Scaling, Mirror Symmetries and Musical Consonances Among the Distances of the Planets of the Solar System

Orbital systems are often self-organized and/or characterized by harmonic relations. Inspired by music theory, we rewrite the Geddes and King-Hele (QJRAS, 24, 10–13, 1983) equations for mirror symmetries among the distances of the planets of the Solar System in an elegant and compact form by using the 2/3rd power of the ratios of the semi-major axis lengths of two neighboring planets (eight pairs, including the belt of the asteroids). This metric suggests that the Solar System could be characterized by a scaling and mirror-like structure relative to the asteroid belt that relates together the terrestrial and Jovian planets. These relations are based on a 9/8 ratio multiplied by powers of 2, which correspond musically to the interval of the Pythagorean epogdoon (a Major Second) and its addition with one or more octaves. Extensions of the same model are discussed and found compatible also with the still hypothetical vulcanoid asteroids versus the transneptunian objects. The found relation also suggests that the planetary self-organization of our system could be generated by the 3:1 and 7:3 resonances of Jupiter, which are already known to have shaped the asteroid belt. The proposed model predicts the main Kirkwood asteroid gaps and the ratio among the planetary orbital parameters with a 99% accuracy, which is three times better than an alternative, recently proposed harmonic-resonance model for the Solar System. Furthermore, the ratios of neighboring planetary pairs correspond to four musical “consonances” having frequency ratios of 5/4 (Major Third), 4/3 (Perfect Fourth), 3/2 (Perfect Fifth) and 8/5 (Minor Sixth); the probability of obtaining this result randomly has a p < 0.001. Musical consonances are “pleasing” tones that harmoniously interrelate when sounded together, which suggests that the orbits of the planets of our Solar System could form some kind of gravitationally optimized and coordinated structure. Physical modeling indicates that energy non-conserving perturbations could drive a planetary system into a self-organized periodic state with characteristics vaguely similar of those found in our Solar System. However, our specific finding suggests that the planetary organization of our Solar System could be rather peculiar and based on more complex and unknown dynamical structures.

Analytical Solution and Quasi-Periodic Behavior of a Charged Dilaton Black Hole

With the vast breakthrough brought by the Event Horizon Telescope, the theoretical analysis of various black holes has become more critical than ever. In this paper, the second-order asymptotic analytical solution of the charged dilaton black hole flow in the spinodal region is constructed from the perspective of dynamics by using the two-timing scale method. Through a numerical comparison with the original charged dilaton black hole system, it is found that the constructed analytical solution is highly consistent with the numerical solution. In addition, several quasi-periodic motions of the charged dilaton black hole flow are numerically obtained under different groups of irrational frequency ratios, and the phase portraits of the black hole flow with sufficiently small thermal parameter perturbation display good stability. Finally, the final evolution state of black hole flow over time is studied according to the obtained analytical solution. The results show that the smaller the integral constant of the system, the greater the periodicity of the black hole flow.

Coincident In-situ and Triple-Frequency Radar Airborne Observations in the Arctic

This paper describes X-Ka-W-band airborne radar observations and almost perfectly co-located in situ microphysical measurements on board the National Research Council Canada (NRC) Convair-580 aircraft from the Radar Snow Experiment (RadSnowExp). Over 12 hours of flight data with more than 3.4 hours in non-Rayleigh regions for at least one of the radar frequencies provide a unique opportunity for studying the relationship between cloud microphysical properties and radar dual-frequency ratios (DFR). The results from this study are consistent with the main findings of previous modelling studies with specific regions of the DFR plane associated with unique scattering properties of different ice habits, especially in riming conditions. Moreover, the datasets could be used to produce look-up-tables for retrieving cloud bulk density and characteristic size.

Temporal trends in primary care-recorded self-harm during and beyond the first year of the COVID-19 pandemic: time series analysis of electronic healthcare records for 2.8 million patients in the Greater Manchester Care Record

