This paper proposes a new method to interpolate between two audio signals. As an interpolation parameter is changed, the pitches in one signal slide to the pitches in the other, producing a portamento, or musical glide. The assignment of pitches in one sound to pitches in the other is accomplished by solving a 1-dimensional optimal transport problem. In addition, we introduce several techniques that preserve the audio fidelity over this highly non-linear transformation. A portamento is a natural way for a musician to transition between notes, but traditionally it has only been possible for instruments with a continuously variable pitch like the human voice or the violin. Audio transport extends the portamento to any instrument, even polyphonic ones. Moreover, the effect can be used to transition between different instruments, groups of instruments, or really any transient-less audio signals. The audio transport effect operates in real-time; we open-source implementation is provided. In experiments with sinusoidal inputs, the interpolating effect is indistinguishable from ideal sine sweeps. In general, the effect produces clear, musical results for a wide variety of inputs.