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A reduced model is introduced to represent an oscillation of a jet by edge tones. The edge tone is one of the indispensable elements in air-reed musical instruments, such as a recorder, a flute, a flue organ pipe, etc. The main approach is to obtain a representation by a one-dimensional partial differential equation (PDE) which is intended to shorten a computational time. Several parameter values are determined through a comparison between model functions and results by two-dimensional fluid mechanics calculations. Through a numerical integration of our model PDE and time measurements, it is shown that this model is applicable to real-time simulations to describe dynamics of air-reed instruments.

The aim of this paper is to shed new light on the tonal grammar of Icelandic and to complement the tone inventory as previously described in the literature (Árnason 1998). Specifically, types of pitch accents and edge tones and their combinations in neutral declaratives and questions, and in utterances containing narrow focus are addressed. Two pitch accent types (H* and L*) and two edge tones (H- and L-) are identified, for which evidence has not been found in previous research. Moreover, the paper shows for declaratives, that along with downstep, Icelandic has upstep across Intonational Phrases. Upstep applies to a series of pitch peaks. It may occur in neutral declaratives and in utterances with final narrow focus. Overall, the results of this study provide a substantial addition to our knowledge of Icelandic intonational phonology.