Jackson, G. - Spiritual Basis of Musical Harmony

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.