Music of the Spheres

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A partir de: FREITAS, Sérgio Paulo Ribeiro de. Que acorde ponho aqui?  Harmonia, práticas teóricas e o estudo de planos tonais em música popular. Tese (Doutorado em Música). Instituto de Artes, Universidade Estadual de Campinas, 2010. p. 434-449.

As Robert R. Reilly mentions “when the forms of musical expression change radically,
it is always because the underlying metaphysical grasp of reality has changed as well. Music is
in a way, the sound of metaphysics, or metaphysics in sound”.

This essay considers two lost paintings of the five senses by Jan Brueghel the Elder and twelve Antwerp masters which were commissioned in 1617 by the city of Antwerp for the governors of the Habsburg Netherlands, Archduke Albert and the Infanta Isabella. Through an examination of contemporary replicas of the lost works it is suggested that, rather than being fully-fledged allegories or representations, they depend upon an ideal of polyphonic harmony akin to that expressed in the concept of the Music of the Spheres. The article explores the different semiotic character of the two pendants and the significance of particular motifs, among them a sheet of paper displaying geometric diagrams from Euclid’s Elements and the Latin phrase 'Utram maius aut minus' (‘which is greater or lesser’). Themes include: the articulation of difference within a regime of resemblance; giving voice to the complex politics of sovereignty and gender in the Habsburg Netherlands; and ways in which these works can be related to the debates surrounding the relationship between the soma and the psyche on the eve of the Cartesian rupture. The pendant Senses are viewed as a response to the threatened harmony between ‘greater and lesser’ to which the Habsburg Netherlands were ideologically committed.

Recent developments within phenomenology have brought to light the indebtedness of phenomenological scientific philosophy to Ancient Greek philosophy. The recent trend that builds on the ancient precedents found in the theories of forms, for example, has demonstrated the importance of the philosophy of Plato and Aristotle for contemporary manifestations of the development of phenomenological eidetic science. This thesis builds on three parallel developments in the phenomenology of time that equally indicate the significance of the ancient Hellenic exact mathematical science of spherical cosmology for the further propagation of phenomenological philosophy. The hypothesis of the infinite sphere gives phenomenology an external foundation capable of accounting for the constitution of the phenomenal universe, possible worlds, and the harmonic continuum of life spanning the inner and outer cosmos. Phenomenological cosmology offers a unified metaphysical framework for first philosophy and the special sciences, with particularly interesting implications for empirical cosmology and theoretical physics. Phenomenology of the spheres brings these phenomenological cosmological insights together in the geometric comprehension of the infinite sphere.

In the 1970s the Chilean biologist Francisco Varela developed a systems theory of life as autopoietic, or self-creating, on the formal basis of the mathematician George Spencer-Brown's 1969 book Laws of Form. Although Varela saw the great power and simplicity of Spencer-Brown' s calculus, he appropriated Spencer-Brown's calculus by adding a third law to the original two laws of form. This law makes self-reference explicit, and I'll argue that it is a redundant addition because self-reference is already implied by indication. The addition of this redundancy has the effect of separating the transcendental realm of constitutive operations from the natural realm of effects. Anna-Teresa Tymieniecka's phenomenology of life as ontopoiesis, on the other hand, succeeds in developing a theory of life on the formal ontological basis prepared by Husserl's phenomenology, transcendental logic, and the living tradition of a mathesis universalis. Tymieniecka's phenomenological theory of life is a breakthrough to life's inner workings, and rests on an ontologically robust foundation. By drawing attention to the calculus behind the calculus, I hope to initiate the interpretation of Spencer-Brown's calculus of indications as an important manifestation of the mathesis universalis, and apply the interpretation to the place prepared by Tymieniecka's phenomenology of ontopoiesis.

