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As far as I know Chopin didn't intend for his Preludes to be played as a complete group and it's only relatively recently(guessing around the last 70 years) that most pianists perform the entire set. Yet the order of the Preludes seems perfectly designed to be played as a full set(contrasting speeds and moods, dramatic finale, introductory first prelude, lengthy Raindrop near the middle).

How does one reconcile these contrasting statements?

Playing the whole set in concert was unheard of in Chopin's day; everything was a variety show. Each piece does feel threaded together intently, but it's never done explicitly in the material. I think it just reflects his improvisational nature. Honestly, I'd be interested to hear a performance where the pianist comes up with their own clever order, as I find the predictability kind of boring now.

the sheer organisation as to tonality and to different temperaments between the pieces really asks for a complete performance, history and actual concertperformance tell us why, any other 'pick' of blossoms in a concert might be right, even as encores, but to stay mainstream: all or nothing.

I’m not sure that’s an established fact. What we know is he never played more than a few of them. But at the time of finishing them (1839) he had an already deteriorated health and would avoid long concerts and would abridge some of his longer compositions when performing them.

So, we don’t know for sure. I personally think they are equally great as a set and as single isolated pieces (some of them being as miniature as a haiku).

A few of the Préludes cannot stand alone because they end inconclusively (e.g. No.23), as if they are, er, preludes to other pieces. Others are certainly complete in themselves - just like a rain(drop) doesn't need the sun to be complete.

But as far as I know, Sviatoslav Richter is the only big-name pianist to play only a selection rather than the complete set in concert.

23 ends in a dominant F7 chord and is “crying” for a Bb maj to follow. But then the 24th starts in Dm which is kind of odd. So, indeed, maybe they were meant to be introductory pieces to other pieces and not to themselves?

There is a bit of a paradox here. If Chopin intended them as standalone pieces, why did he call them “Preludes”? But if he intended them as preludes, then preludes to what?

Well, once you can play them all, they would be preludes to a tremendous technique!

Good questions.

I think Chopin was referring to the Well-tempered Clavier when he wrote the 24 Preludes, so maybe he did think about pairing the preludes with something else, but he never got around to doing it?

There are other composers that published sets of preludes before Chopin, like the 24 preludes by Hummel (in all 24 keys) or the 50 preludes of Moscheles.

The usage of preludes evolved over time. Initially it was played (essentially as an organ prelude) as an introduction to warm up the audience and set the tone for the rest of the liturgical ceremony. That is why one find often sets of preludes in various keys from which the organist can pick the one that works for the ceremony. Later the prelude could also be used as an opening to a suite of pieces.

So the fact that Chopin published a set of preludes is not unusal. Of course by mid 19th century the role of the preludes was completely different. It could be that Chopin intended to play them all together or on the contrary let each player pick some to be used as an opening (or as a rest piece) to a concert to be followed by more meaty pieces. I dont know if there is evidence for a clear answer.

Also contrary to a common idea, the reason why Bach put a prelude before the fugue is purely historical.

Maybe Chopin just wanted to create a set of pieces in all keys. I'm not sure the generic "piece" was used at that time. Not all of them are "miniatures", nor "songs [without words]" or something poetic/lyrical. Could it be as trivial as him calling these pieces "preludes" because he couldn't come up with a meaningful genre classification for a set of pieces? And we, having so much time and wanting to deep-dive at subatomic level of everything, possibly looking for what is not there?

This is true. It was not only a warm-up for the audience, but also literally a warm-up for the player. This is why preludes often feature textures idiomatic to the instrument- chords, broken chords, scales- things to get your fingers warm, to give you a chance to safely try out an unfamiliar instrument and get a feel for its sound and touch, and to set the mood of the key for listeners and for yourself. Couperin explains this in "l'art de toucher le clavecin":
"Non seulement les preludes annoncent agréablement le ton des pièces qu’on va jouer: mais, ils servent à dénouer les doigts; et souvent à èprouver des claviers sur lesquels on ne s’est point encore exercé."
("The preludes not only pleasantly set the tonality of the pieces to be played, but also serve to loosen the fingers and often to test keyboards on which one has not yet practiced.")

