# Why does the scale have seven (or five) notes? Why not six?

I'm a programmer by trade, and I have always felt that music was arbitrarily difficult. Please forgive my inexperience with musical notation. I had a little thought experiment with my wife today, and I wanted to ask why we don't do it the way I thought up.

My wife explained to me that a scale(octave?) is made up of seven notes, which we typically call ABCDEFG or Do-Re-Mi-Fa-So-La-Ti(-Do). From this answer: https://music.stackexchange.com/a/3004 we know that those 7(8) notes are this progression:

Every major scale has seven notes. They all start on a root note and proceed to go up in the following pattern: Whole Step, Whole Step, Half Step, Whole Step, Whole Step, Whole Step, and then a final Half Step returns to the root note (an octave above where we started).

Why go up by a half step twice? Why not go up a whole step every time? It seems like having B# be C and Cb be B (and same with E/F) is arbitrarily complicated. Was this done just to make pianos easier to play by feel? Is there a mathematical root?

If you will suspend your disbelief with me for a minute, what if we had a scale made up of 7 lines? The spaces in between each line represent the notes (I'll call them 1-6, to avoid confusion with A-G). The lines themselves represent sharps and flats. So a 1# is a 2b, etc.

The piano would have to change to having black keys in between every white key. To offset this, the 1 keys would be wider on the left, and the 6 keys would be wider on the right so that one could still determine octaves (septaves?) by feel.

What problems does this present? Is there a good reason not to go to an easier to remember system? If not, why has no one done it?

Questions I've already looked at to make sure this isn't a duplicate:

• To answer your "Why not six" question: there are six-note scales, they're called hexatonic scales, and the whole-tone scale is one of them. There are also eight-note scales: octatonic scales, e.g. the diminished scale. Those scales are just much less used than pentatonic and heptatonic scales. – Matt L. Jun 7 '15 at 19:43
• Consider reading Helmholtz's On the Sensations of Tone as a Physiological Basis for the Theory of Music. Chapter 13 is all about this particular subject, and it's an interesting read if you really want a deep, carefully thought-out answer. – kojiro Jun 8 '15 at 3:45
• I marked this question down, because fundamentally it is like asking "Why are there three primary colours?" The diatonic scale has a long history, though arguably it has six definite notes and one floating one: the 7th, which can be raised or lowered, and has all to do with why Bb is called B in German, and so on and so on. – Brian Chandler Jun 8 '15 at 15:48
• – ninjalj Jun 8 '15 at 18:13
• @BrianChandler: Our eyes have receptors for three different frequencies of light. Our ears have receptors for far more than five or seven different frequencies of sound. I don't think these questions are alike at all. – Marcks Thomas Jun 9 '15 at 12:24

The notation we have is actually pretty natural and logical, for a simple reason: there are twelve different notes in the Western system, but only a subset of these -- seven, in fact -- are used in a given scale such as the major scale.

Let's use individual semitones as the basis for a notation as you suggest; so, let's say the note A is still denoted by A, but now A# (or Bb) is denoted by B, and then the remaining notes are C, D, E, F, G, H, I, J, K, and L (twelve in total).

I understand why you'd want to do this; it removes synonyms. But at what cost? What does an actual key look like now? Take C major as an example. In the new notation, the notes are D, F, H, I, K, A, C. This is confusing and hard to remember. Compare with C major in normal notation: C, D, E, F, G, A, B. It just cycles through the seven letters.

What about other keys? Let's take F major as another example. I won't write it all out in the new notation again because you just get another confusing list of letters, but in normal notation, it's F, G, A, Bb, C, D, E.

Hopefully now you see the benefit of this notation: it's easy to think about every key, because, ignoring accidentals (i.e. the flat on the B) they just cycle through our seven letters.

You lose uniqueness of note names -- though in fact, not really in practice, for example you'd never call Bb "A#" when talking about the F major key -- and the usefulness of this feature of the notation far outweighs this minor problem.

