S0lo wrote:Thats why I'm saying "Variable Slope" not "Variable Asymptotic Value" if that makes any sense. There is no notion of a constant slope over a long range of frequencies in this situation. I'm aware of that.
Yes the ultimate slope of a lowpass filter above a couple of octaves above the cutoff frequency is its order * -6 dB per oct. -6 for 1st order, -24 for 4th order, etc.
If you want to carve out "interesting" slopes over a few octaves in the middle then if your synth architecture will allow it you can do it by feeding filter blocks in series. And you can do it by feeding filter blocks in parallel and then mixing the filter outputs together, possibly also mixing-in some of the original input signal. There are many ways to carve out interesting slopes in the middle. When you start parallel-mixing-in some of the original input signal, the responses can sometimes be various "shelf" shapes.
If your synth architecture will allow it, when parallel mixing it gives more freedom if you can mix each branch either inverted or non-inverted. In simple mixing code, it is convenient to think of positive and negative gain-- For instance something like if Gain_1 = 1.0, Gain_2 = -0.5, etc-- The mixing of each sample would be Output = (Signal_1 * 1.0) + (Signal_2 * -0.5); Which is basically subtracting half of Signal_2 from Signal_1.
Dealing with a "common" mixer GUI calibrated in dB, positive vs negative gain tends to "mean something else": +6 dB multiplies the signal by 2.0 and -6 dB multiplies the signal by 0.5. Both cases are "Positive Gain" in the multiplier sense, but positive dB just multiply to bigger results and negative dB muiltiply to smaller results. So if using a "dB oriented" mixer GUI, maybe the easiest way to include the option of "subtracting rather than adding" is to give each channel strip a phase invert button. Push the phase invert button and then a setting of +6 dB SUBTRACTS [ signal * 2.0 ].
Mixing parallel filters can have lots of shapes, some hard to intuitively predict, because if the filters are tuned different, they have different phase shifts, and when you mix them together the effect of phase shifts can make some frequencies louder or quieter than you may have "intuitively expected". Also why "mixer channel phase invert" for subtraction can be useful, because if the phase differences are radical enough, then subtracting signals may give louder (or more interesting) results than adding the signals!
Apologies belaboring simple obvious points.
The parameter "Q" is most meaningful with 2nd order filters. If series-connecting or parallel-connecting higher order filters, or any filter with something like "resonance" or "bandwidth" knob rather than a Q knob, if not just tuning by ear, it is helpful to watch a spectrum analyzer because it is hard to predict what "middle frequency shape" certain resonance or bandwidth settings would give, and a resonance setting of 0.5 in one synth might not do exactly the same thing as the same resonance setting in some other synth. Each synth designer might have something different in mind when defining his terms.
But if implemented correctly, Q of 2nd order filters we can talk about purt reliably. For lowpass and highpass 2nd order filters, often the value of Q is also the filter gain at the center frequency. A Q of 0.707 is 2nd order butterworth with "sharpest rolloff which is also smoothly falling into the stopband" or something like that. The gain at the center frequency is -3 dB and for the 2nd order lowpass filter, as you trace up from low freq to high freq, the curve steadily decreases all the way up.
Below Q = 0.707 the transition in the middle is more gradual before it settles down to -12 dB per octave. At Q = 0.5, gain - -6 dB at Fc. It takes a couple of octaves below Fc to fall to -6 dB, and it will take a couple of octaves above Fc before the response settles down into -12 dB / oct.
For "carving interesting midrange responses" the Q range from 0.707 to 1.414 deserves attention. I suspect people often either use "little or no resonance" or immediately jump the Q significantly bigger than 1.414, not noticing the subtlty available in that 0.707 < Q < 1.414 range.
At Q = 1.0, Gain at Fc is 1.0. There is a smooth little "bump" approaching from below up to Fc, then it falls off a little faster above Fc, but not a lot.
Here is a dumb example-- If you have two series LP 2nd order filters-- If you set the second LP Q = 1.414 then there is a fairly wide gentle +3 dB gain bump at Fc. There will be SOME noticeable gain going down at least one octave below Fc and gain will stay positive for awhile above Fc before it starts falling off initially "a little steeper" than -12 dB / oct, eventually settling at -12 dB / oct in the high freqs.
So if you tune the Fc of the second LP filter to the -9 dB point of the first LP filter, then the curve is made "more gradual" in the couple of octaves around LP_1's -9 dB point, because of that gentle +3 dB gain bump added by LP_2. But eventually up in the higher frequencies the ultimate falloff is steeper with the two series filters rather than just one.
Higher Q's can also sculpt responses of course, but higher Q's also get narrower and more drastic in effect, so they might not be as useful to sculpt up to a couple of octaves in a cumulative frequency response.
Also of note, if the filters are NOT significantly distorting then the result would be the same feeding [LP_1 -> LP_2 -> Out] OR [LP_2 -> LP_1 -> Out]. So it is only a matter of "easier convenient thinking" to consider that you are using LP_2 to further modify LP_1. OTOH if you distort the filters then different filter routings may give significantly different-sounding results.