The term melodic template or skeleton refers to a basic melody which is subject to variation during a music performance. In many oral music traditions, these templates are implicitly passed throughout generations without ever being formalized in a score. In this work, we introduce a new geometric optimization problem, the spanning tube problem, to approximate a melodic template for a set of labeled performance transcriptions corresponding to a specific style in oral music traditions. Given a set of n piecewise linear functions, we solve the problem of finding a continuous function, f*, and a minimum value, epsilon*, such that, the vertical segment of length 2 epsilon* centered at (x, f*(x)) intersects at least p functions (p <= n). The method explored here also provide a novel tool for quantitatively assess the amount of melodic variation which occurs across performances. (C) 2018 Elsevier Inc. All rights reserved.