Armed with this analysis, and faced with a new input sound from the musician, we analyze the latter and find the `closest' synthetic point. In the simplest realization, we simply choose the synthetic parameters which minimize the Euclidean distance between the analyzed and the resynthesized timbre. This can be done in real time using a linear search through the parameter set, provided that the number of analysis points does not exceed 10,000 or so; we could thus estimate four synthesis parameters simultaneously to 10% resolution, for example.
To get higher resolution in the synthesis parameters we can use one or another interpolation scheme. In the one-dimensional case this is easy: throw a parabola through three neighboring points in the synthesis data set and find the point of closest approach. In higher dimensions there are many possible schemes, and it is unknown which one works best.
To this we might wish to add a scheme for encouraging continuity of the synthesis parameters that come out. A simple, although not entirely adequate, approach is to favor parameter sets that are close to the previous parameter set that was output, by suitably weighting the timbral distance function (that is minimized above) by the distance travelled in the synthesis parameters from frame to frame.
Finally, the loudness of the output is adjusted to match that of the input, by scaling the output so that the 11-band loudness measures match.
An importaant limitation turns out to be closely related to the continuity problem: it could be that the live input changes in a direction which is perpendicular to the surface of synthesizable sounds. Since the input is changing audibly (we presume), the intentionality principle dictates that the output sound should change as well. The (untested) solution is to cheat, locally rotating the path of input so that some change can be heard in the output. At some point, though, we would have to stop rotating; perhaps this is best done at a moment when, despite our efforts to keep the synthesis parameters moving smoothly, it becomes necessary to make a discontinuous change.
No attempt has yet been made in this scheme to deal with the pitch of the sound; it is either considered a byproduct of the process (in which case the performer gives up the possibility of accurate pitch control) or else it must be chosen otherwise (either pre-determined, controlled explicitly, or derived from a separate pitch determination of the performer's input). The desired pitch may be imposed on the synthetic sound either as a post process, or else as a synthesis parameter. In the latter case, it may be desirable to map the synthesis algorithm's timbral behavior for several representative pitches. This will further complicate the problem of making a suitably continuous output.