The mind grows from observing failed attempts, The body grows from observing failed attempts, Topped mid-week both plants Often through our various senses, we receive impressions that bring the pleasure of nature's harmony into our thoughts. At other times we are aware that man has intervened in nature's processes to produce something by art, which to our highly evolved senses seems to rival even the best nature can display of beauty and harmony. We become aware at such times of man's wonderful ability to bring seemingly unrelated elements into harmonic balance, and receive a glimpse into a world where everything exists in conscious sympathetic attunement to everything else. When we listen to a piece of music that seems to strike a beautiful chord somewhere inside us, or view a painting that simply glows with harmonic awareness well executed, we probably do not spare much time to contemplate the wonderfully intricate combination of vibrations that our sensors make it possible for us to perceive. We tend to appreciate the relationship between the parts of something, by an awareness of the harmony or dissonance of the whole. This ability enables us to say "what a beautiful house!" instead of "analysis has proven that this collection of building materials exhibits certain elements of harmonic proportion." While this ability to instinctively appreciate the beauty of true harmony has an important role to play in evolution, a more analytical understanding of the laws involved can be most useful. This is especially so if we wish to create works of art where each part exists in true harmony, not only with the other part of that particular whole, but with the universe within which the creator and the created exist. Everything vibrates. From the most dense matter to the most subtle cosmic rays, everything which our senses allow our thoughts to become aware of, can be specified in terms of wavelength or frequency of vibration. These two terms define the same thing, but from different points of view. The following are the approximate wavelengths of various energy carriers: Cosmic rays 0.000,000,001 mm Gamma rays 0.000,000,1 mm X rays 0.000,500 mm Ultraviolet rays 0.003 mm Visible light 0.006 mm Infrared 0.01 mm Sound waves 1 meter Radio waves 300 meters Violet light 400 nm to 450 nm Blue light 450 nm to 500 nm Green light 500 nm to 570 nm Yellow light 570 nm to 590 nm Orange light 590 nm to 610 nm Red light 610 to 700 nm 1 nanometer (nm) = 0.000,000,1 cm = 1/10,000,000 cm If a guitar string is plucked and we hear a sound, it is not too difficult for the human mind to associate this sound with the vibration of the guitar string. With color it is quite different. It is difficult for us to conceive that the color of a substance is not an inherent property of the substance itself, but an indication picked up by our senses of that substance's ability to absorb or reflect the light which happens to be shining on it at that moment. Neither the matter nor the light is colored. What happens is that the brain learns to differentiate between the frequencies reflected or transmitted by the substance the eyes are focused on. The same thing happens with sound. When we say "Oh! Listen, they're playing my favorite song," what we really mean is: "My brain has stored within it a particular pattern of frequencies. I have compared the new information being received with this stored pattern and have deduced the answer that the two patterns are similar within certain specified tolerances." The 'pleasure' involved could have something to do with our running the pre-recorded pattern at the same time, in 'sympathy' with the new pattern as it is received. The word sympathy describes very well our ability to appreciate color and sound. It also describes the reason behind certain elements of harmony. For instance, if a substance vibrating at 100 cycles per second (tone 1) is in the proximity of another substance vibrating at 200 cycles per second (tone 2), we could perceive, if we had the right equipment, a certain sympathetic relationship between the two. If our equipment was a wave form plotter, we may have a drawing like illustration 2. We will see from this that there is a uniform doubling of the first tone seen in the second. At various points along the waves, the two are the same in amplitude. At other points, they are at opposite poles to each other. This doubled frequency has more points of similarity to the original than any other frequency except the original itself. If the equipment we had available for measuring these two frequencies was a soundboard amplifier and a pair of ears, then we would hear what would sound to us like one tone. If we had the opportunity to hear one at a time, we would hear that although they sound the same, one is higher in pitch than the other. This characteristic of 'the same but different in pitch', musicians have called the octave. Any two tones produced where one has exactly doubled the frequency of the other is called an octave. Speaking in ratios, an octave would appear then as the ratio 2:1 or 1:2, depending on whether we are talking of an octave up or down. A single note produced by almost any instrument will contain more than one wavelength or frequency. It will have a dominant frequency, the wavelength of which we would call the note's 'fundamental' or 1st harmonic. It will also have a varying number of upper harmonics, gradually fading in intensity into infinity or silence. Natural harmonics always have the same pattern of intervals between them. The interval between the 1st and 2nd harmonic is a perfect octave; between the 2nd and 3rd a perfect fifth; between the 3rd and 4th a perfect 4th; and so on, the intervals becoming smaller and smaller until they lose any relationship with the western 12 tone scale as it exists at the moment. Just as an octave has certain elements of sympathy with its fundamental, so some intervals have been noted to be more perfectly in sympathy with the fundamental than others. The ratio of the 'perfect 5th' or interval of 7 semitones, as it occurs in the harmonic series, is 3:2 or 2:3, while that of the 'perfect fourth" is 4:3 or 3:4. All the tones in the western 12 tone scale can be expressed in terms of the ratio between the upper tone and its fundamental. This would seem to be an ideal way of generating a scale from any given fundamental and several attempts have been made to do this, the Pythagorean system being probably the most well known. Although when working with a single tone instrument playing on its own, the Pythagorean formula works wonderfully well, if we had several instruments tuned this way together and asked them to play almost any western music, we would find that at times they sounded quite out of tune to each other. The