Speculative music

According to the Hermetic Tradition, there is consciousness in all of the universe, for The All, known in exoteric monotheist religions by the somewhat limiting term ‘God’ is ever present, and ever aware of everything in creation: even those things that to us are seemingly inert and apparently void of any form of life and understanding are governed, taken care of, and overseen by invisible but ever-present sparks of consciousness emanating from The All, and in constant communion with It.

The exact nature of these sparks of consciousness is still a matter of lively debate among occultists, and several interesting interpretations and proposals of what they might actually be have been put forward recently, in the light of the theories and world views taught by the modern sciences, especially psychology, quantum physics, information systems theory, and even memetics (Blackmore 2000). Yet for many centuries Hermeticists simply considered them as spirits of various kinds: archangels, angels, so called “intelligences,” elementals, demons, and so forth, and dedicated a whole branch of Hermetic magic, that of evocation or conjuration, to the art and practice of establishing safe and productive communication with them.

How music can express the order of the universe, and how everything in the universe may have a musical equivalent that we may or may not perceive through our physical hearing is the subject of study of speculative music (Clark and Rehding 2001).

Since it is the purpose of speculative music to look at the cosmos musically and at music cosmically (Godwin 1982), a speculative music that adopts the standpoint of the Hermetic world view must therefore take serious notice of the spiritual entities that populate the universe according to this mystical and philosophical tradition (Van Den Broek and Hanegraaff 1988).

A lot of musicological work has gone in the analysis and discussion of how composers have used magical squares, sigils or other Hermetic or cabalistic magical material in certain of their compositions, especially in the later twentieth century (Lister 2005; Hirsbrunner 1998; Sherlaw-Johnson 1998; Sterne 1983–84). I am aware of some of this work, but in this article I do not intend to duplicate it, expand on it, or generally collaborate in the project of analyzing or pointing out these mystical/magical/numerological bases of some pieces in the contemporary art-music repertoire. This article is not in any sense analytical or repertoire-based, but centers on the history of ideas, in this particular case of the idea of translating sigils of spirits into pitch rows.

What I am interested in doing in this paper is reviewing the theoretical bases which allow the sigils of spiritual entities as proposed by the Hermetic Tradition to be translated into musical material, limiting the specific scope of this article to the translation of the sigils into pitches. In a way, I am reviewing or proposing some methods to achieve the
“sonification” of the sigils of spiritual entities of the Hermetic tradition, comparable to the sonification of other empirical data observed through the methods of modern science. After all, the Hermeticist, as a sort of occult scientist, considers the entities as separate personalities, and thus the information derived or obtained from them—such as their sigils—as empirical data subject to be interpreted and critically evaluated.

The reasons for the limitation of the present study to pitch include, of course, a consideration on the final length of the paper, but they also constitute my first and germinal musical interpretation of the sigils: as will be discussed later at greater length, most sigils, and certainly the sigils of a planetary nature in particular, tend to be very linear in their design, and this immediately suggests the “line” of a melody, or a tone row, in less traditional terms. The planetary seals proper are constituted of several such lines crossing and locking into each other, in a manner that suggests counterpoint, with its interplay of several simultaneous musical lines, as will be discussed in section V., at the end of this paper.

In the introduction to the Loeb translation of Plato's Timaeus, R.G. Bury notes: 'The primary operation of the Demiurge is to construct the World Soul. In his description of this process, Plato mixes myth with mathematics in a peculiarly baffling way'.
This article will argue that if Plato's mathematics is interpreted in accordance with the Pythagorean tradition and the ancient science of harmonics, the arithmetic quickly ceases to be 'baffling'. The article will also identify a possible Mesopotamian origin for Plato'e mathematical construct.

In an address to Maximilian II, which prefaces his Monas Hieroglyphica (1564), John Dee emphasises that the Monad is not only an alchemical device, but a universal one, with the potential to revolutionise all the arts and sciences. Amongst the examples given are applications to geography, astronomy and music, of which Dee writes:

“How justly may the musician be struck with wonder when here he will perceive inexplicable, celestial harmonies without any movement and sound.” (Josten 1964, 130-1)

Dee’s harmonic conception of the Monad may be interpreted as a progenitor to later alchemical traditions in which music plays an underrated part: music was not only the audible expression of the mathematical, rational world of the celestial spheres, but also of influences the soul, the preparation of which is a necessity for the Great Work (Forshaw 2010, 175). In alchemical practice, ‘speculative music’ potentially bridges the spheres of nature and theology, labour and oratory.

This presentation will summarise the historical and contemporary implications of a musical reading of Dee’s Monad. Commencing with a survey of John Dee’s own musical experience and readings, it will contextualize the philosophical connections between the Monad, alchemy, magic, music, geometry and astronomy.

The concepts of harmonic investigation that characterise Medieval and Renaissance musica speculativa will be applied to the forms and theorems of the Monad as a means of interpreting Dee’s ‘inexplicable, celestial harmonies’. In the spirit of Dee’s age, such an interpretation allows us also to reflect on the tensions between conservative Pythagorean musical mysticism and the more ‘strange and informal’ approaches of composers such as John Dowland: emphasizing  the space between tradition and innovation, wherein Dee’s own work often sits.