Background: Surveillance of clinically treated self-harm episode frequency is an important component of suicide prevention in the dynamic context of COVID-19. Studies published to date have investigated the initial months following the onset of the pandemic, despite national and regional restrictions persisting to Summer 2021. Methods: We conducted a descriptive time series analysis utilising data from the Greater Manchester Care Record, which contains de-identified, primary care health records of 2.8 million patients. Counts of incident and all episodes of self-harm recorded between 1st January 2019 and 31st May 2021 were made for all patients, with stratification by sex, age group, ethnicity, and index of multiple deprivation (IMD) quintile and examination of overall differences by national and regional restriction phases. Findings: Between 1st January 2019 and 31st May 2021, 33,444 episodes of self-harm by 13,148 individuals were recorded. Frequency ratios of incident and all episodes of self-harm were 0.59 (95% CI 0.51 to 0.69) and 0.69 (CI 0.63 to 0.75) respectively in April 2020 compared to February 2020. Between August 2020 and May 2021 frequency ratios were 0.92 (CI 0.88 to 0.96) for incident episodes and 0.86 (CI 0.84 to 0.88) for all episodes compared to the same months in 2019. Reductions were largest among men and people living in the most deprived neighbourhoods. An increase in all-episode self-harm (frequency ratio 1.09, CI 1.03 to 1.16) was observed for adolescents aged 10-17 between August 2020 and May 2021. Interpretation: The COVID-19 pandemic has had a sustained impact on help seeking for self-harm. Reductions in primary care recorded self-harm have implications for clinicians' ability to assess the needs and risks of individuals. Some patients may be experiencing prolonged untreated deterioration in their mental health while other groups are presenting in higher numbers. Our findings have important implications for primary care and mental health services in manging ongoing demand.

Comparison of Dynamic Responses of Parallel-Placed Adjacent High-Rise Buildings under Wind and Earthquake Excitations

Two parallel-placed adjacent high-rise buildings are often linked to each other through passive control devices for vibration mitigation purposes. The mitigation efficiency of these control devices mainly depends on the characteristics of relative dynamic responses, namely, opposite-sign and same-sign responses of the two buildings. The present research first identifies an opposite-sign response factor to estimate the time ratio of opposite-sign responses. Subsequently, a structure comprising two adjacent high-rise buildings (with different natural frequency ratios) subjected to both wind and earthquake excitations is analyzed. Wind-induced responses are evaluated based on wind loads obtained from wind tunnel tests, while earthquake responses are determined through a suite of 44 natural ground-motion records. The results indicate that opposite-sign factors of the displacement, velocity, and acceleration responses under wind loads, especially at across-wind direction, are larger than those under earthquake excitations, and opposite-sign response factors under wind loads are insensitive to variation of the natural frequency ratio of the two adjacent buildings compared with those under earthquake excitations. The conclusions of this research may be helpful for wind-resistant and antiseismic design of parallel-placed adjacent high-rise buildings.

Nikola Tesla’s Theory of Frequency Ratios (369) that Produce Resonances Can Explain How Self Hypnosis can strengthen and Direct the Placebo Effect

Pfizer used 20,000 subjects in the placebo group for Covid vaccinations. When injected with the virus, only 95 of the 20,000 test subjects got sick. A French physician in the 1920’s used self hypnosis to treat his patients and had a 98% cure rate. I believe he found a way to strengthen the placebo (the ability of the mind to heal the body) so that medicine was obsolete.

Mapping of Landslide Susceptible Zones by Using Frequency Ratios at Bluncong Subwatershed, Bondowoso Regency

Landslides are the disasters that frequently happen in Bluncong sub-watershed. These incidents have caused damage and malfunction of road infrastructure, bridges, and irrigation buildings. Therefore, it is important to anticipate landslides through mapping of landslide-susceptibility areas The objective of this study is to map landslide susceptibility at Bluncong sub watershed, Bondowoso, by using Geographical Information System and remote sensing. The landslide susceptibility analysis and mapping are conducted based on landslide occurrences with the Frequency Ratio approach. The landslide sites are identified from field survey data interpretation. Digital Elevation Model maps, geological data, land uses and rivers data, and Landsat 8 images are collected, processed, and then built into the GIS platform's spatial database. The selected factors that cause landslide occurrences are land use, distance to river, aspect, slope, elevation, curvature, and the vegetation index (NDVI). The results show that the accuracy of the map is acceptable. The frequency ratio model gained the area under curve (AUC) value of 0.79. It is found that 9.08% of the area has very high landslide susceptibility. Local governments can use this study's mapping results to minimize the risk at landslidesusceptible zones

Cents versus scale steps: Can we tell the difference between major and minor thirds?

We report an experiment in which participants ( N = 368) were asked to differentiate between major and minor thirds. These intervals could either be formed by diatonic tones from the C major scale (tonal condition) or by a subset of tones from the chromatic scale (atonal condition). We hypothesized that in the tonal condition intervals would be perceived as a function of scale step distances, which we defined as the number of diatonic leaps between two notes of a given music scale. In the atonal condition, we hypothesized that intervals would be perceived as a function of cents. If our hypotheses were supported, we should verify a less accurate performance in the tonal condition, where scale step distances are the same between major and minor thirds. The data corroborated our hypotheses, and we suggest that acoustic measurements of intervallic distances (i.e., frequency ratios and cents) are not optimal when it comes to describing the perceptual quality of intervals in a tonal context. Finally, our research points to the possibility that, in comparison with previous models, scale steps and cents might better capture the notion of global versus local instances of auditory processing.