How many (major and minor) keys are there? Why?

Question

I am wondering about how many major and minor keys there are and why.
Here are some suggestions:

24 keys
One could argue that there should be one major and one relative minor key for each of the 12 equal tempered enharmonic notes, that is for each of
C; Db(/C#); D; Eb(/D#); E; F; F#/Gb; G; Ab(/G#); A; Bb(/A#); B
totalling 24 keys.
This would in some sense be supported by the mere idea of 24-key set compositions such as Bach's The Well Tempered Clavier and Chopin's 24 preludes (although the choice of enharmonic high-number sharps/flats key signatures vary in different composition sets).

26 keys
Sticking to the idea of enharmonic notes and the 24 keys but making a difference between the note names F# and Gb since they require an equal amount of sharp and flat symbols in their major and relative minor key signatures, and in that way seem equally relevant, yields 26 keys.

30 keys
If you count keys while you keep adding sharps or flats, until all seven natural notes (A to G) have a sharp or a flat symbol in the key signature, you end up with 30 keys.
That is the 15 keys
C; F; Bb; Eb; Ab; Db; Gb; Cb(!); G; D; A; E; B; F#; C#(!)
in majors and their relative minors.

42 keys
Counting all seven natural notes (A to G) on their own, as well as their respective flattened, and sharpened notes we get 21 note names as a basis for keys. That is
Cb; C; C#; Db; D; D#; Eb; E; E#; Fb; F; F#; Gb; G; G#; Ab; A; A#; Bb; B; B#.
Major and relative minor keys for each of these 21 gets you 42 keys (indeed with a lot of double sharps of flats in twelve of them).

Infinate number of keys
Albeit seemingly ridiculous someone might amuse himself/herself with for instance "transposing" 'Also Sprach Zarathustra' from C major to A### major¹ ("A triple-sharp major" with 24 sharps in the key signature :-) or use any other super-sharp/-flat key. This is to say that you can invent pretty much as many keys as you please.

THE QUESTION
So, is there a consensus on or a standard answer to how many keys there are?
Or
When asked "How many major and minor musical keys are there?", what is the generally accepted correct answer?
Also
Why, and says who?

I am pretty sure I know what's considered the answer to how many keys there are, but I would like to know why and who settled for this.

In case you find that it matters I'm referring to 12 tone equal temperament. I could otherwise perhaps further have suggested, say, nine (usable) keys for e.g. quarter-comma meantone temperament.

¹ _{I stole the example from a joke by the Finnish orchestra Retuperän WBK.}

Answer 1

I'd say the ENGRAVING standard is 30 key signatures due to standards in scale spelling. This doesn't include all -scales-, just standard #/b -signatures-.

The reason for having half the enharmonic note names undefined is that they have more sharps/flats than their other enharmonic note name and would cause huge numbers of sharps/flats giving no advantage to the alternative note's notation.

We also don't have signatures for any of the non major or minor scales such as the modal scales (when key isn't on, say D of dorian scale, etc), pentatonic, etc.

So there are 12 tones - giving 12 possible keys (enharmonic #/bs ignored as they should be). But there are PLENTY of scale variations that engraving standards do NOT cover. So no standard for all possible scales exists as far as I know. (I am NOT a professional engraver OR piano teacher - I'm a software developer trying to code some FRACKIN standard notation into my app.)

I would LOVE to hear that there ARE standards beyond this, but so far this is all i got.

==================== MAJOR KEYS ===================      ! means PLAIN cuz ksig
            xx      xx          xx      xx      xx       % means natural
flats   KEY m2  M2  m3  M3  4   tri DOM m6  M6  m7  M7   d double flat, x db shp
0       C   db  D   eb  E   F   f#  G   ab  A   bb  B
1       F   gb  G   ab  A   B!  b%  C   db  D   eb  E
2       B!  cb  C   db  D   E!  e%  F   gb  G   ab  A
3       E!  fb  F   gb  G   A!  a%  B!  cb  C   db  D
4       A!  bd  B!  cb  C   D!  d%  E!  fb  F   gb  G
5       D!  ed  E!  fb  F   G!  g%  A!  bd  B!  cb  C
6       G!  ad  A!  bd  B!  C!  c%  D!  ed  E!  fb  F    or F#
7       C!  dd  D!  ed  E!  F!  f%  G!  ad  A!  bd  B!   B in sharps preferred

            xx      xx          xx      xx      xx
sharps  KEY m2  M2  m3  M3  4   tri DOM m6  M6  m7  M7
1       G   ab  A   bb  B   C   c#  D   eb  E   f%  F!
2       D   eb  E   f%  F!  G   g#  A   bb  B   c%  C!
3       A   bb  B   c%  C!  D   d#  E   f%  F!  g%  G!
4       E   f%  F!  g%  G!  A   a#  B   c%  C!  d%  D!
5       B   c%  C!  d%  D!  E   e#  F!  g%  G!  a%  A!
6       F!  g%  G!  a%  A!  B   b#  C!  d%  D!  e%  E!   or Gb
7       C!  d%  D!  e%  E!  F!  fx  G!  a%  A!  b%  B!   Db in flats preferred

