Music, Alchemy, & Projective Geometry

by Michael Theroux

This article was sourced from the Journal of Borderland Research Vol XLVIII, No. 5, Sept- Oct 1992

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INTRODUCTION

In order to fully comprehend this most important correspondence between alchemy and the contrapuntal songform of the Renaissance and Baroque periods and projective geometry, one must be familiar with not only the alchemical process but also understand that the highly developed form of musical counterpoint arose out of the alchemical philosophy of that era. It will be concluded somewhat later that this alchemical philosophy did indeed include a thorough knowledge of the principles employed in projective geometry and that these principles helped in the moulding of a complete cosmological ideology.

Renaissance creativity was driven by the concept that the arts and sciences were inseparable and that spiritual and even non-spiritual truths were discovered only when these two forms of expression mirrored the doings of their supreme guide. Nature, in Her role as supreme guide or spiritual advisor, directed all operations of astronomy, astrology, geometry, architecture, sculpture, music, medicine, etc., hence all of these works were integrated into a cosmic one. As we shall see in the foregoing conclusions, these ideas are once again coming to fruition.

AN ALCHEMICAL REVIEW

”Transmutation and perfection of the soul” or simply “Transformation” are two very similar ideas which may best define what alchemy is in its broadest sense. Here, we are not concerned with the physical transformation of base metals into gold, (although allegorically correct) but with the spiritual chemistry implicit in the Emerald Tablet’s reconciliation of opposites, or more appropriately, the divine union of microcosm and macrocosm. The four elements: Earth, Air, Fire, and Water are at once essential to the alchemical process emerging as they do from the Prima Materia or primordial matter, only to return from whence they came. These elements are in a constant state of transformation as can be seen in figure I .

To continue, from the sum of the four elements is created a fifth element known as the quintessence or spirit, which can be viewed as a mirror image of the Prima Materia (see figure 2). Of still greater significance here, are the myriad triplicities or Tria Prima of the alchemical process, of which salt, sulfur, and mercury form the basis.

Of the most profound consequence is the triplicity involving the three stages of alchemical transformation. The first is that of the nigredo or blackening stage which is an expression of putrefaction or darkness; a breaking down so to speak of a particular essence. The second is that of the albedo or whitening stage denoting revivification and enlightenment and the third and last stage is that of rubedo or reddening which is likened to the perfection of pure gold.

Although this is merely a scant condensation of what may be considered a most penetrating spiritual and scientific discipline, it possesses the prerequisite information needed to understand the following ideas concerning counterpoint and projective geometry. Alchemy is an all encompassing study; one which reveals an unending string of correspondences relating everything micro and macrocosmically. Through actual application of these ideas one may discover the unfolding of an initiatory path of truth and wisdom. For further study one should consult the list of alchemical treatises in the bibliography.

CONTRAPUNTAL MUSIC

The High Renaissance and early Baroque period (roughly 150o to 1700) in Western musical history heralded the advent and development of a style of music which would last nearly two-hundred years. Counterpoint, as this style of music became known, is a translation of the Latin contra punctus and literally means ‘against the point’ (or against the note’ as notes were called points in those days). This music was termed polyphonic as opposed to homophonic and it can be most easily described as a melody accompanied by one or more related, but independent melodies.

The quality of a music may indeed be determined by its actual longevity; the fact that the music of this period is still alive and appreciated today is an excellent testimonial to this idea. Although most modern composers do not engage in this type of writing style, the music of the Renaissance and Baroque masters is continually revived in new recordings and on the concert platform; a veritable proof of its perennial enjoyment (The Academy of St. Martin in the Fields under the direction of Sir Neville Marriner was formed solely to perform and record the works of the Renaissance and Baroque masters and is considered one of the finest groups in the history of classical music). Why is it then that very few continue in the tradition of this contrapuntal composition? As we shall see, this historical period’s musical constructs reflected the philosophical and cosmological disposition of its most creative composers

