A classical topic is the determination of the form of a tensor expressing a physical property and invariant under the point group of a crystal. For example, one finds listings showing 16 distinct forms of the piezomagnetic tensor that can arise in a crystal. Alongside each of these 16 distinct forms is listed the point groups which give rise to that specific form (see Birss (1966) for example). This is a classification of the form of piezomagnetic tensors in crystals. We claim however that this classification is quite ambiguous in the sense that it hides the very difference between microscopic and macroscopic symmetries. The topic of the paper is a clarification of the difference between material and behaviour symmetries and a classification of piezomagnetic tensors in behaviour equivalences classes, found to be 15.
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