art. science. culture.
Natural Music Theory
VIII. The Symphony of Nature: Towards an Integral Music Theory
Hildegard of Bingen, Pythagoras, and the Exegesis of Nature
Note: While this chapter demonstrates the latest, most “green” and freshest synthesis of all that I know to be true about next directions in terms of theory for my musical work, and as such is a demonstration of Integralism in action, it is also raw and incomplete. It will likely not be completed for many years. This raw outline is included at this point as it is an important seed. When this seedling outline has been transplanted to its nurturing ground, the cloistered garden of the Inventing Earth website as a wiki, to be fleshed out by a shared group of invited participants of like mind, it will serve as perhaps our most important Manifesto and contribution to the group conversation emerging about the nature of music and its place in the human experience.
1. Abstract: Music in human kind and animal kingdom demonstrates universal constants not only of the nature of sound and pitch but also principles of perception. Perception of the deep structure of music (the scales and note distances) is automatically understood by humans, and is hard-wired into our brains.
2. The ability to read the existence of pure form, elemental truths, and see in them the evidence of Spirit, is a task that’s carried out by scientists, artists, and spiritual practitioners alike.
Scientists are coming to understand numinous and religious experience from a new angle - that of biopsychological phenomena that occurs in the mind/brain. The ability to understand aspects of the arts via scientific methods results in an understanding of art which is no less numinous but is, rather, now wedded to science as well. (Wilson, 1998)
Thus the work of reading nature as the book of Divine works that Hildegard von Bingen involved herself in is not dissimilar from “hearing” the pure melody underneath musical complexity, and “divining” (interesting choice of words) its existence from the fractal, surface bread crumbs; extrapolating from them the universal truths that exist underneath.
3. Music like all instruments of animal culture evolves and changes over time as for instance in the evolution of bird song. As humans study primates, scientists document how culture evolves and behaviors change as decades elapse, in any species carefully observed – some faster, others slower – as individuals, families, and communities pass on inherited forms and memes, with variation. Bird song evolves even in stable populations.
4. Our interpretation of music from the past takes into account these basic principles of biological and biopsychological change. But musical interpretation begins with the understanding that re-construction of the music of the past is not possible. Honoring the capacities of living musicians and composers and other creators within culture to keep the music alive - to “culture” it – is not only more interesting, but is the only avenue open to us. By offering improvisational and other creative interpretations which will have their own relevance to living and future participants and appreciators, music moves along, an intact instrument of cultural development.
5.The moment that Mozart arrived at in The Magic Flute is instructive. Mozart and his librettist, Schikaneder, demonstrated this exegesis of nature in a symbolic fashion. Papageno’s Pan flute – a pentatonic reed flute, extant from archaic times – signifies Nature, in the Enlightenment’s conception. Nature surges forward in full sensual force, as does Papageno, contrasting with the highly-studied, Platonic, neurophysical, thoughtful, culturally elaborated and highly contemplated structures of the Masonic order, as represented by Sarastro and the silver flute of the “modern” orchestra.
Sarastro’s order exists to teach those who are ready to remove themselves from the sensual experience of form and understand from the realm of mind the esoteric, hidden nature of things. It is no coincidence that Papageno’s character is associated with birds and indeed he uses his flute to catch birds. Mozart is careful to never indicate which flute is the magic flute of the entertainment’s title – the crude bamboo, pentatonic flute of Nature or the mechanical, diatonic, silver flute of Platonic forms and Pythagorean constants – each have their own magical effect and their place in a dualistic cosmos as recognized by Plato, Catharism, etc.
6. African, Australian, Asian music, the history of Indo-European music and its relevance to the study of medieval music: whereas the court music of Asia, the Mideast, and Europe was based on virtuoso playing, and the folk music on dance and storytelling, African music provides an example of polyphonic communal improvisation that we seek to recreate (for instance, Osingolio and Pygmy singing).
7. Music in the Indo-European cultures began as a monophonic tradition all the way from Ireland to India, the only aberration being Western music from the advent of polyphony. In order to do polyphony you had to lose the tertiary colors and the secondary colors had to become equivalent to paint by number of Pantone matching system colors so they could be used interchangeably in notated music. Harmony and rhythm both had to be simplified in order for the polyphony to be heard by untrained ears and sung by people who, unlike the African hunters, had not been born into communal polyphonic singing.
8. In monophony, the rhythms were highly complex. There isn’t anything like that in post-polyphony Western music because the focus became on part-writing, which needed simplified harmony, melody, and rhythm. Much as color and nuance of surface texture is often minimized in sculpture, the three dimensionality which harmonic theory in western music offered was much easier to attain when the elements of rhythm and microtonality were minimized.