==================== MINOR KEYS ===================
            xx          xx      xx          %#      %#
flats   KEY m2  M2  m3  M3  4   tri DOM m6  M6  m7  M7
0       A   bb  B   C   c#  D   d#  E   F   f#  G   g#
1       D   eb  E   F   f#  G   g#  A   B!  b%  C   c#
2       G   ab  A   B!  b%  C   c#  D   E!  e%  F   f#
3       C   db  D   E!  e%  F   f#  G   A!  a%  B!  b%
4       F   gb  G   A!  a%  B!  b%  C   D!  d%  E!  e%
5       B!  cb  C   D!  d%  E!  e%  F   G!  g%  A!  a%
6       E!  fb  F   G!  g%  A!  a%  B!  C!  c%  D!  d%
7       A!  bd  B!  C!  c%  D!  d%  E!  F!  f%  G!  g%

            xx          xx      xx          #x      #x
sharps  KEY m2  M2  m3  M3  4   tri DOM m6  M6  m7  M7
1       E   f%  F!  G   g#  A   a#  B   C   c#  D   d#
2       B   c%  C!  D   d#  E   e#  F!  G   g#  A   a#
3       F!  g%  G!  A   a#  B   b#  C!  D   d#  E   e#
4       C!  d%  D!  E   e#  F!  fx  G!  A   a#  B   b#
5       G!  a%  A!  B   b#  C!  cx  D!  E   e#  F!  fx
6       D!  e%  E!  F!  fx  G!  gx  A!  B   b#  C!  cx
7       A!  b%  B!  C!  cx  D!  dx  E!  F!  fx  G!  gx

rules:
- start with spelling of 7 scale tones per keysig's sharp else flat
- 7 tones of scale ALL on DIFFerent letters
- if minor, M6 and M7 are ALWAYS m6,m7 SHARPED (naturaled flat/doublesharped)
  since "sort of in the scale as almost tones"
- SINGLE LETTER for tonic, dominant - not duped even for tones outside scale
- no letter used 3 times when making outside the scale tones (2 =max=)

checking:
- vertically, sharps should read fcgdaeb
- vertically, flats  should read beadgcf
- cols should have SAME letter:  2,3  4,5  6,7  9,10  11,12

Answer 2

Obviously the answer depends on your point of view, and there probably isn't one "right" answer.

There are 12 unique named tones in Western music; all pitches are one of these 12 tones. Thus, from a purely sonic perspective, there are only twelve starting notes for a key, and with major and minor scale qualities, there are 24 tonally unique keys. For my part, this is my answer; it's the basis of the Circle of Fifths and thus much of Western music theory.

Now, those 12 tones don't each have unique names; each flat note is the adjacent note's sharp (for F and C, their flats are the natural notes E and B) and vice versa. For most of these, such as A#, you have to go more than halfway around the Circle of Fifths, and "double-sharp" or "double-flat" notes in the key signature. Double-sharping and double-flatting is generally frowned on, and is disallowed altogether in key signatures because key signatures are supposed to have only one symbol. Also, in these cases there is a key signature available with far fewer accidentals (A# would require double-sharping F,C, and G, but why have 4 sharps and three double-sharps, when all you need is two flats?)

However, for three of these enharmonic note names (B/Cb, F#/Gb, and C#/Db), a key signature exists that has 7 or fewer sharps or flats, thus not requiring mixed symbols. If we consider major and minor variants of these to be separate nameable keys, there are 30 nameable (engravable) keys that you could conceivably see on a piece of music using the Westen notation system. 6 of them are enharmonic, and four (two key signatures/major-minor pairs) are unlikely to be seen as their enharmonic equivalent alters fewer notes (C# requires seven sharps; Db only requires five flats), but the signatures conform to the notation rules either way.

Virtually all your other possible systems violate the generally-accepted notation standards for Western sheet music (primarily by unnecessarily double-flatting or double-sharping notes). These rules evolved out of a general desire to simplify and standardize notation based on logical symbolic progressions, which also generally followed the math behind the sounds of Western music. There isn't one single person who set them in stone (and indeed many things we consider "rules" can be bent and broken to great effect), but I'll bet that if you handed any professional musician a piece written in A# he'd scratch out all those symbols and write in two flats, and curse your name for wasting his time.

Answer 3

Don't forget there are (at least) 3 minor keys - natural, harmonic and melodic, all using slight variations in their make-up, Yes, all three will be given the same key sig., but actually the 'feel' will be different for each. Whether this difference makes each a different 'key', I'm not sure, but judging by the definitions above, notating each 'key', then maybe it's worth mentioning.