Introduction

I’ve written a number of articles on how the ouroboros, normally a symbol of eternity expressed in endless cycles, can also be used to represent the dialectically unified relationship between opposites. The serpent, coiled into a circle and biting its tail, can represent a continuum that, instead of being conceived as a straight line with both extremes at distant, opposite ends, can also be coiled into a circle, with the opposite ends meeting, where the serpent’s head bites its tail.

I believe that this close relationship between opposite extremes, the one phasing into the other, or the one being an immediate reaction to the other, can be applied universally. I’ve tried to demonstrate this universality with a number of examples, usually Marxist ones, as with dialectical materialism, capitalism, neoliberalism, the workers’ state, and the tendency of the rate of profit to fall.

As for (largely) non-Marxist topics, I’ve also attempted to apply my ouroboros symbolism to more-or-less mystical ideas, to psychoanalysis, and to philosophy. Now, I’d like to try to apply it to music.

What I’m about to attempt here will surely be far from exhaustive, but what follows are, I believe, some quite significant aspects of music, some important parameters of it. These include consonance vs dissonance, dynamics, planned structures vs non-planned ones, rhythm vs arrhythmicality, and simplicity vs complexity as alternating in different periods in music history. I’ll be examining examples from classical music, jazz, and rock. I’ll be discussing the psychological effects of such music more than the actual physical properties of the sounds.

Now, before we begin, I want to state at the outset that I am no trained musicologist or historian of music, so take my opinions here with a generous grain of salt. Just so you know, however, that I’m not a complete musical ignoramus, either, I have demonstrated what musical knowledge I do have, for what it’s worth, in these analyses: on two Gentle Giant albums, three Pink Floyd albums, one by King Crimson, one by Van Der Graaf Generator, one by the Who, by Jethro Tull, by Rush, and by Frank Zappa. I’ve also analyzed works by a number of modern classical composters, including Richard Strauss, Béla Bartók, Charles Ives, Arnold Schoenberg, Alban Berg, Igor Stravinsky, and Edgard Varèse.

Finally, I’ve also composed and recorded (though not always very well) my own music, including mostly modernist classical compositions using Finale software, and pop songs on which I sang and played all of the instruments. For good or ill, all of these will give you an idea of what I know…and don’t know…when it comes to music.

But enough of this. Let’s get started.

Consonance vs Dissonance

As Schoenberg says in his Harmonielehre, one should not think of consonance and dissonance as dichotomous opposites, but rather as on a continuum from most familiar harmony to least familiar harmony: “the distinction between them is only a matter of degree, not of kind. They are no more opposites than two and ten are opposites, as the frequency numbers indeed show; and the expressions ‘consonance’ and ‘dissonance’, which signify an antithesis, are false. It all simply depends on the growing ability of the analyzing ear to familiarize itself with the remote overtones, thereby expanding the conception of what is euphonious, suitable for art, so that it embraces the whole natural phenomenon.” (Schoenberg, p. 21)

The difference, only a relative one, between consonance and dissonance is especially apparent in the contemplation of the overtone series, wherein the first overtones after the fundamental are the octave, the perfect fifth, the perfect fourth, the major third, the minor third,…and only by our reaching of the eighth and ninth harmonics do we come to major seconds, then by the fifteenth and sixteenth harmonics, we get a minor second, the harmonics in between these being microtonal.

So as Schoenberg points out, the only dissonances to be designated as such are the major and minor seconds, and their inversions, the minor and major sevenths respectively, and the major and minor ninths, which are just the seconds plus an octave, as well as the diminished and augmented fourths and fifths, etc. (Schoenberg, p. 22)

Unisons and octaves are, of course, perfect consonances, as are perfect fifths and perfect fourths (this latter particularly if the upper tone is perceived as the tonic). Note how the tense major seconds and their inversions, the minor sevenths, as well as the sharply dissonant minor seconds and their inversions, the major sevenths, are just a step or half-step away from unisons and octaves respectively. In these, we have a basic example of the ouroboros of music, a shift from the bitten tail of extreme dissonance to the biting head of perfect consonance.

