A keyboard with only white keys.
How do you know which is actually C?
But to the answer.
Yes, if a song is purely diatonic (using only the notes from its scale, with no extra # or b.
It can be played in any key out of the 12.
Also, minor tunes will work similarly.
The problem is that some pieces use extra notes that are not from the scale.
For example, in, say, D major, it may modulate to A, and in doing so, use a G# note.
Non diatonic.
Trying to transpose that into C, you'd be looking for F#, which you won't find amongst the white keys.
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For most pieces, no, even if the piece is in C major.
Some chords, like 7th chords, contain accidentals (requiring black keys).
An example of a piece in C Major with black keys is Symphony No. 1 in C Major by Beethoven: it starts off with a C7 chord, C E G B♭ .
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With white keys only, namely a purely diatonic instrument, you are restricted to playing modal songs exclusively.
For the Major mode, that is only an impediment with modulation or intermediate notes present.
For church modes (of which strict Major mode is one), that works as well.
For current-day uses of Minor mode (in its pure form also a church mode), you'll rarely make things fit well since there tend at least to be traces of Harmonic Minor in there, leaving the white-key tonality.
Folk songs are usually good material for going modal.
Greensleeves works reasonably well in Dorian (white keys only starting with D) even though some phrases definitely shift character, but trying to pick a good mode for "Henry Martin" is trickier than it would look.
So generally, you'll likely end up with problems if your whole ensemble is bound to white keys: you are likely going to have to "backdate" songs uncompromisingly, giving them a flavor different from what they were written with.
At least once you go beyond "Major mode".
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Theoretically, no.
Even if a song is in C Major, it may have the occasional alteration.
Often, a C Major song includes a Bb (think of the C7 chord); that usually comes from a modulation, short as it may be, but sometimes that happens.
Many a song modulate from major to minor.
It is a harmonic device to build attention or tension.
However, your white-keys only keyboard is a diatonic instrument, just like a harmonica or a bagpipe.
This means that there are many songs you can play, and you may be able to play more by transposing them - but occasionally you'll find one that doesn't fit.
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Yes, absolutely.
In Equal Temperament, all major scales are mathematically equivalent, in terms of their notes' interrelationships (frequency ratios).
Outside of Equal Temperament, this might not be the case.
This video provides examples of different temperaments from Bach's time.
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You could play any song that used ONLY the notes of the majot scale.
But only very simple tunes are so tightly restricted. '
In C' allows more than just white notes!
music.stackexchange.com/users/17003/Laurence Payne
If you only have the notes of the C major scale available, you are already unable to play every song that's in C major, because 'in C major' does not mean 'using only the notes of the C major scale'.
So, for that reason, having only the notes in the C major scale does not allow you to play a transposed version of every song in a major key.
It does, however, to play a transposed version of every song that sticks to the notes of a major scale.
music.stackexchange.com/users/18896/topo Reinstate Monica
Let's say we have a song in a major key. My understanding is that performing different songs in different major keys just makes the song either higher or lower in pitch. And that's just about the only difference (correct me if I'm wrong).  So let's say for example I just have a keyboard that has white keys (ie C major). Could I theoretically play any song out there? (assuming that whatever I want to play is in some other major key).
Can any song in a major key be performed in C major?
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<theory><scales><key>
music.stackexchange.com/questions/54675
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 Performing a song in a major key in C major, that means using white keys only, and this restricts you to playing modal songs. For the Major mode, that is only an impediment with modulation or intermediate notes present.  For current-day uses of Minor mode (in its pure form also a church mode), you'll rarely make things fit well since there tend at least to be traces of Harmonic Minor in there, leaving the white-key tonality. Folk songs are usually good material for going modal. Greensleeves works reasonably well in Dorian (white keys only starting with D) even though some phrases definitely shift character, but trying to pick a good mode for "Henry Martin" is trickier than it would look. So generally, you'll likely end up with problems if your whole ensemble is bound to white keys: you are likely going to have to "backdate" songs uncompromisingly, giving them a flavor different from what they were written with. With white keys only, you are restricted to playing modal songs exclusively. 
With white keys only, you are restricted to playing modal songs exclusively. Folk songs are usually good material for going modal. Greensleeves works reasonably well in Dorian, but trying to pick a good mode for "Henry Martin" is trickier than it would look. At least once you go beyond "Major mode", you'll likely end up with problems if your whole ensemble is bound to white keys. You are likely going to have to "backdate" songs uncompromisingly.