The Music & Writings of Graham Jackson
CONTENT: Most people know of the overtone series as the basis of harmony. Not so many know of its mirror image, the undertone series, although it has been known for centuries, was written about in the 19th century, was mentioned by Rudolf Steiner, and was in fact the basis of most of the music of the ancients, including the Greeks.
As the overtone series is more easily grasped materialistically, it won the day, but left unsolved riddles which baffled 18th century theorists like Rameau as well as more recent ones like Hindemith and which have still merely been set aside rather than solved.
The OVERTONE SERIES is easily demonstrated on a monochord, or even a guitar. You just have to touch the sounding string lightly at the halfway point and the note an octave higher will sound instead. Touching it then successively 1/3, 1/4, 1/5, 1/6 of the way along will produce the notes of the major triad. The series goes on ad infinitum, producing a kind of major scale then micro-tones, each interval smaller than the one before. Wind players know you can also produce it by “overblowing”--just blowing harder on their instrument.
The overtone series does not, however, produce the minor triad, unless you pick out isolated notes scattered through the upper regions. This has been the first puzzle for the theorists. Even leading musicians have suggested various arbitrary explanations, thinking it suffices to say that simply lowering the third of the triad darkens it, and that is that.
The UNDERTONE SERIES however does create the minor triad, and just as simply. Instead of dividing the string, you just multiply it. Starting with a short bit of string, by strongly damping with a bridge or a finger, you produce a very high note. Sounding twice, then 3, 4, 5, 6 times that length, you produce the same intervals downward as the overtones do, upward. The result is the minor triad. (Frets will frustrate this on a guitar, but a cello will do it.)
Recent theorists have tried to debunk this, saying it doesn’t resonate, does not have enough physical basis, is useless for composition, etc., but these objections all miss the point. Yes, of course it is different, because it is opposite in every way.
THE POLARITY: All phenomena of sympathetic resonance are following the laws of acoustics which are those of the overtone series. And those are the proper laws of sound that resonates in air. But undertones follow laws that come from within, from what we could call the mental or spiritual world.
Consider your inner experience of the two kinds of triad. The major triad is universally characterized as being more cheerful and light. The minor is heard as dark and sad, or at least inwardly pensive. But that is only when we subconsciously feel the chord as based from below, as we have done for several centuries now.
Try to feel yourself based in the high note that is the fundamental of the undertone series, then feel your way slowly down the series. You have to base yourself in something different--not the comfortable feeling of sitting in your body, but anchored in some place in your inner mental or spiritual world. If you start on a C, you will come to a major third between a C and the Ab below it. Feel the outgoing, generous quality of that third, then if you stay based above when you complete the triad with the F, it will not feel sad. You will rather feel as if you are conquering something. You feel confident, happy. And these impressions are strengthened if you continue either series further--in this case to a D and beyond.
Much more can be said about this, and is, in the book. Either series can be experienced in this way from two sides, just as, say, a tragic event can be regarded from your bodily viewpoint as very sad, or possibly from the point of view of your evolving soul, as a valuable learning opportunity.
HISTORY: The research of Kathleen Schlesinger demonstrated over sixty years ago that the music of the ancient Greeks and probably many other cultures was based on these undertones. Covering another hole on a wind instrument is the same as adding a length of string. And if the holes are bored at equal distances, as they were at that time, you inevitably create part of an undertone series. Hence our concepts of the Greek modes need revising.
The real basis of their music however was kept within an inner circle. The same applies to their other approach, closer to the present-day one, and using both series, which was cultivated by the Pythagoreans, and spelled out in enigmatic form by Plato. Although it is clearest in his Timaeus, it seems that when he was writing of different political systems, he was really writing about different musical systems, and their rather outrageously arbitrary aspects were really an inside joke for the musically literate Pythagoreans he was talking to.
We gradually realize that the undertones lend themselves rather to melody, whereas the overtones naturally create harmonies. This plays itself out visibly in subsequent history, as harmony appears in the Middle Ages, and chords are felt as based from below. Scales also now start from the bottom, just as science is then beginning to be based on practical experience in the physical world.
A mysterious maverick manuscript in the British Museum shows that the Celtic bards had consciously used chords many centuries before the official histories, dominated by the Roman Church, spoke of them. Their successors, the troubadours, seem to have used them too. Singing of the Holy Grail, they followed an inner path that linked onto the hidden esoteric tradition always there behind the scenes.
Gradually a system of harmony appears that is crystallized in definitive form by Bach. The book shows how both series are included in that system that, even when elaborated, held for three centuries. It was not fully understood, however, as is seen in the convoluted arguments of the various theorists. Then in the 20th century, it falls apart in a confusing mixture of experimental styles that nevertheless can still be understood in this context. Some believed that the concepts of harmony and dissonance themselves were outdated. The universal lawfulness embodied in the two series however could not be denied, and the last few decades have shown a wish for a return to harmony. Now a way must be found to build it out for the future, for which some tentative suggestions are given.
The last century also saw the enormous rise of jazz, pop and rock in all their many styles, apparently arising from quite a different part of the human psyche. This phenomenon is examined both from a musically technical point of view, and also from how it affects us, trying to see it as objectively as possible. As with all epochs, we realize that music has a profound effect on cultures, preparing the inner ground for what manifests later. Discovering how and why the pop scene, combined with the modern classical scene, has a lot to do with our modern ills of alienation, violence, obsession with sex, etc. on the one hand, and a new idealism and freedom from tradition on the other, can be a liberating experience for oneself.
As with much of the book, the riddles are only solved, and the arguments only carry weight, when a spiritual understanding of the world is brought into the picture. The penetrating researches of Rudolf Steiner are a great help here, as well as of other theosophical viewpoints. The above only mentions some of the main themes. There is much more, about mathematics, melody, rhythm, music of other cultures, different currents in traditions, spiritual mysteries, etc.
The aim of the book is to justify the use of harmony, and by giving its wider context, open the way to new, freer ways for future composers. It also can have quite an awakening effect on the reader, as the person realizes why he/she likes or dislikes this or that kind of music. Whether composer, musician, music-lover, or just interested, it is guaranteed the reader will thereafter never listen to music quite the same way again.