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Music is written in almost every key that corresponds to every note that is on my piano keyboard. There is clearly a C Sharp (black key right of C) on my piano keyboard but I don't recall ever seeing any music written in the key of C-Sharp Major.

Surely the key of C-Sharp Major must exist! So why is it never or rarely used?

Are there situations where the key of C-Sharp Major would be more appropriate than say the key of D Flat Major?

EDIT: I never meant to suggests that you can't find examples of music written in C-Sharp major on Google (as Todd Wilcox pointed out in his comment). It's that it is comparatively rare and I don't find it in any of my many music books among many thousands of songs.

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    You haven't done a web search for "in c sharp major", apparently: imslp.org/wiki/… is the second hit on Google. If you look, you'll see that there are several double sharps. Transcribing it in Db would make those naturals but might involve double flats. – Todd Wilcox Apr 5 '16 at 20:03
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    @ToddWilcox It's interesting trivia brought to my attention by a comment to my answer on another question wherein it was pointed out that my chart left off the C sharp major scale. I attempted to explain why in a comment then it occurred to me that others may have this question at some point. I hope my answer to this question succinctly summarizes the issue in plain English without getting too deep into music theory. – Rockin Cowboy Apr 5 '16 at 20:24
  • Similarly, C flat major/A flat minor is rarely used in the musical literature. A notable exception to this is Poulenc's "C", which was intentionally written by Poulenc in A flat minor. – aeismail Apr 5 '16 at 21:43
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    You haven't found the Well-Tempered Clavier P&F III then (both books)? – user207421 Apr 6 '16 at 9:57
  • @EJP No I am not familiar with the Well-Tempered Clavier. From the title I assume it contains music written for an instrument tuned in other than Equal Temperament. I know that in certain tunings of Clavier that not all keys are available. – Rockin Cowboy Apr 6 '16 at 13:21
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C sharp major has seven sharps, D flat major has five flats. Out of the box, the latter is preferable. The former may be more appropriate when there is more material requiring "flattening" the key signature than otherwise. Now major is a rather sharp mode, so it's not quite unlikely. For example, a "proper" fully diminuished chord in C sharp features C-sharp, E-natural, G-natural, B-flat. The same in D flat is D-flat, F-flat, A-doubleflat, C-doubleflat. If we are talking about the "functional" dominant seventh (G#7, namely G#, B#, D#,F#) replacement, it's actually D sharp dim (D#, F#, A, C) with its enharmonic cousin E flat dim (Eb, Gb, Bbb, Dbb). The former has a lot more reserves for modulation than the latter.

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Yes indeed there is a key of C Sharp Major (C# Major). But the key of C Sharp Major is the “enharmonic equivalent” of the key of D Flat Major.

What that means is that all of the notes in the C sharp major scale sound pretty much exactly the same (to the human ear) as all the notes in the D Flat major scale – only they are notated (written) differently.

The black key to the right of any C key on a piano keyboard is in fact a "C-sharp" and will be most likely be referred to as such when playing a piece in any key that contains a C sharp in the scale or in any key with sharps in the key signature for that matter. But the exact same black key can also be identified as a D flat – and will be referred to as such in pretty much any key with flats in the key signature (with occasional exceptions).

So it may be helpful to understand that on any keyboard instrument (such as piano) or fretted instrument (such as guitar), the notes played in the D-Flat Major Scale will be exactly the same as the notes in the C-Sharp Major scale.

Therefore – given that a particular melody or arrangement of note pitches can be written either as D Flat Major or C Sharp Major and will be played on the same keys or frets either way (and sound the same), most composers will choose D Flat because instead of seven incidentals (7 sharps) to deal with in the key signature for C Sharp Major, there are only five incidentals (5 flats) in the key of D Flat Major.

However, in a case where a musical composition were to modulate (change keys) from another key containing sharps in the key signature, it might be more appropriate to use C Sharp instead of D Flat.

The foregoing also applies to the key of C Flat Major as well - which is the enharmonic equivalent of B Major – only in C Flat Major there are seven flats in the key signature compared to five sharps in the key of B Major.

Interestingly the key of C Flat Major is the only case where the enharmonic equivalent of a Flat key is a Natural key.

Also interesting to note is that the C-Flat Natural Minor Scale contains three double flats in addition to four regular flats (quite cumbersome to notate in a key signature to say the least). Whereas the enharmonic equivalent B Natural Minor scale only has two sharps – yet contains the same note pitches in the same order with the same intervals and sounds the same. But it’s obviously much easier to write.

