April 15, 1980
NEW SOLIDARITY
Page 5
Solving a Musical Puzzle By Leonardo da Vinci by Nora Hamerman
Fig. 1: Leonardo's musical rebus, from a sheet s heet in Windsor Castle (photographed in reverse, since the original was written in "mirror" "mirror" script). Below the rebus Leonardo deciphered it, "Amore sola mi fa remirare, remirare, la sol mi fa sollecita." (Love alone makes me remember, remember, it only makes me alert.) alert.) The rebus and other musical inventions by Leonardo were published by Dr. Emmanuel Winternitz in an essay in the book, The Unknown Leonardo (McGraw-Hill, 1974).
None of Leonardo da Vinci's musical compositions compositions have survived, even though that genius of Europe's "Golden Renaissance" was known, according to the consensus of all the earlier biographers, as the most outstanding improvisational singer and performer on the "lira da braccio," a stringed instrument which is the primary ancestor ancestor of our modern modern violin. But musical notation of a sort from Leonardo's Leonardo's hand does exist; and it gives, on close close inspection, an important clue to the link between music and poetry on the one side and the conquest conquest of physical space on the other. other. It also provides an opportunity for a modern layperson to get "inside" the creative processes that led to seminal discoveries in science in the past, by becoming, as it were, a member of the da Vinci Vinci circle of friends.
Anyone who has closely studied Leonardo's notebooks knows, despite the fragmentary and distorted form in which they have been published, that the British Broadcasting Company's image of the great artist as a fruity recluse "beyond his times" is a total total lie. In addition to the many many outlines and passages from what were intended intended to be major treatises on important important topics, Leonardo's papers are filled with humorous sketches and geometrical and word-games that were clearly destined to sharpen the mental powers of his associates and students. The intimate relationship relationship between these "jokes" "jokes" and "games" and serious scientific inquiry is made evident by the fact that before they were scissored apart in the early 17th century, century, many pages in the note books consisted of caricatures caricatures and witty sayings side-by-side side-by-side with the famous mechanical inventions and studies for important religious and historical paintings. The tradition of using using such "games" to impart advanced advanced knowledge goes back at least half a century, century, when an earlier universal genius, Leon Battista Alberti, Alberti, wrote Ludi Mathamatici ( Mathematical Mathematical Games) Games) in 1450 for the express purpose of teaching geometry to manual craftsmen. Among the notebooks there survive nearly 200 picture "rebuses" by Leonardo, that is, sequences of little drawings of objects which, if named in order, combine to form new new words that form aphorisms. This is familiar to to most people today in the the form of children's games. Leonardo developed developed a very full "vocabulary" of picture-words to use in these rebuses, including the six syllables of the Guidonian musical scale as it was then known—ut, re, mi, fa, so, la. The "ut" was subsequently subsequently replaced with the more pronounceable "do" and the seventh, or leading tone, given the name "si" (or "ti") to form the modern solfege scale. Guido of Arezzo, who invented this system to teach sight-singing, had employed the initial syllables of a well-known well-known Latin hymn. Since Latin and Italian are quite similar, at least in sound-components, there is a large range of available words that can be formed from the Guidonian syllables in Italian. The Leonardo "rebus" which uses the most solfege notations spells out, "Amore mi fa sola remirari, La sol mi fa sollecita." sollecita." To fill it out, Leonardo Leonardo added a doodle of a fish-hook ("amo" ( "amo" in Italian) and wrote in the missing m issing parts of the words (remi)-rari and (sol)-lecita. The aphorism that results can be loosely translated, "Love "Love alone makes me remember (reflect, look back); back); it only makes me alert."
