Equal Ratios Curve

The term “equal ratios curve” was coined by John Rogers and John Rockstroh in a paper entitled “Score-Time and Real-Time” given at the 1978 International Computer Music Conference. Such a curve is, in fact, an exponential curve. Divide the region of the x-axis from A to B into N intervals of equal duration at positions x0, x1, …, xN where x0 = A and xN = B. Then an exponential curve f(x) has the property that

f(x1)/f(x0) = f(x2)/f(x1) = … = f(xN)/f(xN-1)

Such curves are particularly suited to converting “score time” (relative time) in quarter notes to “real time“ (absolute time) in seconds. They produce accelerations which are felt to speed up at a constant pace, or likewise ritards which are felt to slow down uniformly. They are also useful for describing pitch contours such as glissandi.

© Charles Ames Page created: 2015-03-29 Last updated: 2015-03-29