Concerning the matter of "flow" with different keyboard systems you find few keyboards which are independent of what key is used. There are some which may be seen a superior in this case.... like the 5 row button accordion, the Janko piano, the Wicki/Hayden (if large enough) and a couple of others.
The above seems to presuppose that "more independent" ("more uniform"?) is "superior". Even ignoring the question of what definition is used for "independent", I don't believe in that supposition as a fundamental principle. On the contrary, I find "independence" and "superiority" to be quite context dependent, depending especially on what kinds of music or arrangements are being played.
You can probably find several factors included in "flow" ...including relaxed movements and 'speed' of movements.
"Relaxed movements"... definitely. "Speed"? I think that's secondary, not a component of "flow", but a consequence of comfortable flow. As a broad English-language concept, "flow" implies smoothness and continuity, and it can be either fast or slow. In a musical context, I consider it to mean that such smoothness and continuity is possible, but also that it is controllable... i.e., that it is possible to control the amount of smoothness, both legato vs. stacatto and uniformity of note durations. In Irish music, e.g., the durations of individual notes within a measure can vary considerably, even though the individual measures are of uniform duration. "Relaxed" or "comfortable" movements are necessary for such control.
Disregarding the key relations the factors influencing "flow" seem to be the possibility to use regular patterns of finger movements - like climbing a ladder - and using natural positions for fingers - not crossing,twisting or changing direction of movements.
Not all patterns that are "regular" are "comfortable", nor vice versa. For "flow", I think "comfortable" is a relevant criterion, but "regular" -- per se -- is not. There may be other reasons for considering "regular" to be a positive attribute, but I don't think "flow" is such a reason.
I agree that the awkwardness of extremely distorted positions for the hand and fingers hinder "flow", but many conformations that initially seem awkward can become comfortable through practice. Cursive writing with a pen is an example. If we broaden the scope to the rest of the body, proper technique with a tennis racket or golf club and riding a bicycle are others.
The English, the Crane,and the Maccann are all key-dependent for respective "flow" and it also differs between 'whole note' or 'half note' (=chromatic) "flow".
My first reaction was, "So what?" It may take longer to learn to transpose or play in different keys on one system than another, but that doesn't necessarily mean that the quicker-to-learn systems are necessarily more comfortable or "fluid" once learned.
Still, the ability to reach competence without investing too much time or effort is worth something, and a totally random layout of notes would probably be an impediment. So my second reaction is to consider how strong the key dependence of each system is, and how significant that is to learning and playing.
First, I should address the keyboards Göran cites as regular:
... The 5-row CBA (chromatic button accordion) achieves its absolute uniformity by duplicating 2 rows of what is inherently a 3-row system. I don't know of any attempts to implement such a system on a concertina, and I'm not sure that it's possible to do so and still have a reasonable range within reach of the hands. I suspect that if it is, a "handle" system like that on the English concertina would be necessary, as the bar-and-strap of existing duets doesn't provide adequate freedom in the direction parallel to the fingers.
... The Hayden and Janko layouts are essentially the same, differing only in the offset between adjacent rows, so my comments on the Hayden apply to both: To obtain complete uniformity in the same manner as the 5-row CBA, the Hayden layout would have to be 11 buttons wide, something quite unmanageable without some means of shifting the hand sideways relative to the keyboard to play in different keys. I know of no attempts to do this, at least not in a concertina-type instrument; the alternative has been to limit the side-to-side compass, with the result that uniformity exists in at most 6 of the 12 possible key signatures. In existing instruments even this uniformity fails toward both upper and lower ends of the keyboard, as does full chromaticity. Comparisons of actual playing fluidity can be made only on actual instruments, not on theoretical ones, and actual Haydens are a far from the key-independence of the theoretical model.
English - for playing scales in 'natural keys' it is evidently 'designed' firstly for C major and if the outer rows are used Eb major in my view is the next best key.
English - Built around a central diatonic key (usually C), but with the remaining notes of the chromatic scale placed for easy (both conceptual and physical) access both as accidentals in the central key and for transposition into most nearby keys. In fact, 8 of the 12 possible keys (in equal temperament) conform to the same pattern as the central key. In a strict geometric sense the equality is approximate rather than absolute, but approximate equality is the rule in human experience, and exact equality is the exception.
Crane - being quite a bit resembling the English - is typically based on C major and has excellent flow in C major scale.
