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The Oldest Magick

By Lew Paxton Price

Seven: The Diagonal Flute

After the fall of the Old World of science and the burning of the last repository of its knowledge (the library of Alexandria), the old math of music was lost. But just after the peak was reached and Babylon fell, a learned Greek named Pythagoras began to experiment to see what he could rediscover. His primary tools were strings and stringed instruments rather than woodwinds. This was a problem at times because, whereas on a panpipe or simple flute one can see a direct analogy of the wavelengths of the musical scale, strings can give wrong impressions because of their dependency on tension applied or material.

Nevertheless, Pythagoras arrived at some good answers that are very close to what we use today. His scale, the Pythagorean scale, is fine when used with adjacent notes such as singing do, re, me, fa, so, etc. It is very close when used with notes that are not adjacent to one another such as do, fa, ti, etc. However, the Just scale is preferred for notes that are not adjacent. As most tunes are combinations of notes which are both adjacent and not adjacent to one another and to the fundamental keynote, a compromise scale is necessary. This compromise, though first arrived at by ear, was later discovered to be perfect theoretical scale based upon the number two and its roots. We call it the "tempered" scale. The following table illustrates the close similarities of all three scales. It is based upon the standard of C=256 cycles per second (Hertz in today's confusing jargon).

CEF

SCALE GABC

Pythagorean256288324341.33
384432486512
Just 256288320341.33
384426.66480512
Tempered256287.23322.56341.76
384.49430.59483.33512

Since the tempered scale is a compromise to the human ear and brain (it works reasonable well regardless of the note with which one starts) primitive instrument makers, after years of experimenting, usually came up with instruments based upon it. This is true of Old World panpipes and flutes. Consequently, the tempered scale is what we will use when providing instructions on how to make them. We won't use the whole tempered scale in each case, of course, as many old instruments used only a part of it.

The Native American (an imaginary typical human living in one of the Americas) was not fully evolved in the musical sense before the coming of the more advanced civilizations of the areas to the south. In North America, at the time the white man came, few (if any) tribes were fully evolved in western musical terms. Ironically, the Europeans with their evolved scale did not know how to use it in the "magickal" sense, while the Native American, with his primitive scale, did.

The North American tribes were many and were each a culture unto itself. Though some were more evolved in their music than others, generally speaking, their music lacked certain notes and others had not yet evolved into the precise notes that we know. Few tribes used harmony. On the rare occasions they used it, it was more by accident than by design. Without harmony, the scale could not fully evolve. They knew of the natural harmony of the flute (which, when overblown, gives the octave and the musical fifth (fifth note in the diatonic scale)). Many tribes had mastered half steps or half tones up to and including the fifth.

The shaman had dreamed last night. His totem animal has shown him a new way to make magic. It was like a bird and a windblown reed as well. And it was done with cane in a form without nodes.

He fed the fire to make it larger and gathered small stones until the fire was largely a mass of coals. Then he placed the stones in the coals, placed more wood over them, and went off to find some cane. The river was low and the desert was growing warm already, but there was still coolness in the breeze and he had a good feeling. He selected the proper piece of cane and asked the spirit within to give him some of itself for use in summing the higher forces. He cut the cane with his obsidian knife and removed the length that seemed to be right.

Back at the fire, he took the hot stones from the coals with green cane, split to grab such things. He dropped the rocks into the hollow of the piece of cane he had selected. When the nodes were gone, only a hollow tube remained, almost uniform in its inner diameter. He then placed the tube above the coals and slowly turned it until it sweated and changed color. He set it aside, careful not to mar the varnish that had formed on its exterior. After it cooled, he began to blow upon it . . ..

There are many ways to blow on the end of an open ended pipe, but there is one way which is easier than the others. More than likely, this easier way was the first that primitive people discovered.

The shaman was very dizzy. He had slept from his earlier dizzy spells as he continued to blow in various ways on the end of the pipe. He could make the whisper of the wind, but the Coati had promised him more. Once again he turned the pipe and blew. The sound was enough to startle him and he lost it. What a sound! The Coati was right . . ..

There are instruments in the world today that resemble the first open-ended flute. They are played with the mouth at the end, partly covering it but with an opening near the side of the flute. This means that the flute is placed against the side of the mouth and angled away at about 45 degrees from the straight-head position. Such flutes are called "diagonals" because they are played diagonally.

The first diagonal was probably without holes in its shell. It was a simple tube, playing a note for a fundamental, possibly the octave note above the fundamental, the fifth by overblowing, and later the octave note above the fifth. No one knows how primitive people first learned to use playing holes for the fingers.

He was angry. His special flute was ruined. The hours he had spent constructing and consecrating it were wasted. The enemy spear point was still embedded in the flute, broken off so that only the very tip remained. He used a rock to work out the tip, moving it back and forth until it fell free. There was a hole there now.

He blew on the flute. It sounded different. Perhaps it would be better if he plugged the hole. He placed his finger over it and blew. There was the old sound again. He raised his finger and the new sound was back. He moved his finger up and down rapidly. It was like a bird warbling . . ..

Most experts say the placement of holes in Native American flutes is simply according to what feels good to the hand. This supposedly indicates that the Native American had no musical scale, or very little sense of what one should be. In playing replicas of certain flutes, I have found that, whether by accident or intent, each one seems to have been constructed geometrically. Yes, the flutes did fit the individual hand, but they also had holes that had been shifted on the flute between each end and sized to play the fist tetrachord of the diatonic scale in the first octave (five hole version—fewer holes meant a scale with less notes in it), but in a chromatic form with all the half tones included. By tuning the flute in this manner in the first octave, the second octave (which has more notes because of the physics of overblowing) gains note five and note six and a half of the diatonic scale. This would tend to direct the scale of the Indian playing such a flute to the following notes: 1, 11/2, 2, 21/2 (also called the minor third), 3, 31/2, 4 (as the half step occurs here, there is no 41/2 in our scale), 5, 61/2 and 8. This is the entire diatonic scale in half steps of half tones (when in half tones, it is also called the chromatic scale) except for 51/2, 6 and 7. A score of ten out of a possible thirteen isn't bad (this includes the octave note). This might explain why most of the music of this area consisted of the notes of our scale up to the fifth.

Natives in the California area used diagonals for courtship. Some tribes used them for ceremonial music. In most tribes, music was a means of summoning certain spirits. Today, we call it mood setting or altering consciousness. The spirit that the music summons causes certain desired things to happen.