Sequence learning is a fundamental cognitive function of the brain. However, the ways in which sequential information is represented and memorized are not dealt with satisfactorily by existing models. To overcome this deficiency, this paper introduces a spiking neural network based on psychological and neurobiological findings at multiple scales. Compared with existing methods, our model has four novel features: (1) It contains several collaborative subnetworks similar to those in brain regions with different cognitive functions. The individual building blocks of the simulated areas are neural functional minicolumns composed of biologically plausible neurons. Both excitatory and inhibitory connections between neurons are modulated dynamically using a spike-timing-dependent plasticity learning rule. (2) Inspired by the mechanisms of the brain's cortical-striatal loop, a dependent timing module is constructed to encode temporal information, which is essential in sequence learning but has not been processed well by traditional algorithms. (3) Goal-based and episodic retrievals can be achieved at different time scales. (4) Musical memory is used as an application to validate the model. Experiments show that the model can store a huge amount of data on melodies and recall them with high accuracy. In addition, it can remember the entirety of a melody given only an episode or the melody played at different paces.