W.r.t. band coupling/linking, some more info which should help to remove bad options.
Right now there are 4 options:
1 Merging, % (current method for linking)
2 Merging, dB's (current method for coupling)
3 Minimum, %
4 Minimum, dB's
Let's assume 50% band coupling from band 2 to band 1, band 2 is 12 dB more reduced than band 1 without coupling or linking. Now regardless of the level, the relative levels of band 1 and 2 should always remain equal.
So let's examine 2 situations:
- Band 1 at 0 dB, band 2 at -12 dB
- Band 1 at -12 dB, band 2 at -24 dB
Attenuation: 0 dB = 1, -12 dB = 1/4, -24 dB = 1/16.
1 Merging, % (current method for linking)
b1_out = min(b1, b2) * link + b1 * (1 - link)
= min(1, .25) * .5 + 1 * .5 = .625 (for 0, -12).
or min(.25, .0625) * .5 + .25 * .5 = .15625. (for -12, -24)
.15625 * 4 = .625. So this result is EXACTLY 12 dB lower, which is exactly what I want. So this method is ok.
2 Merging, dB's (current method for coupling)
b1_out = 1 / (max(1/b1, 1/b2) * link + 1/b1 * (1 - link))
= 1 / (max(1, 4) * .5 + 1 * .5) = 1 / 2.5 = 0.4
or 1 / (max(4, 16) * .5 + 4 * .5) = 1 / 10 = 0.1
0.1 * 4 = 0.4. So this again results in EXACTLY 12 dB difference. Good.
Btw, .625 corresponds with about -4/-5 dB, 0.4 with about -7/-8 dB. Method 1 and 2 are both ok, the difference (as mentioned earlier, and shown here again) is that method 2 leads to more attenuation if the reduction is big. Will test it below with small values.
Method 3
link_from_band_1 = 1 - (1 - b2) * link
= 1 - (1 - .25) * .5 = 1 - .75*.5 = .625
or 1 - (1 - .0625) * .5 = 1 - .9375 * .5 = .53125
b1_out = min(b1, link_from_band_1)
= min(1, .625) = .625
or min(.25, .53125) = .25
As I wrote earlier, a much deeper band 2 has less effect on band 1. So this version is WRONG.
Method 4
link_from_band_1 = dBs * link
= -6 dB (for b2=-12)
or -12 dB (for b2=-24)
-->
min(0, -6 dB) = -6
or min(-12, -12 dB) = -12
WRONG AGAIN. The difference should be 12 dB, not 6.
Conclusion: Both methods that I'm using now (the one for linking and the one for coupling) are fine, both other methods will fail.
Now for the difference between method 1 and 2. Let's try it again with b1 = 0 and b2 = -3 dB (.707) instead of -12.
1 Merging, % (current method for linking)
b1_out = min(b1, b2) * link + b1 * (1 - link)
= min(1, .707) * .5 + 1 * .5 = .8535
2 Merging, dB's (current method for coupling)
b1_out = 1 / (max(1/b1, 1/b2) * link + 1/b1 * (1 - link))
= 1 / (max(1, 1.41) * .5 + 1 * .5) = 1 / 1.205 = 0.8299
Both values are close to -1.5/-2 dB. So where with a difference of 12 dB the effect in dB is almost doubled in method 2 compared to method 1, for small differences it is not! Method 2 still gives more reduction, but the difference is much smaller. So for very big differences, method 2 gives relatively more effect than method 1. Which was to be expected, and corresponds with what I wrote earlier a few posts ago.
Conclusion: The only thing I need to do is check if I should use method 1 or 2.
Method 3 and 4 are bad.
What remains is this question:
If a band goes down VERY deep, should it pull adjacent bands down equally hard (method 2) or should it pull less hard (method 1)?
In the current implementation, Band Coupling (with the matrix) uses method 2. Band Linking (3->2, 2->1 etc.) uses method 1.
Finally, there's an extra method that has not yet been considered: Coupling a band a constant number of dB's above the level of another band.
Formula: b1_out = min(b1, b2 / link)
So for example,coupling band 1 to 6 dB above band 2 would give:
0, -12 -> -6
-12, -24 -> -18
Which is a 12 dB difference. So this method would also be good.
FINAL CONCLUSION.
There are 3 possible methods that give 'good' results:
1. b1_out = min(b1, b2) * link + b1 * (1 - link)
Effect gets smaller if the relative difference between bands is bigger.
2. b1_out = 1 / (max(1/b1, 1/b2) * link + 1/b1 * (1 - link))
Effect stays the same if the relative difference between bands is bigger.
5. b1_out = min(b1, b2 / link)
Effect is constant at a margin above band 2, only if band 1 gets too loud the level will be reduced further - no smoothing area as in methods 1 and 2.
As said, for Band Coupling I'm now using method 2, and I'm starting to think that I should do the same for Band Linking. Method 2 is closer to Method 3 than Method 1.
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