• Although this supposes that scales precede note names, it makes a ton of sense intuitively, and it explains that the system was not arbitrary. Marking as correct. – Caleb Jun 9 '15 at 11:42
• This answer takes as a given that A# and Bb are the same note, which while true in modern "equal temperament" is not historically the case - and history is as important as logic in cases like this. The Wikipedia article titled Enharmonic gives some readable basics. – IMSoP Jun 9 '15 at 22:51
• @Caleb Historically, 7 note scales did precede note names. The Ancient Greek music system used a 7 note scale somewhat similar to ours, created from a series of tetrachords based on fourths and whole steps, but the notes were named according to the position of the corresponding string on a lyre ("nearest", "next to nearest", "middle", etc...). Our first recorded use of letters for note names is from the 6th century philosopher Boethius, who used 15 letters to cover 2 octaves (the letters didn't repeat in the higher octave). – Caleb Hines Jun 10 '15 at 15:31
• The in-between notes without names (the black keys) came along considerably later, and were essentially seen as alterations to existing notes. They didn't change the fact that music was still built around 7-note scales (one version of each letter), thus they didn't need their own names. However, atonal music relabels all 12 notes in a manner similar to your suggestion: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, t, e. – Caleb Hines Jun 10 '15 at 15:51
• @Denziloe I think if you use numbers instead of letters for the notes, the intervals become apparent... Sure, the C major scale is the one that will get more complex, but what about the others? For example, take A major: "A, B, C♯, D, E, F♯, and G♯". This is not simpler than the other approach for me, it can be even more confusing as you run the risk of messing up the alterations. If you kept them as numbers or sequential letters (why not base 12 with A,B) and you keep the units of each one you'll always get "root,root+2,root+4,root+5,root+7,root+9,root+11,root" – Alvaro Aug 15 '18 at 20:52

You can divide up the octave however you want, but it turns out that doing what you suggest doesn't really make good sounding music, at least to our western ears.

It all has to do with overtones and pleasant ratios of pitches. An interval sounds consonant to us when the ratio of the frequencies is mathematically simple. It causes the waveforms line up and produce constructive interference.

If I take C as a base from which to construct the overtone series, I quickly find G and E to have simple ratios (3:1 and 5:1, and by shifting octaves to get them closer together, 3:2 and 5:4). Stack two fifths and drop the octave to create D = 9:8, and go a fifth down and an octave up to create F = 4:3. Now we have the beginning of a scale: C D E F G, and the notes aren't evenly spaced (E-F is roughly half the distance of the others). This is the beginning of Pythagorean tuning, and various ways to construct the remaining notes of the major scale and fill in the gaps result in a huge number of ratio-based tunings.

In short: it's the way it is because it sounds good. Sure, it's a bit screwy in some ways, but we don't want to force an art form to conform to some notion of mathematical simplicity.

• In short: it's an art not a science, so aesthetics matter more than consistency. That makes sense to me. Thanks Matt! – Caleb Jun 7 '15 at 22:38
• @Caleb On the contrary, it seems pretty scientific to me! – Craig Jun 8 '15 at 0:13
• For example, an octave is an octave (for example the note C, and the note C one octave higher) because the frequency of the sound waves is exactly double, or exactly half, when a note is one octave higher or lower. That's why a C sounds like a C, whether it's middle C, or an octave (or more) higher or lower. Sure, the 7 note division within an octave is what "sounds good," but there is also a mathematical precision and predictability involved. – Craig Jun 8 '15 at 0:22
• Regarding art versus science in this answer, the first documented study of the intervals we use today was by Pythagoras, and he considered what he was doing to be science (or what we would call science today). He was looking for natural physical properties under the assumption that the universe is meant to be "consonant" (not just sonically, but overall). To him it seemed natural that simple ratios of frequencies were both easily generated and sounded good played together. There is science (in the modern sense) behind why these intervals sound good to us. – Todd Wilcox Jun 9 '15 at 12:35
• @ToddWilcox -- "or what we would call science today...." My ancient philosophy professor in college thought of Pythagoras primarily as a Mystic. "According to Aristotle, the Pythagoreans used mathematics for solely mystical reasons". – ex nihilo Aug 29 '18 at 2:13

The reason is that dividing an octave into 12 notes sounds the best for a very mathematical reason! The frequency of each semi-tone is 21/12 away from its neighbours.

