral) factors—harmonicity and spectral pitch similarity—have an impact on affinity. The harmonicity of a single tone is the extent to which its partials (frequency components) correspond to those of a harmonic complex tone (whose partials are a multiple of a single fundamental frequency). The spectral pitch similarity of two tones is the extent to which they have partials with corresponding, or close, frequencies. To ascertain the unique effect sizes of harmonicity and spectral pitch similarity, we constructed a computational model to numerically quantify them. The model was tested against data obtained from 44 participants who ranked the overall affinity of tones in melodies played in a variety of tunings (some microtonal) with a variety of spectra (some inharmonic). The data indicate the two factors have similar, but independent, effect sizes: in combination, they explain a sizeable portion of the variance in the data (the model-data squared correlation is r2 = .64). Neither harmonicity nor spectral pitch similarity require prior knowledge of musical structure, so they provide a potentially universal bottom-up explanation for tonal affinity. We show how the model—as optimized to these data—can explain scale structures commonly found in music, both historical and contemporary, and we discuss its implications for experimental microtonal and spectral music.

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Rupprecht, Philip. "ABOVE AND BEYOND THE BASS: HARMONY AND TEXTURE IN GEORGE BENJAMIN'S ‘VIOLA, VIOLA’." Tempo 59, no. 232 (April 2005): 28–38. http://dx.doi.org/10.1017/s0040298205000136.

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George Benjamin's rich harmonic imagination was apparent from his earliest published works. A distinctive chordal sensibility is already evident in the 1978 Piano Sonata, with its glittering streams of five- or six-pitch clusters; in the hollow bell-chords punctuating the 1979 orchestral score, Ringed by the Flat Horizon; and in the supreme stasis of the A-minor pedal chord (a six-three triad) unveiled by the icy glissandi lines opening A Mind of Winter (1981). All three pieces share a fascination with degrees of chordal resonance – the interplay of upper partials above a fundamental – and a sensitivity to chords as sound objects. True, Benjamin's style, beginning at least with Antara (1987), has shown signs of a more linear-contrapuntal orientation, and less reliance on what one critic terms ‘purely coloristic phenomena’. Yet one could equally claim some continuity between the refined harmonic world of the early scores and the surprising richness of chordal sonority to be heard in a far more recent arrival, the 1997 duo Viola, Viola.

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Walter, Caspar Johannes. "MULTIPHONICS ON VIBRATING STRINGS." Tempo 74, no. 291 (December 19, 2019): 7–23. http://dx.doi.org/10.1017/s0040298219000950.

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AbstractMultiphonics on vibrating strings have been an important element in my compositions since the early 1990s. In order to calculate the frequency components of so-called pure multiphonics (multiphonics consisting of harmonic partials of the fundamental) on vibrating strings, I developed my fraction windowing algorithm. The first section of this article details the use of multiphonics in my compositions and the second section discusses how the fraction windowing algorithm works and its relationship to the closely related mathematical concept of a continued fraction. The article also discusses the online apps I have developed as tools for composers and performers who are interested in using these methods in their own work on string multiphonics.

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Schöön, Daniele, Pascaline Regnault, Søølvi Ystad, and Mireille Besson. "Sensory Consonance." Music Perception 23, no. 2 (December 1, 2005): 105–18. http://dx.doi.org/10.1525/mp.2005.23.2.105.

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THE AIM OF THIS SERIES OF experiments was to determine whether consonant and dissonant chords elicit similar or different electrophysiological effects out of a musical context and whether these effects are similar or different for musicians and nonmusicians. To this end, w e recorded t he e vent-related b rain potentials (ERPs) elicited by the different intervals of the chromatic scale that were classified into three categories: perfect consonances, imperfect consonances, and dissonances. Participants were to decide, on a six-point scale, whether the intervals evoked pleasant or unpleasant feelings. To test the hypothesis that the perception of dissonance results from the superposition of the partials of close frequencies (Helmholtz, 1877), two notes were either played together (harmonic intervals) or successively (melodic intervals). Since, in this latter case, the two notes are played at different points in time, the perception of roughness, if any, should be weaker than for harmonic intervals. In line with Helmholtz's hypothesis, results showed larger differences for harmonic than for melodic intervals, which were mainly found on the N1-P2 complex for musicians, on the N2 component for nonmusicians, and on a later negative component for both musicians and nonmusicians. However, these results also point to the influence of expertise and cultural factors, since different results were obtained when ERPs were averaged as a function of music theory and according to the participants' responses.

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Roberts, Brian. "Effects of spectral pattern on the perceptual salience of partials in harmonic and frequency-shifted complex tones: A performance measure." Journal of the Acoustical Society of America 103, no. 6 (June 1998): 3588–96. http://dx.doi.org/10.1121/1.423086.

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Brunstrom, Jeffrey M., and Brian Roberts. "Effects of asynchrony and ear of presentation on the pitch of mistuned partials in harmonic and frequency-shifted complex tones." Journal of the Acoustical Society of America 110, no. 1 (July 2001): 391–401. http://dx.doi.org/10.1121/1.1379079.

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Zacharakis, Asterios, Konstantinos Pastiadis, and Joshua D. Reiss. "An Interlanguage Study of Musical Timbre Semantic Dimensions and Their Acoustic Correlates." Music Perception 31, no. 4 (December 2012): 339–58. http://dx.doi.org/10.1525/mp.2014.31.4.339.