ALCHEMICAL COMPOSERS

Nearly everyone is familiar with the well known composers of this era. To list a few one might include Handel, Bach, Telemann, Vivaldi, Purcell, etc., and the list goes on. But for our purposes here, a good starting point will be with the works of Monteverdi. Claudio Monteverdi (1567-1643) was not only a an innovative composer but a practising alchemist as well, (being referred to as a ‘Great Master of Alchemy’) and his music is a reflection of the many and diverse philosophical concepts of the time. Already at the age of 19, Monteverdi had composed his first book of madrigals (of which there were to be nine in all) and in 1590 moved from Cremona, Italy (his place of birth and the city of great violin makers) to Mantua.

At this time, the earliest developments of musical style were directly inspired by group studies. One of the most influential organizations of this time was the Florentine Academy. This altogether stuffy fraternal group was involved with the hermetic studies of the Cabala, astrology, and other such metaphysical teachings interwoven with artistic and scientific invention. But the sincerity of their dedication is questionable as they seemed ‘hell bent’ on presenting the idea that there were no conflicts with these teachings and Christianity. Although the Florentine Academy had its inspiring effect on the musical posterity of the time, it was Monteverdi’s involvement with an academic group in the nearby town of Ferrara that helped shape his own musical direction. Known as “Ferrara’s Club of the Fearless”, (so called for obvious reasons) this group joined the forces of scholars and musicians alike in studious discussion and musical performance, and Monteverdi inscribed his fourth book of madrigals to them.

By this time certain forward-looking features of Monteverdi’s style, notably the boldness of prepared dissonances, had begun to annoy a certain Bolognese theorist, Canon Artusi. As the years went by, he publicly attacked Monteverdi, who had to defend his new techniques.

Monteverdi was probably the first and foremost composer of the late Renaissance and early Baroque period to feel caught up in the powerful and inevitable tide that was pulling music away from the old contrapuntal style, to the new ideals of solo melody. Monteverdi referred to the old style as prima prattica, and the new as seconda prattica, avoiding the possibly pejorative and certainly personal attributes of “old” and “new”. Monteverdi experimented more and more with seconda while continuing to use prima as well. But his seconda works were becoming extremely elaborated in technique with the development of the basso continuo; a device involving the free harmonic elaboration of a continuous bass line by a harpsichordist, lutanist or organist. In 1614, (upon receiving a copy of the sixth book of madrigals from onteverdi) the Abbot Angelo Grillo said, ”I can assure you of the eminent worth of your harmonious gift; it seems to me to belong not so much to the earth on which I accept it, as to the heaven in which I listen to it. My monks here first studied it in the most careful manner – for the work requires thorough preparation and then they sang a part of it to me. My heart was as much carried away by the lovely harmony as my mind was refreshed by the newness of the devices. Those new devices included the highlighting of solo voices and duets above a basso continuoli ne of growing significance.

One of the more notable works associated with Monteverdi’s alchemical influences is the secular oratorio II Combattimento di Tancredi e Clorinda, a setting of a long section from Tasso’s Geruselemme Liberata-the vivid description of the fight between the knight Tancred and the warrior maiden Clorinda. In it we fmd a true example of the alchemical wedding between the archetypal symbols of Divine Masculine and Feminine the union of Logos and Sophia. This represents the balance of micro and macrocosmic polarities so common to the ‘reconciliation of opposites’ concepts of alchemical tradition and can be encountered via the intimacy of the White Queen and Red King, the Celtic story of Cuchulain and Aife, and in Maier’s impressions of Hippomenes and Atalanta, to cite but a few. It is in this ‘Western Tantra’ that the real secrets of the highest workings of alchemy may be uncovered. Also, with Combattimento, the beginnings of the three-fold nature of much of the period’s music began to develop. Monteverdi maintained that earlier music expressed only two types of emotion: the prayerful and the temperate. Nowhere to be found was the expression of anger or agitation. Thus, he went on to include the warlike sounds of rage and strife in the rest of his works, metamorphosing his style into the compositional triplicity of concitato, molle, and temperato (agitated, soft, and temperate). Quite obviously this style is in direct sympathy with the three stages of the alchemical process; the nigredo, albedo, and rubedo. One may also note that the three-fold style of composition known as the prelude, fugue, and allegro, as popularized by Bach and many contemporaries, is a somewhat jumbled version of the same idea. Of course, the Christian doctrine of the Trinity (which is certainly not bereft of its own connections to the alchemical triplicities) probably figured more prominently in later works, hence the lack of the seemingly less important order.