A parallel thing happens with respect to the dissonant next-door neighbours of perfect fifths and fourths. The tritone, regarded as strongly dissonant, is only a half-step flat of a perfect fifth, or a half-step sharp of a perfect fourth. Major, and especially minor, sixths are also only a step or half-step above a perfect fifth. Again, perfect consonance and extreme dissonance meet where the ouroboros’ teeth bite its tail.

Unlike the harsh use of dissonance in twentieth-century classical music, the traditional use of dissonance in the art music of previous centuries always kept it subservient to consonance; harmonic tension had to be resolved, and fairly quickly, too. Most people intuitively feel that this subservient role is justified, since we usually can tolerate only so much harshness. This subservience also acknowledges the universal nature of the ouroboros of music: to hear the full range of musical expression, one must pass from the bitten tail to the biting head.

The seventh degree of the major (or melodic or harmonic minor) scale is called the leading tone because, traditionally, one cannot just stop on that note. This tone leads us back to the tonic: it “will bring us back to do,” as Julie Andrews once sang. Incidentally, there’s also a descending, or upper, leading tone, going from a flat second to the tonic. According to Allen Forte, the strongest melodic or harmonic progressions are by half-step, or as I would call it, the ouroboros of shifting from extreme dissonance to the proximate, perfect consonance.

Suspensions and retardations are more examples of shifting from dissonance to consonance, sometimes from extreme dissonance to perfect consonance, as in the 4-3 and 9-8 suspensions by a half-step, or the 7-8 retardation, also by half-step. Again, it’s these stepwise, short distances from dissonance to consonance that demonstrates the ouroboros-like proximity of the harmonic extremes.

A way to intensify dissonance before resolution is to add a minor seventh on top of the leading tone, in the context of a dominant seventh chord. Thus, a tritone, from the third degree of the (Mixolydian) scale (leading tone) to the seventh degree, becomes a major third in the resolution with mere half-step movements in the intervals’ notes closer to (or farther away from, if they’re inverted) each other (or, if the dominant seventh chord resolves to a minor tonic chord, the minor seventh moves by a full step to the minor third of the tonic chord; either way, the movements from dissonance to consonance are only slight). Further, sustained harmonic tension can be created through secondary dominants leading up to the final resolution.

Now, so far I’ve only discussed the relationship of dissonance with consonance largely in the context of diatonic harmony (that is, except for my brief reference to the descending leading tone). The chromaticism of the music of the Romantic period intensifies dissonance all the more (listen to Wagner‘s Tristan und Isolde for a noteworthy example); since this music is still traditionally tonal, though, its necessary resolution to consonance further brings out the ouroboros of extreme dissonance, the bitten tail, to peaceful consonance, the biting head.

The pushing of this dissonant chromaticism takes tonality to its limits in the music of Richard Strauss (i.e., Salome and Elektra) and Gustav Mahler. Then, we get post-Romantic, Impressionist composers like Debussy and Erik Satie, who often sidestep tonality while refraining from harshness. Examples of such sidestepping include Debussy’s use of the whole-tone scale in such compositions as Prélude à l’après-midi d’un faune, and the use of quartal harmony in Satie’s Fils des étoiles.

Matters get even more dissonant, though still rooted in tonality, if in a vague, expanded sense, in Bartók‘s music, as early as such pieces as his first string quartet. His use of axes of symmetry were meant to prove to Schoenberg that one could treat all twelve semitones equally, yet remain tonal. Note how the extreme chromaticism of that string quartet mentioned above resolves with a closing chord, at the end of the final movement, on A, with fifths (E) and ninths (B). Now, such a chord is quite consonant…by Bartók’s standards.

Stravinsky‘s experiments with polytonality, as well as his use, from time to time, of the octatonic scale, in such compositions as The Rite of Spring are nonetheless still basically tonal, and they end in at least relatively consonant harmonic resolution. The same can be said of much of Ives‘s music, in spite of the many clashing independent parts. Dissonance generally is resolved, if imperfectly…a kind of hovering between the bitten tail and the biting head of the ouroboros.