lack of flexibility of the various scale systems based on the harmonic series has led to what is known as the 'tempered' scale. This uses as its primary unit of interval the ratio of the octave or 2:1. It then proceeds to divide the interval between any fundamental and its upper octave into 12 smaller intervals by applying the ratio: two to the one-twelfth power, to one (21/12:1). This equals 1.059463094, so by multiplying any frequency by this number, we will obtain the tempered semitone next up from our fundamental. We will also find that any tone twelve semitones up from any other tone, in a scale generated in this way, will have exactly double the frequency. If we took the note middle C on a piano and halved the wavelength, we would have the note C one octave above. If we halved this, we would have the C above, and so on. However, within about 6 octaves, we would find that although a 'sound' was being produced, no human ear could perceive it. If we kept on going, halving and producing upper octaves of our fundamental C, we would proceed through the infrared band, into the visible light spectrum. If we happened to be outside during the day, we would, for one octave only, see the note C with our eyes. The next octave above would already be in the ultraviolet band, and outside the eye's sensitivity range. If we can think of color as being an indication of a substance's vibratory rate or wavelength, we may begin to see a relationship that could exist between the color and sound spectrums. The logical extension of what has so far been said is that there exists a scale in the color spectrum that coresponds exactly to the scale in the sound spectrum, each color tone being an octave of the equivalent note in the sound range. This is not the end of the story but only the beginning. If we can for the moment accept that any wavelength in one band has upper and lower octave stretching out to infinity, then tne next question is 'fine, but what shall we use as our fundamental? A particular color? A particular sound frequency?' The musicians among us will probably say 'A 440'. This means that the note A should vibrate at 440 Hertz, or 440 times per second. They would tell us that this is standard pitch has been adopted by most orchestras around the world; pianos are tuned to it, instruments are constructed to formulas based on it, and so to them it would probably seem the most appropriate place to begin. Some of these musicians may know of the battle that is still raging with regards to this being the standard, but few would know why A = 440 Hz was chosen except that it werned when it was set to be a suitable compromise between the many different pitches in use at the time. There is also a scientific standard of pitch of C= 512 Hz which, although not in common use in nusic, has a lot of theoretical followers, as it is generated from the lower octave of C = 1 cycle per second and has certain advantages of numerical simplicity in mathematical research. A scale built upon either of these standards will yield an upper octave scale in the color spectrum. However, with the A = 440 Hz scale, we end up with a color series which, although interesting, is hard to relate to any color system or set of values in current use. The C = 512 Hz system, on the other hand, seems a more obvious choice at first sight, having 12 definite color tones and containing the strongest and most pure colors in the spectrum. Further research showed that there were still things not quite right with this system, and has led to a modified version in which correspondences with other systems seemed to fit into place. Of course the proof of the pudding is in the eating and before being accepted this system will need further research to substantiate the correspondences and prove its value to mankind. What follows is a summary of the process used in drawing up this modified scale. The upper octave color of a fundamental of one cycle per second is found to be exactly emerald green, which is recognized as having a wavelength of 511 nanometers (this is at 20o in air). 511 nm is also the color of malachite, or hydrous carbonate of copper occurring as a mineral. It would seem reasonable, given the teachings in the QBL, to associate this with the planet Venus. If we take 1 Hz or its upper octave 512 Hz as our fundamental, then build a scale upon it using our tempered scale 'formula', we will have the following 12 color tones: 723 nm = infrared 682 nm = deep red 644 nm = orange red 608 nm = orange 574 nm = yellow 541 nm = yellow green 511 nm = emerald green 482 rim = green blue 455 nm = royal blue 430 nm = indigo 406 nm = violet 383 nm = ultraviolet There are certain immediate correspondences that become apparent between some of these colors and our teachings in Parachemistry. The yellow here is the color of chromate lead and zinc yellow, the most 'yellow yellow', for want of a better description, to be found in the spectrum. It seems rather logical, if we follow the Queen scale of color, to call this the Sun, or Vulcan, depending on which system we choose to look at. The orange here is exactly the frequency of sulphide of mercury or cinnabar. It would seem appropriate to relate this to the planet Mercury on the tree of life. If we then call the deepest red in our scale Mars and the Royal Blue Jupiter we find a pattern beginning to form. The ultraviolet here is outside our range of color vision and would appear black to us. If we call this Saturn, as Saturn is described as either black or violet, then we have six tones out of the twelve named. Through want of skill and reason's light Men stumble at noon day; Whilst busily our Stone they seek, That lieth in the way. Who thus do seek they know not what Is it likely they should find? Or hit the mark whereat they aim Better than can the blind? No, Hermes' sons for Wisdom ask, Your footsteps she'll direct: She'll Nature's way and secret cave And Tree of Life detect. Son and Moon in Hermes' vessel Learn how the colors show; The nature of the elements, And how the daisies grow. Great Python how Apollo slew, Cadmus his hollow oak: His new raised army, and Jason how The fiery steers did yoke. The eagle which aloft doth fly See that thou bring to ground, And give unto the snake some wings, Which in the earth is found. Then in one room sure bind them both, To fight till they be dead, And that a Prince of Kingdoms three Of both them shall be bred. Which from the cradle to his crown Is fed with his own blood; And though to some it seems strange, He hath no other food. Into his virgin mother's womb Again he enter must; So shall the King by his new birth, Be ten times stronger just. And able is his foes to foil, The dead he will revive: Oh, happy man that understands This medicine to achieve!