"Resembling the English" depends on which features of the English system are used for comparison, and Göran doesn't identify which he means. There's certainly no correspondence to the English feature of notes of the diatonic scale alternating between the ends of the instrument. But there definitely are other similarities:
...1) The "interior" rows (2 in the English, 3 in the Crane) contain the notes of a central diatonic scale (usually, though not always, C in both cases). The "exterior" rows (1 on either side of the button layout) in each contain the accidentals, and (assuming a central key of C) each accidental is located beside an adjacent natural note.
...2) Transposition to a key differing by one accidental (an interval of a fifth in the English, of a fourth in the Crane) is accomplished by shifting the fingers "up" or "down" by one button, and shifting one note of the scale from an interior to an exterior row, or vice versa. (This is the approximate equality mentioned above for the English.)
Beyond these central concepts, the regularity of the Crane layout is less than that of the English, because the English has an overabundance of buttons for accidentals relative to natural notes, while the Crane has a deficit. In the English, each accidental is located beside the same natural note in every octave; in the Crane it is not, and if the keyboard were extended far enough there would not be enough buttons for all the accidentals. However, a range of more than three octaves in a single hand is possible before it becomes necessary to locate an accidental elsewhere than beside an adjacent natural note.
Maccann - despite also 'based' on C major is a bit less dependent on the fundamental key and scales in other keys may be more attractive than with the English or Crane.
"Less dependent"?!! Göran, what do you mean by that? On both the English and Crane there are scales in different keys that have very close -- if not precisely identical -- geomterical configurations. On the Maccann I don't find this to be even approximately true for any two keys.
The greater spread of the fingers and greater key-independent regularity compared with the Crane might speak for Maccann.
The 6-button wide configuration of the Maccann means less extension parallel to the fingers for a given range compared to the 5-wide Crane, which may be an advantage to someone with short fingers. As for "key-independent regularity", I don't believe it exists. But in listening to competent Maccann players, its absence doesn't appear to be a serious obstacle to musical flow. Even though a major emphasis among many Maccann players seems to be toward heavily chordal ("rich", if you like) arrangements, I have heard a couple of Maccann players do beatiful, sparser arrangements, including fine chording against brisk melodies.
A major motive for K.V. Chidley when reforming the Maccann system was getting better "flow" by making the note layout more regular.
While Chidley does claim "flow" to be one of his design criteria, my personal feeling is that the "adjustment" of the pre-Chidley Maccann layout in the upper octave actually improves the "flow" over the strict geometrical duplication (except for the highest C) of the Chidley "improvement". (I do like Chidley's repositioning of the D and D#, however.) Was Chidley known as a performer on the duet? Did/do any of the (other?) known performers prefer the Chidley system?
One more comment regarding "flow": Chidley says, "I mean by 'flow,' that smooth rhythm in scale-playing that is essential for the proper performance of music. The English system has this 'flow' to a high degree." But there is much more to music than scale-playing. Smooth -- or controlled, as I prefer -- playing must not depend on note sequences comprising scales; it must be possible to play a variety and even a majority of arbitrary note sequences fluidly to claim a general quality of fluidity. I think even sequences of 2- and 3-note combinations should be considered in assessing flow.
Chromatic runs are simply a nuisance with all three....
I quite disagree... with regard to all three. While it may take some practice to gain facility with a chromatic scale, I don't find the scale to be inherently awkward on any of them,... nor on the Hayden, for that matter. I personally find it easiest on the English, next on the Crane, and least fluid on the Maccann, but those differences may represent nothing more than my own relative competence on the three instruments.
In my view the best system generally speaking for "flow" used on British style concertinas (if runs in C major with the English are excluded...) was the Wheatstone "Double" but despite being 'based' on chromatism it also presents problems on runs due to the fixed position of the hand compared to the 5 row button accordion (in principle almost the same 'idea')
The "5-row" CBA layout is really a 3-row layout, with duplications. A corresponding duplication in the 4-row Wheatstone "Double" layout would result in a 7-button-wide layout, as uniform as the 5-row CBA. The potential of such a system is interesting, but I don't know that anyone has ever attempted to build one.
At last...it can not be questioned that for single note playing the "flow" of the English is superior to any duet due to the simple fact that two hands may be used for the same job....
Not just for single-note playing, in my experience, but also for certain multi-note arrangements. All duets, on the other hand, should be superior for arbitrary 2-voice arrangements, as long as each part can be confined to a single hand.
(I would, however, dispute the claim that "it cannot be questioned" on general philosophical grounds. There is nothing that cannot be questioned, even though there may be some questions which can be shown to have only one valid answer.)