for crossfeed i can recommend jmeier, 700hz, 7-9db, i think this makes headphone sound more closer to speakers too, tho im still trying around here
The "natural" crossfeed level depends on the spatiality of the music in question. Crossfeed simulates in a very simplified manner the direct sound crosstalk in loudspeaker listening with speaker set at about ±30° angle. According to the science of human spatial hearing the Interaural Intensity Difference (IID) at frequency
f given in Hz can be roughly calculated with the equation:
IID ≈ 1.0 + ( f / 1000 )^0.8 * sin 𝜃
For sound coming from a distant source at 𝜃 = 30° = 𝜋/6 rads angle the natural Interaural Level Difference ILD = 20*log
10(IID) is roughly:
25 Hz: 0.2 dB
50 Hz: 0.4 dB
100 Hz: 0.6 dB
200 Hz: 1.1 dB
400 Hz: 1.7 dB
800 Hz: 2.6 dB
1600 Hz: 3.9 dB
3150 Hz: 5.5 dB
6300 Hz: 7.3 dB
12500 Hz: 9.3 dB
For sound sources closer to the listener there is an additional level differerence due to the distance from the sound source to the ears not being almost the same in comparison to the distance of the listener and the sound source. A fly one inch from the left ear is about 10 times further from the right ear (around the head) and that has a massive effect on ILD! This additional ILD is approximately:
8 meters / ∼27 ft: 0.2 dB
4 meters / ∼13 ft: 0.5 dB
2 meters / ∼7 ft: 0.9 dB
1 meters / ∼3 ft: 1.7 dB
0.5 meters / ∼2 ft: 3.1 dB
0.25 meters / ∼1 ft: 5.2 dB
0.1 meters / 4 inches: 9.1 dB
0.05 meters / 2 inches: 12.2 dB
At the other ear: 19.9 dB
So, for speakers at 30° and 2 meters away from the listener the crosstalk level at 100 Hz is about 0.6 dB + 0.9 dB = 1.5 dB as an example. Of course this analyse is only for the direct sound while the reflections, reverberation and room modes are ignored. The real ILD can be a little bit higher than this and at room mode frequencies possibly much higher depending the position of head, but room modes are undesired problems that harm the fidelity at low frequencies: We are lucky to not suffer from them with headphones! As a rule of thumb, at bass frequencies (below 200 Hz) 1-3 dB of ILD is the "natural" target window. Larger ILD at bass than that indicate sound sources near head which isn't very natural or desirable in music context, but if you want your music "slamming" at your ears then keep ILD large!
Anyway, stereo recordings in general do not contain infinite channel separation: If we set our target at 100 Hz to ILD_target = 2 dB and the channel separation in the recording at 100 Hz is ILD_recording = 8 dB, we need to reduce it by 6 dB. The math isn't very easy at this point, but this is how the calculations go:
We need to calculate the "channel difference ratio" D for the stereo recording. D is the ratio of the side channel level S to the sum of both side and mid channels: D = S / (S+M). For mono (left = right) sound D = 0 and when the right and left channels are completely inverted versions of each other (out of phase), D = 1. For headphone listening recordings should have about D = 0.1 at bass and have D raise to about 0.5 or a bit more at treble. The problem is that when mixing music for loudspeakers, the desired D values are higher than that, especially below 800 Hz, because acoustic crosstalk is taken into account. Channel correlation btw is simply 1 - 2*D. Anyway, in this example case we have:
D = (1-10^(-ILD_recording/20)) / 2 = (1-10^(-8/20)) / 2 ≈ 0.301
We also need the "channel difference ratio" target value T:
T = (1-10^(-ILD_target/20)) / 2 = (1-10^(-2/20)) / 2 ≈ 0.103
From D and T we can calculate the parameter 𝛽 ( = crossfeed level on linear scale):
𝛽 = (D - T) / (D + T - 2 * D * T) = (0.301 - 0.103) / (0.301 + 0.103 - 2 * 0.301 * 0.103) ≈ 0.579
Finally the needed crossfeed level on dB scale is calculated with:
Crossfeed level = 20*log10 𝛽 = 20*log10 (0.579) ≈ -4.75 dB
=> about -5 dB is "close enough."
The closer the recording is the target, the less there is need to crossfeed while hard panned "ping pongy" recording require hard crossfeed. One can learn to hear how much crossfeed is needed (how excessive the spatiality is).
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Before someone comes and writes about how this mathematical model and analyse oversimplifies spatial hearing, I totally know it! Since default crossfeed is also an oversimplification of "loudspeaker spatiality simulation", this math works well with it. It's on the same level of simplification. Many people enjoy basic crossfeed which illustrates how even oversimplified solutions can sometimes work nicely for some people. Not all, but some such as myself...
