Multivariate time series classification (MTSC) has broad applications in numerous domains. Existing MTSC methods typically focus on either temporal dynamics or variable interactions of the data, often overlooking cross-scale couplings among different variables. To bridge this gap, we propose Scale-Variable Graph Learning (SVGL), a novel framework that effectively captures data-inherent scale-variable interactions for MTSC. SVGL begins with spectral analysis to adaptively identify key periodic scales for each variable. A period-aware reservoir computing network is then incorporated to fit the variable at these scales, encoding the sequential and periodic dynamics into multi-scale dynamic representations. Subsequently, we construct a scale-variable graph to model interactions of the encoded temporal dynamics, where nodes represent scale-variable pairs and edges denote their correlations. After sparsely initializing the graph via nearest neighbors, a parallel graph learning architecture is integrated in SVGL, combining global graph convolutional and sample-specific graph attention to aggregate effective features for classification. Extensive experiments on 30 UEA datasets demonstrate that SVGL outperforms state-of-the-art baselines in accuracy and maintains low training overhead.