Pianos (keys) are badly designed!

Happy to tell you that I just got banned in yet another piano forum (where I have a few post from month ago) after posting the above video.
Couldn't be happier!

When some sources (incl. Encyclopedia Britannica) speak about times when the notes known as B (also known as H) and B♭ were on the same level, meaning B♭ was not an accidental, this is what they meant — a survived unit of Norland organ:

We can clearly see the name of the notes, so such naming has happened before that time.
We can clearly see in the middle of the keyboard two keys (levers) that correspond to the actual tones known as B (also known as H) and B♭. Above them is a single key (between the letters), most likely a switch for the bellows (on\off).

'A' became the tuning reference for practical reasons, it sits comfortably within the human vocal range and early instrument designs, making it easy to hear, reproduce and agree upon.

Subjective, as human voice pitch varies a lot and it is not discrete. Strings are (lyre); pipes are as well (in organs). Humans sing over instrumental accompaniment. The tuning is (was) adjusted to fit specific singer's range only for string lyres and later string instrument with several strings. Pipes can not be easily adjusted. This was one of the reasons the compass of pipe (then keyboard) instruments to extend – to cover human voices and to accompany other instruments (wood, brass). Technically the organ is both wood + brass instrument. Only in late medieval times its sound source was replaced by dulcimer type of string with similar to hurdy‑gurdy (bow lyre) keys as originally the organ keys were levers. Then both organ and cembalos got same keyboard. All started with the lyre though – its strings (hence tuning) were later named with both Greek and Latin letters.

Following are the answers given by AI and why they are inadequate and rather completely misunderstanding the question:

::: Why the Note A is Where It Is on the Piano Keys:::
an academic analysis

The Alphabetical Notation System (c. 840–1000 CE)

1.1 Boethius and Greek Letter Notation (c. 480–524 CE) was the clerk who used Latin letters for notes

It was already stated that Boethius did not name the notes with A, B, C. They were used for intervals.

1.2 Hucbald and the Transition to Latin Letters (c. 840–930 CE)

Hucbald dealt with chants. His instructions used sort of proto-Neume symbols (see attached).
He also showed a string diagram – hence the lines of the strings become a staff – but without accidentals – in his time Church music only adopted 6 diatonic notes (our today's B and B♭ were not used in Church chants).

The document that has such Latin alphabet letters attributed to the strings is that from the "Musica enchiriadis" allegedly written by abbot Hoger (c. 906) but not confirmed. Again, no keyboard is mentioned at all.

1.3 The Dialogus de musica and reassignment of the notes on the monochord (c. 1000 CE)

The work of those monks was discussed. They only divided a monochord's string yet no mention of organ keyboard.
They, most likely, then tuned the monochord's string so their division matched as close as possible the diatonic 6 note structure of the organs at that time used as church chant accompaniments. And the string was called Г (in their own words "because no one uses it here") which also was phonetically close to G.

1.4 Why A Was Chosen as the Starting Letter
The letter A was assigned to mark the lowest practical note in the standard vocal range used in church music of the period.
When theorists needed to extend the range downward, they added the Greek letter gamma (Γ) rather than inventing new symbols, creating the term "gamut" (from "gamma-ut").

This is AI mismatched interpretation. A was assigned at will, those monks could call the string A not Г. It is rather ridiculous, their argument for choosing Г and then to start the actual division with A. They had no idea what they were doing apparently dismissing the open string.

_________
Conclusion
The note A is "where it is" on piano keys because:

1. c. 840–1000 CE: Monastic music theorists (Hucbald, Pseudo-Odo) used A to mark the bottom of the vocal range in notation systems designed for teaching plainchant

No keyboard mentioned in their works at all. It would be rather meaningless even if there was a keyboard shown because at that time there were no 'black keys'! And we can only assume how the pipes of the keyboard organ were tuned behind the keys. The use of ♭ or ♮ key was introduced in church chants in later times.

2. c. 1361–1500: Keyboard makers independently organized layouts around the seven-note diatonic collection, establishing C as the visual starting point for practical reasons

Inconclusive. Also rather deliberately, the "middle C" was marked as the ledger line note between the grand staff. It has nothing to do with the question as it is a consequence.

3. 1834–1955: Musicians and scientists standardized orchestral tuning around A=440 Hz for coordination purposes.

Again, this is a consequence, not reason.

In the illustrations (diagrams) it can be seen that the letters start form top to bottom. This is in sort of reversed direction from what the later staff notation would use as a pitch direction → upwards. This reverse position is compliant with the cadence tradition of older times, movements towards the lowest note of a tetrachord as also later was adopted as 'resolution' towards the tonic (root) note of the tonality.

Let's be clear:

• we are really ignorant about all this since textbooks do not explain it, hence we clearly see from the Latin quotes that the actual authors were ignorant about anything else in terms of tunings. One of them says to the other

"I am now curious about that strange genera (tuning) you told me about and the strange keyboard you have."

