Non-Euclidean Biosymmetries and Algebraic Harmony in Genomes of Higher and Lower Organisms

The article is devoted to the study of the relationship of non-Euclidean symmetries in inherited biostructures with algebraic features of information nucleotide sequences in DNA molecules in the genomes of eukaryotes and prokaryotes. These genomic sequences obey the universal hyperbolic rules of the oligomer cooperative organization, which are associated with the harmonic progression 1/1, 1/2, 1/3,.., 1/n. The progression has long been known and studied in various branches of mathematics and physics. Now it has manifested itself in genetic informatics. The performed analysis of the harmonic progression revealed its connection with the cross-ratio, which is the main invariant of projective geometry. This connection consists in the fact that the magnitude of the cross-ratio is the same and is equal to 4/3 for any four adjacent members of this progression. The long DNA nucleotide sequences have fractal-like structure with so called epi-chains, whose structures are also related to the harmonic progression and the projective-geometrical symmetries. The received results are related additionally to a consideration of DNA double helix as helical antenna. This fact of the connection of genetic informatics with the main invariant of projective geometry can be used to explain the implementation of some non-Euclidean symmetries in genetically inherited structures of living bodies.

Harmonic Progression in Bioinformatics and Recurrent Series in Inherited Biostructures

The article is devoted to the study of new approaches to the development of mathematical models in genetic biomechanics, which studies the structural relationships of the genetic coding system with genetically inherited biological forms. More specifically, we are talking about models based on the recurrent harmonic progression whose connection with the information sequences of DNA molecules in the genomes of higher and lower organisms was recently revealed. In particular, the article describes previously unknown connections of the function of natural logarithms with the structures of the molecular genetic system, which allow modelling the main psychophysical logarithmic law by Weber-Fechner and also many other logarithmic structures in genetically inherited biological systems. In physics, the harmonic progression is traditionally considered, first of all, as related to standing waves in resonators. Our results are correlated with Frohlich’s vibration-resonant theory about collective quantum effects and long-range communication in biological systems.

Revision of the Imitation Rules in the Madrigals of Luca Marenzio and Carlo Gesualdo

Статья посвящена пересмотру правил строгого стиля в имитационном письме мадригалов Луки Маренцио и Карло Джезуальдо. Показаны основные признаки мадригальной имитации: 1) особые типы соджетто, которые можно объяснить воздействием идеи imitazione delle parole: соджетто-возглас (с текстом Ahimè, Io moro и т. п.) и звукоизобразительное соджетто; 2) предельная краткость имитационных построений и их группировка по принципу имитационного «ядра» и имитационного «развертывания»; 3) контрастные сопоставления смежных имитационных групп; 4) паузирование во всех голосах ансамбля как один из приемов такого сопоставления; 5) окказиональный характер интервалов имитации, определяемых гармонической вертикалью, идеей хроматического порядка тонов в каждой партии ансамбля (у Джезуальдо) и т. п. This article focuses on the imitative writing in the madrigals of Luca Marenzio and Carlo Gesualdo. Many of the properties of these imitations do not conform to the rules of strict style. Among special features of madrigal imitation are: 1) new types of soggetto which can be attributed to the influence of the idea of imitazione delle parole: soggetto-exclamation (with the text Ahimè, Io moro, etc.) and sound-visual soggetto; 2) the utmost brevity of the imitative section; 3) the opposition of the adjacent imitative sections; 4) simultaneous rests in all the voices of the ensemble at the moment of such opposition; 5) occasional intervals of imitation caused by the harmonic progression or chromatic order of the tones in each voice of the madrigal (Gesualdo), etc.

Hyperbolic Rules in Genomes, the Harmonic Progression and Recurrence Sequences in Algebraic Biology

The article is devoted to biological models using recurrence sequences, which are connected with the harmonic progression 1, 1/2, …, 1/n, and some cooperative properties of genomes. The harmonic progression is itself one of the recurrence sequences based on the harmonic mean. This progression appears in the hyperbolic rules of oligomer cooperative organization in eukaryotic and prokaryotic genomes. This allows thinking that the harmonic progression is also related to inherited physiological systems, which must be structurally consistent with the genetic coding system for their transmission to descendants and survival in evolution. The harmonic progression is one of historically known mathematical series, whose features were studied by Pythagoras, Leibniz, Newton, Euler, Fourier, Dirichlet, Riemann. It is widely used in many known algorithms and is closely related to some other important mathematical objects, for example, the function of the natural logarithm and harmonic numbers. Accordingly, the article describes the possibilities of using these interrelated mathematical objects to model biological structures, including logarithmic spirals and some other. Modeling inherited spiral configurations seems to be a particularly urgent task, since they are extremely common at all levels of organization of living bodies and, according to Goethe, are lines of life. The principle of a recurrence similarity, that is a special similarity of parts and transformations presented in recurrence sequences of numbers and matrix operators (the scale similarity and scale transformations are only particular cases of such similarity), is considered as one of the key principles of structural organization of living bodies.