This little saying has a particular charm, because it goes to the very heart of Leonardo da Vinci's Vinci's philosophy. philosophy. As he repeatedly stated and demonstrated, the process of love and the process of scientific knowledge are inseparable. He wrote elsewhere that it is only through in-depth knowledge of the beloved that one can truly love; here, he turns the same concept concept on its head to say that thinking, reflecting, and being mentally alert, are only brought about through the impetus of love. This means that the ordinary notion of love, the banalized, infantile kind of personal gratification, or or fantasy-dominated love, is inadmissible inadmissible to Leonardo—otherwise, as Freud pointed out in a perverse misunderstanding of Leonardo's psychology, psychology, such love would never stand up to the test of constantly expanding knowledge of the beloved. On the other hand, of course, it also means that the piecemeal, "collecting" approach to knowledge associated classically with Aristotle, in which the universe of knowledge is built up of logical blocks, is also inadmissible. Leonardo has thus by himself refuted the oft-repeated allegation that he was an Aristotelian. 'Rebuses' and Mentation
Not by accident Leonardo's Leonardo's disciple Raphael, in his famous painting of of the "School of Athens" where Plato and Aristotle dispute their opposing worldviews in the midst of an imaginary gathering of history's most famous philosophers, painted Plato with the features of Leonardo Leonardo da Vinci. Vinci. The love-knowledge equation put forward by Leonardo is distinctively Platonic and had been extensively discussed by the Florentine Platonic Academy during Leonardo's youth in Florence. In his paintings Leonardo gives a concentrated expression of the preconscious mental activity— the process which Plato termed "hypothesizing the higher hypothesis" which allows the mind to make new discoveries by conceptualizing a problem problem from a higher level. Unfortunately, Unfortunately, this expression is not readily accessible to most people today, today, because the Renaissance concept of painting as a "Platonic dialogue" in visual terms has been deliberately destroyed. But a path has been provided to such knowledge knowledge by Leonardo's musical rebus, which requires no high level of visual literacy.
Fig. 2: Leonardo da Vinci was a leading leading member of the Platonic faction, despite modern efforts to characterize him as an Aristotelian. In Raphael's celebrated celebrated Vatican Vatican fresco of the "School of Athens," painted during Leonardo's lifetime, the head of Plato is identical to the drawing traditionally believed to be Leonardo's Leonardo's self-portrait (inset). (inset). Plato points skyward as he holds the Timaeus, in a famous Leonardesque gesture, appearing in many paintings by Leonardo himself.
Let us look more closely at the the rebus in Fig. 1. First, there is the literal literal "picture." However, However, the picture does not stand for the object as meaningful meaningful in itself—it stands as the name of the object. The minute you have named named the object, it disappears disappears into a sound pattern. The sound pattern then brings forth a different "object." In the case of the cited musical rebus, the new "object" is something totally abstract—a concept. "Love alone makes my mind work!"
By transforming objects into sounds, and then sounds into different meanings—an elaborate pun—Leonardo triggers in his audience/viewers (they are both at once) the sensation of the mind at work, leaping over particulars to form new concepts. concepts. This happens in any of of his rebuses. With the musical-syllable rebus, the process is raised to an even more complex level. First, a sound is transformed into a visual symbol (notes on the staff, identified as being in the the F-major scale by the symbol on the left). Then, this symbol is transformed mentally back into sound—the associated solfege syllables. These sounds are added to the additional pictogram—the pictogram—the fishhook —and the letters, to add up up to "Love alone makes me remember, remember, it only only makes me alert." Leonardo understood very intimately the fact that creative mentation in composing music, poetry and geometric construction or painting was the same process. Moreover, he deliberately used the the evocation of this process process in one medium to raise the dimension of understanding of a different medium. What he was doing was focusing focusing his audience's attention attention on the hypothesis-forming activity which underlay all art and science. The Poetic Principle