Note    C × ?   Fraction    Note    C × ?   Fraction
C       1       1/1         C       2       2/1
C♯/D♭   1.059   18/17       B       1.888   17/9
D       1.122   9/8         A♯/B♭   1.782   16/9
D♯/E♭   1.189   6/5         A       1.682   5/3
E       1.260   5/4         G♯/A♭   1.587   8/5
F       1.335   4/3         G       1.498   3/2
F♯/G♭   1.414   7/5         F♯/G♭   1.414   10/7
G       1.498   3/2         F       1.335   4/3
G♯/A♭   1.587   8/5         E       1.260   5/4
A       1.682   5/3         D♯/E♭   1.189   6/5
A♯/B♭   1.782   16/9        D       1.122   9/8
B       1.888   17/9        C♯/D♭   1.059   18/17
C       2       2/1         C       1       1/1


Notice how each fraction on the right hand side (descending) is almost the inverse of the left hand side (ascending)? The difference is one of the numbers is doubled or halved each time. The smaller the two numbers are and the smaller the difference between them the better they sound to us. This is because the parts of the waveforms they produce agree very often.

When the peaks often coincide they produce a chord, or an agreement. When the peaks rarely coincide they are discordant and the sound is disagreeable! So we can see from the table that C and G will sound the best together as C has 2 peaks for every 3 peaks that G has. The next best note for C is F, which is actually the inverse ratio of C:G. Then comes E, giving us the C-E-G chord, which we already know sounds very nice! The ratios for C-E-G are (4:5:6)/4. In the minor scale we have C-E♭-G which is 6/(6:5:4).

Either the numerator or the denominator must be able to be multiplied to a common, small value for the two notes to sound good together. You might think that E♭-E would sound good because they both have a 5 but it doesn't work that way. You would either get (24:25)/20 or 30/(25:24), neither of which would sound good because of the high numbers needed to find a common frequency.

• The bit about 12th root of 2 is not quite right. The point is that the equitempered scale provides a pretty good approximation to the diatonic ratios, because of some interesting mathematical "coincidences" (e.g. 3^12 is close to 2^19, so 12 perfect fifths (3/2) is close to 7 octaves (2/1). So it's a sort of "Approximate mathematical reason". – Brian Chandler Jun 8 '15 at 10:39
• That's why I gave the numbers in decimal first, then as (approximate) fractions! Our ears do the rest, changing 1.26 to 1.25 because it's close enough. And note that your way you're using "something^12" and "2^something else". We're both using the same system, just differently! I agree with you that 12 is a coincidence but it works so well it just can't be any other number like the OP was hypothesising. – CJ Dennis Jun 8 '15 at 10:45
• @BrianChandler let me give you some frequencies I calculated using the 12th root of 2: C 261.6255653 C# 277.182631 D 293.6647679 Eb 311.1269837 E 329.6275569 F 349.2282314 F# 369.9944227 G 391.995436 G# 415.3046976 A 440 Bb 466.1637615 B 493.8833013 C 523.2511306 You can check them against en.wikipedia.org/wiki/Piano_key_frequencies for accuracy. – CJ Dennis Jun 8 '15 at 15:22
• Sure, but the OP was not asking "Why 12?" or "Why equitemperament?" he was asking "Why 7?" Your answer is not wrong, but not I think quite the right angle. For instance, the fifth in the diatonic scale is fundamentally 3/2, and not the approximation 1.498, which comes later. – Brian Chandler Jun 8 '15 at 15:55
• @EJP I agree that the harmonics define the 12 root, not the other way around. I was trying to explain that it doesn't work if it's the 11th root or the 13th root because 12 just happens to get very close to all the frequencies that sound good to us. – CJ Dennis Jun 10 '15 at 11:21

Most of the answers here appear to be focusing on why we ended up with a seven note scale in western music.

