Chregg
what i did was tune one z3ta with a sine to 435 and another left it at 440, playing E on both of them, there was a 4 hz difference ??
Depends, there is a 5 hz difference between 435 and 440 (the two types of A's) but the problem or beauty of the hertz scale is that it is logarithmic. So the same difference between A440 and A435 up an octave is A880 and A870, so in that octave the same two notes are 10 hertz apart. They are not any further apart sonically however, it is just the nomenclature of the scale. The distance between 100 hz and 200 hz is one octave (double the hertz to get the octave.) Like wise the distance between 10,000hz and 20,000hz is also one octave. The 10,000-20,000hz octave is not any further apart (obviously) then the 100-200hz octave, it just how the scale works. So 5 hz difference in the 0-20 hz is a big change, a wide interval, but 5 hz difference in the 10,000 hz range is barely perceptible if in fact at all. So maybe there is around a 4hz distance between two E's (one with A 440 and one with A 435) with E being normally 329.63 in A440, but obviously there would be a greater difference between those two E's up on octave at 659.26. If there is a 4hz difference between the two E's in one octave, it will be 8hz difference in the next octave, 16 hz difference in the one after that. Conversely it will only be a 2hz difference in the octave below the initial two E's that are 4hz apart.
As far as a half step, the octave is divided equally into 12 equally distant notes in the equal tempered system. A, A#, B, C, C#, D, D#, E, F, F#, G, G# (and repeat back to A)
a half step is the distance between any note and its direct neighbor right next to it. A whole step you skip one note. So A to A# (or Bb) is a half step, as well as E to B is a half step. A to B or E to F# is a whole step. It is named this way because of the way western music theory formed, based off of scales. Before the equal tempered tuning popularized by Bach we did not tend to think chromatically. Actually we did not tend to think chromatically until the 19nth century. Hope that helps.