well, its really application specific. when you design generalized filters you assign goals. you can define a filter by an arbitrary cutoff point, but for most things, its assumed to be -3dB. The biggest example is the Linkwitz Riley crossover which has a -6dB cutoff.
@OP -- please add info regarding the dB scale. you have information about octaves, but not dB.
a nice guide, not cumbersome. at this point i like to classify crossovers into categories:
1.) preamplifier, active analog. (like amplifier crossovers)
2.) preamplifier, passive analog. (fmods)
3.) preamplifier, digital (HU filters using DSP)
4.) postamplifier, electrical (passive crossover)
5.) postamplifier, acoustic (using acoustics to give a desired response).
maybe i'll add some generalized filter stuff, because it comes up ALL the time:
most filters are defined by a combination of 1st (-6dB/oct) and 2nd (-12dB/oct) networks. 1st order filters are not resonant and cannot really favor one specific frequency more then other. 2nd order filters can either be two 1st order filters (Q 0.5). a high Q* filter is highly resonant, favoring one frequency more then others -- possibly even more then other frequencies in the passband.
4th order networks (-24dB/oct) can thusly be made from 2 2nd order filters. typically it will be a filter with a higher Q (maybe 1.6) and a filter with a lower Q (maybe 0.6). this ends up not favoring any specific frequencies, but also gives a sharp cutoff.
--------------- main point ---------------
This is important becuase EVERYONE asks if you can combine filters. YES you can. BUT not with the intended results. The final filter will be the product of all the filters. thus if filter A is -10dB at 80hz, and filter B is -0.1dB at 80hz, the final result will be -10.1dB @ 80hz. if both filters A and B are -3dB at 80hz, the result will be -6dB @ 80hz. if you were defining a cutoff at -3dB, then the resulting filter's cutoff is not 80hz.
further, just because you have maybe a 4th order filters (made from 4 1st order stages) doesn't mean it will be good. the slope WILL eventually make it to -24dB/oct, but it may not change from -0dB/oct to -24dB/oct in a small bandwidth. i assume this is why some concider fmods to be -6dB/oct filters.
New developments in crossovers are there in digital filters as well as combining bandstop filters with normal filters. the bandstop creates a high slope but only in a small band. the argument is that you can get a filter that is -60dB/oct, and always at or below -30dB in the stopband. CDT and NTM use these filters. NTM has a patent on applying the hourglass filter to audio systems. I also had this same idea, but never finished working on it.
* -- Q refers to the "quality" of a resonator. basically how well it favors a single frequency. a high Q filter may not be desired if the filter is to affect a wide bandwith.
