The globular flute is a very old instrument. Egg-shaped forms of it come down to us from Old China and the pre-Columbian South American natives were adepts of creating vessels to hold and vary the rates of vibrating air.

Sometime in the mid-1960s, a relatively-young English mathematician, John *****, studied a number of South American globular flutes (achronically now known as ocarinas) and concluded that there was some sort of pattern, that the different sizes of the fingerholes had some functional purpose.

It wouldn't surprise me, given the results, that John was already familiar with recorders and their "cross fingering", for he went on to develop a little four-holed globular flute....the holes of progressively larger size. Different combinations of open holes---- behold the mathematician at work!--- in series would produce an almost entire chromatic scale over the range of one octive.

The form of these little creatures was streamlined, made most attractive, and suspended by a cord around the neck of their purchasers, thanks to an additional hole which did not communicate with the interior chamber of the instrument.

My sister, Susan, showed me one of these in 1974. Her cello teacher had lent it to her. Susan also plays the recorder and cross-fingering was therefore no mystery to her. She demonstrated the scale. I memorized the intervals of the four holes, opened progressively with no cross fingering: DO, RE, LA, DO.

At that particular time, I had become tired of making simple six-holed bamboo flutes. Moreover, I had discovered to my disgust that I had worked for some four years, producing tens of thousands of such flutes, without ever really having understood the law of proportions----although I thought I knew all about it. I should like to say that the fault was not my own stupidity, but the fact that my prestigious education had taught me how to perform mental gymnastics to please my masters, not how to think for myself. In any case, it was my use of elementary statistics to record sales data and project craftshow needs based on such which brought me to finally apply mathematics to the making of the flutes themselves. The simplicity and obviousness of the results were so patent that I felt like a fool and still do. It was time to get out of the flute-making business and do something more challenging.

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