I will also explore Dee’s Monad into more contemporary areas, based on my use of the text and symbol in my own composition and music-making. The compositional and technological approaches behind a number of my own pieces will be outlined, for example: spectral transformation and the Monad’s proportions in The Great Chord (2012); the relationship between geomancy and the Monad in Horizon of Eternity (2006); the Monad as a graphical sequencer in Hieroglyphic Pathwork (2016); and the use of alchemical cabala in the work of Dee and Pantheus in Osiro Ngatso Nutu Marthek Dei (2016). Many of these works use the aesthetic of drone to provide sonifications of alchemical and Monadic concepts, to create contemplative spaces in which to consider the relationship between alchemy, music and the soul.

References
Forshaw, Peter. 2010. ‘Oratorium-Auditorium-Laboratorium: Early Modern Improvisations on Cabala, Music, and Alchemy’ in Aries, vol. 20.2, pp. 169-195.

Josten, C.H. ‘John Dee’s Monas Hireoglyphica’ in Ambix, vol. 12, pp.84-221.

This article reviews four 20th century proposals by theoreticians
of speculative music whose work has focused on
assigning pitches to the letters of the Hebrew alphabet,
with the intention of being able to deduce the musical
equivalence of texts written in Hebrew, often used in Hermetic,
magical and cabalistic rituals, seals, or talismans.
This first part deals with the direct attributions of letters
to pitches; that is to say, the kind of attribution that is not
based on gematria or cabalistic numerology, which will be
discussed in a later piece.

Este artículo reseña cuatro propuestas realizadas en el siglo
xx por teóricos de la música especulativa, cuya intención
ha sido relacionar las alturas musicales con las letras del
alfabeto hebreo para deducir la equivalencia musical de
textos hebreos utilizados en rituales, sellos o talismanes
cabalísticos y de la tradición Hermética del esoterismo
occidental. En esta primera parte se examinan las atribuciones
“directas”, (las que no utilizan el valor numérico de
las letras hebreas como factor intermedio de conversión)
comparables a sistemas de decodificación criptográfica.
La gematría musical se discutirá en una segunda parte.

Si bien no toda la música tiene la intención de expresar algo externo a sí misma, también es cierto que existen innumerables piezas que hacen referencia a materiales externos a la información puramente musical codificada en la partitura: la música vocal es un claro ejemplo de ello, pues por lo general quienes musicalizan un texto están buscando expresar el contenido lingüístico de éste a través también del nivel musical.

Pero esto no se da únicamente en música con texto cantado: la llamada “música programática”  busca expresar un sub-texto – generalmente narrativo (Almén, 2008) que no está lingüísticamente explicitado en ninguna parte de la música (a veces ni siquiera en su título) sino que hace referencia a un discurso diferente, que en ocasiones se ofrece como complemento a la experiencia musical, por ejemplo como notas de programa (Kregor, 2015). Investigar los nexos entre estos diferentes textos (el musical y el no musical) es una de las áreas de estudio del campo teórico de la semiótica musical (Tarasti, 1995, 2002).

Durante mi trabajo doctoral investigué la música con sub-textos místicos y esotéricos, indagando por el problema de cómo diferentes compositores han articulado y relacionado los sub-textos esotéricos de partida a su material musical, cuando el texto en sí mismo no se explicita en las obras musicales. Como resultado de esta indagación desarrollé una categorización de tres niveles de expresión de estos contenidos extra-musicales dependiendo de qué tanto afectaban el sistema de composición musical, es decir, qué tanto de los materiales musicales se derivaba o desarrollaba a partir del tema o sub-texto esotérico. En mis resultados identifiqué tres niveles: un primero en el cual es simplemente la “atmósfera” de la obra que hace referencia a esos sub-textos, sin que el material en sí mismo se pueda diferenciar de materiales musicales utilizados en otros contextos; el segundo nivel apela al nivel simbólico, en el cual ciertas relaciones importantes para el sub-texto esotérico están también codificadas de manera explícita en el texto musical; y en tercer nivel que deriva el material musical radicalmente (en el sentido literal) del material pre-musical incluido en el sub-texto esotérico.

Speculative music, or music theory with an esoteric base,
has existed since ancient times in parallel with more
mainstream aspects of music theory and musicology. Far
from becoming extinct after the scientific revolution of
the 16th and 17th centuries, speculative music has survived
modernity, and recurs in times of cultural crises,
repeatedly offering hopes of a spiritual and humanistic
renewal through the return to more “natural” forms of
music, closer to the physical and acoustical bases of sound
than the elaborate and “artificial” intellectual constructs
developed during “high modernism”. This article offers a
general overview of this less known aspect of musicology
and musical theory, in its conceptual, historical, and
current aspects.

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.