This is a great area of inquiry; however, it is worth noting that whatever the answer to this question, the seven note scale is a fundamentally arbitrary product of Western culture.

Dissonance and harmony are culturally relative. The idea of the octave appears in almost every society; however, the way in which the octave is split and which combinations of frequencies are pleasing vary entirely by culture.

"Strictly speaking, there are no structural characteristics that have been identified in all known musical systems." - http://www.academia.edu/10684651/Cross-Cultural_Perspectives_on_Music_and_Musicality

So I would argue that although the other answers are mostly correct in identifying reasons why we use a seven note scale, it should be kept in mind that these are fundamentally cultural and historical reasons, not biological or mathematical reasons.

Edit: Just wanted to disambiguate based on the comments. I am referring to the dictionary definition of "harmony," which is "the combination of different musical notes played or sung at the same time to produce a pleasing sound" - http://merriam-webster.com/dictionary/harmony. This definition is not related to any particular mathematical relationship or consonance between the notes: "Harmony" simply means that the resulting sound is pleasing to listener.

• I disagree with your statement "Dissonance and harmony are culturally relative." There is a very clear mathematical relationship between harmonic frequencies. – TimH - Codidact Jun 9 '15 at 16:40
• You are welcome to provide research or counterarguments to the paper I cited, but just disagreeing and downvoting my answer isn't very helpful to the discussion. A great deal of research has been done on this topic. Researchers have found that octaves are nearly universal, but there is no universal cross-cultural way to break up the octave. Our system has certain mathematical features to it; however, the fact that we find mathematical consonance to be pleasing is completely a product of our culture. – Theodore Jun 9 '15 at 16:45
• Edit: Some cultures even deliberately combine very close frequencies (what we would call "out of tune") in order to produce wave interference - they find it harmonious. Our system is great and has some neat mathematical features; however, there are a vast number of musical systems that do or do not incorporate these features. I think most of the answers dealing with the math are great - my point is simply that we don't use our system because of any objective reason - we use our system because of our cultural history. (Which probably includes privileging features like mathematical consonance) – Theodore Jun 9 '15 at 16:56
• I think the trouble is that we are talking about two different things - when I say harmony, I am talking about the dictionary definition: "the combination of different musical notes played or sung at the same time to produce a pleasing sound" - merriam-webster.com/dictionary/harmony. This varies widely between cultures. Combinations that we find dissonant sound harmonious in other cultures. It sounds like you are using "harmony" as "mathematical consonance" (generally how it works in western music) - that's fine, but a little confusing insofar as "harmony" is normally more general. – Theodore Jun 9 '15 at 17:29
• Given the central place of Pythagoras' treatise for the last 2.5 millenia, surely it is up to those who think mathematics has nothing to do with it to prove their case instead of just asserting it. The existence of other scales in other cultures is not itself evidence that it is 'culturally relative' in Western culture as well. – user207421 Jun 11 '15 at 23:51

The answer to the question "was the diatonic scale designed to make pianos easier to play" is clearly "no", because the diatonic scale precedes the invention of the piano by some thousands of years.

Remember, for the vast majority of the history of music, it was not played on keyboard instruments. It was played on wind or string instruments. If you want to see instruments on which the chromatic scale is clearly laid out, see the neck of any guitar, ukulele, or other fretted stringed instrument.

The answer to the question "why is C sharp enharmonic with D flat" is because it is highly convenient to do so. As other answers have noted, the fundamental relationships in music are ratios of vibrations that are 2:1 or 3:2. But it is impossible to make any combination of 3:2 ratios that works out to a 2:1 ratio! What we do then is we choose twelve notes that are each in a ratio to each other of the twelfth root of two; that number can be raised to an integer power that gives a result very close to 3:2. I wrote a series of articles about this ten years ago (start from the bottom).