So given a choice between notating a musical composition using a key that includes 7 incidentals (sharps or flats) in the key signature versus notating the same note pitches using a key with only 5 incidentals, most composers will choose the one with only five (in most cases)!

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    Did you mean "accidental" instead of "incidental"? I'm not used to seeing the latter. – Todd Wilcox Apr 5 '16 at 20:29
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    @ToddWilcox Well I actually meant to use incidental (as in incidental to the key) to contrast with "accidental" which Wikipedia defines as "In music, an accidental is a note of a pitch (or pitch class) that is not a member of the scale or mode indicated by the most recently applied key signature". I know that it is common to refer to sharps and flats as "accidentals" regardless - but I think that usage likely evolved from the fact that whenever a # or b or natural symbol is written on a staff outside the key signature it is called an accidental - so the name stuck (albeit incorrectly). – Rockin Cowboy Apr 5 '16 at 20:38
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    @ToddWilcox Searching on Google for the word for the collective sharps or flats in a key signature which can't be accidentals because they are on purpose - I came across this on Stack Exchange (music.stackexchange.com/a/5240/16897) – Rockin Cowboy Apr 5 '16 at 20:47
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    @ToddWilcox Check out the new answer I just posted to that age old question on Music SE that I stumbled across on Google search. (music.stackexchange.com/a/43296/16897) – Rockin Cowboy Apr 5 '16 at 21:28
  • Hahaha. Those two comments are so much like click bait. "Three answers to a question you never thought to ask, the accepted answer will shock you!" "You'll never guess who asked a question combining group theory with 12 tone composition. Or who argues about which stack it should be on!" – Todd Wilcox Apr 6 '16 at 1:13
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The other upvoted answers here are good and I don't want to repeat them, but I think that there is a lot to add.

Surely the key of C-Sharp Major must exist! So why is it never or rarely used?

There are several factors that need to be taken into consideration. Here I list a few:

Historical

To understand modern scales you need to look at how they originated. This can be fairly technical so I will give the short version. Before the major/minor system there were hexachords - scales built from 6 pitches with 1 tone steps except for a semi-tone in the middle, 3-4. In the Middle Ages, music used 3 hexachords:

  • hexachordum naturale: C D E F G A (semitone in E-F)
  • hexachordum durum: G, A, B♮, C, D, E (semitone in B♮-C)
  • hexachordum molle: F, G, A, Bb, C, D (semitone in A-Bb)

In the 15th century or so more hexachords were added using the same process which results in sharps and flats being added one by one. Eventually, you could have one that looks like this: C#, D#, E#, F#, G#, A# (semitone in E#-F#). It's a bit like the circle of fifths in equal temperament where you add a sharp (flat) for each modulation up (down) a fifth.

Note that in these eras there is no equal temperament yet, so C# and Db hexachords (or even major scales) do not sound the same. In general, I will consider equal temperament when answering your question.

The point is that not all scales were treated equally. Those with less accidentals had historical preference and it took time until those with more accidentals were "discovered" and used. And we all know that old standards stick and have heard at some point the answer: "because of historical reasons".

"Color" and meaning of a scale

This is a bit more fuzzy. There were (are?) notions of different "colors" and meanings for scales.

"Color"

You might have heard things like "F major is very bright [compared to, say, Bb major]" or "C# minor is very dark [compared to A minor]". It could be that this was the acoustic result of the tuning system and instrument building at the time (remember that the instruments evolved with the expansion of hexachords, so before the 14th century instruments didn't need/have a D# pitch, for example).

Meaning

Sometimes different scales mean or symbolize something for composers. You sometimes hear "Beethoven chose insert scale here because it was associated with freedom [or something]". For example, Beethoven saw C minor as "powerful and emotionally stormy".

It will require digging to figure out what each scale was associated with at each musical era or for different composers. I have yet to see any such association/symbolism for C# major, nor a "color".

The scale in which we hear

Again, this topic is a bit fuzzy, but I will make my point clear. Most (all?) of us, when we compose music in our heads, do it in one of just a few scales. Try to compose a few tunes in major and minor on different days (don't listen to anything tonal beforehand) and be faithful to the key you hear them in. You "should" find out that you don't hear the music in your head in 10 different scales - you stick to a few.

