|
The Oldest Magick
Lew Paxton Price
Six: The In-Between Notes
Ashar awoke with a realization in the back of her mind—she didn't quite have it yet, but it was there. This was the second night she had slept since she had made the new set of pipes with seven distinct pitches for an octave. Her subconscious was still reminding her of something important. Generally speaking, the pipes in the new set were even at the top as usual. And the bottom of the pipes formed, for the most part, a regular pattern, a gentle, sweeping curve—except for four pipes that created two intervals that did not conform. The second pipe was substantially shorter than the first. The third pipe was substantially shorter than the second. But the fourth pipe was only slightly shorter than the third and the same was true of the relationship between the eighth and the seventh. The distance between the lower ends of the third and fourth and the distance between the lower ends of the seventh and eighth seemed to be about half what each should be.
Furthermore, when she angled the pipes so that their bottoms were farther away from her, their notes would "blend" and go down for what sounded like a halftone. This halftone would be right between the normal tones of the pipes with two exceptions. The normal tone of the fourth pipe could be bent down what seemed to be the usual halftone, but this halftone would be the same as the normal tone for the third pipe. And the normal tone of the eighth pipe could be bent down what seemed to be the usual halftone, but this halftone would be the same as the normal tone for the seventh pipe.
All these clues seemed to mean that there might be tones between tones that could be used for some purpose. What this purpose could be, she did not know. She resolved to consider the matter for a while.
The diatonic scale is a strange thing because of the inherent math of music. It is composed of notes that sound right to the human ear, and it sounds right because of the mathematical ratios between the frequencies of the notes. However, the notes are not evenly spread. At two places in the octave, there are notes that are only a halftone apart. One such place is between the third and fourth notes and the other is between the seventh and the eighth notes—as Ashar discovered. The Greeks later divided the diatonic scale (octave note included) into two parts that were the lower four notes (eight notes total). Each division was called a "tetrachord" meaning "four notes." But a tetrachord was not just any four notes. It was four notes in a particular pattern. (The Greeks may not have been the first to discover this pattern—they may have just introduced it to the west.)
A tetrachord consists of a pattern of four notes separated by three intervals that might be called "steps." A tone can be linked to a step on a stairway. This stairway might consist of whole steps (or tones) eight inches high, or half steps only four inches high. A tetrachord consists of a note separated from the next note by a whole step, a separation between the second and the third notes of a whole step as well, and then a separation between the third and the fourth notes of only a half step. Then there is a whole step between the lower and the upper tetrachords and the pattern of the tetrachord repeats in the upper half of the diatonic scale.
Lower Tetrachord:
whole step, whole step, half step
(whole step between tetrachords)
Lower Tetrachord:
whole step, whole
It was several months later when Ashar began to suspect a purpose for the in-between notes she had envisioned. Certain voices in the clan could not sing certain songs that were begun with the notes in which they had been first composed. However, the same voices could duplicate the songs perfectly by beginning on a different note. When a set of pipes was played to duplicate the notes sung by the singer, the pipes had to be angled to bend certain notes downward. When Ashar analyzed this phenomenon, she understood why. She now knew why the in-between notes were necessary. Today, we call this transposing from one key to another.
The note names a key in which a tune is played that is the dominant one in the tune. Usually, it is the note on which the tune begins, on which the tune ends, and which is used most in the tune. Not all voices have the same range. For example, we have sopranos, second sopranos, altos, second altos, tenors, second tenors, baritones, basses, and deep basses in most sing groups. Most of the time, sopranos take the melody, but not always. When a lower part takes the melody, this often requires a change of key.
When a change of key occurs, the half steps in the musical scale change positions. This means that the in-betweens notes that Ashar discovered must be used, the panpipes must be angled, black notes must be placed on the piano keyboard as well as the white notes. For every key to be available for use, we must have a musical scale of twelve notes, each separated by only a half step—the chromatic scale. This chromatic scale is what we use today. It is the same scale (centuries old) of the Chinese and Sumerians who assigned one note of it to each of the twelve months (or signs).
Some form of this scale occurs nearly everywhere in the world. Due to certain mathematical difficulties, some cultures add notes as compensating measures, but fundamentally they still use what we call the chromatic scale. The chromatic scale is basically a convenience for shifting the diatonic scale from one key to another. So one might say that the diatonic scale is really the world's fundamental scale.
Lesser scales, various forms of the pentatonic scale, still exist in primitive areas of the world. Given enough time, they will probably evolve into diatonic and, eventually, the chromatic scales. This is logical because: music is the half step frequencies that the ear preceives, sound frequencies are pure mathematics carried by physical molecules, and all people have similar ears and brains.
The musical scale is not an accident. It is a natural consequence of pure mathematics and nature. It was discovered, not invented. It is even more precise than so far described in this series. And its effects are more far-reaching than most of us have ever imagined.
Ashar accepted the new in-between notes she had found and began to make sets of pipes that played the in-between notes. Once she had made several sets in other keys, it was difficult to tell which key was the one that she had found first. Only the distinctive appearance of the oldest set could tell her where the starting point was, unless she chose to use her measuring stick. The scale seemed to have no beginning and no end . . .. | 
