It may be of interest that the ever-rising tone phenomenon springs can be viewed as an application of the fact that a typical helix curve in R^3 (e.g., h(theta) = (cos(theta), sin(theta), theta) ) can be thought of as a fibre bundle whose total space is the helix, base space is the circle, and fibre is the group Z of integers. The bundle projection, from the total space to the baseb is just p( (cos(theta), sin(theta), theta)) = theta.mod (2pi). I think the idea such "instrument" would play a "chord" of 11 or 12 octaves of a given tone simultaneously at equal volumes -- since the human range of hearing is often cited as between 20 and 20,000 cps, a factor of 1000 ~ 2^10. It might be fun to hear music written specifically for this circular range of tones. --Dan A.
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