Amplitude Panning
Materials
Just stereo?? (different miking techniques)
Panning
- constant gain
- constant power (sin^2 + cos^2 = 1)
- velocity and energy vector optimizations
("magnitude" vector - intensity = velocity; power = energy)
- two channels: velocity vs. energy mismatch; Gerzon: three channels (center speaker)
- four channels, five channel optimization (mix)
- azimuthal harmonic optimization
(Thesis: Five Channels Panning Laws, by by James R. West, start reading at Panning Laws in Chapter 3)
VBAP
The original article on VBAP by Ville Pulkki
Concepts
- two dimensional amplitude panning
- two speakers, not more than 60 degrees apart
- gain factors: g1, g2
- for constant power g1² + g2² = C (C = volume control for the source)
two dimensional vector base, the base being defined as unit length vectors pointing to the loudspeakers:
l1 = [l11 l12]T l2 = [l21 l22]T (T = matrix transposition)
The source unit vector p is:
p = [p1 p2]T
So:
p = g1 l1 + g2 l2
Same as:
pT = g L12 (g = [g1 g2]; L12 = [l1 l2]T)
So:
g = pT L12^-1
Once we find the inversion of the matrix that describes the speaker vector base a simple matrix multiplication will give us the gain coefficients for the speakers involved
Gain coefficients should be scaled according to:
The extension to 3D does the same on triads of adjacent speakers:
Unequal spreading, see: another Pulki article
Examples
I have not been able to find a VBAP Ugen for SC...Some relevant SuperCollider panners...
- Out
- Pan2
- Pan4
- PanAz