The Oldest Magick
Chinese Changes and the Ti
Lew Paxton Price
In any circle of fifths based upon the two-thirds ratio, the thirteenth pipe or string does not turn out to be the perfect note maker for the octave. It will be a bit sharper than it should, when the two-thirds ratio is rigidly adhered to throughout the circle. Multiples of pipes going up higher and higher will not help. Indeed, in theory they will only compound and magnify the error. However, because of slight variations in the inner dimensions of pipes and, possibly because of errors in hearing each pipe, the nature of the thirteenth pipe can vary. It may have been this variation that encouraged Ching Fang in 45 BCE to add more notes (called lu) to the official scale. Very likely, the legendary magic of the number sixty may have influenced him as well because sixty was the total number of notes that the scale now had. At least this is what most authorities consider being correct.
It seems more logical to me to assume a different reasoning for going to sixty lu in lieu of twelve. I believe it was done because someone heard that it had been done in the Middle East. The people of Sumer were very good at pure math. Very likely they had discovered the secret of what we call the tempered scale. This secret would have allowed them to go to a system of sixty notes to the octave. Why? Why would they want so many notes? Probably because they were doing something very similar to the Chinese who were using music to augment the seasonal influences by officially changing keys at certain times. But the Chinese did not have the secret of the tempered scale and would have failed miserably in developing a workable sixty lu system. This frustration, coupled with the desire to have a different note for each degree in the zodiac, led to the 360 lu system started by Ch'ien Yueh-Chih in about 438 CE.
The next eleven and a half centuries must have been terribly frustrating for Chinese musicians because the 360 lu system would have been much less accurate than even the 60 lu system because of the nature of simple mathematics. The problem was resolved in 1596 CE by Prince Chu Tsai-yu who established the tempered scale in China. They had finally discovered the secret about one hundred years before the Europeans learned it. The prince also restored the twelve note scale to the relief of everyone concerned.
The Huang Chung had changed somewhat from time to time because of the emperor's desire to keep the status quo. When the Huang Chung was about nine inches long, it had tone equal approximately to F#. The last Huang Chung had a frequency of about 601.5 cycles per second according to some, and this is about D#. On the Chinese calendar, F# was the first sign after the vernal equinox. So D# would have been the first sign after the winter solstice. Again, we see the two starting points for the year that began (or was earliest recorded) in the Middle East.
There seems to be an apparent attitudinal schism between East and Middle East. This has come down to us today as between East and West, because most of our Western tradition began in the Middle East. The notes assigned to the Chinese calendar were for going along with the vibrations of the zodiac. When the sun was energizing a certain sign, the Chinese music was played to augment or magnify its effect. However, the Middle Eastern system seems to be to use the complementing note that would tend to balance the effect of the activated sign. This same tendency is here today. The Oriental way is to accept and go along with authority. The Western way is usually not the same. There is something to be said for both systems.
The flute of China, commonly called the ti, is a transverse flute like the Aryans or Hurrians used. The diagonal flute of the Middle East does not seem to have been adopted in any form by the people of the East. The appearance of the traditional ti is almost symmetrical, which means that the tuning must be adjusted with the lip. The ti was usually made of bamboo wound with thread or fine string, and might have ends made of another material. However, its most distinctive feature was a hole located between the blowhole and the closest finger hole.
This hole was probably added to increase the volume of the flute because that is what it doesand it also creates a buzzing when properly used, which causes it to sound a bit like a clarinet. The hole itself must be covered with a small piece of rice paper, moistened with water or saliva to hold it in place. It is the rice paper that actually buzzes in resonance with the note being played.
The traditional ti is longer than necessary, providing an end with two holes for a cord (with which to hang it) and two more holes to tune it properly during its manufacture. The opposite end is also long, probably to provide a more symmetrical appearance. There is a winding between each of the playing holes, and many windings between the blowhole and the nearest end. The holes may be oval or round, and are usually all the same size.
To make a working ti, you may make a normal transverse flute (see NMR 4:1) and add a hole that is the same size as the normal playing holes, located about a quarter of an inch closer to the open end from a point midway between the blowhole and the first playing hole. This is the hole to cover with rice paper or a similar resonating material. If you don't want the resonator, modeling clay or scotch tape over the hole will allow you to play the ti like any other transverse folk flute.
1989 by Lew Paxton Price
On this example, the ends are bone and the windings appear to be hemp. There are two holes for a hide thong, and two tuning holes (one visible), six finger holes, one blow hole and one hole for rice paper (resonance).