I'm not sure what kind of bias it has or what the statistics are. I'm just noting that, again, not all scales are treated equally.

Ease of use

Scales with less accidentals are easier to read and play. It's also easier to modulate around them. Just as an example from A-sharp minor: "A♯ major, usually replaced by B♭ major, since A-sharp major's three double-sharps make it impractical to use." I wouldn't take Wikipedia as a gospel, but "impractical to use" is somewhere in the right direction. Nevertheless, Chopin modulates to A# major in one of his pieces.

Both C# and Db major have a lot of accidentals.

Conclusion

Any combination of the above can give you the answer. There are certainly many instances where those keys are used, either as the base of the piece or in a modulation, but they are truly less abundant than the scales we usually see (hear). Just remember that C# major is not the scale with most sharps as you can always take enahrmonic scales like A# major and these are used even less.


Are there situations where the key of C-Sharp Major would be more appropriate than say the key of D Flat Major?

While the previous question would be more in the area of musicology, this one is much more technical and one has to look at theory. I won't go deep, but the answer is "yes". Here is a simple example:

You write a piece in Binary form in F# major. You modulate to the fifth, which is C# (not Db) major. You then modulate back to F# major and finish the piece. This is a regular I-V-I form.

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    Wow - such a detailed and comprehensive answer. And great job for going beyond what some of the other answers mentioned. Hope to see you participating more on this site in the future. – Rockin Cowboy Apr 7 '16 at 23:37
  • @RockinCowboy Thanks, this is more or less my standard for answers (on other SE sites as well). I would like to participate more, but most of the questions on this site are about amps for electrical guitars and the like and only a handful are about musicology, performance or theory. – user1803551 Apr 8 '16 at 9:42
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    Stick around. They come in spurts. There will be more questions about musicology and theory. As you probably know you can set up e-mail alerts for questions with certain tags such as "theory", "Key", "Scales" etc. – Rockin Cowboy Apr 12 '16 at 0:05
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    I'll second the Cowboy here- a great answer. If I may, I'd just like to add a bit on the point about ease of play. Especially for many woodwinds, there's a real physical difference between playing a C major scale and a C # major scale, since most have their "natural scale" somewhere close to C major, where you don't have to use those side keys as much. Even though any good woodwind player can rattle off a C # major scale about as fast as C major, it's not as easy, and the further you go back in history, the less easy it becomes. This of course ties in with the evolution of the scale. – Scott Wallace Feb 21 '17 at 12:53
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    @ScottWallace Not only is does it become harder, it can become impossible. The very early clarinet did not have the ability to produce its middle B note (the long left pinky bridge wasn't invented yet). Molter, having written what might be the first clarinet concertos, had to content with not using the middle B in the solo part, affecting his choice of scale. Indeed, D major was used for the first 4 concertos, where B is not as dominant as in other scales of the time. – user1803551 Feb 21 '17 at 13:25
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The white key to the left of c# is actually B#. The one to the left of that is actually C flat. Alto sax has to play F# and C# keys all the time. Darn Transposition.

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one reason could be - especially for brass instrument arrangements:

Cornets, Flugelhorns, Baritones, Trombones are tuned in Bb, Tenor Horns (Alto-instruments) in Eb. Bass in Bb and Eb. Mind that they have already to read with 3 sharps while other instruments in C have no signs ...

Why didn't Bach notate the C#-prelude in Db?

enter image description here

I would prefer to read the first page in Db major but near the end as it modulates to c# minor there there are some chords: e,c#,a,f#,d#,b# this would be Fb,Db,Bbb,Gb,Eb,C and more difficult for reading and analyzing.

a propos analyzing: This is a lot easier in C# major - as you can drop all signs (7 sharps and read it in C major and understand it much better.

btw. there's actually a transposition in Db on the IMSLP

enter image description here

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Shorter answer: Every note in a scale must be named A, B, C... etc. in ascending order but with as many accidentals like sharp and flat as necessary.

Therefore, the note before C# (major 7th) is B sharp (the same as C natural), and E# (same as F natural) is the third which is annoying to work with.

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    Actually B double-sharp is a C#, since there is no separate B# key. B# is the same as C natural. In the key of C# major, E and B are both sharp, so one plays notes enharmonic to F natural and C natural, respectively. – Todd Wilcox Apr 6 '16 at 11:58
  • Yes, you're right. You get both E# and B#. Also annoying – Ryan Hancock Apr 6 '16 at 13:32

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