Originally posted by falconeye
and (f', N', iso') totally describe a photo in EVERY aspect (framing, noise, depth of field, diffraction etc.) and no dependency on the crop factor whatsoever remains.
Based on this simple piece of background knowledge, most discussions of differences of formats become useless.
What you are describing is not equivalence, it is DOF wide open equivalence and should be labeled so (in fact this equivalence isn't really a DOF equivalent either as equivalent lenses after this principle will not give the same image at the close focusing distance cross formats with real world lenses).
As others have pointed out elsewhere an image is an exposure that is defined by Aperture, shutterspeed and sensitivity of the medium (ISO). You cannot keep these constant or equivalent if you like while maintaining the same image cross formats. Nor can you change one of them without effecting at least one of the other. Hence, true equvalency across formats is practically impossible.
In fact any other constant is just as valid as reference points for equivalence; like exposure equivalence. Thats is same exposure cross formats. It is the latter equivalence that most people actually buy lenses after; eg someone having the 16-50/2.8 for the K-5 will most likely want a 24-70/2.8 for an FF camera in order to use both at their best advantage and either work around or with any DOF issues. Or they simply buy it cause it is available.
No one choose a format according to "equivalence". They choose them cause they are not equivalent. Generally larger formats yields better image quality than smaller.
In addition, no one actually shoot after the "law of equivalence". People will use their camera to their best advantage regardless of format; they will not try to equalize them in real life. Eg if you stand in front of a beautiful landscape with camera on a tripod, whether it is the Q, K-5, FF. 645 or 6X7, you'll use it at its finest ISO value to maximize quality and give a damn about equivalency. Likewise, if you want to freeze action you will do whats necessary while trying to maintain best possible image quality results. What you can say though, is that the bigger the format the bigger the chance to be forced to boost ISO in order to get the shot.
As other have pointed out; DOF wide open equivalency is the wrong math. To illustrate this is the fact that there are no 28-70/4 (FF) equivalent budget lens for the Pentax 6X7 which according to you should be in fact cheaper then the budget 28-70/4 lenses for FF ($100 perhaps?). Apart from the fact that they wouldn't be any cheaper, no one would buy such a 56-140/9.5 (or 11 or whatever) for the 67 cause people aren't interested in DOF wide open equivalency; they want exposure equivalency. Trying to market such a lens in the film days by claiming at was a kit lens equivalent to the 28-70 lenses for the 35mm format, and that you can work around its slow speed by using 3200ISO film would make people laugh.
Treating camera as a DOF (wide open) measuring device is missing the point. The camera is a tool for creative image making where photographers use whatever formats to the best of its advantage.
In addition, absolute DOF, except for having enough of it, is not a useful measure. This is because the degree of out of focusness or subject separation is highly subjective and not neccessarily highly critical in absolute values; eg. thinner DOF do not necessarily give better subject separation. And there are situation when you want subject separation but still want to show what the environment is like.
While this equivalency debate may be interesting, it is of little practical value. I feel it is a bit like posting the following statement on a sailing forum: "Circumnavigation is an impossibility provided the earth is flat". Possibly correct, but of little value to sailors.