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A study of musical timbre semantics was conducted with listeners from two different linguistic groups. In two separate experiments, native Greek and English speaking participants were asked to describe 23 musical instrument tones of variable pitch using a predefined vocabulary of 30 adjectives. The common experimental protocol facilitated the investigation of the influence of language on musical timbre semantics by allowing for direct comparisons between linguistic groups. Data reduction techniques applied to the data of each group revealed three salient semantic dimensions that shared common conceptual properties between linguistic groups namely: luminance, texture, and mass. The results supported universality of timbre semantics. A correlation analysis between physical characteristics and semantic dimensions associated: i) texture with the energy distribution of harmonic partials, ii) thickness (a term related to either mass or luminance) and brilliance with inharmonicity and spectral centroid variation, and iii) F0 with mass or luminance depending on the linguistic group.

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Zacharakis, Asterios, Konstantinos Pastiadis, and Joshua D. Reiss. "An Interlanguage Unification of Musical Timbre." Music Perception 32, no. 4 (April 1, 2015): 394–412. http://dx.doi.org/10.1525/mp.2015.32.4.394.

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The current study expands our previous work on interlanguage musical timbre semantics by examining the relationship between semantics and perception of timbre. Following Zacharakis, Pastiadis, and Reiss (2014), a pairwise dissimilarity listening test involving participants from two separate linguistic groups (Greek and English) was conducted. Subsequent multidimensional scaling analysis produced a 3D perceptual timbre space for each language. The comparison between perceptual spaces suggested that timbre perception is unaffected by native language. Additionally, comparisons between semantic and perceptual spaces revealed substantial similarities which suggest that verbal descriptions can convey a considerable amount of perceptual information. The previously determined semantic labels “auditory texture” and “luminance” featured the highest associations with perceptual dimensions for both languages. “Auditory mass” failed to show any strong correlations. Acoustic analysis identified energy distribution of harmonic partials, spectral detail, temporal/spectrotemporal characteristics and the fundamental frequency as the most salient acoustic correlates of perceptual dimensions.

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Kopiez, Reinhard. "Intonation of Harmonic Intervals: Adaptability of Expert Musicians to Equal Temperament and Just Intonation." Music Perception 20, no. 4 (2003): 383–410. http://dx.doi.org/10.1525/mp.2003.20.4.383.

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This study examines the deviation in the intonation of simultaneously sounding tones under the condition of an embedded melody task. Two professional musicians (trumpet players) were chosen as subjects to play the missing upper voice of a four-part audio example, while listening via headphones to the remaining three parts in adaptive five-limit just intonation and equal temperament. The experimental paradigm was that of a controlled varied condition with a 2 (tuning systems) ×× 5 (interval categories) ×× 5 (renditions) ×× 2 (players) factorial design. An analysis of variance showed a nonsignificant difference between the average deviation of harmonic intonation in the two systems used. Mean deviations of 4.9 cents (SD = 6.5 cents) in the equal-temperament condition and of 6.7 cents (SD = 8.1 cents) in the just-intonation condition were found. Thus, we assume that the musicians employed the same intonation for equaltemperament and just-intonation versions (an unconscious "always the same" strategy) and could not successfully adapt their performances to the just-intonation tuning system. Fewer deviations could be observed in the equal-temperament condition. This overall tendency can be interpreted as a "burn in" effect and is probably the consequence of longterm intonation practice with equal-temperament. Finally, a theoretical model of intonation is developed by use of factor analysis. Four factors that determine intonation patterns were revealed: the "major third factor," the "minor third and partials factor," the "instrumental tuning factor," and the "octave-minor seventh factor." To summarize, even in expert musicians, intonation is not determined by abstract tuning systems but is the result of an interaction among compositional features, the acoustics of the particular musical instrument, and deviation patterns in specific intervals.

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Gregory, Andrew H. "Timbre and Auditory Streaming." Music Perception 12, no. 2 (1994): 161–74. http://dx.doi.org/10.2307/40285649.

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Listeners rated the subjective difference between pairs of different synthesized orchestral instrumental timbres. They then reported their perception of variations on crossing ascending and descending musical scales played in different timbres. With little or no timbre difference between the scales, auditory streaming by pitch led to the perception of separate high and low halfscales. Increasing timbre difference led to the perception of the complete scales played by each instrument, particularly if the two scales were in distant keys or temporally interleaved rather than simultaneous. If the notes of each scale alternated between two instruments, then perceptual separation by timbre would result in the perception of the "jumping" sequence of notes played by each instrument. This sequence was perceived only if the scales were discordant or temporally interleaved. Multidimensional scaling of the difference ratings led to three dimensions, which were correlated with acoustic parameters resulting from spectral analysis of the sounds. The most important aspects of timbre for perceptual separation were the proportion of energy in the lower partials and, for discordant scales, the duration of the decay. Auditory streaming by timbre thus depends on particular dimensions of timbre and on musical factors such as harmonic relation, simultaneity, and continuity.

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Johnson-Laird, Phil N., Olivia E. Kang, and Yuan Chang Leong. "On Musical Dissonance." Music Perception 30, no. 1 (September 1, 2012): 19–35. http://dx.doi.org/10.1525/mp.2012.30.1.19.

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psychoacoustic theories of dissonance often follow Helmholtz and attribute it to partials (fundamental frequencies or overtones) near enough in frequency to affect the same region of the basilar membrane and therefore to cause roughness, i.e., rapid beating. In contrast, tonal theories attribute dissonance to violations of harmonic principles embodied in Western music. We propose a dual-process theory that embeds roughness within tonal principles. The theory predicts the robust increasing trend in the dissonance of triads: major < minor < diminished < augmented. Previous experiments used too few chords for a comprehensive test of the theory, and so Experiment 1 examined the rated dissonance of all 55 possible three-note chords, and Experiment 2 examined a representative sample of 48 of the possible four-note chords. The participants' ratings concurred reliably and corroborated the dual-process theory. Experiment 3 showed that, as the theory predicts, consonant chords are rated as less dissonant when they occur in a tonal sequence (the cycle of fifths) than in a random sequence, whereas this manipulation has no reliable effect on dissonant chords outside common musical practice.

