Nancarrow piano studies collections: why are they ordered that way?

[an attempt to reply to your question, though I feel a whole doctoral disertation could easily be dedicated to this subject alone!]
You have 2 questions about the Nancarrow Piano Studies which are intrinsically linked: their chronology and ordering in cd.

The most discussion I found about the chronology are from: Dated and annotated list of the works, premieres and arrangements of the music of Conlon Nancarrow [well worth a read]

The main points I gathered from this were:

• a number of people put together different chronological lists over time and came to different conclusions.
• there are three types of score for most of the studies:
  1. a pre-punching score as a guide
  2. a piano roll
  3. a standard music notation score
• between about 1960–1965 he worked mainly catching-up writing music notation scores for the already made piano rolls.
• (Gerhard) Trimpin* during 1988–1992 converted all the piano rolls to the midi file format.
• There's an impressive chronology list of all works known at the end at the above web page.

* simply known as Trimpin.

From the same site, different page: Interviews with Conlon Nancarrow (1980-1993) by Monika Fürst-Heidtmann [Various interviews on June 1987, Jan. 1980, May 1984, Nov. 1993 and Oct. 1991 and letters between 1980 and 1993]

I don’t remember any dates, but the sequence of the numbered pieces (Studies for Player Piano) is more or less regular, except that occasionally I would go on to a new number before finishing a previous one, and later return to it. Also there was a period of about five years when I didn’t do any pieces (1960-1965?).

It further explains:

• earlier pieces done on a machine that could only punch relations of sixteenth notes.
• After study 21 has new machine that can move to any point in the roll (not limited to the sixteenth notes).
• Earlier pieces in standard notation, no drawing on the roll.
• Renumbered 38 & 39 to 43 & 48.
• 45 split into five pieces
  • renumbered three of the five
  • rewrote one of the five
  • withdrew [implied] one of the five

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Recordings of Nancarrow's Complete Studies

This seems to be the first complete set of the studies and this is were the original ordering of the 50-odd studies seems to come from.
[Cn = Catalogue Number; rd = release date; ts = tracks]

1750 Arch Records Volumes recorded 1977

• Vol. 1, cn: 1768, rd: 1977, ts: no. 3a–e, 20, 41a–c.
• Vol. 2, cn: 1777, rd: 1979, ts: no. 5, 6, 14, 22, 26, 31, 35, 4, 32, 37, 40a–b.
• Vol. 3, cn: 1786, rd: 1981, ts: Sonatina. no. 1, 2, 7, 8, 10, 15, 21, 23–25, 33.
• Vol. 4, cn: 1798, rd: 1984, ts: no. 9, 11–13, 16–19, 27–29, 34, 36.

Wergo Studies For Player Piano (various volumes), recorded 1988 [various recordings, rd: 1990 seems earliest]

• Vol. 1, ts: no. 3a–e, 20, 44, 41a–c.
• Vol. 2, ts: no. 4, 5, 6, 14, 22, 26, 31, 35, 32, 37, Tango?, 40a–b.
• Vol. 3 ts: no. 1 2a, 2b, 7, 8, 10, 15, 21, 23, 24, 25, 33, 43, 50.
• Vol. 4 ts: no. 9, 11, 12, 13, 16, 17, 18, 19, 27, 28, 29, 34, 36, 46, 47.
• Vol.5 rd: 1991 seems earliest, ts: no. 42, 45a–c, 48a–c, 49a–c.

Other Minds cn: OM1012/15-2, rd: 2008 (re-release but remastered of 1750 Arch Records recorded 1977)

In Other Minds liner notes [archive.org site, pdf file]
[from original 1750 Arch Records, Volume 1, James Tenney, 1977, p15]:

"Nancarrow is unusually reticent about the history of his work, both in terms of biographical information ("it's nobody's business") and with respect to any precise chronology of the Studies themselves (the scores are not dated, and he says "it doesn't matter much").... Nancarrow ...[numbered] ... the Studies although ... [the numbers do] ... not always correspond exactly to the chronological order in which the pieces were composed. ... [E]arlier pieces ... have been withdrawn from the set ... Nos. 40 and 41 ... may have been completed before earlier-numbered pieces were finished (... Nos. 38 and 39). ... I think it's safe to assume that the numbering of the Studies may be taken as at least an approximate indication of their chronological order ...."

So the complete ordering comes from the 1750 Arch Records recordings. I'd speculate the numbers for each were given in 1977, 1979, 1981 and 1984.

The Wergo liner notes [archive.org site, pdf file] are totally amazingly analytical, but I don't see much more than already said.

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Kyle Gann (an authority on Nancarrow since at least 1995 when he published The Music of Conlon Nancarrow) suggests that, among many things, Nancarrow:

• Called studies a higher number than what they were to give the impression he composed more than he did to get comissions

• basically has year of composition and number of study all over the place, not corresponding to each other at all

• from Outside the Feedback Loop: A Nancarrow Keynote Address

  I’ve looked it up, and no calculator available in the 1970s was capable of cube roots. How did he do it? He didn’t remember.

  A "Nancarrow" search on Kyle Gann's Postclassical blog

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I do wonder if the 1750 Arch Records 1977 recording was all recorded at the same time, in 1977, since 1977 to 1984—seven years—is a long time to released a product that is very near to completion.

There is also the idea that later pieces had a flavour of earlier pieces with a Spanish influence and Jazz. Could these later pieces have not been later reworkings of old pieces already written?

I agree that the liner notes would be a good starting place. A music school library would be a good place to look. (The music school library near me is temporarily, but indefinitely, closed. If and when possible, I'll update my answer with what I find there. The CDs, and presumably the booklet, are in their collection.)

Another place to look would be reviews of the collection. Here are the ones I've found:

• Scholz, Carter. 1992. "Book Review: Conlan Nancarrow: Studies for Player Piano, Vols. 1-5". Leonardo. 25 (2): 231-232.
• Fürst-Heidtmann, Monika. 1991. "Book Review: Studies für Player Piano, Vol. III & IV". Neue Zeitschrift Für Musik (1991-). 152 (5): 51-52.

As far as overall considerations, aesthetics could certainly be one. Since it's a CD release, the overall timing would be an issue, making sure the music fits efficiently on a given disc. Other considerations could be musical or compositional relationships between studies, such as instrumentation or compositional focus.

Finally, I stumbled onto this, which might interest you. The site indicates that "the studies are presented in their original order, selected by the composer."