ok, I have posted a million jillion times I think on long poem, series, and sequence, and since I read a Cati Porter query on facebook (am a mututal admiration society of Cati, including the spelling her name, and the Riverside Art Museum)
first, my princeton poetcs encyclopedia is checked. well, the library is mirrored now. feng shui says the mirror is amplifying the artists' monographs etc. on the south wall, helping our investments and fame, even though the flying yellow star with move in there next week
ok, so this means, I'm going to start where I start, which is etymology and time, space, whatnot. so, without checking, a sequence is , well (chronologically usually) "one step leads to another" sequential. a series is looser. items in a series have more latitude to be arrayed according to more different types of ... formulae. (5, 12, 62, ...)
(I don't know if there is sufficient patterning there, but I think I've used a format that indicates patterning, even if not actually forming anything)
vs. 1, 2, 3.
and a long poem is extetended, proceeding anyhow. it is not in sections or whatever that are in series or sequins, though long poem could be in sections... looong sections.
new computer not doing oed or online etymology dictionary well, we got
Se"ries\, n. [L. series, fr. serere, sertum, to join or bind together; cf. Gr. ??? to fasten, Skr. sarit thread. Cf. Assert, Desert a solitude, Exert, Insert, Seraglio.] and to look at ser- (indo european)
in my unpublished OOD, sequel to DaDaDa, part of Confiteor, I just switched the old last poem to be the new first poem because the end of that poem is "she's a series"
it is mathematical series here, a conflation of the two meanings
(Math.) An indefinite number of terms succeeding one another, each of which is derived from one or more of the preceding by a fixed law, called the law of the series; as, an arithmetical series; a geometrical series.
sequence is different -- merely following
now, one could argue a sequence is MORE powerful because you can just follow A with "frog" with [the artist formerly known as unpronouncable sign but now known as Prince again. Or Sheppy to those who love him.] But one could say, nope, because the only thing that is important is the FOLLOWING, which, FOLLOWING, is a more simple relationship.
c.1200, "continue, persevere," from Anglo-Fr. suer "follow after, continue," from O.Fr. sivre, later suivre "pursue, follow after," from V.L. *sequere "follow," from L. sequi "follow" (see sequel). Sense of "start a lawsuit against" first recorded c.1300, on notion of "following up" a matter in court. Sometimes aphetic for ensue or pursue.
but you see the series/sequence blur.
another distinction is often interdependence / independence
oddly? perhaps understandably, this is most frequently distinguished in terms of separate publishability or publishing history: the pisan cantos vs. poems x y and z cobbled together under a rubric
as someone who writes things published as both, I would say that some of this is the result of writer insistence, or perhaps design in advance or foreknowledge or plan of final result of a process
some of these is the result of lack of acceptance or encouragement by the publisher of a larger rubric
I could go on giving other options, but, I think we can see that much about publishing history is accident, and much has to do with its relation to process or process' relationship to thew writing of the poem(s).