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Carterette, Edward C., Kathryn Vaughn, and Nazir A. Jairazbhoy. "Perceptual, Acoustical, and Musical Aspects of the Tambūrā Drone." Music Perception 7, no. 2 (1989): 75–108. http://dx.doi.org/10.2307/40285453.

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The basso continuo principle, as embodied in Rameau's theory of functional harmony, was paralleled by the introduction of drone instruments in the classical music of India. In order to understand how these two systems are tied together in human music perception, we studied the role of tambūrā interactions with North Indian rags played on the sitār. Raman (1914-1922) had applied his theory of discontinuous wave motion to mechanical and musical properties of the strings of the violin. He noted the remarkable, powerful harmonic series that arose from the nonlinear interaction of the tambürã string and grazing contact with its curved bridge. We analyzed the waveforms of the most common drone tunings. Each of the four strings was played with and without juari ("life-giving" threads). The upward transfer and spread of energy into higher partials imparts richness to tambūrā tones and underlies the use of different drone tunings for different rags. Specific notes of rāg scales are selectively and dynamically enhanced by different drone tunings. Based on coincident features of spectral and musical scale degrees, we computed an index of spectral complexity of the interactions of tambūrā tunings with rãg scales. We speculate that the use of juari contributes to stable pitch centers, implied scale modulation, and an improvisational flexibility.

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Badugu, Jayababu, Y. P.Obulesu, and Ch Saibabu. "Harmonic Analysis of Three-phase Fixed Capacitor–thyristor Controlled Reactor under Balanced and Unbalanced Conditions." IAES International Journal of Robotics and Automation (IJRA) 7, no. 1 (March 1, 2018): 67. http://dx.doi.org/10.11591/ijra.v7i1.pp67-76.

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Three-phase Fixed Capacitor Thyristor Controlled Reactor is widely used for reactive power compensation in power systems because of reduced cost and high reliability. The problem with FC-TCR is that to generate current harmonics when it is partially conducting. When this harmonic current is interacted with system impedance, voltage waveform will distorted. This harmonic pollution is undesirable in power systems. Therefore, it is important to know the harmonic behaviour of three-phase FC-TCR before they can be used in a power system network. This paper presents the harmonic analysis of three-phase FC-TCR operating under balanced and unbalanced conditions. This analysis is useful to design the harmonic filter to reduce the harmonic pollution in power systems.The proposed work is implemented in MATLAB environment.

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Fishman, Yonatan I., Igor O. Volkov, M. Daniel Noh, P. Charles Garell, Hans Bakken, Joseph C. Arezzo, Matthew A. Howard, and Mitchell Steinschneider. "Consonance and Dissonance of Musical Chords: Neural Correlates in Auditory Cortex of Monkeys and Humans." Journal of Neurophysiology 86, no. 6 (December 1, 2001): 2761–88. http://dx.doi.org/10.1152/jn.2001.86.6.2761.

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Some musical chords sound pleasant, or consonant, while others sound unpleasant, or dissonant. Helmholtz's psychoacoustic theory of consonance and dissonance attributes the perception of dissonance to the sensation of “beats” and “roughness” caused by interactions in the auditory periphery between adjacent partials of complex tones comprising a musical chord. Conversely, consonance is characterized by the relative absence of beats and roughness. Physiological studies in monkeys suggest that roughness may be represented in primary auditory cortex (A1) by oscillatory neuronal ensemble responses phase-locked to the amplitude-modulated temporal envelope of complex sounds. However, it remains unknown whether phase-locked responses also underlie the representation of dissonance in auditory cortex. In the present study, responses evoked by musical chords with varying degrees of consonance and dissonance were recorded in A1 of awake macaques and evaluated using auditory-evoked potential (AEP), multiunit activity (MUA), and current-source density (CSD) techniques. In parallel studies, intracranial AEPs evoked by the same musical chords were recorded directly from the auditory cortex of two human subjects undergoing surgical evaluation for medically intractable epilepsy. Chords were composed of two simultaneous harmonic complex tones. The magnitude of oscillatory phase-locked activity in A1 of the monkey correlates with the perceived dissonance of the musical chords. Responses evoked by dissonant chords, such as minor and major seconds, display oscillations phase-locked to the predicted difference frequencies, whereas responses evoked by consonant chords, such as octaves and perfect fifths, display little or no phase-locked activity. AEPs recorded in Heschl's gyrus display strikingly similar oscillatory patterns to those observed in monkey A1, with dissonant chords eliciting greater phase-locked activity than consonant chords. In contrast to recordings in Heschl's gyrus, AEPs recorded in the planum temporale do not display significant phase-locked activity, suggesting functional differentiation of auditory cortical regions in humans. These findings support the relevance of synchronous phase-locked neural ensemble activity in A1 for the physiological representation of sensory dissonance in humans and highlight the merits of complementary monkey/human studies in the investigation of neural substrates underlying auditory perception.

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Gutlyanskii, Vladimir, Olga Nesmelova, Vladimir Ryazanov, and Artem Yefimushkin. "Boundary value problems for the generalized analytic and harmonic functions." Proceedings of the Institute of Applied Mathematics and Mechanics NAS of Ukraine 33 (December 27, 2019): 66–82. http://dx.doi.org/10.37069/1683-4720-2019-33-5.

