1The Momel algorithm models a fundamental frequency (f0) curve as the interaction of two components, a smooth and continuous macromelodic component, corresponding to the underlying intonation pattern, and a micromelodic component, corresponding to the deviations from the underlying curve caused by the effect of individual speech sounds, in particular voiced and unvoiced stops and fricatives. The algorithm is often referred to as a technique of stylisation but is more accurately described as a technique of modelling since the raw f0 curve is factored into two components without any loss of information.
2The macromelodic component is modelled as a sequence of anchor points, linked by monotonic parabolic transitions, constituting a quadratic spline function. The microprosodic component can then be derived as the residue of the raw fundamental frequency curve with respect to the macromelodic component (Hirst 1981). In its earliest implementation in the 1980s, the anchor-points defining the underlying curve were assigned manually, by clicking on selected points on a representation of the raw f0 curve on a video screen. The points were then connected by the quadratic spline function and the original utterance could then be resynthesised (using PSOLA resynthesis), replacing the original f0 by the quadratic spline function, making it possible to evaluate the adequacy of the modelled curve. It was then possible to modify the anchor-points until a satisfactory fit had been obtained.
- 1 F-measure is a statistic commonly used in information retrieval and binary classification tasks and (...)
3After several years of experience modelling f0 curves manually, an automatic version of the algorithm was developped (Hirst & Espesser 1993) using a variety of robust quadratic regression. The algorithm was later evaluated during the course of the Multext European project, on a corpus of read speech in five languages: English, French, German, Italian and Spanish (Eurom1 corpus), together with a corpus of spontaneous speech in French (Véronis, Hirst, and Ide 1994). Evaluators were instructed to add or delete anchor points of the modeled speech only when such corrections made an audible improvement to the resynthesis of the speech. The results of the evaluation were very encouraging. The Fmeasures1 for the different languages showed a global efficiency of around 95 percent, and even the corpus of spontaneous French showed an F-measure of 93.4 percent even though the algorithm had not at all been specifically optimized for spontaneous speech.
4Most of the cases where the correctors had felt the need to add an anchor point which was not predicted by the algorithm, concerned an utterance with a rising pitch before a silence. Often, in this case, only the starting point of the rise was detected. The Momel algorithm was later implemented as a Praat plugin Hirst (2007), which allows users to use its functions directly from the Praat menus without needing to handle scripts directly. The plugin allows users to analyse recordings either individually or by batch.
5The systematic error mentioned above was corrected by a special treatment before silent pauses. The concave part of the pitch rise was extended to include a similar shaped convex portion. In other words, in order to obtain the best fit for this pitch rise, a high anchor point is calculated, situated in the silent pause and as near as possible to the previous low anchor point. The anchor point is calculated so that the concave portion of the pitch rise follows the raw data points as closely as possible.
6An evaluation of the improved algorithm was carried out on a corpus of read speech in Korean (Hirst et al., 2007). It showed a significant and systematic improvement as compared to the older version of the algorithm.