9. The pentatonic scale is fairly universal both in nature and in human perception (use examples) AUDITORY AND VISUAL EXAMPLE HERE Reference some of earliest musical instruments bone flutes from 20-30,000 years ago which were pentatonic including the Neanderthal which is a different species. Point to arguments that say pentatonic is universal. Mash in Bobby McFerrin video.
Pythagoras and others moved musical theory into the direction of the diatonic using the circle of fifths. EXAMPLES HERE. Talk about examples of music of the day versus his machinations. Progression of Pythagoras's ideas up until Bach and well-tempered tunings. [see http://www.medieval.org/emfaq/harmony/pyth.html
10. AND TALK ABOUT THE COMMA - mathematics is about describing pure forms, the beauty of perfection but in an imperfect world, with imperfect minds to perceive, it never totally accurately describes a perfect system. Talk about the “comma” and the problem of notes being unevenly spaced, making Pythagorean scales difficult for harmony -only the octave, the fourth, and the fifth work, and not across many octaves because of the drift.
11. Monophony of monody is defined as melodic music, a single line, which is played or sung simultaneously by all instruments or voices. In musical practice at the time of Pythagoras and throughout history in Indo-European music until advent of polyphony.
12. The import of Pythagoras’ discoveries was all about melodies, not about harmonies. Conceptually, the musica universalis was constant and simultaneous. But application of his theories meant playing notes in a sequence, and finding “perfect” or universal or magical sequences which reflected the harmony of the spheres. In practice, harmony would be revealed as the result of a beautifully sequenced melody, played on a mathematically designed instrument. In perfectly constructed instruments and music the harmony was an internal resonance that happened in the consciousness; if one could hear a pure tonic and a pure fifth or dominant shortly after, the tonic was held in mind when the fifth (the dominant) was played and the harmony was a time-based rather than simultaneous experience of harmony. In this way the listener achieved godlike powers, conflating time and space.
Musical practice did not conflict with theory because one did not actually play chords in the music of the time. It was improvised with microtones in the melodic sequence, a tradition we see still extant although with various evolutionary modifications in Persian, Arabic, and Indian music. The early Western theorists including Guido d’Arezzo discuss the widespread use of the drone, but not chords per se.
13. The drone, where it exists in any world music externalizes, gives opportunity for common shared perception of, the internal constant of the tonic or the tonic plus the dominant, instantiating the sustained internal sense of harmony and placement of the tonic the dominant and the relationship of all the other notes to this constant. This is why it is used in trance; it holds the tonic for the listener, rather than the listener having to hold it in memory. A drone allows the singer to sound and the listener to hear every possible dissonance in an acceptable context for harmonious resolution in the ear. Thus, for audiences familiar with drones, no sound is an unexpected dissonance - despite the protestations of the theorists - except those without proper approach or resolution.
14. Microtones become a beautiful caressing of that held drone. In monophonic-style music microtones and rhythmic complexity are the color, the beauty and nuance which adorns the scaffolding of a familiar tone sequence (and the typically limited one to two octave range of traditional instruments), and demonstrate the skill and individuality of the performer.
15. The Greeks were aware of the overtone sequence. What Pythagoras was doing was explaining the overtone sequence that some people can hear very clearly as distant notes. This is naturally occurring harmonic sequence. In human evolution when the noise level and quality of sounds which one was subjected to on a daily basis would have been entirely different, and music was so much more spare, it is likely that people heard very differently and perhaps understanding of and hearing of the overtone sequence was part of the common experience.
16. The diatonic scale fills in the blanks in the pentatonic scale and is as such intrinsic is to human perception (it’s a mathematical variation of the pentatonic, which if it is expanded into a circle of fifths, demonstrates a serious of relationships that reflect the overtone sequence and the nature of the mind - that to to some degree the mind probably does automatically look for to some degree VISUAL EXAMPLE HERE
17. It would be interesting to examine whether or not the maquams are an expansion of the circle of fifths beyond the diatonic scale. Worth examining. It is quite possible that that is how they were derived.
18. To use a synaesthetic metaphor: Let’s call the pentatonic scale the primary colors and the diatonic scale the secondary colors; let’s call microtonal variations, i.e. the sounds heard in maqam, dastgah, and raga, as tertiary colors.
19. Scales in Birdsong and other animal sounds have also been shown to follow these basic diatonic scales and other simple constants EXAMPLES HERE.
