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

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.

• What started my thinking was this answer as well as the question is G# major a real key. Sep 24, 2012 at 12:16
• The thirty keys are pretty standard. Sep 24, 2012 at 15:27
• @Luke: Why? Who set the standard? When? And what about G# being a key - this does not fit within 30! - as by the question I linked in the previous comment? Maybe there is no clear answer to these questions, but then I'd like to know that too. :-) Sep 24, 2012 at 16:39
• Eh, I think it's just squabbling over nothing, confused by history and varying conventions. Much like grammar discussions ;). In 12-tone equal temperament there are obviously 12 tones, and having two names for each is just silly; there is no functional difference between C# and Db (etc.). Yet people insist on distinguishing them because they have nothing better to do! :P
– user28
Sep 24, 2012 at 16:48
• you MAY need to specify whether you want -keys- or -key signatures-. A -Key- could ignore the scale: there are obviously only 12 of them, possibly enharmonically named. A -key signature- includes the spec of the scale. There are a HUGE number of those (all possible combinations of a set of 12). Sep 26, 2012 at 22:43

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.

• This explanation of 24 or 30 keys, and why, seems eminently sensible. It is perfectly sensible also, though, to name keys such as G# Major (dominant of C# Major) or Fb Major (subdominant of Cb Major), entered via a modulation in an actual piece of music. Without using these names, one can't fully describe/analyse such music. Of course you can't have a practical key signature for such keys. More info about this is here: music.stackexchange.com/a/5660/9198 Apr 2, 2014 at 13:47
• True, however the question specifically asked for a number of major and minor keys, which imply the Ionian and Aeolian diatonic modes respectively. Any additional diatonic mode you want to include as a key, like Dorian, Phrygian or Lydian, would add 12 tonally unique and 15 engravable keys (though the signatures would not change). Add non-diatonic scales with non-standard key signature patterns, like Ascending Melodic Minor, Harmonic Minor, Hungarian Minor, Phrygian Dominant, and Arabic/Byzantine semitonic, and you can easily arrive at a total number of tonally-unique keys in the hundreds. Jul 8, 2014 at 16:54
• There are not 12 unique named tones. That is, on a standard keyboard there are 12 unique tones, but there are not 12 unique names for those tones. For example, while a piece would be played the same whether written in F sharp major or G flat major, it would be written differently in those two keys. In other words, I would remove the word "named" from the first sentence of the second paragraph. Sep 22, 2021 at 10:26

I hadn't really thought about the "engraving" standard, but in the diatonic tonal world, there are two answers:

1. In equal temperament there are 24 "keys", if by key you mean tonal structure based on some transposition of the major or minor scale.

2. In non-equal temperament, especially in pure just intonation, there are no enharmonic equivalents (Gb ≠ F#), and so there are, theoretically, an INFINITE number of keys. You can keep modulating around the cycle of fifths forever and you will never return to the exact pitch from which you started.

You will slowly drift either up or down in frequency by a Pythagorean comma (don't ask) until, ten of thousands of modulations later, you exceed the human ear's limits.

Trippy...

• Enharmonic equivalence does not depend on equal temperament. F sharp and G flat are the same in every twelve-tone temperament, whether the temperament is equal or not. Sep 22, 2021 at 10:28

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
- cols should have SAME letter:  2,3  4,5  6,7  9,10  11,12
```
• Not sure why you used ! in place of #/b on your chart... seems to confuse things, and you could probably still use single characters and use the nonstandard ones for the more infrequent double-sharps/flats. Sep 25, 2012 at 19:21
• But more importantly, the engraving explanation is a good one. Start from C#/Cb, and then go through the circle of fourths/fifths until you get to the other side! Sep 25, 2012 at 19:22
• sorry bout the ! stuff - that's what the c++ in my app needs :) (and, by the way, trying to FIND these standard-ish rules was like pulling teeth) Sep 25, 2012 at 21:08
• You miss D# minor and A# sharp minor Apr 3, 2014 at 17:47

If you use equal temperament there will be 12 major keys and 12 minor keys, or 24 all together, as others have said on here. If you use unequal temperament there will be a lot more, since C♯ and D♭ etc. will be different notes (C♯ will be slightly higher than D♭).

• The criterion is not whether the temperament is equal but whether it has 12 tones. Some of those temperaments have fewer than 24 usable keys, but they all have 24, and in some temperaments all 24 are usable (see J. S. Bach's Well-Tempered Clavier). The inequality of popular temperaments in the 17th and 18th centuries was intended to approximate just intonation, in which major thirds are narrower than equal or Pythagorean, so in those contexts where separate pitches for (e.g.) C♯ and D♭ are possible, C♯ will be rather lower than D♭ rather than higher. Sep 22, 2021 at 10:39
• @phoog Well sometimes C♯ will be higher than D♭, other times it will be lower. It depends on the circumstances. I play the violin and on violin you use different intonation types depending on the circumstances. Sometimes your intonation is Pythagorean, sometimes it is Just-intonation, sometimes it can be equal temperament intonation and furthermore it can also be expressive intonation like playing leading notes up very sharp and leading notes down very flat or if you play blues you can play the blue notes as blue as you want, like playing a blue note extremely flat. Dec 29, 2022 at 15:51
• @LarsPeterSchultz I did say "in these contexts." With a keyboard, however, you can't adjust your intonation depending on context; there are twelve tones, period, unless you have a keyboard with more than 12 keys per octave, in which case the context is meantone temperament, where C sharp is lower than D flat (if that is one of the split keys). Dec 30, 2022 at 21:51
• @phoog OK, on any keyboard you can of course only play those notes that are available on that keyboard. Dec 30, 2022 at 22:16

You have C Major that has no sharps and then you have seven scales that go from one sharp to seven sharps. You also have C major that has no flats and then you have seven keys that go from one flat to seven flats.

That gives you 15 keys but as you know you only have twelve notes in the chromatic scale. That is why you have three pairs of keys that are enharmonically speaking identical.

Those are Gb Major and F# major, Cb Major and B Major and C# Major and Db Major. So now you have a system where all the twelve notes in the chromatic scale have a corresponding key (Some have two) and you have keys that vary from 0 - 7 sharps and the same for flats. All your bases are covered now

As for the relative keys each one of the 15 has its own relative key, so now we are talking about 30 keys for both minor and Major.

Practical soul that I am, I say there are as many keys as there are notes in the chromatic scale, times the number of modes. That gives me 84, if my arithmetic skills serve me correctly. Of course, if there are only two modes anymore, then the number is 24.

One way of looking at it would be this: There are 12 different pitches in relative pitch, so a major and minor for each of these means there are 24 keys. However, each of these (apart from C and Am) is in a sharp or flat key, so there is an enharmonic key for each of these with the opposite, either flats or sharps. As for C and Am, these are not either sharp or flat keys, and so need a sharp and flat key each. This leaves us with 50 different keys. However, this also leaves us with keys such as G double-sharp minor, which has 2 sharps and 5 double-sharps.