'Music is existence. ' Sun Ra In this paper, I want to outline how 'sacred music' and 'performance' might be understood in the broadest possible terms -as nothing less than a description of reality itself. This may seem a grandiose -not to say ridiculous -claim; nonetheless, by concentrating on the Timaeus, I want to show that, for Plato, the cosmos is musically 'constituted' by a divine creator and that, as such, its fundamental operation is to be understood as a mathematico-harmonic performance.

This article focuses on twelfth-century philosophical theories of cosmological harmony, built on mathematical proportions. The late-ancient authors Calcidius, Macrobius, and Boethius are the background of the twelfth-century harmonic cosmos. Mathematical proportions underlie the constitution of the world-soul and of world. The four elements bind them through mathematical proportions, and different parts of cosmos and their rational animals.

Este artículo presenta un barrido bibliográfico a través de la metodología de lectura crítica y posterior catalogación de los diversos modelos que se han desarrollado en Occidente, desde el siglo I hasta finales del siglo XX, con la meta de tratar de interpretar las posiciones o velocidades de los planetas como alturas musicales. Se concluye que estos modelos pueden catalogarse en tres grandes familias: derivados de la interpretación de las velocidades orbitales de los planetas como frecuencias más altas o más
bajas, derivados de las proporciones de las distancias de los planetas entre sí (para interpretar dichas distancias como intervalos musicales) y derivados de una combinación entre ambos cuando ni las distancias ni las velocidades son fijas, como en el caso del modelo de órbitas elípticas y las tres leyes de movimiento planetario de Kepler. El aporte original de este artículo consiste en que presenta dichos modelos en un texto compacto y su clara clasificación, lo que facilita enormemente su utilización práctica
para la creación musical, o bien en composición preescrita, o bien para extemporización en tiempo real, y así posibilita la utilización artística de modelos cuyo alcance histórico ha estado circunscrito al ámbito teórico de la música especulativa o de la percepción sonora de modelos cosmológicos.

The deduction, calculation or assignment of musical parameters to the celestial bodies is known as the ‘tradition of music of the spheres,’ and, in the West, it goes back to the Pythagorean school of the sixth century BC. In this article, several proposals in this regard will be reviewed, cataloged and discussed, starting from the first century with the proposals of several authors of the Roman world, until the end of the 1980s, with the proposal of Swiss mathematician Hans Cousto. Here, I will limit myself to the proposals that assign the height parameter to the celestial bodies, and save for future publications the topic of the rhythm of celestial bodies, also addressed by the tradition of the music of the spheres, but which will not be covered here. I have grouped the reviewed proposals in four groups, based on their theoretical and procedural base perspective: either interpreting the translational speeds of the celestial bodies as musical heights, interpreting the orbital distances between them as musical intervals, or combinations between both parameters (as in the case of Johannes Kepler’s proposal in his book The Harmony of the World, of 1619), or a more radical Pythagorean-Platonic perspective that ignores the observational and assigns these equivalences between music and celestial bodies from proportional mathematics and pure music theory.

La comprensión metafísica de la música no es en ningún caso susceptible de ser limitada a la interpretación o al análisis de una forma artística. Prueba de ello es el trazo epocal que se podría reservar desde Pitágoras hasta Heidegger, y más acá. Pero también más allá: todo el pensamiento occidental parece conferir un estatuto excepcional al sonido musical y a su audición, en la medida en que siempre parece conducir al terreno propio de la especulación, en donde es preciso abandonar al sonido sensible para intentar escuchar un sonido ideal, inaudible perceptivamente. Pero más allá, en la hipótesis sobre el origen de la escritura cuneiforme en Mesopotamia se puede alcanzar algunas conjeturas que sitúan, en el seno de la gestualidad sensible que produce la escritura, una explicación de un sonido que inaudible por su falta de sentido, permanece guardada en toda voz y en todo sentido.

