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