Abstract
FluidHarmony is an algorithmic method for defining a hierarchical harmonic lexicon in equal temperaments. It utilizes an enharmonic weighted Fourier transform space to represent pitch class set (pcsets) relations. The method ranks pcsets based on user-defined constraints: the importance of interval classes (ICs) and a reference pcset. Evaluation of 5,184 Western musical pieces from the 16th to 20th centuries shows FluidHarmony captures 8% of the corpus's harmony in its top pcsets. This highlights the role of ICs and a reference pcset in regulating harmony in Western tonal music while enabling systematic approaches to define hierarchies and establish metrics beyond 12-TET.

Abstract
The extraction of harmonic information from musical audio is fundamental for several music information retrieval tasks. In this paper, we propose novel harmonic audio features based on the perceptually-inspired tonal interval vector space, computed as the Fourier transform of chroma vectors. Our contribution includes mid-level features for musical dissonance, chromaticity, dyadicity, triadicity, diminished quality, diatonicity, and whole-toneness. Moreover, we quantify the perceptual relationship between short- and long-term harmonic structures, tonal dispersion, harmonic changes, and complexity. Beyond the computation on fixed-size windows, we propose a context-sensitive harmonic segmentation approach. We assess the robustness of the new harmonic features in style classification tasks regarding classical music periods and composers. Our results align with, slightly outperforming, existing features and suggest that other musical properties than those in state-of-the-art literature are partially captured. We discuss the features regarding their musical interpretation and compare the different feature groups regarding their effectiveness for discriminating classical music periods and composers. © F. Almeida, G. Bernardes, and C. Weiû.

Abstract
In this article, a proof-of-concept study on the use of a hybrid design technique to reduce the number of phase shifters of a beam-scanning reflectarray (RA) is presented. An extended hemispherical lens antenna with feeds inspired by the retrodirective array is developed as a reflecting element, and the hybrid design technique mixes the lenses with the microstrip patch elements to realize a reflecting surface. Compared to the conventional designs that only use microstrip antennas to realize a reflecting surface, given a fixed aperture size the presented design uses 25 percent fewer array elements while shows comparable beam-steering performance. As a result of using fewer elements, the number of required phase shifters or other equivalent components such as RF switches and tunable materials is reduced by 25 percent, which leads to the reduction of the overall antenna system's complexity, cost, and power consumption. To verify the design concept, two passive prototypes with a center frequency at 12.5 GHz were designed and fabricated. The reflecting surface was fabricated by using standard PCB manufacturing and the lenses were fabricated using 3D printing. Good agreement between the simulation and measurement results is obtained. The presented design concept can be extended to the design of RAs operating at different frequency bands including millimetre-wave frequencies with similar radiation performances. The presented design method is not limited to the microstrip patch reflecting elements and can also be applied to the design of the hybrid RAs with different types of reflecting elements.

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