Las relaciones entre música y poesía son de sobra conocidas y los poetas recurren a
la música en su proceso de escritura o incluyen a menudo referencias musicales en
sus poemas, como es el caso de Gonzalo Rojas. El poeta chileno, además, posee un
especial sentido del ritmo y la sonoridad que lo hace especialmente “musical”.
El presente trabajo plantea el análisis de la configuración del poema “Cítara mía” desde
una perspectiva interdisciplinar, a través del comentario de las referencias y símbolos
musicales (ilustrados con ejemplos de la Historia del Arte) y, en menor medida, de
sus cualidades rítmicas.
Palabras clave: poesía chilena, música y poesía, comparación de las artes.
The relationships between music and poetry are well known and poets often turn to
music in their writing process or include musical references in their poems, as is the
case of Gonzalo Rojas. The Chilean poet also possesses a special sense of rhythm
and sonority that makes his work especially musical. This work proposes an analysis
of the configuration of the poem “Cítara mía” from an interdisciplinary perspective
through a commentary on references and musical symbols (illustrated with examples
from art history) and, to a lesser extent, its rhythmical qualities.
Keywords: chilean poetry, music and poetry, comparison of arts.

Olomouc Úvod Hledání harmonie světa je velmi stará záleţitost. Začíná u pythagorejců, kteří věřili, ţe svět byl stvořen nejdokonalejší moţný, a proto proporce uţité při jeho stavbě jsou ty nejharmoničtější. Právě v hudbě pythagorejci objevili harmonické proporce, protoţe dokonalé poměry tvoří konsonance, zatímco nedokonalé poměry dávají disonance. Prakticky to můţeme pozorovat na napnuté struně. Prázdná struna zní základním tónem, kdyţ ji rozdělíme v harmonickém poměru a drnkneme na takto oddělenou část struny, dostaneme harmonický interval k základnímu tónu. U toho ale pythagorejci nekončí. Celý kosmos podle nich neustále zní harmonií dokonalých poměrů, hudbou sfér. Není totiţ moţné, aby se tak velká a rychlá tělesa jako planety pohybovala po svých drahách neslyšně. To jen my je pro velkou vzdálenost neslyšíme. 1 Tato práce sleduje Keplerovu téměř celoţivotní cestu k vlastnímu pojetí harmonie světa, cestu, na níţ jako milníky stojí tři zákony planetárního pohybu nesoucí Keplerovo jméno. Mysterium Cosmographicum Keplerova první práce, kterou vydal roku 1596 jako pětadvacetiletý, nese obšírný název, zkracovaný obvykle jako Mysterium Cosmographicum (dále MC) a popisuje Keplerův první model kosmu. Základem pro tento model byla tzv. Platónská tělesa, totiţ jediných pět mnohostěnů, jejichţ stěny jsou shodné pravidelné mnohoúhelníky přiléhající k sobě pod shodnými úhly, a jejichţ všechny vrcholy leţí na povrchu koule, která je jim opsána, a středy jejich stěn se dotýkají koule, která je jim vepsána. 2 Platón tato tělesa prohlašuje v dialogu Timaios 3 za základní stavební jednotky světa, jakési atomy, z nichţ kaţdý druh tělesa náleţí podle svých vlastností jednomu elementu: čtyřstěn ohni, krychle zemi, osmistěn vzduchu a dvacetistěn vodě. Tato čtyři tělesa mají strany ve tvaru čtverce (krychle) nebo rovnostranného trojúhelníka (všechna ostatní). Pátým tělesem je dvanáctistěn, který má jediný strany ve tvaru 1 Rozlišit, co je pythagorejská filosofie a co ne, je nelehký úkol, vzhledem k tomu, ţe neznáme s jistotou ani jména většiny pythagorejců. Co se týká konceptu harmonie světa, uţ od středověku jsou informace o něm čerpány ze spisu Severina Boethia De institutione musica libri VI., z nějţ je pravděpodobně znal i Kepler. Srozumitelný výklad číselných poměrů, které tvoří hudební intervaly poskytuje např. APEL, Willi. Mathematics and Music in the Middle-Ages. In: BINKLEY, T. E. (ed.). Willi Apel: Medieval music. Collected articles and reviews with a foreword

"Show (between 45' and 1h25) created by Guy Boistel and Stéphane Le Gars in 2011. Around KEPLER's Harmony of the World.
— When Jazz brings to light the harmony of the spheres and explains the movement of the planets, and vice-versa — !
Show for all audience.
Pictures gallery, audio and video pn our wix.com page below.

