I hate math

It has been described in terms of whether or not there is overshoot of the impulse, and whether or not there is ringing.

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Yeah, though I grew up with critically damped = max flat/0.707; 0.5 = transient perfect.
And which of the following step responses is "transient perfect"?
The plots show the step responses of second-order high-pass filters with values of Q = 0.7071, 0.5, and 1.0. Note that each of the high-pass response functions have the same a –3dB point: 50Hz. In this comparison, the Q = 0.7071 response has the shortest settling time, but it has the second-largest oevershoot in the negative direction, but not by a very great amount.

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And which of the following step responses is "transient perfect"?
None actually since there can't be anything below the line according to both a local Altec engineer and an old local curmudgeonly E.E. that worked at W.E. in the early days of cinema sound circa '66 that noted the best we can do 'perfect' in sound reproduction was a 'euphonically' distorted response, which IME 0.5 is my 'perfect' transient response based more on the much better hearing of young females than my then youthful hearing already damaged from game hunting, auto racing and several other hearing damaging hobbies/endeavors.