The ninth-century treatises Musica and Scolica Enchiriadis are the first musical writings in the West to present a theory of organum, a mode of plainchant performance that is the earliest known form of Western medieval polyphony. The fundamental principle of this theory is that the intervallic relationship between the simultaneous melodic lines be one of "consonance" . Nevertheless, intervals arise between the voice-parts that are not symphoniae; the theory responds to this, not by explicitly invoking the concept of dissonance, (...) but by excluding these non-symphonic or non-consonant intervals from the concept of "organum." Through close analysis of the relevant texts, the dissertation seeks to explicate this concept of organum as symphonia in terms of a "metaphysics of consonance" that the Enchiriadis theorists took over from the most influential of the musical writings of late Antiquity, the De institutione musica of Boethius. ;The metaphysics of consonance projected therein is a particular development of the Pythagorean-Platonic conception of music, in which the symphoniae, because of their simple numerical ratios, represent the universal, divinely ordained rational principles of cosmic order and harmony. After a section devoted to showing that such "speculative" ideas about music formed the basis of the "practical" theory of the Enchiriadis treatises, the dissertation goes on in Part II to find that the relationship between consonance and dissonance in the Boethius Musica is structured as an unequal, hierarchized opposition, in which consonance holds the dominant position in particular because of its virtual identification with the metaphysical ideal of unity. Conversely dissonance, the opposed term of the hierarchy, represents the negative values of duality and difference, and hence discord, conflict, and disorder. Consequently, through various textual strategies, consonance is identified with "music" itself, while dissonance is effectively excluded from that domain. ;The concept of organum in the Enchiriadis treatises is found to be determined by this same metaphysics of consonance, with its consequent tendency to exclude or marginalize dissonance, a conceptual pattern that has resonated throughout the subsequent history of polyphonic theory and practice in the West. (shrink)

Reinvention of the form of expression is a conceptual approach characteristic for the evolution of all arts. This research study provides one such step forward in the advancement of scientific paper, a standard form of expression in natural sciences, toward more progressive terrains. The paper adopts the form of a theatrical play where a scientific family of four attempts to find the way around a writer’s block (Act I). Their idealess sense of confinement is overcome through arts or, more specifically, (...) through scientific research implementing the aesthetics of music as its key element. The characters record compositions differing in the degrees of consonance, rhythmicity and tonality, and play them to birds to observe their vocal and behavioral responses (Act II). They note that the birdsong volume drops significantly when the piano tunes, especially the compositionally complex ones, are played to the birds and increases signifcantly when the white noise of ocean waves is played. The bird count experiment proves indirectly that the birdsong volume reduction is an auditory response of the birds to music rather than the effect of their migrating to or away from the sound source. This science with the flavor of art elevates the characters beyond the limits of their confinement and they, exalted and uplifted, gain ideas for creative research in their own disciplines of biomedical science (Act III). They relinquish the newly gained freedom in favor of embracing love for humanity that underlies medical research and return to their confinement, where they conduct, in the coda of the paper, a series of experiments that venture beyond musicology and ornithology and fall in the domains of tissue engineering and drug delivery, but also psychology (Act III). First, sparrow nests are used as templates for tissue engineering constructs, which facilitate the growth of human fibroblastic cells better than their artificial, gridded replicas. Next, the shell of an Easter egg, predominantly calcite in composition, is used with success as a drug delivery carrier. Lastly, the bird nest drawing experiment demonstrates a greater mental health of children than that of the adults, correlating with one of the overarching points of the paper, which is to present children as a model for grownups to follow rather than the other way around. Over the course of the play, the characters discuss the value of the various fusions between art and science, question the limits of human language and repeatedly go off-topic to celebrate the freeness of the creative thinking process. The play reports on real-life research methods and scientific results through a narrative, without diminishing their empirical rigor and analytical accuracy. (shrink)