It’s when we come to the Second Viennese School that we have the “emancipation of the dissonance.” Not satisfied with the use of the whole-tone scale and quartal harmony in his Chamber Symphony No. 1, Schoenberg wanted to treat all twelve semitones as equals. His experiments with atonality led to a need to structure the apparent melodic and harmonic chaos with his twelve-note system. Though I have a deep appreciation for this kind of music, unfortunately, most listeners have untrained ears, and therefore they find it virtually impossible to distinguish the tone rows used in it. One often cannot even make sense of the unresolved dissonance; to the average listener, this music sounds as if it has no beginning, middle, or end. One languishes, it seems, at the bitten tail of discord.

The ‘chaotic’ sense of modernist dissonance is more apparent in such music as George Antheil‘s Ballet Mécanique, much of the music of Varèse and Messiaen (this latter’s especially since the 1940s), and Stockhausen works like Gruppen and Kontakte. As a result, the classical avant-garde has been unpopular, and the average listener drifted away from it and towards jazz and rock ‘n’ roll.

Though these two popular forms started out with harmony that’s simple enough to follow, they, too, grew more dissonant over time. Examples in jazz start out with the altered and extended chords played by Thelonius Monk; dissonance later intensified with the avant-garde and free jazz of players like Cecil Taylor, with his flurries of tone clusters on the piano, or Ornette Coleman‘s improvising in no recognizable key.

Rock music grew more harmonically adventurous first with the Beatles, who proved that pop can embrace a whole world of harmony beyond twelve-bar blues and clichéd progressions like I-vi-ii-V. This experimentation continued in the psychedelic era, with Frank Zappa‘s music, and ultimately with progressive rock in the 1970s, with bands like King Crimson and Gentle Giant in particular daring to play harsh dissonances. In all of these examples, we can see a cyclical movement all the way around the body of the ouroboros of music, from the bitten tail of extreme dissonance to the biting head of simple harmony, then along the serpent’s coiled body back towards the tail–that is, more and more harmonic adventurousness in both jazz and rock.

Sometimes, the extreme dissonance of modernism in postwar classical music simply leads to, largely if not absolutely, an abandonment of sounds of definite pitch, as can be heard in such examples of music exclusively for percussion as Varèse’s Ionisation, John Cage‘s Constructions, Stockhausen’s Zyklus and Mikrophonie I and II, and Iannis Xenakis‘s Psappha. After hearing a litany of screaming cacophony, the sound of pitchless instruments can feel restful in comparison, a shift from the serpent’s bitten tail to its biting head.

Dynamics

As far as going from one extreme of dynamics to the other, from absolute silence–the serpent’s bitten tail–to deafening loudness–the biting head–is concerned, we find ourselves starting and ending with the postwar avant-garde. That is to say, we can start with Cage’s ‘silent’ works, his 4’33” and his 0’00”, and end with examples of danger music, which sometimes uses sounds so loud that they may risk deafening the listener and/or performer. Loudness leads to silence.

Less extreme manifestations of this sort of thing can be found in dance clubs and rock concerts, in which the booming music may not cause permanent, profound deafness, but it may weaken one’s hearing, requiring one, for example, to turn up the volume to an extreme loudness, just to be able to hear the talking on the TV with reasonable clarity.

Extreme loudness, the serpent’s head, leads to the silence of the hearing impaired, the tail, then to extreme loudness again, turning up the volume as a movement along the serpent’s coiled body from its tail back to its head.

From Planned Sounds to Non-planned Ones

The dialectical relationship between what is planned in music and what isn’t manifests itself in many forms. Though music is notated, there’s also plenty of room for interpreting how exactly to play those notes from performance to performance, even in precisely notated classical music or film scores.

Part of the great skill of jazz musicians is to be able to improvise, to invent melodies on the spot during a live performance. If they play a wrong note, it’s advisable to play it loud, to give off the illusory impression that they “meant to do that.”

As for soloing in rock music, the playing is largely prepared and practiced, with a little wiggle room for impromptu variations on a few notes here and there. Zappa noted this general tendency among rock guitarists while contrasting it with his own, totally improvised playing, not knowing at all what notes he would play until the very moment he began the solo onstage, fully aware of the risk of making the occasional mistake in front of his fans.