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The study of the Dirichlet problem with arbitrary measurable data for harmonic functions is due to the famous dissertation of Luzin. Later on, the known monograph of Vekua has been devoted to boundary value problems (only with H\"older continuous data) for the generalized analytic functions, i.e., continuous complex valued functions $h(z)$ of the complex variable $z=x+iy$ with generalized first partial derivatives by Sobolev satisfying equations of the form $\partial_{\bar z}h\, +\, ah\, +\ bh\, =\, c\, ,$ where $\partial_{\bar z}\ :=\ \frac{1}{2}\left(\ \frac{\partial}{\partial x}\ +\ i\cdot\frac{\partial}{\partial y}\ \right),$ and it was assumed that the complex valued functions $a,b$ and $c$ belong to the class $L^{p}$ with some $p>2$ in the corresponding domains $D\subset \mathbb C$. The present paper is a natural continuation of our articles on the Riemann, Hilbert, Dirichlet, Poincare and, in particular, Neumann boundary value problems for quasiconformal, analytic, harmonic and the so-called $A-$harmonic functions with boundary data that are measurable with respect to logarithmic capacity. Here we extend the correspon\-ding results to the generalized analytic functions $h:D\to\mathbb C$ with the sources $g$ : $\partial_{\bar z}h\ =\ g\in L^p$, $p>2\,$, and to generalized harmonic functions $U$ with sources $G$ : $\triangle\, U=G\in L^p$, $p>2\,$. It was also given relevant definitions and necessary references to the mentioned articles and comments on previous results. This paper contains various theorems on the existence of nonclassical solutions of the Riemann and Hilbert boundary value problems with arbitrary measurable (with respect to logarithmic capacity) data for generalized analytic functions with sources. Our approach is based on the geometric (theoretic-functional) interpretation of boundary values in comparison with the classical operator approach in PDE. On this basis, it is established the corresponding existence theorems for the Poincare problem on directional derivatives and, in particular, for the Neumann problem to the Poisson equations $\triangle\, U=G$ with arbitrary boundary data that are measurable with respect to logarithmic capacity. These results can be also applied to semi-linear equations of mathematical physics in anisotropic and inhomogeneous media.

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Mignolet, Marc P., Wei Hu, and Ioan Jadic. "On the Forced Response of Harmonically and Partially Mistuned Bladed Disks. Part II: Partial Mistuning and Applications." International Journal of Rotating Machinery 6, no. 1 (2000): 43–56. http://dx.doi.org/10.1155/s1023621x00000051.

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This series of two papers focuses on the determination and clarification of the characteristics of the forced response of bladed disks that exhibit a mistuning pattern that is either harmonic or partial. Harmonic mistuning refers to single wavelength variations in structural properties along the disk while partial mistuning is associated with blade characteristics that are random in a specific sector and tuned elsewhere. The results of this analysis demonstrate that many features of the response of these simple systems match not only qualitatively but also quantitatively their counterparts on randomly mistuned bladed disks. Relying on these similarities, simple and reliable approximations of the localization factor and of the mean response are easily derived that exemplify the usefulness of harmonic and partial mistuning patterns. Finally, it is demonstrated both theoretically and by comparison with simulation results that the maximum amplitude of response of a disk closely follows a Weibull-type distribution in all coupling situations, from very weak to very strong.

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Chiou, S.-T., and T. H. Davies. "Partial cancellation of shaking force harmonics by cam modification." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 211, no. 4 (April 1, 1997): 253–63. http://dx.doi.org/10.1243/0954406971522024.

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An optimization procedure for minimizing the shaking force harmonics of machinery is described. Because of constraints imposed by the specification, optimization is unlikely to make any significant reduction in the fundamental, machine frequency, term of the shaking force. That term, normally the largest, must be substantially reduced by other means for the procedure described here to be cost effective. Earlier work describing methods of reducing the fundamental term are cited. An extrusion press machine incorporating two planar mechanisms, one crank driven and one cam driven, provides an example. Two designs of the cam-driven mechanism, referred to here as cams 1 and 2, are in use in installed extrusion press machines. Harmonic analysis of the shaking force as a function of time shows that cam 2 produces smaller amplitudes of shaking force harmonics. The ten variables used in the optimization process are the amplitudes and angles of the first five terms of a trigonometric series defining the acceleration of a reciprocating mass driven by a hypothetical third cam, cam 3, which is similar to cam 2 but stripped of all harmonics of order higher than the fifth. The objective function is the sum of the amplitudes of the horizontal components of the second to fifth shaking force harmonics on the machine as a consequence of accelerations of the moving parts of both mechanisms. Several equality and inequality constraints must be met. For the extrusion press machine the result is a reduction in the amplitudes that would be created if cam 3 were to be used by approximately 10, 75, 65 and 100 per cent respectively. The improvement over cam 1 is greater. The procedure is particularly suited as a retrofit measure where the number of installed machines is large in relation to the future rate of production of new machines: a cam that has been removed from one machine can be re-cut for use on another machine.

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Yang, Ruixuan, Fulin Zhou, and Kai Zhong. "A Harmonic Impedance Identification Method of Traction Network Based on Data Evolution Mechanism." Energies 13, no. 8 (April 13, 2020): 1904. http://dx.doi.org/10.3390/en13081904.

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In railway electrification systems, the harmonic impedance of the traction network is of great value for avoiding harmonic resonance and electrical matching of impedance parameters between trains and traction networks. Therefore, harmonic impedance identification is beneficial to suppress harmonics and improve the power quality of the traction network. As a result of the coupling characteristics of the traction power supply system, the identification results of harmonic impedance may be inaccurate and controversial. In this context, an identification method based on a data evolution mechanism is proposed. At first, a harmonic impedance model is established and the equivalent circuit of the traction network is established. According to the harmonic impedance model, the proposed method eliminates the outliers of the measured data from trains by the Grubbs criterion and calculates the harmonic impedance by partial least squares regression. Then, the data evolution mechanism based on the sample coefficient of determination is introduced to estimate the reliability of the identification results and to divide results into several reliability levels. Furthermore, in the data evolution mechanism through adding new harmonic data, the low-reliability results can be replaced by the new results with high reliability and, finally, the high-reliability results can cover all frequencies. Moreover, the identification results based on the simulation data show the higher reliability results are more accurate than the lower reliability results. The measured data verify that the the data evolution mechanism can improve accuracy and reliability, and their results prove the feasibility and validation of the proposed method.