20. The maqams similarly fill and color the diatonic. Arabic maqam, Persian dastgah, and Indian raga (rag) are all pleasing to the ear but most especially, the mind -- the intellectual capacity -- because they engage an internal dialogue with the pentatonic and diatonic hardwiring, the Platonic ideals, which exist in perception as reflections of the hardwiring of the equipment of the ear/brain apparatus. In other words, the musician, and thus the audience, feels/hears/translates how the not-quite half-and-whole steps, the quarter and 3/4 notes, relate to the pentatonic and diatonic scales that the ear/mind expects. This is not unlike the way we “hear” the relationship between the note that “should” be there when a note is being slid or bent in jazz and blues. In similar fashion, it relates to the way we “hear” how an improvisation on a melody relates to the original melody. In a sense, the internal perception “creates” a harmony and polyphony by offering up the internal scales on a mental level when improvisations and variations of them are heard.
21. At first blush Arabic and Persian music may seem simplistic as compared to Western music in its lack of what we would consider sophisticated harmony and counterpoint. The tendency is for each instrument to play the same melody line, in “unison”, with each instrumentalist improvising on it simultaneously. This stretches the ear more and more to hear the relationships between what is being heard/played and what IS, the internal pentatonic/diatonic scale, the standard, or golden rule which exists in the mind’s eye and is fundamental to perception of music.
22. (Visual example here - showing where the notes are on the pentatonic scale, then overlaying a diatonic scale, then overlaying more than one maqam, then another diagram showing the pentatonic, diatonic, and a maqam family used in one song, being played by multiple musicians, all improvising on it simultaneously). The pentatonic scale becomes the backbone of the fern, the stem, with level of variation being seen to be the fronds (the invisible diatonic scale that the exists in perception as an item to build upon) the frond-lets (the notes of the maqam trichords, tetrachords, and pentachords that overlay one another to make up the scales), and the improvisation of the musicians (the leaves on each frondlet, etc.).
23. Arabic and Persian music theory both built on the work of the Greeks in finding the mathematical correlates to and “reason” behind Music, the work of people like Pythagoras, who demonstrated that the diatonic scale emerges from the circle of fifths and the scale emerging from the overtone sequence (describe this here and show diagrams.) Everybody after Pythagoras drew on Pythagoras in theory but practice varied widely.
24. The idea that the deep structure of music (the scales) is inherently understood in the human mechanism, our shared bio-psychological heritage, relates to the mystic concept that nature is a book and one can exegete, or interpret, or “divine” Divine Truths, from nature. Thus the work of reading “nature as the book of Divine works” that Hildegard involved herself in is not dissimilar from “hearing” the pure melody underneath musical complexity, and “divining” (interesting choice of words) it’s existence from the fractal, surface bread crumbs, extrapolating from them the universal truths that exist underneath. through science the work of observation and experimentation, numinous and religious experience as understood through the arts is converted into a replicable experience that is still no less numinous but is now wedded to science as well as art.
25. This is where Spirit, Art, and Science converge; for the Divine Truths, in this case - the mathematical and physics/physical constants underlying music -- are matters of both Art and Science.
26. It also relates to divin-ation -- the ability to read the existence of pure form, elemental truths, and see in them the evidence of Spirit, is a task that’s carried out by scientists, artists, and spiritual practitioners alike.
27. No one actually knows what music of Europe in the Middle Ages sounded like. No one actually knows what scales sounded like, and how ornamentation was used. Musicians of the time did not tune according to replicable or still-extant constants (such as would exist if they used, for example, tuning forks of a specific, weight, shape, size, metallurgy, etc) nor were tuning or scales consistent from time to time or place to place. In fact the use of a scientific, measurable constant like A440 did not come into vogue in Western music until the early 1800s.
28. Musical notation at the time of Hildegard was crude, with no time signatures, only the primitive forebears to key signatures in the form of medieval church modes; with grace notes, (flats and sharps) included sporadically, and with ornamentation (presumably microtonal in some cases) described by mysterious neumes, some of which are yet to be deciphered and others of which we will never know if they were deciphered correctly. we observe that it would be extraordinary if the western modes weren’t originally microtonal based on what we have observed here. it’s completely implausible that the western modes before polyphony were microtonal. Assuming they were microtonal, we can only guess what they might have sounded like.
29. We do know that music of the time was widely improvised, as music all over the globe is, in the vast majority of indigenous traditions.. To assume that Western musicians, who adopted many/most of their instruments from Middle Eastern and Asia, would go against nature and the music that their music derived from or at least that they came in contact with over centuries, and play/create a music which was based solely on the pure scales taught by (but not used exclusively by!) the classic Greek philosophers, would be to assume that Westerners were exceedingly dull, extraordinarily well-educated and indoctrinated so as to be able to deny natural tendency so completely, and profoundly stubborn.