As Lyndon LaRouche has emphasized in a series of ground-breaking articles on the poetic principle, the division between "art" and "science" is an artificial one fostered in the late 17th century by British empiricism, with the aim of crippling creative advances advances in both areas. The British, nominalist nominalist delusion that no lawfulness participates in the original features of ordering of works of art has its exact parallel in the delusion that the physical universe is ordered, at least in the large scale, by predetermined, fixed laws. In this universe there can be, ultimately, neither love nor knowledge—it is the existentialist nightmare so appropriately reflected in the typical 20th century Cubist or Expressionist painting, where the human figure and its surroundings are depicted from the standpoint of a scientifically objective axe-murderer. In reality, reality, as LaRouche has demonstrated, the physical universe is configured by a series of efficiently-connected "Riemannian" "Riemannian" manifolds or domains, which are connected by a developmental principle identical to that which governs human human creative thought. thought. Man's own existence—his existence—his successive conquest of qualitatively higher levels of energy throughput
through the realization of new technologies, is the proof that this, and not any fixed law, law, is the "law" of the universe. The task of the great artist is to elicit the actual knowing of a creative discovery in the the audience. LaRouche reminds us of the common experience experience of a thought sought in in memory and "on the tip of of one's tongue." The process of giving a name to that thought is the completed preconscious thought, LaRouche stresses. This condition, this moment of seeking seeking the name in memory, memory, is a "universal with respect to all the predicates that might properly be attached to it." This principle was consciously applied by the great Renaissance artists from Dante in the early 1300s through Leonardo, two centuries later. later. Muriel Mirak, in her forthcoming article "How Dante Used Poetry to Start the Scientific Renaissance" (Campaigner ( Campaigner , May 1980), demonstrates that the poetic imagery and language-creation language-creation within Dante's Dante's epic poem, the Commedia, Commedia, acted to trigger the understanding in Renaissance artists of the scientific concepts of perspective that were otherwise available, but less accessible, in the form of treatises treatises on optics and geometry. geometry. She argues that the mind brings forth new ideas first as sounds, and that therefore the process of abstraction that poetry poetry effects on the intonation intonation patterns of of a language as a whole was essential in order to mediate these geometric ideas so that they could be applied in new forms. f orms. Leonardo would have agreed with this view, view, but probably would have made an important modification of it. He would have said said that the process of moving from an insight in one physical medium (sound) to that in another (space) crucially effects the mind's ability to make new scientific and creative breakthroughs. The way he would have read Dante, especially especially the Paradiso, Paradiso, would have been to point out that it is the way Dante indissolubly links the imagery of light and sound that allowed the creative breakthroughs in all fields of thought to take place in the ensuing Golden Renaissance. Not only, only, in the Paradiso the Paradiso section, does Dante repeatedly stress the simultaneity of musical and light sensations in celebration of the creative principle (God), but he invents new words, especially especially verbs, made up of combinations that contain the "idea" of light and also "sound like" light. One example is the new verb "sfavillar" " sfavillar" which contains the noun "favilla," or spark, which happens to be extremely close to "favella," or language, and is given the extra "charge" "charge" of the beginning "s" prefix. prefix. In Italian this prefix
adds force to a verb. But it also heightens heightens the sense of motion, conveyed conveyed throughout the Paradiso the Paradiso by words with the maximum number of combinations of "s," "f," and "1," all consonants that flow into their adjoining vowels rather than stopping the tone abruptly. abruptly. It is therefore not the priority of sound which is critical, but the transformatransforma tion process shared between vision and hearing that forces the reader of the Commedia to move to a higher dimension of conceptualization conceptualization that encom passes both as particular phenomena. phenomena. Leonardo argues in the following way in one of his many m any discussions of painting and music: The Painter Measures of Distance of Things as they Recede from the Eye by Degrees just as the Musician Measures the Intervals of the Voices Heard by the Ear. Although objects observed by the eye touch one another as they recede, I shall nevertheless found my rule on a series ser ies of intervals measuring 20 braccia [a measure roughly equal to 17 inches—ed.] each, just as the musician who, who, though his voices are united and strung together, has created intervals according to the distance from voice to voice, calling them unison, second, third, fourth, and fifth and so on, until names have been given to the various degrees of pitch proper to the human voice. If you, O musician, musician, say that painting is a mechanical art because it is performed with the use of hands, you must admit that music is performed with the mouth which which is also a human organ. organ. And just as the mouth is not working in this case for the sense of taste, just as the hands while painting do not work for the sense of touch! Words are of less account than performances. But, you, O writer on the sciences, do you not, like the painter, painter, copy by hand that which is in the mind? If you say that music is composed of proportion, then I have used similar meanings in painting, as I shall show. show. Music and Perspective