Such is the yin-and-yang relationship between planned and unplanned music along the coiled body of the ouroboros. As far as the area of the meeting extremes is concerned, where the head bites the tail, we can return to the postwar avant-garde. On the one hand, there is total organization in the form of total serialism in the 1950s music of composers like Boulez and Stockhausen, as well as the player piano music of Conlon Nancarrow; on the other, there’s the aleatoric music of composers like Cage, the extreme of which is noted in the aforementioned ‘compositions,’ 4’33” and 0’00”.

Rhythm vs Arrhythmicality

The basic units of rhythm can be broken down to twos and threes, resulting in simple duple or triple times, then compound times. Common time can be subdivided into twos and threes, such as eighth notes of 3 + 3 + 2, or sixteenth notes of 3 + 3 + 3 + 3 + 2 + 2, or into other syncopations. We follow the beat hypnotically, not needing to think about it.

Next, we have odd time signatures, such as 7/8, 5/4, 11/8, or 13/8, as commonly heard in progressive rock and jazz-rock fusion. Then, to make rhythm even more irregular, we can have constantly changing time signatures, as we hear in The Rite of Spring. Now, instead of being hypnotized by the beat, we have to think about it and figure out all of the changes in order to follow and understand the music. Unconscious listening has thus changed to conscious listening.

Matters get even more complicated when we throw in irregular subdivisions of the beat, beyond triplets and going into quintuplets, septuplets, etc. An extreme example can be heard in that opening set of seventeen rising diatonic notes played at extreme speed on the clarinet from Gershwin‘s Rhapsody in Blue. The legato notes are played so fast that they sound like a glissando. We pay no attention to the rhythmic values of these notes, because quite simply, we can’t.

Then there’s the serialism of rhythm, or ‘modalizing’ of it, as heard in pieces like Messiaen’s “Mode des valeurs et intensités,” the second of his Quatre Etudes de rythme, for piano. The accents and durations of the notes are completely divorced from conventional notions of ‘expressivity,’ but they must be played exactly and figured out by the listener (following the music with the score in hand, no doubt!) in order to understand what is being heard. The same basic understanding of how to hear the accents, durations, etc., of total serialist compositions is to be kept in mind when listening to such music by Boulez, Stockhausen, etc.

Rhythmic irregularity, though precisely planned, as noted in the above-mentioned music by Messiaen, Boulez, and Stockhausen (as well as in the player piano music of Nancarrow), next shifts to a total lack of perceived rhythmic pulse, as in free jazz and the avant-garde experiments of Cecil Taylor. Taylor’s Units would play seemingly endless flurries of atonal phrases backed by drum rolls and arhythmic licks (notably by Andrew Cyrille). One doesn’t tap one’s foot to this music, yet perhaps one will sway one’s head and shoulders in circles to it.

As a result of these extremes, one goes back, from consciously working out a planned but extremely complex rhythm, to unconsciously listening to arrhytmicality. The ouroboros of music has come full circle once again.

Historical Cycles of Simplicity and Complexity

We can find these cyclical moments in the history of Western music at a number of times, especially in the modern era, but I’ll point out a few, when music rose in complexity to an extreme that was eventually felt to be excessive (the biting head of the ouroboros), and then there was a reaction against it, a return to simplicity (the serpent’s bitten tail).

In early Western music, we had monophony, as has mostly been the case in traditional forms of music in the rest of the world. From the monophonic singing of the old Church modes in Gregorian Chant (which used melisma to add sophistication and musical interest), complexity began in the use of organum (perfect fourths and fifths sung parallel to the original melody), which was the beginning stage leading to polyphony. When parallel melody was felt to be rather ‘primitive’ sounding, an interest in creating independent, but harmonious, melodic lines began.

Now, the fascination with experimenting with polyphony, which included polyphonic settings of sacred texts, led to increasingly complex music. Consider the wildly experimental, expressive, and chromatic music of Gesualdo in the late Renaissance period as a noteworthy example.

The Church became concerned with all of this growing complexity in its sacred music, since it became difficult to make out the religious texts sung in all of those intricate vocal lines. (The fact that secular tunes were being mixed into religious music didn’t ease the minds of Church authorities, either.) So there was an urge, at the time of the Counter-reformation and the Council of Trent, to simplify sacred music and tone down all of the tangled vocal polyphony. Such composers as Palestrina were considered ideal in the simplicity of their sacred music.

