I was thinking how Equal Temperament (ET) is really not an appropriate term for how pianos are actually tuned. It would require that at least one interval have a beatrate that doubled every octave. No intervals display this feature on an actual piano.
Of course if the beatrate of an interval was zero, it could double every octave and still remain at zero. Zero times two equals zero. But then this interval would not be tempered at all and ET would still not be an appropriate term. Since what is usually considered to be the nearly coincident partials, actually are coincident, Zero Actual Coincidence (ZAC) would be more appropriate.
But there is still a problem. If, let’s say, a 5th or 12th or 19th is chosen as the beatless interval, there are many possibilities of how the other intervals can be tempered. The resulting beatrates could make any number of patterns like square waves, or sine waves. These patterns would repeat according to how many semitones the zero beating interval spans. To designate a smoothly progressive beatrate curve it could be called Progressive Zero Actual Coincidence (PROZAC).
Do you think the name could catch on?