Leonardo's interest in the processes which are in common between music and painting goes much deeper than a mere facility in in both fields. He was preoccupied with the solution to a paradox, which was how to convey convey the
concept of motion in the static medium of the arts of design, whether it be painting, sculpture or or architecture, but especially especially in painting. This is the real key to Leonardo's revolution in the concept of the painter's perspective. Before Leonardo the highest highest level of Renaissance art art theory could be characterized by the great painter Piero della Francesca's De Prospectiva Prospectiva Pingendi, Pingendi , a treatise on perspective. Piero's concern was to apply all that was known of projective geometry to painting in a systematic systematic way. way. He—like Leonardo subsequently—decried subsequently—decried painters who were not expert expert geometers, who ignored ignored science. Every object could be portrayed essentially as the section of the "visual cone" of light entering the eye, according to its shape, distance, and angle at which it is seen. His exposition is far more detailed detailed than the earlier treatments of of perspective construction by by Alberti and Ghiberti, Ghiberti, and quickly became authoritative. Piero begins his treatise: Painting consists of three principal parts, which we name drawing, measurement, and coloring. By drawing we mean profiles and outlines which which contain the objects. objects. By measurement we mean the profiles and outlines placed proportionately in their places. By coloring we mean how how colors show themselves on the objects: light or dark, changing according to the light. He then goes on: Of these three parts, I intend to consider only measurement, which we call perspective, mixing in some parts of drawing, because without this, this, perspective cannot be be employed practically. practically. We shall omit coloring and shall consider that which can demonstrate with lines, angles, and proportions (emphasis added). Now this should be directly directly compared with the the surviving fragments of Leonardo's Treatise on Painting , in which he approaches the same question in the following way. way. Rather than speaking of painting as being made up of drawing, measurement and coloring, he states that:
the first thing in painting is that the objects it represents should appear in relief and that the grounds surrounding surr ounding them at different distances should appear to extend (three dimensionally) right into the wall on which they are painted, with the help of the three branches of perspective, which are: the diminution in the the forms of the objects; the diminution in their magnimagnitude; and the diminution diminution in their their color (emphasis added). Thus, what were the "three parts of painting" for Piero della Francesca, become "three branches of perspective" perspective" for Leonardo, which all all contribute to the illusion illusion of three dimensional dimensional relief on the painted surface. Perspective, for Piero, geometric construction of measured spaces, has been transformed and broadened into something which is no longer essentially metric, but comprises an entire system of of spatial representation. But while perspective's domain expands, thereby changing the concept of perspective itself, color has taken on critical importance as one of the scientifically determining aspects of painting. painting. This is a revolution over over Piero's "We "We shall omit coloring." However, However, this is not the end of Leonardo's reconceptualization of the ingredients of painting. painting. Because in order to have discovered the transfinite "perspective" conception by which he has now subsumed measurement, outline, and color it was necessary for him to introduce a "fourth" dimension into painting. And this, he specifies, is motion: The second essential in painting is appropriate action and a due variety in the figures, so that the men m en may not all look like brothers, etc. And in fact, elsewhere in his treatise tr eatise Leonardo spends a great deal of time explaining that the purpose of painting the human figure is to depict the "motions of the soul." Not only does this this purpose tax the physical physical limitations of the itself-motionless itself-motionless canvas or panel; it also taxes the nature nature of visual phenomena on a deeper level, since the soul, unfortunately, unfortunately, does not always manifest its motions motions on the surface. Therefore, the artist's job, says Leonardo, is to discover how an idea can be conveyed through physiology, physiology, gesture, interaction, etc. etc. And this in turn demanded demanded a fully unified continuous continuous space—the "three kinds of perspective." perspective." Why? Leonardo specifies that while his "first" kind of perspective, the diminution of size, derives mainly from the physiology of the eye, the second and third