It was therefore perfectly normal for players of any instrument- lutenists, cellists, harpsichordists, and later pianists- to "prelude" (the Germans use the verb "preludieren", and the French "préludier") before launching into a set of dances, a fugue, or a more substantial work, whether in private or public performances. Preludes were also commonly used to modulate from the tonality you just ended in to the key of the next work, to make sure you keep listeners with you ("in order to avoid cooling the audience if one stops, or shocking the ear if one does not stop" (Chaulieu)). Ideally, this should be improvised, but composers also wrote ready preludes that can be used for this purpose, sometimes as blueprints for further improvisation or with the aim of teaching the art of preluding- Louis Couperin's unmeasured preludes are one such example. French composer and pedagogue Charles Chaulieu explained it in his book to teach Composition:

In settings where a keyboard player is an accompanist or a leader of an ensemble, "preluding" had other functions: establishing the key for the singer, or allowing other instruments a chance to tune, as in church music ensembles.

This practice gradually fell out of favor in the 20th century- not very long ago. Some of the last examples can be heard in simple preluding, mostly arpeggiating, done before and between pieces in Backhaus and Lipatti's concerts (Lipatti's preluding before Chopin and Schubert has unfortunately not survived in the recordings). It is interesting to think of the reasons, but it is in any case unfortunate for both pianists and audiences, I think.

Within the context of this performance practice, Chopin might have wanted to compose preludes in all keys to be used before any piece, and he ended up cleverly linking them with the circle of fifths. And this was probably him thinking originally: why always "prelude" in the tonic- why not prelude in the relative major? Or in the supertonic (e.g. E minor) when the next piece starts on the dominant of its key (A in D major)? To fully explore the potential of these relationships, he made each prelude a prelude to the next. Scriabin used the same key logic in his own 24 Preludes. I think it would be interesting to start using these pieces as preludes again- to cleverly pick from Bach, Chopin, Rachmaninoff, Scriabin before larger works in concert. I know one pianist who does this before his concertos, sometimes improvising his own preludes.

^ This would all make sense if there weren't some pretty long preludes there too, such as the Raindrop. Why would that serve as an introduction to another piece if it's so long? And this entire theory about preludes being something to test your fingers or establish the tonality doesn't quite fit with some of the preludes which are not just some arpeggios to test your fingers.

Let's look at WTC. Do you really think the preludes are introductions to the fugues? I don't think so. Most of them are equal pairs to their fugues, not mere "introductions". I believe even with Bach the prelude "genre" is already a generic notion of a keyboard piece without any specific form (in contrast to the fugue). So, in Bach's case we have keyboard piece pairs, both equal in impression, one non-polyphonic and one polyphonic. And so, IMO, prelude means that, a keyboard piece. And Chopin wanted to create the same set of pieces in all keys, however the fugue was so badly out of fashion that he omitted the fugues Why do we have to desperately explain the semantics of the word Prelude? How is a ballade different than a fantasy, a scherzo and an impromptu?

shame...I'd love to hear a fugue by Chopin.

The prelude is one of the oldest form in keyboard music, the first one named as such is dated 1448. So it was already a genre in itself well before Bach and it was played at the beginning of various liturgical ceremonies. By mid 17th century these preludes typically had several sections, the first ones being in free form like tocatas and the next ones in imitative form and later in fugal form. When the fugue part started to be quite developped and formalized, it took a life of its own and it made sense for a certain type of preludes to have 2 well separated segments, the prelude in free form followed by the fugue. Thats why they are paired in the wtc.

But the prelude as a standalone piece continued also, there are preludes which are short and other very long. And Bach like many other composers wrote also many of those standalone preludes, like his chorale preludes.

By Chopin time, the prelude like the fugue lost completely its original meaning anyway. So whatever it is that Chopin wanted to do when composing them, it was in a completely different context and for a different purpose. Forms are like other things, they evolve and they also die, like the fugue and the sonata form.

As I said in my OP, to the best of my knowledge, Chopin didn't intend for his Preludes to be played as a set and for a long time they were not played that way. That's what makes the fact that they work so well together as a set so befuddling. I think the idea of each Prelude being a prelude to the next in the set makes little sense. I think he just arranged them is a circle of fifths and their relative minor keys.

I can't imagine the preludes were meant to be used as a prelude to some other work. Many are far too long and even the shorter ones would distract from what went before or after. The few examples I've heard of early pianists' preluding are very short and non descript.

Sidokar, thanks, very informative.

Chorale preludes were and are used to introduce a hymn in a liturgical service or to start a service.

Performing them all as a set turns them into a virtuoso showpiece, hence the popularity to do so by pianists having the technical facility to do so.