Nature has many ways of disclosing musical direction to composers and it is here that we turn to the most highly developed form of alchemical expression in this era’s music. It was Count Michael Maier (1568-1622) who said, ”Let Nature be your guide, and with your art follow Her closely. Without Her you’ll err.” This revealing wisdom comes from his monumental work entitled Atalanta Fugiens,. which is an edition of 50 fugues, emblems, and epigrams first introduced in 1617. In it, Maier sets to music the classical myth of Atalanta and Hippomenes; the huntress Atalanta representing the fleet-footed Mercury; Hippomenes, the fiery male force of Sulfur, and the Golden Apples (with which Hippomenes used to bait Atalanta) depicting the balancing force of salt. Thus, the three alchemical raw materials were each personified and then interpreted by a musical voice. These pieces of music are actually an early form of fugue, having canons in two parts over a cantus firmus. The cantus firmus is a plainsong theme, which represents the Golden Apple, and is used throughout the work, while the other two voices, representing Atalanta and Hippomenes, are woven above, below and around the them.

ALCHEMY AND MUSIC

Although Maier did not possess the compositional agility of Monteverdi or his contemporaries, his creations stand out as incredible alchemical masterpieces of song. It is with Maier that we see the emergence of the contrapuntal songform as an actual tool of the art whose usefulness becomes apparent in the alchemical workings of the day. As each fugue represented a particular alchemical concept, so each individual melody within the composition acted out (physically) the process and when combined with the other melodies became an intricate interplay of musical forces. That music of this kind should be wholly integrated into the workings of alchemy is not unfounded. Alchemy’s mystical relationships relied heavily on the mathematics derived in part from Cabalistic sources. In the gematria of the Cabalists, words can be represented by numbers. For instance, gold, having the value of 192 (1 x 2 x 3 x 4)8 is directly related to the four-lettered Tetragrammaton (IHVH). Also included in the mystical groups of four were the four elements, the four seasons (of which Vivaldi was no stranger), the four directions, the four worlds, etc. It may also be noted that as far as numerical relationships are concerned, that within Rudolf Steiner’ s four ethers, the chemical ether is also known as the number or tone ether.

Music, from the most ancient times has always played an important part in the rituals of religion and magic. The earliest record of the musical associations of alchemy appears to come from Arabic origin as far back as the 1Oth century. Abou-Nasr-Mohammed-IbmTarkan, known as al-Farabi is said to have flourished is Asia Minor and Syria about thisperiod and is represented as an author of works on alchemy and music. He was also an accomplished lutanist. According to A. E. Waite, ”At the request of the Sultan (of Syria) he produced a piece of his own composing, sung it, and accompanied it with great force and spirit to the delight of all his hearers. The air was so sprightly that even the gravest philosopher could not resist dancing, but by another tune he as easily melted them to tears, and then by a soft unobtrusive melody he lulled whole company to sleep. Here again we see the triune structure emerging in its early stages. In Celtic myth these three forms of music are always to be found in the harper’s repetoire as the smile-strain, the wail-strain,  and the sleep-strain respectively.

The qualitative and energic properties of each of the three musical elements also found their place here:

1. Rhythm — Related to the function of time. Melody and harmony appear to be dependent upon rhythm.

2. Harmony— Related to the function of space. Through the combination of interval relationships — form in space is created. This is a molding process which most often shapes from the periphery inward but can take on characteristics of counter-Euclidean geometries which involves an interplay betwixt the peripheral and centric planar themes. It most often accompanies the horizontal patterns of time.