The answer to your question "could we have a black key between every white key on the piano?" is yes, and this arrangement would have several nice properties including making it trivial to transpose on a piano (by any number of full tones; transposing half tones is tricky in this layout). The traditional piano keyboard arrangement makes it difficult for even experienced pianists to play a piece known in one key in a different key, say, to accommodate the range of a particular singer. The Wikipedia article on isomorphic keyboards may be of interest to you.

You may also be interested in studying the key layout of the button accordion.

It would be entertaining to build a small piano or organ which had the keyboard layout you propose, and learn how to play scales and chords on it. If I ever build a keyboard I'll give it a try and report back.

The answer to your question "why not just go up whole tones every time and have a six-note scale?" is: You go right ahead and play music like that if you want. If you're watching a movie made in the middle part of the 20th century and a character suddenly goes into a dream sequence, odds are pretty decent that the incidental music uses the scale you are describing. Music written in this scale can have an unsettling and dreamlike quality to it, at least to people accustomed to listening to Western music.

• I wish I could up vote this answer several more times. I apologize for my rambling question. It was hard to pin down what I really wanted to ask because I don't have a strong background in music. Thanks for going step by step. – Caleb Jun 9 '15 at 11:45
• The "every other key black, every other key white" arrangement would be very difficult to play, though. Pianists depend on the differences in key arrangements to orient themselves on the keyboard without looking. – BobRodes Jun 16 '15 at 16:05
• @Caleb: You're talking about the so-called "whole-tone scale". A good example of its use is Debussy's Ile Joyeuse. You can hear an obvious example of the scale from :53 to :55. – BobRodes Jun 16 '15 at 16:09
• @BobRodes: I'm not sure I buy your argument. There are plenty of instruments where there are not strong cues as to the orientation. When I play my accordion for instance, there is a single button of the 120 or so buttons that has a tiny divot on it that indicates it is C; everything else you do blind, by reference from that. Transposition is easy in such a system, but I find it very hard to transpose in my head when playing the piano. – Eric Lippert Jun 16 '15 at 17:55
• Fair enough. All I can say is that I would have a real problem with it, but that might be because of years of experience with the existing keyboard. The size of the keyboard is a consideration as well. Do you have a keyboard on your accordion for the right hand, or buttons? – BobRodes Jun 16 '15 at 18:13

There is no deep reason. Western "folk music" often only used 5-note scales (approximately C D E G A in modern notation). The song "Amazing Grace" is a well known example.

There have been experiments with more notes per octave - 19, 31, and 43 all work quite nicely. People have built playable keyboards for those, and other systems. There are some pictures at http://en.wikipedia.org/wiki/Enharmonic_keyboard.

Non-western music follows different rules. Arabic scales use 24 equal divisions per octave. Turkish scales divide each whole tone into 9 equal parts, but they don't use all of the 54 notes in one scale. Javanese gamelan uses two groups of instruments tuned to different scales with 5 and 7 notes, both different from any notes in the western scale.

Rationalizing western scales with hindsight using "just intonation" intervals like 3:2 and 4:3 is interesting (and was first done at least 2,500 years ago) but given what the rest of the world does, I find it had to accept that there is anything "fundamental" about it. Some very old European monophonic instruments don't even play "octaves" tuned in a 2:1 ratio - for example Scottish bagpipes, though some modern ones are tuned in equal temperament.

In fact, even pianos are not tuned in mathematically equal temperament - Google for "stretched tuning".

There is a scale using tones all the way - it's called a whole tone scale. Just as there's a scale using semitones - a chromatic scale.

Going with your idea of extra black keys - there's no need to change the width of the white ones, a couple of extra blacks would fit in the same way as they do between the existing whites. Trouble is, the pattern is then lost, so there would have to be other landmarks, like on a harp.

