Sunday, October 08, 2006

Musical Implications of the Harmonic Overtone Series: Introduction


"There's this thing called the overtone series..." - Leonard Bernstein

The above quotation is from a videotaped interview with the late Maestro, during which the interviewer asked him why he never joined his contemporaries in the atonal avant garde. Say what you will about the man's pecadillos: He was nonetheless far more attuned to the implications of the overtone series than almost any of his peers. From his autumnal interpretations of Brahms - a man I sometimes think was fathered by the series - to his own compositions, this came through again and again over the course of his long and distinguished career.


My quest to understand music on the most fundamental level possible is a path that I have been travelling for over thirty years now. During that time I have amassed an extensive music library, liquidated the undesirable texts from it, and I am now left with what I believe to be the indespensible essentials: Riemann's The History of Music Theory, Zarlino's The Art of Counterpoint, Fux' Gradus ad Parnassum, Rameau's Treatise on Harmony, Gedalge's Treatise on Fugue, Schoenberg's The Structural Functions of Harmony, Taneiev's Convertible Counterpoint and The Doctrine of Canon, The Schillinger System of Musical Composition, Schenker's Free Composition and Five Graphic Music Analyses, Seigmeister's Harmony and Melody and - my theory teacher from graduate school days - Dr. Gene Cho's Theories and Practice of Harmonic Convergence. There are many more garden variety text books in my library, of course, but the aforementioned are the ones that I consider to be of note, and that have helped form my current understanding. I have been through them all; some several times.

Lacking in all music theories that I am aware of from Western history is a neat and tidy description of why music works, and why it has evolved as we see from the historical record. There is no Einsteinian General Theory of Musical Relativity... yet.

For such a proposed theory to be compelling, it would have to relate directly - in all of its aspects - to the very nature of sound itself. Harmony, counterpoint, rhythm, melody, and form would all have to be explained as having originated within some feature that God and nature have given to sound, and sound alone. There is only one candidate for the feature I am describing, of course, and that is The Harmonic Overtone Series.


The harmonic overtone series is present in each and every sound you hear: From birds chirping to sirens blaring, anywhere periodic vibrations are generating sound, the series is present. Musical instrument design is positively dominated by the series and its implications: The nodes on every vibrating string and in every oscillating column of air generate it, and instrument design is impossible without the understanding of it. As a guitarist, I can touch the series: I can touch each and every node up to the eighth partial and make them all ring out. I can hear the series in a direct and immediate way, and I use it in the music I write. It is no minor phenomenon of little import. On the contrary, every aspect of music is implied in the series, and every aspect of music is predicted by the series, as I shall demonstrate.

My fascination with the series and its implications began almost from the first time I chimed a harmonic on the guitar, but it really came to fruition during my years as a Synclavier owner/programmer/guitarist in the 1980's. In those days I was in a band and had a management contract, and I did Synclavier programming on the side. I was paid to practice and create and produce new and interetsting sounds. Some days I'd spend eight hours or more just programming timbres on the Syncalvier. I was positively addicted to the thing.

Since the Sync's voice architecture was a combination of additive synthesis and frequency modulation, I was able to reach into the chest cavity of sound and touch its heart. I could grab each harmonic by the throat and adjust its amplitude. I could nudge each harmonic in relation to its neighbors by shifting its phase. I could crossfade several waveforms in sequence to allow the different series iterations to do the bump and grind against each other. I learned about the nature of sound under the tutlage of sound itself.

Though my intuitive understanding of sound - the harmonic series and its implications - was quite well developed by the time I returned to school for a graduate degree at the end of the 1980's, my ability to articulate that understanding and to convey it to others was nearly totally absent. Like many artists, I'm sure, my ability to understand my art and my ability to describe that understanding are two very different things: My abstract reasoning abilities are way beyond my verbal talent, so please be patient and excuse the linguistic crudities and misspellings that you are bound to encounter.


Though I had heard a little twentieth century atonal stuff - I can't call it music - when I was attending Berklee, it was easily ignored. I was into jazz and rock music, and there weren't really any raging proponents of twentieth century "serious" stuff there. At least, none that I can recall. In any event, twentieth century music struck me as decidedly unmusical from my first encounters with it, but I didn't really put any thought into why I found it distasteful. That all changed when I returned to school to pursue a Master of Music degree.

I'll never forget the first time some pompous gasbag said to me, "You just don't understand this music." when I dismissed an atonal work as inherently anti-musical. Being the hot-head rock guitarist I was, I was furious, of course. My reply was something along the lines of, "I understand it perfectly well, and it's $#!*!" I had no doubt but that I was correct in that assessment, but I was bothered by the fact that I couldn't explain - in irrefutible terms - exactly why that piece was... er... excrement.


By this time (Circa 1990) I was well aware that the harmonic overtone series was a big, fat major minor-seventh chord - or dominant seventh - and that this overtone chord's inherent instability predicted harmonic progression dynamics. As I got further into it, I realized that traditional functional harmony was a product of nature, and not artifice. As has always been the case, the struggle I had was not with understanding, but with developing concise terminology: Terminology which would allow for the utmost economy of expression in articulating these discoveries, and which would also allow me to explain the musical proofs I was beginning to develop in as exact and scientific a manner as possible.

The key to reaching a critical mass of understanding as well as to developing the required terminology turned out to be... this weblog. In explaining various aspects of music theory here over the past +/- eighteen months, I have narrowed down my choices for verbiage and have homed in on how to realate eveything back to the musical godhead. Obviously, the tipping-point was the recent Harmonic Implications series.