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De Barros, Allan, and Ivan Chabu. "Modeling of airgap flux density for the study of stator core vibration in low speed synchronous machines." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 39, no. 4 (June 5, 2020): 839–52. http://dx.doi.org/10.1108/compel-01-2020-0012.

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Purpose This paper aims to develop models and simulations focused on the prediction of electromagnetic forces acting on the stator core of a synchronous machine. It contributes to the study of stator core vibrations. Design/methodology/approach An analytical model based on the rotating fields’ theory including the damper winding contribution was developed. Such model allows the comprehension of airgap magnetic field distribution and the consequent pressure distribution. Focus was given to the pressure sub-harmonics due to the usual fractional winding configuration of low speed machines. A comparative numerical model was also developed and applied to an example laboratory machine. Partial validation measurements were performed. Findings The paper provides the predicted electromagnetic forces and the relative influences of damper winding and teeth tangential forces on each pressure harmonic. It is shown by how much such effects can influence the amplitude of pressure sub-harmonics from a fractional stator winding. Research limitations/implications The performed validation measurements were based on the airgap field distribution, but the resulting core vibration at load was not measured. Therefore, researchers are encouraged to perform additional tests for improved validation. Practical implications The obtained models and results are of great importance for the design phase of new generators and for the diagnosis process of existing machines with core vibration problems. Originality/value As a contribution of this paper, the magnitude of indirect effect of tangential forces and the effect of damper winding are comparatively quantified for each pressure harmonic. The given approach contributes to the relative evaluation of these effects especially on the sub-harmonics from the fractional stator winding.

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Meyer, Fernando, Sérgio Ossamu Ioshii, Eduardo Wei Kin Chin, Danielle Mussoi Esser, Renata Tomasetti Marcondes, Andressa Hubar Patriani, and Bruno de Figueiredo Pimpão. "Laparoscopic partial nephrectomy in rats." Acta Cirurgica Brasileira 22, no. 2 (April 2007): 152–56. http://dx.doi.org/10.1590/s0102-86502007000200014.

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PURPOSE: To establish an experimental model of laparoscopic partial nephrectomy (LPN) in rats and to analyze morphological alterations in the renal parenchyma utilizing an electric cautery and harmonic scalpel. METHODS: Forty Wistar rats were used, divided in 2 experiments with 20 rats each: experiment I, LPN was performed with an electric cautery and the rats were subdivided into groups A and B; experiment II, LPN was performed with a harmonic scalpel and they were subdivided into groups C and D. The animals in groups A and C were sacrificed shortly after surgery and the remnant kidney was removed to study the following variables: necroses and degeneration. In groups B and D a laparatomy was performed for retrieval of the remnant kidney on the 14th day after surgery to analyze fibrous scarring. RESULTS: For the variables necroses and fibrous scarring, the electric cautery creates, on average, greater width than that produced by the harmonic scalpel (p=0.0002 and p=0.0068 respectively). Regarding the variable of degeneration, we found no significant difference between the two types of scalpels (p=0.1267). CONCLUSIONS: LPN in rats is an adequate and feasible experimental model. The electric cautery caused greater damage to remnant renal tissue when compared to harmonic scalpel.

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Jia, Xiu Fang, Shao Guang Zhang, and Hai Qing An. "Partial Linear Method for Background Harmonic Voltage Estimation." Advanced Materials Research 960-961 (June 2014): 710–15. http://dx.doi.org/10.4028/www.scientific.net/amr.960-961.710.

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The linear regression method which will be influenced by fluctuations could only calculate constant background harmonic voltage. To make up the limitation, this paper studies partial linear method. The method expands fluctuant background harmonic voltage at a time in accordance with Taylor series. On the basis of least sum of square error, the objective function selected by the method considers the influence of weight and uses bandwidth control each size of weight. This method can calculate fluctuant background harmonic voltage accurately. A case study based on the IEEE 14-bus test system is conducted and the results indicate that fluctuant background harmonic voltage can be obtained effectively and accurately by the proposed method.

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Du, J., C. Chen, V. Lesur, and L. Wang. "Non-singular spherical harmonic expressions of geomagnetic vector and gradient tensor fields in the local north-oriented reference frame." Geoscientific Model Development 8, no. 7 (July 7, 2015): 1979–90. http://dx.doi.org/10.5194/gmd-8-1979-2015.

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Abstract. General expressions of magnetic vector (MV) and magnetic gradient tensor (MGT) in terms of the first- and second-order derivatives of spherical harmonics at different degrees/orders are relatively complicated and singular at the poles. In this paper, we derived alternative non-singular expressions for the MV, the MGT and also the third-order partial derivatives of the magnetic potential field in the local north-oriented reference frame. Using our newly derived formulae, the magnetic potential, vector and gradient tensor fields and also the third-order partial derivatives of the magnetic potential field at an altitude of 300 km are calculated based on a global lithospheric magnetic field model GRIMM_L120 (GFZ Reference Internal Magnetic Model, version 0.0) with spherical harmonic degrees 16–90. The corresponding results at the poles are discussed and the validity of the derived formulas is verified using the Laplace equation of the magnetic potential field.

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Ramesh, T., R. Saravanan, and S. Sekar. "Analysis of ANFIS MPPT Controllers for Partially Shaded Stand Alone Photovoltaic System with Multilevel Inverter." IAES International Journal of Robotics and Automation (IJRA) 7, no. 2 (June 1, 2018): 140. http://dx.doi.org/10.11591/ijra.v7i2.pp140-148.