Homophony, beginning in sacred music, came to replace polyphony as the dominant form in European art music, the simplicity of one melody over a chordal accompaniment being preferred over the complexity of many independent melodic lines heard all at once. Small wonder JS Bach’s music, with its contrapuntal intricacy, wasn’t appreciated during his life, but rather the homophonic music of his sons, Johann Christian Bach and CPE Bach, was preferred back then.

By the Romantic period, the strict adherence to classical forms, such as the sonata form, binary form, minuet and trio, and rondo was beginning to be felt to be too limiting, and so 19th century composers were using these forms in looser and looser ways. Combining this growing freedom with more emotional expressivity and chromaticism, Romantic-era music was getting more complex.

By the 20th century, these movements towards more and more freedom, expressivity, and chromaticism was making music so eccentric, complex, and dissonant that it was beginning to alienate audiences. Some composers, like Stravinsky and Hindemith, were already toning down their modernism by resorting to neoclassicism, finding musical inspiration in the more remote past, though still presenting it with a quirky, modernist slant.

Postwar avant-garde classical music, such as the aforementioned total serialism and aleatoric music of the 1950s, as well as such developments as the micropolyphony of Ligeti, was also alienating listeners with what was perceived as its excessive complexity. And so by the 1960s, a new kind of music began: minimalism, with its simple, repetitive melodies as composed by such musicians as Steve Reich, Philip Glass, and Terry Riley.

In jazz, the complicated riffs of jazz-rock fusion in the early-to-mid 1970s were soon replaced by such leanings as simple, often Latin American, styles. One might think of how the jazz-fusion of groups like the Mahavishnu Orchestra and Return to Forever, with their flashy, virtuosic solos and tricky time changes, was a hot thing in the beginning, but then got simplified by the late 70s. Similarly, the popular Latin American simplicity of mid-to-late 70s Weather Report replaced the band’s originally intense experimentation early in the decade.

The peak of progressive rock experimentation had come by the mid-70s; then punk rock and new wave came along, and their popularity forced the prog dinosaurs to simplify their sound by the late 70s, as can be heard in the shift in musical style by bands like Genesis, Gentle Giant, Jethro Tull, and even UK (consider the difference between their first and second studio albums, from original drummer Bill Bruford‘s subtle use of dauntingly tricky meters to Terry Bozzio‘s more extroverted, but simpler, harder-hitting style). Yes’s 90125 was also essentially a pop album (as was Big Generator), with only the instrumental passage at the beginning of “Changes,” written by Alan White, sounding like prog, with its shifting from a bar each of 4/4 to 6/8, then from a bar of 4/4 to two bars of 6/8.

Asia, though being a prog supergroup with members like John Wetton, Steve Howe, and Carl Palmer, were essentially known for playing pop songs, such as their hit single, “Heat of the Moment.” The 80s King Crimson, like JS Bach in his own day, were a band born too late, as it were: the complexity of their music required too much intelligence for the average listener to appreciate, so they could only be a short-lived cult band. Still, even they wrote a few songs that could be deemed more or less radio-friendly, like the funky “Elephant Talk” and “Sleepless,” and the pop-oriented “Heartbeat.” King Crimson were the exception that proved the rule, as far as 80s pop was concerned.

Since the simplification of 80s pop and rock, some examples of a return to complexity (to an extent) have existed, i.e., the odd time signatures that Soundgarden liked to play in the 1990s, among other examples. But mainstream rock since then has simplified again, with a few exceptions here and there, along with the hybrid prog/metal of groups like Dream Theater.

Conclusion

I hope the examples I’ve shown have demonstrated how the dialectical relationship between opposites, as I symbolize with the ouroboros, can be applied to a number of aspects of music and music history: consonance vs dissonance, loudness vs softness, rhythm vs non-rhythm, and simplicity vs complexity in music history.

The wave-like, or serpentine, motion between opposites is, I believe, one of the keys to understanding all of life…rather like listening to…the music of the spheres, if you will.