In this outing, I will relate everything to the series except for perhaps melody and form. I am developing some extrapolated deductions pertaining to melodic and formal implications of the series - and I'll certainly present them at least in passing at appropriate points - but I'm not certain my conclusions yet merit entire chapters in this book. However, they very well may be sufficiently developed by the time I get to that point; I'll just have to wait and see.


As it stands now, there will be nine more posts in this series:

01) The Descent of Tonality and Modality

02) Root Progression and Transformation Types (Root Progression Dynamics)

03) The Secondary Dominant System

04) The Series' Prediction of Integrated Modality

05) The Series' Prediction of Canon (Harmonic Canon)

06) The Secondary Subdominant System

07) Contrapuntal Implications of the Series

08) Rhythmic Implications of the Series

09) Simple Musical Examples

A chapter on melody would make for the perfect ten, so I'm hopeful that will materialize, but I remain uncertain. The next step will be to enter all of these posts into Word, along with cleaned-up versions of the musical proofs, and publish it as a monograph. Perhaps I'll get that done before I go on tour next year.

In any event, those who have an ear to hear and a mind to understand - and who are able to see behind their musical and societal indoctrinations - will be able to reach no other conclusion than I have at the end of this series: If it's called "atonal music," then it follows logically that it must also be "amusical tone."

En garde!


Anonymous Anonymous said...

Hucbald Baby - welcome to your 21st century incarnation, man! You are definitely cool in my book of musical thinkers! I'd love to plagiarize you!
(But I promise fair credit and a link.)

Jack from GVR

5:50 PM  
Blogger Hucbald said...

LOL! Thanks, Jack.

Cool deal you have going on down in Old Mexico. I'm only 75 miles to the Texas side of the Rio Grande, so perhaps I'll come down sometime.

PS. Not only is there a special place in Hell for plagiarists, but my manager is a lawyer. ;^)

6:23 PM  
Anonymous Anonymous said...

The harmonic overtone series, correct me if I'm wrong, exists in many sounds that we consider tonal, but not in all sounds. For instance, a conga open tone has a different harmonic series, the saron in Gamelan orchestras do not have the harmonic series, and the sound of boots trampling dry leaves definitely do not contain the harmonic series. But it is true that most "tonal, consonant" sounds exhibit at least an approximation to the idealized case.

1:03 PM  
Blogger Hucbald said...

J Mack,

The only PITCHED sound that does not have the overtone series associated with it is a synthesizer generated sine wave. Other than that exception, it's just a matter of degree: A tuning fork is close to a sine wave, and has very weak overtones, while an oboe is pungent because it has strong overtones.

Non-pitched percussion sounds have overtones, except they are not grouped around a SINGLE fundamental. Again, dull thuds have disorganized overtones that are weak, while cymbals have disorganized overtones that are strong.


3:04 PM  
Anonymous Anonymous said...

Dear Hucbald,

Personally I believe the answers are all in the music. Perhaps that's why Bach refused to write a treatise, and why Mozart considered it but never did. The whys and wherefores of tonality become self-evident during the study of counterpoint. I believe music is a craft, not a system. That said, Cherubini's practical treatise is useful, as is Taneiev's beast: Convertible Counterpoint and The Doctrine of Canon. Schillinger was a madman, though I like the idea of interference of periodicities, his assumption that pitch scales are the tonal 'foundation' of music is a complete misconception; scales are simply the tones that can be extracted from melody.


R.C Sotorrio

10:37 AM  
Blogger Hucbald said...

Hi R.C.

This is the first rough draft of my work, and when I finish with some practice and recording projects I'm in the middle of, I'm going to write a second version.

As with all things of this nature, it is constantly evolving in my mind. Here, I just went through it in a stream-of-consciousness way and actually made a lot of discoveries in the process. As a result, some of the topics could have been explained better, and the overall organization could be a lot tighter.

The next version will be entitled, "The Natural Laws of Musical Motion: The Harmonic Overtone Series and Musical Context."

It is my contention that the overtone generates all of the baseline contextualizations that appear in music: pure modal, tonal, and poly-modal. It is how closely or distantly related to these baseline contexts that a composer's work is that allows for musical affect and effect. I have developed more efficient ways of demonstrating this, which I am anxious to get to present.



11:31 AM  
Anonymous Anonymous said...

I am a Berklee grad as well, film scoring, so we studied the twentieth century stuff, and I find it quite useful as a way of generating ideas and opening your mind. I also spent eleven years in the Navy music program and took quite a few semesters of learning to arrange on the fly. The key to arranging on the fly is that the next written note most be in the overtone series of the one preceding it, or there will be dissonance. They called them avoid tones. While rehearsing one day with a vibraphonist for a job at the Admirals house, I played a pitch on the last note of the song that blew the vibist away. The following day, he called me and said I do not know what I am doing, because that note was an avoid tone. It sounded good because no other note followed it.

9:26 PM  
Anonymous zimk said...

Hi Hucbald.
It was such a pleasure to find your blog. Me too, I try to understand harmony to its basic level and "this thing called the overtone series..." is the answer for so many mysteries. Thank you so much for sgaring your thoughts and knowledge.

1:39 PM  
Blogger zimk said...

Hi Hucbald.
I've been a regular visitor of your blog. It's a really inspiring place for those who investigate the musical implications of the overtone series. In my blog I linked to your posts hoping that my students go there.
Thanks for the great work
José (from Portugal)

8:19 AM  
Anonymous phil klein said...

Considering what these discussions are all about, I'm surprised to see no comments about Rob McConnell, his sound and his mentor: Gordon Delamont, one of the great teachers of all time. I am speaking as a pianist and music theory teacher, with a harmonic background as a pianist. I had a lengthy conversation with McConnell regarding his education and his marvelous Canadian teacher (who has several fabulous theory books on the market. Phil Klein

7:18 PM  

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