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The keyboard has these notes:

A, A#, B, C, C#, D, D#, E, F, F#, G, G#

Why do B and C and E and F not have a sharp note between them? If they did, the keyboard would look like this:

A A# B B# C C# D D# E E# F F# G G#

Bold being black keys.

Would this make a piano harder to play in some way? This would also change the frequency of the notes after B# as it would be equal to was it now C and E# to F, correct?

Is there anything in music theory, as it stands, that prevents these notes? If not, why don't they exist and why aren't they used more often?

To write what would be B# in our current notation system, you'd use B 1/2 sharp (which would be indicated by the sharp sign with an extra "|" through it), correct?

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Note: For the sake of discussion, I'm limiting myself here to equal temperaments, which is the most common way of tuning keyboards. Other systems exist, of course, but would probably only confuse the matter.

Why do B and C and E and F not have a sharp note between them?

Simply because, acoustically speaking, there is no room in our current system for another pitch between B and C, or E and F.

The scale was originally conceived of as a 7 note scale, with the notes A, B, C, D, E, F, G. However, these 7 notes are not equally distributed throughout the octave. Most of these pitches are a whole step above the previous one, but there is only a half step between the B and C, and between the E and F.

But sometimes, we want to move around where this half step occurs. For example, if we were playing in the key of G, we want a half step between the F and the G, but not between the E and the F. The solution is to bump up the F's pitch by a half step, which makes it a whole step higher than the E, and just a half step under the G. This "bumped up" higher version of F, we call F♯. A sharp always refers to raising the pitch by a half step, and a flat always refers to lowering the pitch by a half step. This is true regardless of whether the resulting pitch is a white or black key on the keyboard.

From this, you can see that a B♯, for example, is a half step higher than a regular B. But you'll notice there is already a key on the keyboard that sounds a half step higher than B -- we usually call it C, but B♯ is also a perfectly valid name for that note, in the proper context (for example, the key of C♯ would contain a B♯ -- this occurs in Beethoven's Moonlight Sonata). Similarly, the note B can be called a C♭ in the proper context (such as in an A♭ minor chord). Granted, these don't come up very often, because writing in a key that requires them means reading/playing a lot of sharps or flats, which can often be tricky, but they do show up when needed.

Would this make a piano harder to play in some way?

This brings up an interesting question. If you wanted to, you could lay out the keyboard so that it consists of perfectly alternating black and white keys. However, what you would have to do is make F, G, A, and B become new black keys, and make the three black keys in between them become new white keys. This would leave you with 6 black keys and 6 white keys, which would look a bit like this:

[C] [C♯/D♭] [D] [D♯/E♭] [E] [F] [F♯/G♭] [G] [G♯/A♭] [A] [A♯/B♭] [B].

In some ways, this kind of keyboard would actually be a better representation of the "shape" of the musical scale. So why don't we use it? I can think of two reasons.

The first, obviously, is historical reasons. Never underestimate the importance of tradition. As I mentioned earlier, music was originally (and still is) based around a seven note scale, as depicted by the white keys. The earliest tuning systems didn't really permit the use of playing other keys (that's why everything was limited to modes), so it made no sense to treat the black keys as equal. In fact, the keyboard seems to predate the use of sharp and flat notes, although the current arrangement of keys is very old, and has survived the test of time (see: Origin of the asymmetrical keyboard layout of a piano).

The second reason is simply because it is useful to have these gaps -- it provides tactile feedback to help a player orient themselves along the scale. Pretty much the first thing every piano student learns is to locate "C", to the left of the two black keys. If we had a perfectly symmetrical layout (like a guitar fretboard), it might be easier to lose track of where you are in the scale.

Is there anything in music theory, as it stands, that prevents these notes?

As mentioned above, notes like B♯ do already exist, and do get used, but they do not need a separate key on the keyboard, because B and C are already only a half step apart, so a B♯ is effectively the same pitch as C.

If you were to add new keys, you would have to figure out how you wanted them tuned, because in the current system of 12 equally-spaced half steps, there is no room for another note in between B and C, or E and F. This introduces the somewhat esoteric concept of microtonality, and multiple tunings, of which there are an infinite number of possibilities. I'll only mention two obvious choices, for brevity.