3. Melody— Related to the functions of extra dimensions. Melody always involves change which in its randomness (especially in improvisation) makes it intangible in form and can only be grasped in association with the horizontal rhythmic element (unless the rhythms are of a vertical nature such as the palindromic or non-retrogradable patterns).This, of course, does not express that these qualities are fixed or dogmatic, but that they are purely a matter of observation.

A most prominent association betwixt alchemical laboratory operations and music comes from Norton’s Ordinall of 1477:

Joyne your elements Musically,
For two causes, one is for Melody:
Which there accords will make to your mind,
the trewe effect when that ye shall finde.
And also for like as Diapason,
With Diapente and with Diatesseron,
With ypate ypaton, and Lecanos muse,
With other accords which in Musick be,
With their proporcions causen harmony,
Much like proportions be in Alkimy …

This bit of prose was actually acquired from John Read’s Prelude To Chemistry. ⁹ Mr Read’s interpretation was that Norton was emphasizing Pythagorean values based on string lengths, but actually Norton was, on a larger scale, revealing that there is a direct relationship between the alchemical process and the contrapuntal songform. The first thing Norton places significance on is melody and rightfully so, as melody is the true being which may leave its indelible impression on the subconscious, thus giving it its extradimensional quality. True to the period, melody was placed above harmony, setting it apart from the later periods’ emphasis on harmonic development. In the other part of  Norton’s prose he speaks of the” other accords” which link the proportions of harmony to the proportions of alchemy and this is in reference to  the contrapuntal interplay of melodies being like that of the contrapuntal interplay of forces in alchemy.

THE PROJECTIVE GEOMETRY OF THE ALCHEMISTS

He who attains to the great secret will come to know how the fire spirit hath its root in the spiritual fire earth, and receive from it a secret influx. Nay, more he will know while all influx of fire descends (against the nature of fire) coming downwards from heaven and while the same fire having found a body ascends again towards heaven and grows upwards.

This quote comes from the alchemist Thomas Vaughan (1626-66). Although he stayed away from actual laboratory research (he most knowledgeably felt an aversion from what he called the ‘torture of metals’), his alchemical prose reveals a profound wisdom not seen in others’ works of the time. In this small quote he speaks of a descending and ascending cosmic periphery which envelops the earth– which is expressed as a result of the immediate outcome of a mystical communion with nature. It is no accident that these Renaissance alchemists speak in such paradoxical parables for they understood wholly the concepts of a projective geometry from the direct observation of nature. Other Renaissance figures such as Da Vinci and Dürer with their naturalistic art and sciences penetrated the secrets of nature and developed the science of perspective vision. It was their practical and æsthetic application of perspective vision which gave birth to projective geometry. This new geometry in art and science not only included the finite elements of Euclid’s space but included infinite distance in space with vanishing lines of perspective. Now the fixed forms such as the square or circle were cast aside in favor of mobile types of form taking on geometrical transformation in the diverse aspects of perspective. The section of the conic can be considered the resident glyph of projective geometry in that all organic forms arise from its transformative properties. One may cite Wilhelm Reich’s theory of Cosmic Superimposition¹⁷ where he arrives at the same conclusion from actual observation and experimentation. Projective geometry produces
a quality of spatial thinking which is synonymous with the metamorphoses of living form.

It is fact that Renaissance wisdom produced this ideology- and this was very much due to geocentric orientation. There is a certain rhythmic interplay between point-centered forces and the peripheral forces in much of Renaissance creation. For instance, this underlying polarity of expansion and contraction can easily be viewed in the works of Robert Fludd (1574-1637). In the many engravings accompanying his works we see the forces of nature expanding toward the heavens in concentric spheres, but at the same time contracting in a most anthropocentric fashion. The two basic entities of space, namely the point and plane, are defined projectively in these spheres. As they expand toward the periphery, they create the plane, and likewise their contraction reveals the point.