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<p>This work presents a unique combination of an boost converter run by a set of two photovoltaic panels (PV) with a MPPT, suitable to guarantee MPP even under partial shadowed conditions, managed by an adaptive neuro fuzzy inference system (ANFIS) trained by the training data derived from a Perturb and observation (P&O) conventional algorithm. The single phase cascaded H bridge five-level inverter (CHI) driven by the individual outputs of the boost converter, with selective harmonic elimination scheme to eliminate typically the seventh order harmonics. Simulation was carried out in the MATLAB/SIMULINK environment validated the proposed scheme. It has been thus established; by both simulations the ANFIS model of MPPT scheme outperforms other schemes of conventional control algorithm.</p>

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31

Gergün, Seçil, H. Turgay Kaptanoğlu, and A. Ersin Üreyen. "Harmonic Besov spaces on the ball." International Journal of Mathematics 27, no. 09 (August 2016): 1650070. http://dx.doi.org/10.1142/s0129167x16500701.

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We initiate a detailed study of two-parameter Besov spaces on the unit ball of [Formula: see text] consisting of harmonic functions whose sufficiently high-order radial derivatives lie in harmonic Bergman spaces. We compute the reproducing kernels of those Besov spaces that are Hilbert spaces. The kernels are weighted infinite sums of zonal harmonics and natural radial fractional derivatives of the Poisson kernel. Estimates of the growth of kernels lead to characterization of integral transformations on Lebesgue classes. The transformations allow us to conclude that the order of the radial derivative is not a characteristic of a Besov space as long as it is above a certain threshold. Using kernels, we define generalized Bergman projections and characterize those that are bounded from Lebesgue classes onto Besov spaces. The projections provide integral representations for the functions in these spaces and also lead to characterizations of the functions in the spaces using partial derivatives. Several other applications follow from the integral representations such as atomic decomposition, growth at the boundary and of Fourier coefficients, inclusions among them, duality and interpolation relations, and a solution to the Gleason problem.

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32

Leroy, Stephen S., Chi O. Ao, Olga P. Verkhoglyadova, and Mayra I. Oyola. "Analyzing the Diurnal Cycle by Bayesian Interpolation on a Sphere for Mapping GNSS Radio Occultation Data." Journal of Atmospheric and Oceanic Technology 38, no. 5 (May 2021): 951–61. http://dx.doi.org/10.1175/jtech-d-20-0031.1.

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AbstractBayesian interpolation has previously been proposed as a strategy to construct maps of radio occultation (RO) data, but that proposition did not consider the diurnal dimension of RO data. In this work, the basis functions of Bayesian interpolation are extended into the domain of the diurnal cycle, thus enabling monthly mapping of radio occultation data in synoptic time and analysis of the atmospheric tides. The basis functions are spherical harmonics multiplied by sinusoids in the diurnal cycle up to arbitrary spherical harmonic degree and diurnal cycle harmonic. Bayesian interpolation requires a regularizer to impose smoothness on the fits it produces, thereby preventing the overfitting of data. In this work, a formulation for the regularizer is proposed and the most probable values of the parameters of the regularizer determined. Special care is required when obvious gaps in the sampling of the diurnal cycle are known to occur in order to prevent the false detection of statistically significant high-degree harmonics of the diurnal cycle in the atmosphere. Finally, this work probes the ability of Bayesian interpolation to generate a valid uncertainty analysis of the fit. The postfit residuals of Bayesian interpolation are dominated not by measurement noise but by unresolved variability in the atmosphere, which is statistically nonuniform across the globe, thus violating the central assumption of Bayesian interpolation. The problem is ameliorated by constructing maps of RO data using Bayesian interpolation that partially resolve the temporal variability of the atmosphere, constructing maps for approximately every 3 days of RO data.

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Yoneda, Rikio. "A CHARACTERIZATION OF THE HARMONIC BLOCH SPACE AND THE HARMONIC BESOV SPACES BY AN OSCILLATION." Proceedings of the Edinburgh Mathematical Society 45, no. 1 (February 2002): 229–39. http://dx.doi.org/10.1017/s001309159900142x.

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AbstractWe characterize the Bloch space and the Besov spaces of harmonic functions on the open unit disc $D$ by using the following oscillation:$$ \sup_\{\beta(z,w)\ltr\}(1-|z|^2)^{\alpha}(1-|w|^2)^{\beta}\biggl|\frac{\hat{D}^{(n-1)}h(z)-\hat{D}^{(n-1)}h(w)}{z-w}\biggr|, $$where $\alpha+\beta=n$, $\alpha,\beta\in\mathbb{R}$ and $\displaystyle{\hat{D}^{(n)}=(\partial^{n}/\partial^{n}z+\partial^{n}/\partial^{n}\bar{z})}$.AMS 2000 Mathematics subject classification: Primary 46E15

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HU, Z. D., Z. M. SHENG, W. J. DING, W. M. WANG, Q. L. DONG, and J. ZHANG. "Electromagnetic emission from laser wakefields in underdense magnetized plasmas." Journal of Plasma Physics 78, no. 4 (March 15, 2012): 421–27. http://dx.doi.org/10.1017/s002237781200027x.

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AbstractThe laser wakefield structure in a magnetized underdense plasma is studied analytically and numerically. Because of the DC magnetic field perpendicular to the laser propagation direction, an electromagnetic component appears in addition to the normal electrostatic component. This electromagnetic component can transmit partially into vacuum at the plasma–vacuum boundary as shown by particle-in-cell simulation. It is found that the emission has components both at the fundamental plasma frequency and its harmonics if the wakefield is driven at a high amplitude. Comparing with the emission at the plasma frequency, the harmonic emission depends weakly upon the density profile at plasma–vacuum boundary and it can pass through the boundary almost without energy loss, providing a new method for the diagnostic of wakefields.