Resumen:El presente artículo busca dar a conocer la importancia del trabajo de Johannes Kepler en la actualización, modificación, continuidad y transmisión posterior de las teorías de correspondencias entre planetas y alturas musicales en la tradición de la "Música de las Esferas", noción que para él tenía mucha importancia dentro de su concepción teológica del funcionamiento del cosmos. Lejos de desbancar esta antigua idea que en su origen funcionaba dentro del paradigma cosmológico geocéntrico, Kepler la adapta al sistema heliocéntrico copernicano y a sus propias propuestas de órbitas elípticas de los planetas, notando que estos nuevos modelos cosmológicos requieren de una nueva teoría de la música de las esferas: dado que se deduce que la velocidad de los planetas no es constante, esto tiene implicaciones importantes en los "tonos" (o dicho actualmente "alturas" o "notas") de cada planeta, que dejan de ser una altura única, como en los mode...

Throughout history, astrology has influenced many aspects of Western culture, including music. Indeed, through the doctrine of correspondences of the Renaissance and its forerunner in Antiquity, the neo-Platonic via positiva of analogical and symbolic thinking, music and astrology have been linked since ancient Greek times by means of sets of tables of correspondences and equivalences based on different logics of analogy, comparison and similarity. These range from neo-Pythagorean geometry and ratio theory to Theosophical eschatology, passing through scientificist extrapolations of Kepler’s theories and even statistical approaches to the quantification of appearances of musical keys in canonical classical music repertoires related to the planets or constellations.

El presente artículo busca dar a conocer la importancia del trabajo de Johannes Kepler en la actualización, modificación, continuidad y transmisión posterior de las teorías de correspondencias entre planetas y alturas musicales en la tradición de la “Música de las Esferas”, noción que para él tenía mucha importancia dentro de su concepción teológica del funcionamiento del cosmos. Lejos de desbancar esta antigua idea que en su origen funcionaba dentro del paradigma cosmológico geocéntrico, Kepler la adapta al sistema heliocéntrico copernicano y a sus propias propuestas de órbitas elípticas de los planetas, notando que estos nuevos modelos cosmológicos requieren de una nueva teoría de la música de las esferas: dado que se deduce que la velocidad de los planetas no es constante, esto tiene implicaciones importantes en los “tonos” (o dicho actualmente “alturas” o “notas”) de cada planeta, que dejan de ser una altura única, como en los modelos de órbitas circulares, para convertirse en toda una gama musical. El desarrollo y evolución de la tradición de la Música de las Esferas es un largo capítulo en la historia de las ideas, de la ciencia y de la teoría musical (pues abarca desde Pitágoras hasta el presente), y hace parte de la llamada “música especulativa”, que indaga las relaciones entre la teoría musical y sistemas considerados esotéricos o místicos.

Este escrito aspira a contribuir, inicialmente a partir de la revisión de la literatura relevante, a este campo menos estudiado de la historia de la ciencia de la modernidad temprana desde el modelo medieval del quadrivium (aritmética, geometría, astronomía y música).

This paper wishes to bring to a wider audience the importance of Johannes Kepler’s efforts in the updating, modification, continuity and transmission of the theories of musical correspondences between the planets of the Solar System and the pitches of the musical scale. This tradition is known as “The Music of the Spheres”, and its evolution and development constitutes a long chapter (from Pythagoras to the present day) in the history of ideas, science, and musical theory, through the area known as “speculative music”, which researches on the connections between music (especially musical theory) and the occult, esoteric or mystical. As such, it warrants further research from the perspective of history of mentalities (understood in this case as a double take from both historical musiclogy and the history of science), and this is precisely the approach that his paper aims at.