30. When the Gregorian modes were adopted in 7th through 9th centuries in ragged fashion they were not based on the equal-temperament, A440 scales which we have now which did not emerge for many centuries. We do know that the Gregorian were written and down and codified by Pope Gregory in the 600s but they were in constant evolution until the 13-1400s when polyphony really blossomed, in the Ars Nova period, the late Middle Ages. The biggest changes happened in the couple hundred years around the invention of polyphony. We postulate that rhythmic and modal structure were radically simplified to make polyphony and possible. Between the late 900s and early 1300s was the most profound shift in Western music and it is why Western music is so different from all other Indo-European music forms.
31. Prior to polyphony, “western” music was modal, microtonal, and improvisational in the same way as all world music, and would have sounded much more similar to Arabic music than western post-polyphony. To hear pre-polyphonal western music, you just need to listen to Byzantine chant, Hebrew cantillation, and Arabic and Persian music, and then extrapolate.
32. We have multiple accounts of Westerners listening to music on pilgrimages to the Mideast or through contact with musicians as a result of the Crusades, and the music is never described as “strange, exotic, hard to hear”, or in any way unusual, so the likelihood is that it would have sounded more like that music, which has not undergone the radical transformation that Western music has through the development of the arts of notation and harmonic theory.
33. According to McGee, however, everyone who was considered a composer was experimental with polyphony and experimenting with multiple voices, even According to McGee, they were all doing polyphony, they just hadn’t started writing it down yet. McGee documents that there were two kinds of composition, performance composition and written compositions. The descriptions in theoretical treatises of music in performance composition indicate that it was composed in multiple lines. The practitioners did not devise write down a method of writing down polyphony for several generations ,until it was a well-established practice. Hildegard was in that period as it was becoming an established practice but it was not yet written down. they had not yet devised a method for writing down a polyphony. she was in that two-generation period between the wide practice of polyphony and the notation of it. When it was first written down it was the organum which was written down. The organum is a simple plainchant melody, several notes sung very slowly with an improvised descant on top of it, a well established practice before it was ever written down. (A practice that lives on in Taizé music, interestingly enough.
34. We must imagine Hildegard’s highly ornamented and complex music against a simple plainchant ground with the rhythmic and microtonal colors of the modes because it was still just two lines. but as you added a third voice and a forth voice, as things went on into the 1200s and 1300s like the Machau Mass and the intense polyphony of the1300s. That’s when the colors were stripped out and the modes (scales) became much more uniform. They lost the microtonal colors because they didn’t make sense in these long harmonies. The big change was with the Countenance Angloise. The change was complete and the microtonal colors were completely gone by then.
35. The loss of the improvisatory tradition, while it can be expected when music made a turn towards standardization for the sake of musical notation and the development of theory of harmony, it is a great loss in the Western tradition and should be explored and re-instated as the birthright of makers and performers of music the world over -- an essential human music-making capacity whose origins extend far back into the animal kingdom (for instance, the pentatonic scale).
36. Thus it is unlikely that medieval music sounds the way it is most often played in the twenty-first century, transcribed as it has been to modern notation and in scales that did not exist, and performed by classical musicians with no understanding of either improvisatory traditions and approaches of the Medieval period or indeed, any theory of improvisation whatsoever. This is a tragedy of modern music education.
37. The beauty of music which is based on improvisation and subtlety of variation is that it, like nature, never stops evolving. The maqams as first recorded in the 1930s, have changed in less than a century as musicians add keyboards and fretted instruments.
38. This is the nature of culture, which in the scientific sense, is something that grows. While we can never go back, it may be more respectful of the past to interpret music not as we imagine it might have been, but more in the spirit of imagination and adding something of ourselves -- improvising upon and creating with the skeletons left us by history, to cultivate a new and living music which honors its ancient and deeply interwoven roots across the eons and cultures.
39. Hildegard wrote about the Symphonia of nature, saw the natural world as a reflection of the Divine, with all of Nature resonating to the Harmony of the Spheres, and the human world as potentially able to resonate in kind, in harmony [BBS: this is also a shamanic principle, I believe, that Eliade talks about]. In her works of healing, Physica, and Causae et Curae (Berger, 1999), she catalogued, ambitious naturalist that she was, hundreds of species of plants and animals, and their usefulness and relationship to the human. She sought to explain the physiology of psychological types using humor theory, demonstrating an inclination to somatic psychology and psycho-physiology.
