A Simplified Introduction to Music Algebra: from the Scale Vectors to the Modal Tensor

In this paper we take a step forward towards the attainment of a formalism that allows to establish a deeper connection between Music and Algebra. Starting from the writing of the Ionian Scale as a Vector, we define the Ionian Modal Tensor. We prove that all the Scales that derive from the Ionian Mode, as well as all the corresponding Seventh Chords, herein considered as being Scalars, can be obtained from the above-mentioned Tensor by resorting to the concepts of Standard Basis and Dot Product.Moreover, by opportunely summing the Vectors of the Standard Basisto each other, we define some interesting Fundamental Vectors such as the "Monk – Powell" Vector and the "Guide Notes" one

Towards a Music Algebra: Fundamental Harmonic Substitutions in Jazz

In this paper the most common harmonic substitutions, at least as far as jazz music is concerned, are unconventionally addressed. The novelty consists in introducing a new method finalized to formally defining and logically applyingall the fundamental harmonic substitutions, by exploiting anunusually rigorous notation. After defining the substitutions and discussing their applicability, we resort to them in order to modify some simple harmonic progressions substantially based upon a banal major turnaround. As explicitly suggested by the title, the modifications are carried out by following an extremely formal line of reasoning: all the logic passages are accurately described by resorting to a notation so similar to the one commonly employed in mathematics and physics, that the harmonic analysis of a song turns out to be de facto comparable to the demonstration of a theorem

On the Schwarzschild Solution: a Review

In this paper the well-known Schwarzschild Solution is discussed. In the first section, by resorting, as usual, to the Einstein Field Equations, a short summary of the conventional derivation is provided. In the second section, we carry out an alternative derivation of the Schwarzschild Metric. The above-mentioned procedureis based upon several noteworthy hypotheses, among which the existence of a further spatial dimension stands out. Initially, we postulate a Universe identifiable with a 4-ball, homogeneously filled with matter, whose radius equates the Schwarzschild Radius. Then, in order to obtain the vacuum field, all the available mass is ideally concentrated in a single point.By imposing a specific condition concerning the measured radius, we deduce a metric that, if subjected to an appropriate parametrization, allows us to finally obtain the Schwarzschild solution

Is the EM-Drive a Closed System?

Since its disclosure, the so-called EM-Drive, an apparently reactionless electromagnetic thruster conceived by Roger Shawyer, has simultaneously caused wide scepticism, related to the physical principles that may allow its functioning, and understandable enthusiasm, by virtue of the astonishing scenarios potentially offered by such a device. On the one hand, thrust without exhaust is de facto impossible, unless we deny the Law of Action-Reaction, whose evident violation would result in acknowledging the concrete need for a new Physics; on the other hand, it would appear that opportunely shaped resonant cavities, when fuelled with microwaves, deliver a certain thrust, apparently without a detectable exhaust. In this paper, instead of discussing the validity of the various tests to date independently carried out, speculating about misleading side-effects or inadequate instrumental precision, we simply suppose that the thrust may be an actual phenomenon. Therefore, we try to provide a qualitative explanation to the functioning of the alleged reactionless device, by resorting to a theory elsewhere proposed and herein briefly discussed

The “Light Clocks” Thought Experiment and the “Fake” Lorentz Transformations

In this paper an alternative version of the well-known “light clocks” experiment is discussed. The so-called Lorentz transformations, backbone of the Special Relativity theory, are herein deduced by resorting to the above-mentioned experiment, albeit with a different meaning. Time dilation and length contraction are not considered as being real phenomena. Time, in fact, is peremptorily postulated as being absolute. Nonetheless, this strong assumption does not imply that instruments and devices of whatever kind, finalized to measure time, are not influenced by motion. In particular, although the “light clock” in the mobile frame ticks, so to say, more slowly than the one at rest, it can be easily shown how no time dilation actually occurs. The apparent length contraction is considered as being nothing but a banal consequence of a deceptive time measurement

Music Algebra: Harmonic Progressions Analysis and CAT (Cataldo Advanced Transformations)

