## 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 g1Â² + g2Â² = 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 Pulkki article

### Examples

Some relevant SuperCollider panners...

- Out
- Pan2
- Pan4
- PanAz

An implementation of VBAP for SuperCollider can be found here

- http://www.beast.bham.ac.uk/research/mulch.shtml (and scroll down to "BEASTMulch SuperCollider UGens")

#### Zirkonium

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 ZKMâ€™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 Zirkoniumâ€™s panning capabilities into his or her preferred environment (including Digital Performer, Logic, Max/ MSP, SuperCollider, etc.)"*