From recent mathematical conversations, I have heard that when Leray first defined spectral sequences, he never published an official explanation of his terminology, namely what is "spectral" about a spectral sequence.
In Timothy Chow's relevant article, he writes
"John McCleary (personal communication) and others have speculated that since Leray was an analyst, he may have viewed the data in each term of a spectral sequence as playing a role that the eigenvalues, revealed one at a time, have for an operator."
This certainly seems like a reasonable answer, but are there any other plausible explanations? Did Leray ever communicate, perhaps in personal correspondences or unpublished manuscripts, why he chose that particular term? Does anybody have a better explanation for the origin of the adjective "spectral" in spectral sequences?