The magical, the occult and the esoteric have been a constant fountain of inspiration for composers and music theorists of all times. From the Florentine Intermezzi about the music of the spheres and the magical powers of music and Kepler's translation of his astronomical observations to 'cosmic music', to Stockhausen's Gnostic operas about angels and Messiaen's symphony on cosmic unity, passing through the Masonic works of Mozart, the theosophical ones of Scriabin and the astrological suite of Holst, composers of all styles, aesthetic affiliations and varying
degrees of commitment to occult movements and systems have drawn inspiration from the mystical and occult for their works.

This paper argues that a careful study of the classical repertoire based on or inspired by occult themes will show that there are three main levels of representation of the occult in music, and that the decisions on the level of representation that a composer makes while working on a piece may modify the musical material, from a mere thematic or otherwise extra-musical connection in some of the subtler approaches, to a complete re-appraisal and re-design of the whole musical system and theory in the more radical ones. The paper also proposes that this is seems to
be dependent on the level of familiarity of the composer with the chosen occult system or theme, and perhaps also with his ideological commitment to it.

Tendo por intuito a revalorização da tradição "musica speculativa" no século XIV, Jacobus Leodiensis (c. 1260 - c. 1340) visou demonstrar em seu tratado "Speculum Musicae" como ela poderia manter-se pertinente ao ser inserida no quadro de pensamento da escolástica aristotélica e tomista (associados ao século XIII). Jacobus Leodiensis - em plena congruência com o programa pedagógico das "artes liberais" e com o programa de "Itinerário da mente para Deus" presentes na especulação filosófica e teológica da Idade Média - considerava o estudo da música especulativa como uma ferramenta epistemológica através da qual o homem poderia ser introduzido ao estudo da Filosofia e da Teologia. Desse modo, o homem poderia ser conduzido a partir do espelho das coisas sensíveis (incluindo aí o "espelho da música") à contemplação das coisas invisíveis, e, sobretudo, à contemplação de Deus.

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

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...

Este articulo resena cuatro propuestas realizadas en el siglo xx por teoricos de la musica especulativa, cuya intencion ha sido relacionar las alturas musicales con las letras del alfabeto hebreo para deducir la equivalencia musical de textos hebreos utilizados en rituales, sellos o talismanes cabalisticos y de la tradicion Hermetica del esoterismo occidental. En esta primera parte se examinan las atribuciones “directas”, (las que no utilizan el valor numerico de las letras hebreas como factor intermedio de conversion) comparables a sistemas de decodificacion criptografica. La gematria musical se discutira en una segunda parte.

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.

Boring Formless Nonsense intervenes in an aesthetics of failure that has largely been delimited by the visual arts and its avant-garde legacies. It focuses on contemporary experimental composition in which failure rubs elbows with the categories of chance, noise, and obscurity. In these works we hear failure anew. We hear boredom, formlessness, and nonsense in a way that gives new purchase to aesthetic, philosophical, and ethical questions that falter in their negative capability. Reshaping current debates on failure as an aesthetic category, eldritch Priest shows failure to be a duplicitous concept that traffics in paradox and sustains the conditions for magical thinking and hyperstition. Framing recent experimental composition as a deviant kind of sound art, Priest explores how the affective and formal elements of post-Cagean music couples with contemporary culture’s themes of depression, distraction, and disinformation to create an esoteric reality composed of counterfactuals and pseudonymous beings. Ambitious in content and experimental in its approach, Boring Formless Nonsense will challenge and fracture your views on failure, creativity, and experimental music.

Chapter from 'Parametric Composition' (Morgan & Legard, 2017).

Throughout this book, we have often presented code by way of small, illustrative script snippets alongside occasional longer pieces, such as the 12-tone invention in chapter 10. Longer pieces, such as the aforementioned invention, often demonstrate a fairly linear flow of list processing as a way of demonstrating the technique and thinking behind scripted composition.
However, there will be many compositional situations in which the making of the final piece will not necessarily follow such a linear 'waterfall' coding approach, and may need to make use of loops, logic and the preparation of bespoke functions (we encountered some of these in chapters 7, 12, 16 and 21). This chapter explores the use of logical mechanisms and mathematical operators.

O tratado Speculum Musicae do Magister Jacobus de Ispania (ou Jacobus Leodiensis) não recebeu a devida visibilidade nas instituições de ensino e de investigação intelectual tanto de sua época quanto posteriormente. A partir da segunda metade do século XX o tratado foi gradualmente ganhando maior visibilidade e nos últimos anos tem recebido por parte de diversos estudiosos um maior esforço de investigação. A presente dissertação visa expor o contexto filosófico e teológico desse tratado, investigando os seus principais conceitos norteadores a partir de uma leitura dos primeiros capítulos do seu primeiro livro. A partir da exposição dessas concepções fundamentais, buscamos então esclarecer algumas das questões mais fundamentais a respeito da musica speculativa, a saber, sua função no programa das artes liberais, sua concepção enquanto ciência e sua relação com a teologia sagrada.

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...