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35

Porwal, Saurabh. "Partial sums of certain harmonic univalent functions." Lobachevskii Journal of Mathematics 32, no. 4 (October 2011): 366–75. http://dx.doi.org/10.1134/s1995080211040184.

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Ragusa, Maria Alessandra, Atsushi Tachikawa, and Hiroshi Takabayashi. "Partial regularity of $p(x)$-harmonic maps." Transactions of the American Mathematical Society 365, no. 6 (October 4, 2012): 3329–53. http://dx.doi.org/10.1090/s0002-9947-2012-05780-1.

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37

Aldweby, Huda, and Maslina Darus. "Quasi Partial Sums of Harmonic Univalent Functions." Revista Colombiana de Matemáticas 53, no. 1 (January 1, 2019): 15–25. http://dx.doi.org/10.15446/recolma.v53n1.81035.

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38

Porwal, Saurabh, and Kaushal Kishore Dixit. "Partial Sums of Starlike Harmonic Univalent Functions." Kyungpook mathematical journal 50, no. 3 (September 30, 2010): 433–45. http://dx.doi.org/10.5666/kmj.2010.50.3.433.

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39

Yao, Guowu. "$\overline {\partial }$-energy integral and harmonic mappings." Proceedings of the American Mathematical Society 131, no. 7 (October 24, 2002): 2271–77. http://dx.doi.org/10.1090/s0002-9939-02-06757-6.

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40

Yaşar, Elif, and Sibel Yalçın. "Partial sums of starlike harmonic multivalent functions." Afrika Matematika 26, no. 1-2 (July 27, 2013): 53–63. http://dx.doi.org/10.1007/s13370-013-0188-9.

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41

Gong, Yu Long, Jin Xi Guo, and Hong Fu Guo. "Feature Extraction Based on the Multiple Harmonic Analysis of 2-Dimensional Pattern of Partial Discharge." Applied Mechanics and Materials 303-306 (February 2013): 478–81. http://dx.doi.org/10.4028/www.scientific.net/amm.303-306.478.

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Partial discharge will cause deterioration of insulation of high-voltage electrical equipment, resulting in insulation breakdown and short circuit accident. In order to ensure the normal operation of the high-voltage equipment, it is necessary to detect partial discharge online. By using Ultra High Frequency (UHF) defection method, statistical 2-dimensional (2D) patterns of partial discharge are obtained. Extracting the envelopes of the 2D patterns, we do the harmonic analysis for patterns’ envelopes, and the harmonic components are used as a characteristic parameter for defect type’s recognition. The results show that the harmonic components can be used as characteristic parameter for defect types’ recognition. This method has the characteristics of strong real-time and simple operation.

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42

Li, Xiang, Min You Chen, and Yong Wei Zheng. "Assessing the Harmonic Emission Level Based on Partial Least-Squares Regression with Data Envelopment Analysis." Advanced Materials Research 989-994 (July 2014): 3367–70. http://dx.doi.org/10.4028/www.scientific.net/amr.989-994.3367.

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A novel method is used for assessing the harmonic emission level, which is based on the partial least-squares (PLS) regression with data envelopment analysis (DEA). Based on measuring the harmonic voltage and current at the point of common coupling (PCC) and removing the inefficiency data with DEA, regression coefficients are worked out through partial least-squares algorithm. Consequently the harmonic emission level of customer is calculated.The proposed approach removes the effect of outlying data points and gets accurate estimation results. The simulation results prove that the proposed method is more effective than PLS.

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Setter, Eyal, Izhak Bucher, and Shimon Haber. "Propulsion at low Reynolds numbers by multiple traveling waves." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 228, no. 16 (February 12, 2014): 2938–49. http://dx.doi.org/10.1177/0954406214523580.

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Microorganisms or micro-robotic swimmers employ traveling waves as a common swimming mechanism involving time-irreversible deformations of their outer surface. Normally, the deforming surfaces constitute of multiple spatial waves, some standing and others propagating forward or backward. A unique technique is developed here to experimentally decompose a waving surface into its spatial wavelengths in each time instance by processing a sequence of photographs. This information is curve fitted to yield the phase velocity, frequency, and amplitudes of the propagating and receding waves of each component. The significance of the harmonic decomposition is demonstrated using an experimental macro-scale swimmer that utilizes small amplitude circumferential waves. A numerical image processing and curve-fitting procedure is shown and a theoretical model is also developed to account for the hydrodynamic effects of multiple wavelengths. The theoretical results fit well with the experimental data at low speeds, although the contribution of higher harmonics was small in experiment, but the higher harmonics are clearly visible and successfully identified. Still, the importance of the multiharmonics analysis for swimmers, which utilize traveling waves mechanisms, found both in nature and in man-made machines, was formulated and partially verified.

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Jung, Soon-Mo, and Byungbae Kim. "Simple Harmonic Oscillator Equation and Its Hyers-Ulam Stability." Journal of Function Spaces and Applications 2012 (2012): 1–8. http://dx.doi.org/10.1155/2012/382932.

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45

Branding, Volker. "On Finite Energy Solutions of 4-harmonic and ES-4-harmonic Maps." Journal of Geometric Analysis 31, no. 8 (February 25, 2021): 8666–85. http://dx.doi.org/10.1007/s12220-021-00610-7.

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Abstract4-harmonic and ES-4-harmonic maps are two generalizations of the well-studied harmonic map equation which are both given by a nonlinear elliptic partial differential equation of order eight. Due to the large number of derivatives it is very difficult to find any difference in the qualitative behavior of these two variational problems. In this article we prove that finite energy solutions of both 4-harmonic and ES-4-harmonic maps from Euclidean space must be trivial. However, the energy that we require to be finite is different for 4-harmonic and ES-4-harmonic maps pointing out a first difference between these two variational problems.