40. Hildegard’ is a music that requires us to be aware of our nature as living creatures of flesh even as she strains the sinews in her aspiration to reach the Heavens with her invocations. Her music stretches the strings of the human instrument to their limit, with its leaping intervals, rapidly-changing modes, two and a half octave ranges, extended, lung-defying melismas, and exotic and complex ornamentation. it appears to be an intensely physical, visceral music to engage. Within her own musical melodies she demonstrates an intuitive grasp of the endless variations upon a theme which nature provides for us, using centonized segments of melody, short melodic phrases, in seemingly endless combinations, and varying them as well throughout. One can only imagine the nuance in interpretation she added and encouraged in her nuns.
41. But even more so, her music is like a bare branch in spring outlined against a winter sky, a sketch for us to interpret, inviting variation, interpretation and leafing out with our own Viritidas, the force of renewal flowing through in our own lives and artistic inspirations. It is only respectful for us to approach her music with an understanding of her unique place and moment in time in the evolution of culture and music.
42. However perhaps even a larger view is in order. Perhaps by returning to an understanding of music through the lens of human nature and culture we can, as good naturalists of music, understand the specie of Hildegard’s music in like form, and interpret it through the lens of the living, eternal verdancy, the Viriditas of the branch that she extends for all who follow in her footsteps.
43. To put the leaves back on that branch we have to hear her specie as a monophonic tradition right at the beginning of polyphony. . she was at that intense moment when they were doing polyphony, and it sounded really weird because it was rhythmically and microtonally complex, but also starting to be multi-voiced.
44. We are not saying that Hildegard wrote in 20th Century Arabic modes, or that they are relevant to her music today. we are saying that these monophonic traditions preserved in Indian, Arabic, Persian, eastern European, and Judaic vocal and instrument music are helpful to a modern interpreter in providing a bridge back to the common, pre-polyphonic, western monophonic tradition of which Hildegard was one of the last practitioners.
45. the Jewish tradition is incredibly important all the way through the history of Western music up to the present day, a constant source of innovation and color. We believe that this is in part so because the pre--polyphonic tradition is preserved in Hebrew cantillation as a parallel thread which interweaves with the western music at key points through out its history - for a Jewish musician, indeed, every Sabbath. In Eastern Europe, its heard through the Byzantine chant traditions that preserve some microtonal color and certainly some flavor of the medieval maqams and modes.
46. With greater understanding of the history of music, perhaps Hildegard von Bingen’s, written as it was just as polyphony and harmony were emerging in Western Europe (Organum, n.d.) with its arcing, poignant melodies and complex, sensual, and mysterious ornamentation (neumes), can be played with more of the passion, subtlety, and spirit of exploration of the divine truths as hidden in nature which Hildegard herself believed in.
47. The Hockett - organized collective activity, with its naturally occuring mimicry, leads to polyphony, a la the Medieval Bird Song book.
In Summary - Towards a Natural Music Theory
A “natural” music theory would be based not only on the physical properties of sound (waves, pitches, harmonic theory) but also on human, animal, and plant biology. Some writers have suggested that music arose from speech. Others might suggest that speech arose from music. Do pre-speech/non-speaking animals make music? Is there a meaningful distinction between music and speech? In the human species, music and speech have co-existed for several hundred thousand years so speech and music in modern homo sapiens should be regarded as co-developed phenomena. Further, since humans co-evolved with other species possessed of language, music and vocal communication capacities, the co-evolution of music between species cannot be ignored.
· What the ear finds pleasing is in alignment with some physical constants -- these are the physical properties of sounds and the sensory apparatus of humans, animals, and plants. That what pleases the ear aligns with the constants found in math and physics was observed as far back as Pythagoras, maybe further.
· Musical constants arise from properties found in the physical world. Cite several specific cases where vocalizations for speech and music mirror sounds that exist in physical world. The hearing and sound processing of animals affects vocalization and communication.
· Various musical systems throughout human history reflect physical and biological realities to greater and lesser extents. Summarize in brief several examples of closer or more distant reflections.
· Based on a rational understanding of music based in biology and physics and evolution, we propose a deliberate movement of the Western ear by making music based on physical-linguistic theory. if music arises from speech, and speech from music: What’s next in human evolution?
· Perhaps we learned to sing and co-learned this capacity in dialogue with birds and other animals - as all God’s creatures singin’ in the choir.
· Perhaps Hildegard was right.
© 2012 Created by Ben Sargent.
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