Texto sobre la obra gráfica de Eduardo Chillida, publicado en el catálogo de la exposición "Oihartzunak · Resonancias, 26 obra grafiko eta artista liburu bat / 26 obras gráficas y un libro de artista", celebrada en el Museo de Historia y Arte de Durango (Bizkaia) entre el 25 de enero y el 11 de marzo de 2018.

El presente artículo busca dar a conocer la importancia del trabajo de Johannes Kepler en la actualización, modificación, continuidad y transmisión posterior de las teorías de correspondencias entre planetas y alturas musicales en la tradición de la “Música de las Esferas”, noción que para él tenía mucha importancia dentro de su concepción teológica del funcionamiento del cosmos. Lejos de desbancar esta antigua idea que en su origen funcionaba dentro del paradigma cosmológico geocéntrico, Kepler la adapta al sistema heliocéntrico copernicano y a sus propias propuestas de órbitas elípticas de los planetas, notando que estos nuevos modelos cosmológicos requieren de una nueva teoría de la música de las esferas: dado que se deduce que la velocidad de los planetas no es constante, esto tiene implicaciones importantes en los “tonos” (o dicho actualmente “alturas” o “notas”) de cada planeta, que dejan de ser una altura única, como en los modelos de órbitas circulares, para convertirse en t...

This paper concerns a rare visual representation of “voice and musical key (ἡ φωνὴ, [ὁ] τόνος)” that is embedded within a full-page arc diagram, which demonstrates the harmonic-tone system attributed to Pythagoras.
The diagram, which was endowed with exceptional pictorial quality, belongs to a larger image cycle inserted into a fourteenth-century Greek manuscript, Marc. Gr. 516 (=904), one of the many manuscripts Cardinal Bessarion famously donated to the Biblioteca Marciana.
The voice is personified as a male figure clad in a garb articulated with heavy folds of drapery, which derives from classical models. The figure is represented with a peculiar gesture that further hints to its identification: he cups his mouth in a way to help extend the voice. Fitted snuggly on the lower inner margin, between the graph and the outer edges of the folio, the personification of voice is turned inwards and faces another figure, which is identified as “the most wise Pythagoras” (ὁ πάνσοφ[ος] πυθαγόρας).
The aim of this paper is to unravel the epistemic role of these marginal pictorial elements, namely the personification of voice and the figure depicting Pythagoras, which flank the full-page diagrammatic representation of the musical canon. It argues that the spatial relationship of the pictorial elements vis-à-vis one another on the one hand, and with respect to the diagram, on the other hand, conveys the foundational theoretical principle of Ptolemy’s Harmonics: “a commitment to the authority of mathematical principles with a healthy respect for the data of perception (things that were simply ‘sensed’)” (Barker 2000).