7 lectures, Torquay, UK, August 12-20, 1924 (CW 311) These seven intimate, aphoristic talks were presented to a small group on Steiner's final visit to England. Because they were given to "pioneers" dedicated to opening a new Waldorf school, these talks are often considered one of the best introductions to Waldorf education. Steiner shows the necessity for teachers to work on themselves first, in order to transform their own inherent gifts. He explains the need to use humor to keep their (...) teaching lively and imaginative. Above all, he stresses the tremendous importance of doing everything in the knowledge that children are citizens of both the spiritual and the earthly worlds. And, throughout these lectures, he continually returns to the practical value of Waldorf education. These talks are filled with practical illustrations and revolve around certain themes--the need for observation in teachers; the dangers of stressing the intellect too early; children's need for teaching that is concrete and pictorial; the education of children's souls through wonder and reverence; the importance of first presenting the "whole," then the parts, to the children's imagination. Here is one of the best introductions to Waldorf education, straight from the man who started it all. German source: Die Kunst des Erziehens aus dem Erfassen der Menschenwesenhiet (GA 311). ∞ ∞ ∞ SYNOPSIS OF THE LECTURES LECTURE 1: The need for a new art of education. The whole of life must be considered. Process of incarnation as a stupendous task of the spirit. Fundamental changes at seven and fourteen. At seven, the forming of the "new body" out of the "model body" inherited at birth. After birth, the bodily milk as sole nourishment. The teacher's task to give "soul milk" at the change of teeth and "spiritual milk" at puberty. LECTURE 2: In first epoch of life child is wholly sense organ. Nature of child's environment and conduct of surrounding adults of paramount importance. Detailed observation of children and its significance. In second epoch, seven to fourteen, fantasy and imagination as life blood of all education, e.g., in teaching of writing and reading, based on free creative activity of each teacher. The child as integral part of the environment until nine. Teaching about nature must be based on this. The "higher truths" in fairy tales and myths. How the teacher can guide the child through the critical moment of the ninth year. LECTURE 3: How to teach about plants and animals (seven to fourteen). Plants must always be considered, not as specimens, but growing in the soil. The plant belongs to the earth. This is the true picture and gives the child an inward joy. Animals must be spoken of always in connection with humans. All animal qualities and physical characteristics are to be found, in some form, in the human being. Humans as synthesis of the whole animal kingdom. Minerals should not be introduced until twelfth year. History should first be presented in living, imaginative pictures, through legends, myths, and stories. Only at eleven or twelve should any teaching be based on cause and effect, which is foreign to the young child's nature. Some thoughts on punishment, with examples. LECTURE 4: Development of imaginative qualities in the teacher. The story of the violet and the blue sky. Children's questions. Discipline dependent on the right mood of soul. The teacher's own preparation for this. Seating of children according to temperament. Retelling of stories. Importance of imaginative stories that can be recalled in later school life. Drawing of diagrams, from ninth year. Completion and metamorphosis of simple figures, to give children feeling of form and symmetry. Concentration exercises to awaken an active thinking as basis of wisdom for later life. Simple color exercises. A Waldorf school timetable. The "main lesson." LECTURE 5: All teaching matter must be intimately connected with life. In counting, each different number should be connected with the child or what the child sees in the environment. Counting and stepping in rhythm. The body counts. The head looks on. Counting with fingers and toes is good (also writing with the feet). The ONE is the whole. Other numbers proceed from it. Building with bricks is against the child's nature, whose impulse is to proceed from whole to parts, as in medieval thinking. Contrast atomic theory. In real life we have first a basket of apples, a purse of coins. In teaching addition, proceed from the whole. In subtraction, start with minuend and remainder; in multiplication, with product and one factor. Theorem of Pythagoras (eleven-twelve years). Details given of a clear, visual proof, based on practical thinking. This will arouse fresh wonder every time. LECTURE 6: In first seven years etheric body is an inward sculptor. After seven, child has impulse to model and to paint. Teacher must learn anatomy by modeling the organs. Teaching of physiology (nine to twelve years) should be based on modeling. Between seven and fourteen astral body gradually draws into physical body, carrying the breathing by way of nerves, as playing on a lyre. Importance of singing. Child's experience of well being like that of cows chewing the cud. Instrumental music from beginning of school life, wind or strings. Teaching of languages; up to nine through imitation, then beginnings of grammar, as little translation as possible. Vowels are expression of feeling, consonants are imitation of external processes. Each language expresses a different conception. Compare head, Kopf, testa. The parts of speech in relation to the life after death. If language is rightly taught, out of feeling, eurythmy will develop naturally, expressing inner and outer experiences in ordered movements--"visible speech." Finding relationship to space in gymnastics. LECTURE 7: Between seven and fourteen soul qualities are paramount. Beginnings of science teaching from twelfth year only, and connected with real phenomena of life. The problem of fatigue. Wrong conceptions of psychologists. The rhythmic system, predominant in second period, never tires. Rhythm and fantasy. Composition. Sums from real life, not abstractions. Einstein's theory. The kindergarten--imitation of life. Teachers' meetings, the heart of the school. Every child to be in the right class for its age. Importance of some knowledge of trades, e.g., shoemaking, handwork, and embroidery. Children's reports-- characterization, but no grading. Contact with the parents. QUESTIONS AND ANSWERS: The close relationship of Multiplication and Division. How to deal with both together. Transition from the concrete to the abstract in Arithmetic. Not before the ninth year. Healthiness of English weights and measures as related to real life. Decimal system as an intellectual abstraction. Drawing. Lines have no reality in drawing and painting, only boundaries. How to teach children to draw a tree in shading, speaking only of light and color. (Illustration). Line drawing belongs only to geometry. Gymnastics and Sport. Sport is of no educational value, but necessary as belonging to English life. Gymnastics should be taught by demonstration. Religious Instruction. Religion lessons in the Waldorf school given by Catholic priest and Protestant pastor. "Free" religion lessons provided for the other children. Plan of such teaching described, of which the fundamental aim is an understanding of Christianity. The Sunday services. Modern Language Lessons. Choice of languages must be guided by the demands of English life. These can be introduced at an early age. Direct method in language teaching. Closing words by Dr. Steiner on the seriousness of this first attempt to found a school in England. (shrink)