You might try tuning these new keys exactly in between the existing two pitches (and keep all the other pitches the same). In this case, you've just added notes that are a quarter step away, but there are no other quarter steps anywhere on the keyboard, so you'd be introducing microtonalism in a very restricted way. Why should quarter steps only exist between those two pairs of notes, instead of between every pair of notes a half step apart? If you do that, you've just recreated 24-tone equal tuning (you aren't the first). This doubles the amount of notes available to you, so what are you going to do with them all? I believe you are correct about the symbol for the B half-sharp, but note that this would not be equivalent to B♯ (which is still equal to C).

Another option is to notice that you've now got 14 notes in each octave, and split the octave into 14 equal parts (moving the pitches of all the existing notes accordingly), unfortunately, such a scale does not do a good job of approximating many consonant intervals, and it would not be very suitable for traditional western music. Experimental musicians have used it though.

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The layout of a piano keyboard always puzzled me. For many years I asked music professionals why was it so illogical - no one seemed to know. Eventually, the best answer I found was that early harpsichord type instruments had only white keys. They consisted of banks of seven notes. Each bank formed a scale which 'sounded pleasing and natural to the ear', with the an eighth note finishing off the scale and beginning a new tonal scale higher than the last. Hence the 'octave', (Greek origins for eight.) Each note was denoted by an alphabetic letter; A B C D E F G A

So, there was a kind of 'natural ear' logic to the seven note scale but when half tone notes were introduced, what was natural to the ear, and what was mathematically true, uncovered two different realities.

This can be best highlighted by visually seeing and counting the semitone (half tone) divisions on the fret board of a stringed instrument such as the guitar. Mathematically, there are twelve semitones in an octave; six whole tones and six semitones on a single string. This is unarguable, they're 'just there'. What (or how) they are named, is where the real problem lies. Working from logic it would be best to number them 1 to 12, with the 13th note being the first note of the octave above.

The reality is, that the transition from note B to note C, and the transition from note E to note F, are mathematically actually only semitone steps, not whole tone steps.

The problem lies with the fact that the original layout of the harpsichord had seven 'whole' notes (white keys) already physically in place, and to make up the full compliment of twelve semitones, required the addition of only five black keys. Hence, the odd spacing system of seven and five to make the 12 semitones.

It would have been more logical to re-jig the keyboard layout at that point, into a symmetrical system of six white notes and six black notes. If the alphabetic nomenclature was still used, logically it should have been re written as; A A# B B# C C# D D# E E# F F# A. However, it seems that history, tradition, laziness or un-willingness to change won out, and we have an odd key layout, with a dogs breakfast of a nomenclature system, and complex transposition rules for changing keys.

Some have suggested that it would be difficult to navigate a symmetrical keyboard. This could be overcome by colour coding or tactile coding of certain notes as a reference point. Musicians can be very adaptable in any case.

The advantages of a symmetric keyboard is that finger positions for chords and scales would be more consistent and transposition from one key to another would be easier.

  • love this answer, explains the fact that B and C are not the same interval as C and D, and it explains how it got that way – Some_Guy Sep 23 '16 at 9:46
  • Your second para. There were already half tone (semitone) notes existing in the '7 note scale' you mention: assuming a major scale, between notes 3&4, and 7&8. Doesn't this fact muddy the water somewhat? – Tim Sep 23 '16 at 17:16
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If you are talking about microtonality - of which I know little, there will have to be a lot more than just changes to E/F and B/C. It's possible to have notes between any adjacent semitones. There could be as many extra notes between G and G# as between E and F. It just happens that it's accepted (and has been for centuries) that the note called F is effectively E# = and needs to be called one OR the other due to its technical position in a tune. Note that on some instruments,e.g. violin, F and E# will be slightly different in pitch anyway.

The OP's theory, I'm guessing, is to make a keyboard white, black, white, black, etc., but at the same time, trying to put in B half-sharp and E half-sharp. Difficult to find one's way around, and two notes only from a microtonal system. Makes it unwieldly and the two microtonal notes would hardly fit for 'ordinary' playing.

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There are some ambiguities in the way your question is stated. It is difficult to interpreted it in a non-arbitrary way; if you suggest adding one key for E# in addition to the present F key why not suggest for example the addition of two keys for B-flat and A-sharp respectively? And if you suggest reinterpreting E# as the quarter-tone between E and F, why not add a bunch of other quarter-tones to the keyboard?