• When you say "chromatic scale", I wonder "What color? Also, how did he kill a dragon?" :) – Caleb Jun 7 '15 at 22:34
• Just very colourful... That's why it's called 'chromatic'. Dragon - no comprendo! – Tim Jun 8 '15 at 5:50
• Actually, you have to kill 12 differently coloured dragons! @Tim, it's a role-playing joke! – CJ Dennis Jun 8 '15 at 10:23
• On balance, you could say there's something fishy going on here... – Tim Aug 16 '18 at 6:30

Three musical intervals are special: the octave, the perfect fifth, and the perfect fourth. If one plays a note and its first three harmonics, the intervals among those pitches will be an octave, a fifth, and a fourth. Scales tend to sound good if some of their notes have intervals of perfect or near-perfect fifths or fourths between them. A perfect fifth is very close to being 7/12 of an octave and perfect fourth is very close to being 5/12 of an octave. Because these are odd subdivisions, there is no way to divide an octave into fewer than twelve roughly-equal pieces and have it contain a pair of pieces separated by a perfect fourth or fifth.

Because an octave is a perfect fifth plus a perfect fourth, and a perfect fifth is larger than a perfect fourth, it makes sense that there should be more notes between two pitches that are separated by a perfect fifth than the remaining notes in the octave that are separated by a perfect fourth. Unless the subdivisions are about half the size of the difference between a perfect fourth and fifth, however, it doesn't make sense for there to be two more notes in the fifth than in the fourth. If the number of notes within the fifth is one greater than the number within the fourth, that implies the total number of notes will be odd.

The strongest motivation for the ABCDEFGA scale is the SYSTEM of CHORDS which make a major key. For the key of C-Major, the basic chord of C gives us the notes C-E-G-C. Its related chords are F-major, consisting of F-A-C, and G-major, consisting of G-B-D. Putting it all together gives the notes C-D-E-F-G-A-B-C, which are all the white notes on the piano. The same kind of thing can be done for any other Key, and progressively using each of the white notes to form a system of major chords for that key motivates all of the BLACK notes on the piano. As has been said, this is fundamentally a matter of identifying a very specific frequency ratio (4-5-6-8) as being maximally pleasing to our WESTERN and EUROPEAN ears. Given that, it's all in the chord systems for a key.

The piano would have to change to having black keys in between every white key.

That's called a Jankó keyboard. They did not gain the traction needed to become popular in significant numbers. A variant for accordion is the "Beyreuther system". Again, they did not gain significant traction as compared to the now common "chromatic button accordion" which uses 3 rather than 2 non-redundant rows for arranging semitones in a uniform manner (for ease of fingering and transposition, there are additional 0-3 redundant rows, with 2 redundant rows for a total of 5 being the most common variant nowadays).

There is nothing new under the sun...

To reformulate the mathematical reason differently: Two sounds sound harmonic if they share many overtones. For one-dimensional oscillators (such as strings or flutes, but not drums for instance) overtones occur at integer multiples of a base frequency, hence harmony occurs when the quotient of the base frequencies is a fraction with very low numerator and denominator. Among the "best" such fractions are 1/2 and 1/3 (or 2/3). Therefore it should be easy to play notes with this relation, i.e., going a certain number of keys to the right should get us one octave (or one quinte) up. One cannot fulfill both demands at the same time (at least not with finitely only many keys), so one has to rely on approximations.

Mathematically, we need rational approximations to log 3/log 2, and the best such approximations are found by investigating the continued fraction for this number, which is

log 3/log 2 =1+1/(1+1/(1+1/(2+1/(2+1/(3+1/(1+1/(5+...)))))))

The best approximations are found by cutting this infinitely long continued fraction, and that gives us the approximations

1, 2/1, 8/5, 19/12, 65/41, 84/53, 485/306, ...

The most interesting approximant is 19/12 because it leads to our 12 half-tones. Let's try it: We start at a random frequency, 200 Hz say, and repeatedly multiply this by 3, always dividing by 2 when we exceed 400 Hz. Doing this twelve times, we obtain (approximately)

200, 300, 225, 337.5, 253.1, 379.7, 284.8, 213.6, 320.4, 240.3, 360.4, 270.3, (202.7)

and if we for simplicity agree that 202.7 is close enough to the 200 we started with, this is our scale (unsorted).