Many pioneers of the Scientific Revolution such as Galileo, Kepler, Stevin, Descartes, Mersenne, and others, wrote extensively about musical theory. This was not a chance interest of a few individual scientists. Rather, it reflects a continuing concern of scientists from Pythagorean times onwards to solve certain quantifiable problems in musical theory. One of the issues involved was technically known as ‘the division of the octave’, the problem, that is, of which notes to make music with. Simon Stevin's contribution to (...) this issue, in his treatise Vande Spiegheling der Singconst , is usually conceived of as a remarkably early plea for equal temperament, which is the tuning system we nowadays all take for granted. In this paper I show that, even though it is true that Stevin calculated the figures for what is now known as equal temperament, in fact the subject of temperament has almost nothing to do with his accompanying considerations, and that, therefore, his calculations served another purpose. A careful analysis of the problem situation in the science of music around 1600, reveals that Stevin's treatise highlights a particular stage in the history of what has always been the core issue of the science of music, namely, the problem of consonance. This is the search for an explanation, on scientific principles, of Pythagoras' law: ‘Why is it that those few musical intervals which affect our ear in a sweet and pleasing manner, correspond to the ratios of the first few integers?’ Through an analysis of the source material available we find that Stevin's theory, which makes no sense if interpreted as an early stage in the ‘evolution’ of equal temperament, was meant as a solution—as freshly original as it was wrongheaded—to this perennial problem of consonance, which has continued to baffle some of the best scientific minds from the very beginning of science to the present day. (shrink)

.In this paper, I address Descartes’ claims that sensory perceptions function to aid and preserve the subject in interacting with the world, and focus specifically on the ‘valence’, or agreeable/disagreeable quality, that characterizes many sensations. I show how Descartes considers this aspect of sensation to be a significant factor in the ecological role of sensory perception and I then turn to a kind of case that seems to pose a problem for this view: that of aesthetic pleasure. I consider Descartes’ (...) remarks on a particular kind of aesthetic pleasure – that found in musical consonance – and argue that his discussion of this phenomenon reveals that he distinguishes between two distinct kinds of valence – evaluative sensory valence and aesthetic valence – only one of which functions to report directly on ecological evaluation. Further, I suggest that the best way to understand the distinction between these is by appealing to Descartes’ three grades of sensory perception. (shrink)

1. In the Physics and Metaphysics, Aristotle lays out four kinds of causes and provides examples of each. Bronze and silver are offered as examples of the material causes of artefacts, the father a...