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The structural relationship between the periodicity (denoted ch) of the host structure along the tunnel and the periodicity (denoted cg) of the guest molecules along the tunnel is incommensurate if no small integers p and q satisfy the relationship pcg = qch. Thus, cg/ch is not equal to a rational number with a small denominator. In contrast, if small integers p and q satisfy the relationship pcg = qch, then the structure is commensurate and the host and guest substructures share a common periodicity cs = pcg = qch along the tunnel (if p > 1 and/or q > 1, then the common periodicity cs is typically called a "superstructure"). General aspects concerning the nature of incommensurate versus commensurate behavior in tunnel inclusion compounds are discussed in the following papers
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