Amplitude Panning


Just stereo?? (different miking techniques)


  • 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)


The original article on VBAP by Ville Pulkki


  • 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


        p = g1 l1 + g2 l2

    Same as:

        pT = g L12
        (g = [g1 g2]; L12 = [l1 l2]T)


        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 Pulkki article


Some relevant SuperCollider panners...

  • Out
  • Pan2
  • Pan4
  • PanAz

An implementation of VBAP for SuperCollider can be found here


A complete system for the Mac that does VBAP (and more) is here at ZKM.

""Zirkonium is a program for sound spatialization originally developed for the ZKM Klangdom, a 47 loudspeaker environment installed in the ZKM’s Kubus, but designed to work with other loudspeaker environments as well. The aim of the software is to simplify the use of space as a compositional parameter. It can be used as a stand-alone application for creating multi-track, spatialized compositions or as a 3D panner, receiving audio from another program. Zirkonium also accepts control data via Open Sound Control (OSC). Thus, the user can incorporate Zirkonium’s panning capabilities into his or her preferred environment (including Digital Performer, Logic, Max/ MSP, SuperCollider, etc.)"