If we leave out your suggested changes to the keyboard layout the question is clearly about a seemingly inconsistent system behind the keyboard layout. And I'll try to address that.

There are historical and physical reasons to why the keyboard looks the way it does, but alternative systems are possible and have indeed been used to a small extent (for example there have been experiments with quarter-tone pianos).

One alternative that I think is in line with your question is not to have seven white keys and only five black keys but have an equal distribution with every other key as white and every other as black.

A A# B C C# D D# E F F# G G#

(The bold are again black.)

Note that the keyboard layout now effectively mimics the two whole-tone scales.

Leaving out (most) of the mentioned historical and physical reasons I think it could be productive to think of the differences between transposed and untransposed instruments. The idea behind transposing instruments is basically this: The notation system is built around the scale of C major in the way that it has no sharps and flats and is thus easier to read. If an instrument is built around another scale (for example by ease of fingering), it can be more practical to sync the notation with the instrument by transposition.

For untransposed instruments the easiest scale is in fact C major or presumably it doesn't matter (or it doesn't matter enough...). For a keyboard it is easy to see that the former is the case - the keyboard layout mimics the notation system with the white keys as unaltered notes and the black keys as sharps or flats. And that is I think in very short the answer to why the keyboard layout looks the way it does.

I'm well aware that this forwards a bunch of questions from the keyboard layout to the notation system, but that not was not really put to question in the OP as I read it.

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    OP doesn't know that B and C is a semitone and C and D is a whole tone. Even though it's taken for granted by the musically trained, it isn't self-evident from the nomenclature – Some_Guy Sep 23 '16 at 9:47
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I think you are focused on the wrong question. You want to render the piano keyboard more regular by fitting in the "missing" black-between-white notes. But if you take a look at the wooden levers leading away from the keys to the strings, there are no gaps. And if you pluck the strings that the levers lead to, their progression is completely straightforward and you won't be able to spot any "gaps" where a black note would be missing: there are twelve notes per octave spaced all the same, mechanically and acoustically. The only irregularity are the actual keys attached to the notes.

There are regular keyboards, like with a chromatic button accordion, basically the only regular chromatic keyboard in wide-spread use. If you play a chord or melody on such a keyboard, you can transpose it arbitrarily by moving anywhere else and playing the same "shapes" as long as there are buttons underneath (only the first three rows have unique notes, the others are repetitions for facilitating this kind of transposition). The cost for that is that all scales are equally hard: C major already requires a zigzag traversal of three rows (just follow the white buttons in the first three rows).

Buttons would not work well for the striking and graded action of a piano, but there are some other arrangements (most notably the Jankó keyboard) that are similarly regular. None have caught on.

And I suspect that the main reason for the comparative success of the chromatic button accordion is not because of its regular semitone layout but because the keyboard is so much more compact, adding about two more octaves of notes as compared to a similarly sized piano accordion.

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The simple answer is that the layout of the piano keyboard is the most useful and efficient possible for playing in equal temperament. If you want to play music in all 12 Major and all 12 Minor keys, this is the keyboard you need.

As another answer has observed, our notation system is centered on the key of C Major, so it is only natural that the keyboard should be as well. Thus between adjacent white keys there is an interval of either a whole or half step, depending on what is needed in C Major. The half step is the smallest interval admitted by equal temperament, so a black key between E and F and between B and C is not needed -- in fact, would be a nuisance -- because there is no tone to sound.

But perhaps an equally compelling fact is that if there were a black key between EVERY white key, it would be impossible to orient ourselves visually to the keyboard. A pianist can tell at a glance what pitch will be sounded when she strikes a particular key. A BLIND pianist can tell by touching the keyboard. This is entirely due to the layout of the black keys. It would be MUCH harder to play a keyboard that lacked the [2,0,3,0] pattern of black keys.

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    "the piano has been designed explicitly for playing the equal-tempered repertoire" -- This is wrong in a few ways. First, the current layout of the keyboard can be traced back to at least the 14th century, used in organs & harpsichords, predating the 18th century piano. Second, even in pianos, equal temperament was not widely adopted until the 19th century. For much of this period, some variation of meantone tuning or well temperament was used. Well temperament (used by Bach) was not equal temperament. It'd more accurate to say that ET was developed as a concession to keyboard instruments. – Caleb Hines Jul 6 '15 at 17:10

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