("aerial" perspective) derive from the effect of atmosphere on the world of visual perception. Since spatial recession is depicted depicted by these means means used coherently together, together, the coherency between the workings of the perceiving mind and the "outside" physical universe is thus powerfully, powerfully, even if preconsciously, preconsciously, reinforced in his paintings. paintings. Again, the analogy to to music and poetry is most appropriate. appropriate. The infant learns to speak, as Dr. Mirak explains in the cited article, through singling out particulars (words) from what the child first learns as an intonation pattern of the particular language language as a totality. totality. In the same way, way, the mind "tunes" its ability to work on visual phenomena on the basis of harmonic relations or proportions that are not self-evident in the visual data but must be abstracted from it by a higher higher principle. To actually function in the world, the child must have an intuitive grasp of the laws which govern projective geometry. geometry. Leonardo's Music
Leonardo strictly followed the analogy to poetry and music that he discussed in his theoretical writings in order to introduce the "motion of the soul" into painting. It was the discipline of music, his celebrated adeptness adeptness at improvising verses and accompanying himself on the lira da braccio (an instrument which he not only played, but also made), that instructed him in the notion of creating higher and higher levels of freedom fr eedom within lawfulness ("O marvelous Necessity," Necessity," as he called it). In turn, Leonardo knew that the development of music demanded a "spatial" quality that is not physically physically intrinsic to the musical medium. The notion of cross-voice relationships, to which he alluded in the passage on musical and pictorial intervals, implies implies that music is created in space space and not merely in time. The relationship was also demonstrated by one of the musical inventions of Leonardo, a music box which would play a four-voice canon. On the likely hypothesis that Leonardo's musical rebus implied an experiment to be carried out by his students and friends; friends; this writer has created a canonical interpretation for the aphorism, "Amore sola mi fa remirare." The first step was to fill out the line with notes notes where pictures or words, not solfege syllables, were given in the original rebus. It seemed only natural to start by establishing the tonic ("ut," or in modern usage, "do") so that the piece the piece is in a definite definite key, key, and also, of course, to end end the song on the tonic. Beyond that, one of of the most interesting but problematic aspects
of Leonardo's "theme" is the series of jumps of a fourth interval, from "re" to "sol," then from "la" to "mi" in the scale. In my solution, I made these fourth-intervals into a prominent feature of the song, by adding yet another, another, "sol-do," at the beginning. After an initial rather straight-forward rendering rendering of the two two lines. I repeated them with with variations. The most important is a key change at the beginning beginning of the third line, to the key of C, and a rearranging of the word (and solfege syllable) order, to "Amore mi fa sol," which in Italian I talian gives, "love alone makes me." The last line has returned to the key of the piece, F-major.
Fig. 3: A canon composed by the author using Leonardo's musical musical rebus.
With the second voice, sung as a canonical counterpoint to the thusreconstructed da Vincian Vincian tune, I took more liberties—all of them, I believe, implied in the first voice. And I also translated the words into English, in
several variants which bring out some of the multiple interpretations possible from Leonardo's aphorism. aphorism. Out of the key-change to C-major which occurred in the first voice, came a whole new geometry of possible tonalities expanding from the diatonic melody in the first voice through through chromatic half-step shifts. shifts. Thus in addition to the obvious C-major, one hears its relative minor A-minor, and subdominant B-flat major, and G minor as well. These key changes play off the words as well, especially in the place where the English word "reconsider" coincides with a redefinition of the tonality from F-major, as it would sound from the first voice sung alone, to G-minor as "reconsidered" by the second voice that lands on an F-sharp, the leadingtone to the key of G and a note that is not not in the F-scale. This shows that an entire continuous universe of tones can be built out of such a simple little solfege "joke." The result is singable; and from the standpoint of of an amateur with no experience in composing music, it is a useful experiment in getting inside the mind of a Renaissance genius and beginning to understand how such geniuses can be reproduced again today. today.