In this article we formally introduce an original method, the purpose of which fundamentally lies in providing musicians with a reliable instrument that may effectively assist them in carrying out, as simply and intuitively as possible, the analysis of whatever chord progression, without resorting to the so-called "modal interchange". Net of a single exception (a routine named "structure reduction"), the whole method is based on a series of harmonic transformations. The above-mentioned transformations, named CAT (the acronym stands for Cataldo Advanced Transformations), turn out to be nothing but inverse chord substitutions characterized by specific conditions and restrictions. The method arises from the analysis of a considerable number of chord progressions, devoting particular (although not exclusive) attention to traditional jazz compositions: in this regard, it is worth highlighting how a significant improvement of CAT has been achieved by conducting an extremely thorough analysis of the so-called LEGO Bricks (public domain harmonic patterns)

Natriuretic peptides and cardiovascular damage in the metabolic syndrome. Molecular mechanisms and clinical implications

Natriuretic peptides are endogenous antagonists of vasoconstrictor and salt- and water-retaining systems in the body's defence against blood pressure elevation and plasma volume expansion, through direct vasodilator, diuretic and natriuretic properties. In addition, natriuretic peptides may play a role in the modulation of the molecular mechanisms involved in metabolic regulation and cardiovascular remodelling. The metabolic syndrome is characterized by visceral obesity, hyperlipidaemia, vascular inflammation and hypertension, which are linked by peripheral insulin resistance. Increased visceral adiposity may contribute to the reduction in the circulating levels of natriuretic peptides. The dysregulation of neurohormonal systems, including the renin-angiotensin and the natriuretic peptide systems, may in turn contribute to the development of insulin resistance in dysmetabolic patients. In obese subjects with the metabolic syndrome, reduced levels of natriuretic peptides may be involved in the development of hypertension, vascular inflammation and cardio vascular remodelling, and this may predispose to the development of cardiovascular disease. The present review summarizes the regulation and function of the natriuretic peptide system in obese patients with the metabolic syndrome and the involvement of altered bioactive levels of natriuretic peptides in the pathophysiology of cardiovascular disease in patients with metabolic abnormalities

Magneto-Electric Effects on Sr Z-type Hexaferrite at Room Temperature

In this paper, magnetoelectric effects of Sr Z-type hexaferrite, Sr3Fe24Co2O41, at room temperature is measured. The change in remanence magnetization was measured by applying a DC voltage or electric field across a slab of hexaferrite. Changes of ~ 18% in remanence was observed in an electric field of 10,000V/cm implying a similar change in the microwave permeability at frequencies below 3GHz. Also, a change in dielectric constant at 1 GHz of ~16% in a magnetic field of only 320 Oe was measured. In these types of measurements high resistivity is critical in order to reduce current flow in the hexaferrite. The resistivity of the hexaferrite was raised to 4.28x10^8 ohm-cm by annealing under oxygen pressure. The measurements indicate that indeed electric polarization and magnetization changes were induced by the application of magnetic and electric fields, respectively. The implications for microwave applications appear to be very promising at room temperature.Comment: 8 pages, 3 figures, MMM conference and Journal of applied Physic

Magnetic fields generated by r-modes in accreting millisecond pulsars

In millisecond pulsars the existence of the Coriolis force allows the development of the so-called Rossby oscillations (r-modes) which are know to be unstable to emission of gravitational waves. These instabilities are mainly damped by the viscosity of the star or by the existence of a strong magnetic field. A fraction of the observed millisecond pulsars are known to be inside Low Mass X-ray Binaries (LMXBs), systems in which a neutron star (or a black hole) is accreting from a donor whose mass is smaller than 1 $M_\odot$. Here we show that the r-mode instabilities can generate strong toroidal magnetic fields by inducing differential rotation. In this way we also provide an alternative scenario for the origin of the magnetars.Comment: 6 pages, 3 figures, Proceedings conference "Theoretical Nuclear Physics", Cortona October 200