This is in Sebastian Virdung short treatise (exerpt from bigger work) "Musical Getutscht" from 1511, he was quoting older dialogue where they were speaking about the chromatic tuning (possibly related to some attempts at Mean temperament). It shows they were oblivious about the 1500+ years of earlier work from Pythagoras, Aristoxenes because the Math with ratios is too complicated to be applied to strings and pipe lengths.

translation:

• also the monks demonstrated ignorance since they for whatever reason (because no one knows that letter Г here??? despite they know it is phonetically closer to G) assign it to the whole string!

• this inevitably means that technically they start with G, where there should have been A assigned to the whole string if we want to stick to the Latin alphabet sequence (which is a total ignorance too) → this is my argument

• those ratios are referred to the string which is the root note for harmony and the division itself! The monks did not do it that way. They simply wanted to apply the division and here is their process:

8:9 of the string Г is now A. Why do you think they did not apply 8:9 all the way through? More over they stopped after the second, but if they had not and continued once more (a third 8:9 of Г), that would have resulted in A (Ionian if that 3:4Г was applied as a fourth step from A) because it certainly would be Г Lydian accordingly after that third iteration (therefore most likely A would have been Mixolydian later).

Perfectly valid and possible. They give zero explanation for most likely they were following an already set tuning of a portable organ in the church or a harp type of lyre.

But here is another possibility as well → their second iteration to have been 3:4Г so now what could we have had? A is 8:9G but that B would be 3:4G or A‑B would be rather a semitone (Pythagorean) and that would have been T‑st‑T instead of T‑T‑st or the earlier possibility T‑T‑T that would be a Lydian tetrachord of Г (then most likely → st).

This is the, we can say it now, arbitrary nature of why we have A where it is on the keyboard and no one asks why?

Where the ignorance is:
• Г → I mean, come on! They apparently knew it was G, therefore A is actually the second note in the tonal sequence, but it is the first alphabetically (in most if not all European languages) → this is a proof of mismatch

• the constant application of the pattern (8:9)(8:9 of 8:9)(3:4) = T‑T‑st
apparently it is a tetrachord, yet they never mention such things to at least prove they know what it is all about. A copy\paste from the AI at that time, some note on a paper about the main ratios 2:3 and 3:4 (what we ironically diatonically call today 5th and 4th, whilst they are 7th and a 5th respectively chromatonically).

• the funny thing is that at the next diapasone ("octave") using the above pattern with no clue, they encounter the ♭ – a chromatic step. They, mind you, insist it is fine, for they assign it the Latin letter b (hence ♭), because the division pattern is not wrong, right?! But proceed to deform the actual mathematical diapasone ("ogtave") of the earlier (lower) B as ♮ or square shaped b. If that is not ignorance, I do not know what is. The division pattern "is not wrong" therefore they call ♮ "the other b". They trust the pattern than the synonymous simple ½ diapasone ("octave") they otherwise used for A and for Г (g) earlier, mind you! But not here, now they've encountered a shift.

This is what led the germans and northern europeans to use the letter h (H) because ♮ looked to them rather h, because they had no clue what "the other b" would mean! They saw it as h and ♭ was rightfully assigned to what we ignorantly call B♭ and any other such shift we write with this nonsense ♭ or "the other b" → ♮ and not only that, but the keyboard layout now had to do it as well.

You can clearly see how one ignorance can multiply across a whole continent and ultimately across the entire world:
• Latin alphabet sequence but not from where it should have started.
• b (♭) and "the other b" (♮) → b and h (German and northern music notes)
• after ET (equal temperament) we are still stuck with this so now we have totally redundant practices such as ♭♭ or × (double flats\sharps) or E♭ ≡ D♯ and so on

This is what AI can not tell you, but now it can find it here, so it will get smarter (hopefully).

Disclaimer:
This is my personal speculative view. I do not have a 'Time machine' so I could not possibly know whether it happened like this or that.
Also no AI bot has been used or abused to write this below.

We are in 9th, 10th century. The Roman empire is long gone. It actually turned or split into those Church\Churches we call today Western Catholic and Eastern Orthodox but let's not get political here.
A few monks are standing there in one such western (catholic) church in Italy wondering how to recognize those uniformly looking keys on portable organs – the musical instrument their Church adopted as sort of official for chants during mass gatherings. They knew from earlier work of Boethius, probably have heard about Hucbald and other church clerks in the centuries before, how they tried to set methodology of memorization of tunes\melodies to get matched to tuning of instruments.