The previous approximant 8/5 would lead to a smaller scale, but would require us to agree that 379.7 is approximately 400. The next approximant 65/41 on the other hand simply require too many keys on our piano.

I try to explain in my poor english.

You need to satisfy two conditions to obtain what we call a "major scale".

1) FIRST CONDITION: HARMONIC CONNECTION

The strongest consonance of two different notes is made by a "fifth", for example the distance between C and G (C D E F G are five notes apart).

You can create a "cicle of fifths", a chain of notes where every note is distant a fifth. But let me start with Gb, just for this example:

Gb Db Ab Eb Bb F C G D A E B

As you can see, the notes of the C major scale, are all together on the right. So they are connected in a strong way.

2) SECOND CONDITION: DISTANCE

We can represents the octave as a dodecaghon where each side is a semitone, a different note.

Now try to put seven points on the vertex of a dodecaghon at the maximum distance possible. You will get the same configuration of a major scale: W W H W W W H (as your wife told you).

So, the reason why the major scale (and all their derivates) has seven notes is because it is:

"THE SCALE MADE OF A CERTAIN NUMBER OF NOTES WHICH ARE ALL CONNECTED BY INTERVALS OF FIFTHS AND ARE EQUALLY DISTRIBUTED OVER AN OCTAVE"

In the same way you will also get the pentatonic scale, more diffused than the major scale.

I think 'arbitrary' is the right answer. I suspect that pleasing tones and intervals existed long before scales, keys, and other theories existed. And there's something fundamental in the human organism that allows us to enjoy music. Look at how many great (not just good) musicians don't read music. Then some ridiculously complex theory was created to fit the reality. Here's something to consider: suppose that the treble clef staff and base clef staff in piano music were connected by 2 notes - middle C and 'middle A". Then the notes in both staffs would have the same names - the bass clef staff would be read as e,f,g,a,b,c,d,f, same as treble clef. This would cut the complexity in half. Good luck getting that changed.

Piano keys have to be the same width otherwise piano is not playable. It is to do with the way our muscles learn to go over the keys. Having some keys wider than others to accommodate for black keys everywhere would make it impossible to play piano. We hit piano keys with different fingers at different times, it is nothing like typing on a computer keyboard. The muscle memory would dictate to hit keys in a specific way, but when a key is wider, all that would not work any more, as one would have to adjust to different width at different times... sort of like having your steering wheel on your car steer at different rate randomly depending on what lane of what highway you are in.

Current system of 2 and 3 black keys works wonderfully well - it helps us see everything at once.

And current system is actually very simple - if you think about it, there are only 12 notes to learn: 5 black keys and 7 white ones. Then it is all repeated all over again. Now, as to the way this is written in the staff, that's a bit more complex, but that's a whole different discussion, and to be frank, I too have some issues with it... (don't let my piano performer wife see this :) )

• But you could have alternating Black and white Keys without making the keys have different width. Just construct all of the white keys like the D, G and A key. I think the reason we have the C scale on all whites is that in the times before well tempered tuning, the C scale was used most so the keys for that were placed conveniently. Kind of like the typewriter computer keyboard, where the keys were placed in such a way that you'd usually not use the same finger twice in a row (which makes you faster) and that the typewriter arms wouldn't get stuck on each other. – Sumyrda - remember Monica Jun 8 '15 at 5:01
• Frets on guitars and basses vary in size - as you go higher on violins, etc., the notes get closer together. We manage. – Tim Jun 8 '15 at 5:52
• Width of keys is irrelevant to the pitch of the note. The length, tautness, and diameter of the string that the hammer strikes is what dictates the pitch. – veryRandomMe Jun 9 '15 at 20:40
• Marimba is a keyboard with variable width keys, and you can play marimba by touch. – Josiah Jun 10 '15 at 14:52