Peter Byrne Manchester's 2005 book The Syntax of Time identifies a lost doctrinal source for the ancient precedents to pure phenomenology. This lost work is called the spherics, and I will describe the historical evidence first. Manchester develops a phenomenology of time by expanding Aristotle's physics to include the Pythagorean spherics that Aristotle’s account of physical time begins by rejecting (Physics, IV.10, 218b). Manchester’s phenomenology of time employs a technique of expanding the spanned interval of the now in a way that scales and frames it to fit the paradigm of eternity as a sphere. The formulations “Sphere of the All” and “Sphere of the All One” are used  throughout the book to describe this ultimate framework. The former term has a Stoic connotation, and the latter is Plotinian, but an important citational reference uses “Sphere of the Paradigm” (Sambursky 1971, 2) to mean the same, in a more strictly Timaean context. Manchester’s goal is to operationalize the intuition that time is the life of the soul (Manchester 2005, 86), and to reactivate the ancient spherics as an intuition more original than the reductive linear conception of temporality that has become the natural attitude of our analytic logistic. This goal is approached by considering the pairs of opposites that constitute the cosmological syntax or arrangement and figuration (schemata) of the full dimensionality of lived experience as opposites only in their synthesis in a continuum that he calls the disclosure space. This technique calls for a generalization to all dimensions of space-time. I would like to suggest that this generalization is already underway in the phenomenologies of possible worlds of Anna-Teresa Tymieneicka and James G. Hart. In this presentation, I will focus on the application of Manchester’s insights to the history of geometry given in Dietrich Mahnke’s 1937 Unendliche Sphäre und Allmittelpunkt, and Hedwig Conrad-Martius’ 1950s phenomenology of space-time categories. With the illuminating effect of Manchester's historical identification of the spherics, I will use Mahnke's book to identify the history of this ancient paradigm as it plays out in the history of Platonic mysticism. Mahnke’s earlier book on the subject of synthesis in Leibniz will be shown to be an influence on Tymieniecka’s early book on the same topic, where she first develops her “multi-spherical” model (Tymieniecka 1964, 5) of monadological scaffolding. Hart’s description of Husserl’s reconstructive metaphysics of the Ich-All and extension to the life-world attributes the extension to a Leibnizian “scaffolding” (Laycock and Hart 1986, 103-4), while Dermot Moran attributes the adoption of Leibnizian monadology in the Cartesian Meditations to Dietrich Mahnke’s direct influence (Otten and Allen 2014, 623). The role of Leibniz in the reactivation of the spherics will be explored in connection to the issue of analytic and synthetic method in the mathesis universalis. Finally, I will consider the spherical world-model of Hedwig Conrad-Martius' 1950s phenomenology of space-time; Die Zeit (1954), Das Sein (1957), and Der Raum (1958). The structures of world-center, world-periphery, and world-disk frame a disclosure space very similar to Manchester’s framed and scaled spanned interval of his own disclosure space. The reactivation of the original intuition of sphericity can establish a phenomenology of the spheres that positions our world in the all-encompassing ontological framework of a unified cosmological phenomenology. The issue of analysis and synthesis in the conception of a mathesis universalis, the role of the monad and indefinite dyad in both number and figure, and the sphere as the ultimate metrological unit, are themes that will be systematically explored as we prepare to reenter the paradigm of the sphere through the Sphere of the Paradigm.

“Follow me, modern musicians, and express your opinion on this matter by means of your arts,” wrote astronomer Johannes Kepler in Harmonices Mundi (1618). Having demonstrated that the orbital speeds of the planets reflect divine musical ratios, he called for a partnership between composer and astronomer that would declare the beauty and reason of God’s creation through translation of his theories into polyphony. Kepler considered this treatise his most important work, which included his third law of planetary motion mentioned almost in passing, and it culminated a lifetime of studies devoted to redefining the Music of the Spheres.
Harmonices Mundi has received increasing scholarly attention, but several of Kepler’s earlier foundational musical writings, found in astrological treatises, personal letters, and meteorological predictions, remain largely unexamined. I address this lacuna by surveying Kepler’s musical writings, concentrating on how his changing understanding of music theory influenced the development of his astronomical hypotheses. I examine, for instance, his evolving beliefs regarding the relationship between musical intervals and astrological aspects, influential angles formed by two planets. Introduced by Claudius Ptolemy (c. AD 90 – c. 168), the theory held that the effect on the earth caused by planetary aspects was directly associated with specific intervals. In his early writings Kepler was an ardent supporter of this theory, but in Harmonices Mundi his thinking had markedly changed, leading to a profoundly different understanding of the Music of the Spheres. I explore causes for his shift in thinking, and the resulting developments in Kepler’s influential musical cosmology.