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The dynamics of glycolytic waves in a yeast extract have been investigated in an open spatial reactor. At low protein contents in the extract, we find a transition from inwardly moving target patterns at the beginning of the experiment to outwardly moving spiral- or circular-shaped waves at later stages. These two phases are separated by a transition phase of more complex spatiotemporal dynamics. We have analyzed the pattern dynamics in these three intervals at different spatial scales by means of a Karhunen-Loeve (KL) decomposition. During the initial phase of the experiment, the observed patterns are sufficiently described by the two dominant KL modes independently of the spatial scale. However, during the last stage of the experiment, at least 6 KL modes are needed to account for the observed patterns at spatial scales larger than 3 mm, while for smaller scales, 2 KL modes are still sufficient. This indicates that in the course of the experiment, the local glycolytic oscillators become desynchronized at spatial scales larger than 3 mm. Possible reasons for the desynchronization of the glycolytic waves are discussed.