THE WILL OF THE TONES

Today's musical tones have evolved since the beginning of mankind, in primitive and civilized cultures all over the world. Primitive peoples instinctively produced the same basic tones that scientists and philoso-phers discovered intellectually. This is not surprising since the musical tones used today and for centuries all over the world are based on har-monics, the mathematical divisions of a vibrating string. The string is divided into halves, thirds, fourths, fifths, sixths, sevenths, eighths, and

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so on. The lower the number dividing the string the more universally used is the note derived from that division. For example, the string di-vided into two parts gives us an octave. Since women^'s voices are natu-rally an octave higher than men's voices, singing in octaves occurs quite naturally in any kind of group singing, whether primitive chanting or contemporary folk song.

The string divided into three parts gives us the note sol or the perfect fifth. This musical interval of the perfect fifth is the most universally used interval. It is found in all types of music including Classical, Jazz, Chinese, Turkish. Indian, etc. The string divided into four parts gives us the note fa (¾^ths of the string). This is the next most universally used tone.

As the divisor increases, it is less and less commonly used. The mathematical ratios for our Western system of twelve tones are:

do2 1:1

The lower the ratio, the less dissonant (tense, active, needing to move) the note. The higher the ratio, the more dissonant the note. When we hear music we are hearing mathematical ratios which correspond to many other naturally occurring phenomena.

Of all these tones, do is the fundamental tone or center of gravity from which the other tones are derived and also the place to which they return. In any piece of music do is the final note and the center of grav-ity around which the other tones resolve. Each of these other tones has a definite will of its own and its own special place in the musical hierar-chy.

To understand the musical concept of "center of gravity,” we can use the analogy of a giant clock having one hand that weighs fifty pounds. The hand is not connected to any mechanism inside and can be moved freely. It naturally falls to the 6 o'clock position because of grav-ity. As the hand is moved in a complete circle, different dynamics of weight are experienced at different places. To move the hand from 6 o'clock to 7 o'clock will be considerably easier than moving the hand from 8 o'clock to 9 o'clock. Once the hand is in the 12 o'clock position

it is again "weightless^" and can be balanced there. Past this position it will move by itself gaining in momentum until it reaches bottom. Each point in this 360° circle will have had a different dynamic quality. In the same way each musical tone has its own dynamic quality in relation to do. For instance, the reason that the audience at a concert knows the symphony is over is not related solely to the fact that the musicians have stopped playing. Rather, the music has reached a conclusion that sounds like a conclusion to the listeners. That conclusion derives di-rectly from this “will of the tones.”

Tones themselves are representations in sound of cosmic laws which manifest themselves in everything, including music, color, geometry, physics, and the human body. Thus can music be what it is to us—

satisfying, unsatisfying, predictable, unpredictable, harmonious, disso-nant, beautiful or ugly. Of course the art of music also depends on the state of the listener and their level of attention, conditioning, and famili-arity with the work itself or with similar musical compositions.

HARMONICS

Is there an objective connection between music and the heavenly bod-ies? Where is the hidden key to the philosopher's dream of the Celestial Music, the music of the spheres? The answer may lie in one word that is used in both the science of music and the science of astrology: harmon-ics.

Ask any string player to explain a harmonic, and they will tell you that it is a note produced as if by magic from a certain place on the in-strument touched very lightly. (Usually one must press down tightly to get a note to sound clearly.) This celestial sounding little note audibly occurs at the basic divisions of the instrument's string. The more simple the number, the louder and clearer the harmonic. The harmonics occur in order of loudness and simplicity of number: ½, ⅓ and ⅔; ¼ and ¾; ¹/_5,

2/_5, ³/₅, and ⁴/₅; ¹/₆ and ⁵/₆ (³/₆ equals ½ and ²/₆ equals ⅓, etc.).

At each of these points there is both a harmonic that results from a light touch, and a stopped note produced by pressing firmly. At the very basic numbers, these notes are one and the same. Beyond the sim-ple fractions, the harmonic and stopped note produce different notes but have a definite relationship. Once past the basic numbers, the mathe-matics gets very complex. This stopped note and partner note of each harmonic both equal the whole. For example, a planetary angle of 60º degrees is also 300º, and an angle of 40º is also 320º. In the same way a note played on the guitar for example ¹/₆^th of the way down the string, has a partner note of ⁵/₆. It also has relative notes (as in family relatives) of ½, ²/₆, (⅓), and ⁴/₆, (²/₃).

The entire family of sixths is shown on the next page.

The harmonic sol3 is produced by touching lightly at any of the

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sions except at the point ³/6, (¹/2), where it is drowned out by the louder harmonic do2 existing there, and at the points ²/6 (⅓) and ⁴/6 (²/3) where it is drowned out by sol2. This is because the basic numbers are the loud-est, and decrease in volume by approximately 30% to 50% at each higher harmonic. For example, if do₁ were given a volume rating of 100, do₂, which is based on the number 2, would have a rating of 70;

sol₁, based on the number 3, would have a volume rating of 40; do₃, based on the number 4, would have a volume rating of 20, and so on.

By pressing tightly at these points the following notes occur.

At ¹/₆ we get sol₃, which is identical to the harmonic since it is the family ruler. (All family rulers have stopped notes identical to their harmonics.) At ²/₆ (¹/₃) sol₂ is produced. Note that ²/₆ is twice the length of ¹/₆, thereby sounding the same note an octave lower. In other words in this family of 6 the law of 2 is also involved. As we go higher in number the interrelationships increase rapidly. At ³/₆ (½) we have do2, at ⁴/6 (²/3) we have sol1 and at ⁵/6 we have mib1.

To sum up, each division of a musical string has a partner note, a harmonic, a stopped note, and a family of related notes. For example a division of ¹/6 has a partner of ⁵/6; together they equal the whole. The harmonic at ¹/6 is sol3, the stopped note is sol3, and the family relatives are do1 (all), ¹/6 sol3, ²/6 sol2, ³/6 do2, ⁴/6 sol1, and 5/6 mib1.