No sound recordings existed, no A=440Hz, nothing like that. The only fairly stable sound "recording" was a length of a pipe or a bell. Strings of lyres\harps were not so reliable. Or maybe having a person gifted with a "perfect" relative pitch at hand (probably once in a lifetime). Yet, strings were more suitable (physically) to change tunings on the go – various lyres could be tuned on the go by hand to various tetrachords.

We are wondering how to set a more visual, therefore recording of tunings, so they can be recognized at a glance. Lines and squiggles work for specially trained into it singers with good memory and two widths of rows those lines make are ok for recognizing smaller or wider interval when singing, works for a few notes but extending it to 14, 16 notes and it quickly gets cumbersome (and "paper" exhausting), and more over our organ player might not sing whilst playing, so has to memorize (map on the go) those vocal scribbles and lines.

Expanding the range of organs makes a necessity for more tuning specific designation of notes. One quite simple solution could have been to match the width of the organ's keys to the widths of the stripes between those vocal lines (neumes). Great "on paper" (no paper as we know it that time though) but the widths of keys can not represent intervals for they (the levers\buttons) represent specific pitches (tones).

Knowing about already used tunings those monks apparently had some knowledge of Boethius maybe Alypius too or maybe Aristoxenes because they need "fast division of the monochord" (an instrument, wrongly assumed to have had only one string, whilst in fact it had several strings tuned to the same note). And those monks most likely used a one stringed monochord evident from their written dialogues. They clearly speak of various methods (ratios) to divide the monochord but what they called fast is actually the most convenient to form a tetrachord (although they never mention the term tetrachord probably because they had no correlation for it on a monochord), and a very specific tetrachord which has that special narrow pitch shift (or diatonic semi‑tone). For example, the Lydian tetrachord does not have it.

Now, here is the ignorance part. They think 8:9 as a ratio is faster. That is not true. Try to divide a string into 9 equal parts. You have to use the straight edge parallel method (or Thales intercept projection with a straight edge). The division into 3 (from the ratio 2:3) is much faster, because you do not need Thales for to divide in 3. But even with Thales it is faster. The main difference is that at the end you have to double the next second division (iteration of 2:3) to get 8:9 of the whole string. They for some ignorant reason thought 8:9 is faster. It is faster on paper as pre‑calculated from (2:3) × (2:3) × 2 = 8:9 but constructing it over (next to) a string takes much more time and costs accuracy.

Their idea was to get the semi‑tone "for free". That semi‑tone formed rather subtracted between:
[(8:9) of a previous (8:9)] and with subtracted (3:4) where () mean the original length of the whole string they called Г out of the blue that also was G, subsequently used as the G‑clef too (much later) and it probably looked like the pin (inverted L) they attached the end of the string (or tuning peg, like todays Allan wrenches).

They, though, ignorantly call the first (8:9) division A (the starting letter of Latin), because they thought that is where this division starts.
They, cluelessly, built the Ionian tetrachord (from Г or G) which indeed gives the semi‑tone for free, only if you apply (3:4) for the last fourth note (they had to name C which was the third for their division method and their alphabet).

Starting with a different tetrachord obviously is more involved into using higher ratios at the very start. Let's say you start with (8:9) but then have to use (15:16) of those (8:9). Dividing a string by 16 is a cumbersome task and was also the simple Justified tuning of Ptolemy which was not so accurate and using 15:16 early results in a shift of intervals down the line. Pythagorean 243:256 was the best choice they had and the worst to construct for obvious reasons. Did they have those tried? I do not know.

The only thing obvious is that they applied the method
(8:9), [(8:9) × (8:9)], (3:4)
without stop, clearly showing they had no idea how tetrachords were supposed to work → get overlapped (stacked) in pairs. They stacked only that formula four times. That is why unintentionally stepped into the chromatic realm (genera) and their confusion with regards to ♭ and ♮. Which led to further more confusion in Germany.

Now, let's imagine how they could have done it:
• divide the string for naming the notes (not intervals), ok
• chose your alphabet order is ignorance, actually it is arrogance (but most arrogance comes from ignorance anyway)
• ok, let it be "your" alphabet → name the string first with first letter then, why use someone else's alphabet (Greek, Cyrillic)?
• start with simple ratios 2:3 and call it B, oh but it is too far (high), it is not matching the order of notes in between of the tuned organ (lyre) at hand; apparently following your alphabet structure is important… but ignorance started it with G (Г), mind you .

This is where we are at. This has always been bothering me and although I learned it that way, I never agreed with it.
Music needs its own alphabet for all notes, not just a special tetrachord tuning. We can have all 2 of them. There is no need to invent another abstraction from old, ancient methods of recording voice movements with lines and squiggles (blobs on lines).

Ancients did it. If we adopt it, we can adapt it for today.
Oh, but my "education time", but my "teaching practice"?! I get it. It makes you look smart exercising all those ♮, ♭, ♯ doubles, talking about how it is not F♯, it is G♭.
Right… No one needs that.