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46

Ito, Shota, Hideki Kandori, and Victor A. Lorenz-Fonfria. "Potential Second-Harmonic Ghost Bands in Fourier Transform Infrared (FT-IR) Difference Spectroscopy of Proteins." Applied Spectroscopy 72, no. 6 (February 13, 2018): 956–63. http://dx.doi.org/10.1177/0003702818757521.

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Fourier transform infrared (FT-IR) difference absorption spectroscopy is a common method for studying the structural and dynamical aspects behind protein function. In particular, the 2800–1800 cm−1 spectral range has been used to obtain information about internal (deuterated) water molecules, as well as site-specific details about cysteine residues and chemically modified and artificial amino acids. Here, we report on the presence of ghost bands in cryogenic light-induced FT-IR difference spectra of the protein bacteriorhodopsin. The presence of these ghost bands can be particularly problematic in the 2800–1900 cm−1 region, showing intensities similar to O–D vibrations from water molecules. We demonstrate that they arise from second harmonics from genuine chromophore bands located in the 1400–850 cm−1 region, generated by double-modulation artifacts caused from reflections of the IR beam at the sample and at the cryostat windows back to the interferometer (inter-reflections). The second-harmonic ghost bands can be physically removed by placing an optical filter of suitable cutoff in the beam path, but at the cost of losing part of the multiplexing advantage of FT-IR spectroscopy. We explored alternatives to the use of optical filters. Tilting the cryostat windows was effective in reducing the intensity of the second harmonic artifacts but tilting the sample windows was not, presumably by their close proximity to the focal point of the IR beam. We also introduce a simple numerical post-processing approach that can partially, but not fully, correct for second-harmonic ghost bands in FT-IR difference spectra.

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Gutlyanskii, Vladimir, Olga Nesmelova, Vladimir Ryazanov, and Artyem Yefimushkin. "Logarithmic potential and generalized analytic functions." Ukrainian Mathematical Bulletin 18, no. 1 (March 9, 2021): 12–36. http://dx.doi.org/10.37069/1810-3200-2021-18-1-2.

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The study of the Dirichlet problem in the unit disk $\mathbb D$ with arbitrary measurable data for harmonic functions is due to the famous dissertation of Luzin [31]. Later on, the known monograph of Vekua \cite{Ve} has been devoted to boundary-value problems (only with H\"older continuous data) for the generalized analytic functions, i.e., continuous complex valued functions $h(z)$ of the complex variable $z=x+iy$ with generalized first partial derivatives by Sobolev satisfying equations of the form $\partial_{\bar z}h\, +\, ah\, +\ b{\overline h}\, =\, c\, ,$ where it was assumed that the complex valued functions $a,b$ and $c$ belong to the class $L^{p}$ with some $p>2$ in smooth enough domains $D$ in $\mathbb C$. The present paper is a natural continuation of our previous articles on the Riemann, Hilbert, Dirichlet, Poincar\'{e} and, in particular, Neumann boundary-value problems for quasiconformal, analytic, harmonic, and the so-called $A-$harmonic functions with boundary data that are measurable with respect to logarithmic capacity. Here, we extend the corresponding results to the generalized analytic functions $h:D\to\mathbb C$ with the sources $g$ : $\partial_{\bar z}h\ =\ g\in L^p$, $p>2\,$, and to generalized harmonic functions $U$ with sources $G$ : $\triangle\, U=G\in L^p$, $p>2\,$. This paper contains various theorems on the existence of nonclassical solutions of the Riemann and Hilbert boundary-value problems with arbitrary measurable (with respect to logarithmic capacity) data for generalized analytic functions with sources. Our approach is based on the geometric (theoretic-functional) interpretation of boundary-values in comparison with the classical operator approach in PDE. On this basis, it is established the corresponding existence theorems for the Poincar\'{e} problem on directional derivatives and, in particular, for the Neumann problem to the Poisson equations $\triangle\, U=G$ with arbitrary boundary data that are measurable with respect to logarithmic capacity. These results can be also applied to semi-linear equations of mathematical physics in anisotropic and inhomogeneous media.

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48

Moore, F. K. "Weak Rotating Flow Disturbances in a Centrifugal Compressor With a Vaneless Diffuser." Journal of Turbomachinery 111, no. 4 (October 1, 1989): 442–49. http://dx.doi.org/10.1115/1.3262292.

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A theory is presented to predict the occurrence of weak rotating waves in a centrifugal compression system with a vaneless diffuser. As in a previous study of axial systems, an undisturbed performance characteristic is assumed known. Following an inviscid analysis of the diffuser flow, conditions for a neutral rotating disturbance are found. The solution is shown to have two branches; one with fast rotation, the other with very slow rotation. The slow branch includes a dense set of resonant solutions. The resonance is a feature of the diffuser flow, and therefore such disturbances must be expected at the various resonant flow coefficients regardless of the compressor characteristic. Slow solutions seem limited to flow coefficients less than about 0.3, where third and fourth harmonics appear. Fast waves seem limited to a first harmonic. These fast and slow waves are described, and effects of diffuser-wall convergence, backward blade angles, and partial recovery of exit velocity head are assessed.

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49

Hong, Min-Chun. "Partial regularity of stable p-harmonic maps into spheres." Bulletin of the Australian Mathematical Society 76, no. 2 (October 2007): 297–305. http://dx.doi.org/10.1017/s0004972700039678.

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Xavier, Lucas Santana, Allan Fagner Cupertino, Heverton Augusto Pereira, and Victor Flores Mendes. "Partial Harmonic Current Compensation for Multifunctional Photovoltaic Inverters." IEEE Transactions on Power Electronics 34, no. 12 (December 2019): 11868–79. http://dx.doi.org/10.1109/tpel.2019.2909394.

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Journal articles on the topic 'Harmonic partials'

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