Commentary on Shaffer et al.: A cluster analysis of harmony in the McGill Billboard dataset

This short commentary on the target paper by "A cluster analysis of harmony in the McGill Billboard" by Shaffer et al. starts with observing that not all harmonic progressions that are theoretically possible are equally common. Instead, some progressions are more popular than others in popular. In fact, certain harmonic progressions are closely associated with specific styles and sub-genres and it is the aim of the target paper to provide a meaningful classification system for harmonic progression. The commentary identifies several strengths of the target paper, including a nice balance between rigorous empirical work and providing a context and interpretations that are musicologically well-informed. In its critique the commentary points to the limitations of only using harmonic bigrams (i.e. the transitions between two chords) as the empirical data and the missing link to related literature on harmonic modelling in the music information retrieval community.

Hyperbolic Rules of the Oligomer Cooperative Organization of Eukaryotic and Prokaryotic Genomes

The author's method of oligomer sums for analysis of oligomer compositions of eukaryotic and prokaryotic genomes is described. The use of this method revealed the existence of general rules for cooperative oligomeric organization of a wide list of genomes. These rules are called hyperbolic because they are associated with hyperbolic sequences including the harmonic progression 1, 1/2, 1/3, .., 1/n. These rules are demonstrated by examples of quantitative analysis of many genomes from the human genome to the genomes of archaea and bacteria. The hyperbolic (harmonic) rules, speaking about the existence of algebraic invariants in full genomic sequences, are considered as candidates for the role of universal rules for the cooperative organization of genomes. The described phenomenological results were obtained as consequences of the previously published author's quantum-information model of long DNA sequences. The oligomer sums method was also applied to the analysis of long genes and viruses including the COVID-19 virus; this revealed, in characteristics of many of them, the phenomenon of such rhythmically repeating deviations from model hyperbolic sequences, which are associated with DNA triplets. In addition, an application of the oligomer sums method are shown to the analysis of the following long sequences: 1) amino acid sequences in long proteins like the protein Titin; 2) phonetic sequences of long Russan literary texts (for checking of thoughts of many authors that phonetic organization of human languages is deeply connected with the genetic language). The topics of the algebraic harmony in living bodies and of the quantum-information approach in biology are discussed.

The Thanatotic and the Tonnetz

The chapter describes how the Andante from Josef Suk’s Asrael Symphony is a funeral march in all but name. It celebrates the lives of Suk’s teacher Dvořák and his wife Otilie, whose death during the work’s composition famously changed the projected optimistic tone. The various moods of this movement hang together because of a heavily asserted inner pedal of d♭, heard prominently in various instruments throughout. This pitch is never dissonant, and chords are constructed around it in such a way as to replicate a perfect hexagon on the common neo-Riemannian graphical Tonnetz. The associations of death with limited harmonic progression are aligned with Freud’s essay “Mourning and Melancholia.” The same compositional technique occurs in each of the five pieces from About Mother, Op. 28. The dual association held by this technique between maternal warmth and death leads to a critique of the basic Freudian death drive inspired by Lacan, Deleuze, and Lyotard. A flexible approach to the Tonnetz is adumbrated, which allows for the integration of tense tetrachords.

A Linguistic Theory of Chromatic Harmonic Substitution and Progression in the Diatonic Unconscious

The chapter constructs an energetic model of harmonic progression in which tense chords are signifiers of tonal functions (Riemann’s T, S, and D functions). The paradigm adopts the linguistic axes that Lacan mapped as metaphor and metonymy, which were crucial to the formation of a human subject at whose center lies désir. The theoretical claims build on the recent work of David Lewin (2007), Richard Cohn (2012a), Steven Rings (2011a), Dmitri Tymoczko (2011a), Brian Hyer (2011), and others but also reevaluate the earlier work of Ernest Kurth (1920), Hugo Riemann (1893), and Ernö Lendvai (1993). The chapter seeks to account for voice leading, modulation, and tonal diversity in a broad range of works

Hyperbolic Rules of the Oligomer Cooperative Organization of Eukaryotic and Prokaryotic Genomes

The author's method of oligomer sums for analysis of oligomer compositions of eukaryotic and prokaryotic genomes is described. The use of this method revealed the existence of general rules for cooperative oligomeric organization of a wide list of genomes. These rules are called hyperbolic because they are associated with hyperbolic sequences including the harmonic progression 1, 1/2, 1/3, .., 1/n. These rules are demonstrated by examples of quantitative analysis of many genomes from the human genome to the genomes of archaea and bacteria. The hyperbolic (harmonic) rules, speaking about the existence of algebraic invariants in full genomic sequences, are considered as candidates for the role of universal rules for cooperative organization of genomes. The described phenomenological results were obtained as consequences of the previously published author's quantum-information model of long DNA sequences. The oligomer sums method was also applied to the analysis of long genes and viruses including the COVID-19 virus; this revealed, in characteristics of many of them, the phenomenon of rhythmically repeating deviations from model hyperbolic sequences; these deviations are associated with DNA triplets and should be systematically analyzed for a deeper understanding the genetic coding system. The topics of the algebraic harmony in living bodies and of the quantum-information approach in biology are discussed.