## 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

#### 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.)"