Another point worthy of mention is that Fludd also studied Paracelsian medicine. Paracelius’ s medicine was the alchemical forerunner of today’s homeopathy and the similarities exist not only in the treatment of like with like, but in the utilisation of rhythmic and projective forces. In homeopathy, the rhythmic process of dilution or potentisation of a substance calls forth the etheric-peripheral healing forces which tend toward germinating point-centers of life.

It therefore becomes obvious that a perfect association between the contrapuntal songform and alchemical works must exist.  As each melody is formed from individual points (notes), a plane (melodic) is created and the interplay between these peripheral planes (melodies) will create ætheric forms in space necessary for certain operations. These musical talismans indeed can be likened to the peripheral forces at work in a homeopathic remedy and likewise to Radionic rates that ‘tune in’ the geometries particular to an individual ætheric form. These musical radionic rates have quite a different quality than the simple inertial forms associated with radionic machinery in that they are animated through the mobility of song. Although it may appear somewhat complex, much work is being performed and simplified in this field today.

CONCLUSION

The common thread which has woven these ideas together would appear to rest in the art of a new and more profound geometry. This geometry has always been overlooked and mostly cast out by mechanistic science in favor of analytic (I would call it chaotic) mathematics. These scientists also tum up their noses at alchemy– as they find it nothing more than an oddity of idiots playing with retorts and metals in attempt to become wealthy. Their misconceptions only contribute to their demise. We may conclude that there is something wholly vital and organic in the three disciplines discussed – Alchemy, Contrapuntal music, and of course, Projective geometry. Maybe anew Renaissance will take charge with this knowledge in hand and mold it toward the future. Fortunately, fertile ideas are not alone. That which is seemingly original has always been defined in some fashion before – but when it arises anew, it will be certain to bring with it the fresh insights of
rebirth.

REFERENCES

1. The Western Way- Vol. 2, The Hermetic Tradition, by Caitlin and John Matthews 1986 Arkana.
2. Warriors of Arthur by John Matthews and Bob Stewart. 1987 Blandford Press.
3. The Elements of The Celtic Tradition by Caitlin Matthews. 1989 Element Books.
4. Atalanta Fugiens, by Michael Maier– Translated and edited by Jocelyn Godwin. 1989 Phanes Press.
5. Robert Fludd — Hermetic Philosopher and Surveyor of Two Worlds by Jocelyn Godwin. 1991 Phanes Press.
6. The Elements of Alchemy, by Cherry Gilchrist 1991 Element Books.
7. Alchemy by E. J. Holmyard. 1990 Dover.
8. Alchemy – Science of the Cosmos, Science of the Soul, by Titus Burckhardt 1986 Element Books.
10. The Coelum Phllosophorum by Paracelsus, Translated by A. E. Waite 1894.
9. Prelude to Chemistry — An Outline of Alchemy by John Read. 1936 G. Bell & Sons, Ltd.
11. The Story of Great Music from the Renaissance by Denis Stevens. 1967 Time, Inc.
12. The Illustrated Encyclopedia of Music edited by Alan Isaacs & Elizabeth Martin. 1990 Gallery Books.
13. Counterpoint* – Strict and Free by H. A. Clarke. 1991 Borderland Sciences.
14. Projective Geometry– Creative Polarities in Space and Time by Olive Whicher. 1971, Rudolf Steiner Press.
15. The Idea of Counterspace by Olive Wbicher. Anthroposophic Press.
16. Physical and Ethereal Spaces by George Adams. 1965, Rudolf Steiner Press.
17. Ether, God and Devtl/Cosmic Superimposition by Wilhelm Reich. 1973 Noonday Press.
18. The Science and Philosophy of the Drown Radio Therapy* by Ruth B. Drown. 1980 Borderland Sciences.