Why is music theory built so tightly around the C Major scale?

Question

Lately, I'm trying to study deeper into music theory, learning Intervals, key Signatures, Chords, Progressions etc. I can see that everything is built around the 'normal' notes that belong to the C major scale, and everything in-between is an inconvenient anomaly. I just feel there is a whole lot of unreasonable extra work and trouble coming out of this convention, that feels wrong.

1. You have the normal/natural notes, and the 'accidental' ones. The staff has no place for them, so you have to draw extra symbols around them, relative to the closest 'natural' note. Practically the staff behaves like it's offended by the accidental's existence. Or like it's punishing you for using them.
2. Naturally, you have to avoid using the accidentals, as much as you can. So G# is different than Ab, despite being (tonally) the same note, because practically it allows you using fewer accidentals. I understand how that works, but it still feels weird.
3. And instead of writing the key in the start of the sheet, you'll have to guess it by reading the accidentals right next to the clef, and memorize 30 different key signatures. Note that the signature is defined from the accidentals. Oh yes, there are shortcuts by using the circle of fifths. and a poem with Charlie's Father. I'm starting to understand how this works, but I still don't like the fact I have to memorize something.
4. Then you have the Intervals, that are initially based on ignoring the accidentals (Generic Intervals), then we re-introduce them by valuing the Specific intervals and defining 'Interval Qualities' (perfect, major, minor, diminished, augmented etc).

Now that I've stated some inconveniences of this system, I'm wondering what are the benefits that make all this memorizing worth the trouble. The only thing I can guess, is that the piano - probably the most important/common/traditional instrument for a classical composer - uses the black keys for the accidental notes. Of course this will not necessarily benefit other instruments.

But leaving the individual instruments and the easiness of reading music sheets, out of the scope of this question, what are the benefits of the the accidentals to the evolution of Music Theory itself?

I made some serious Edits out of the initial question, trying mostly to filter out my ranting :).

Answer 1

1. Bias against "unorthodox" notes

Western music tradition (and some others) was, and to a large extent still is, based on heptatonic scales, that is, seven unequal divisions in an octave. So, in a given musical context, all twelve notes are not created equal. For instance, in a musical phrase in C major, natural notes (ones with no accidentals) are the norm, others are there to add color (hence the name chromatic, from the Greek word for color).

So, treating these extra notes as second class citizens makes a lot of sense. For guitar, you position your hand and set your mind to the scale given in the key signature and only break the pattern when you encounter an accidental. The presence of an "alien" accidental makes it obvious that you're breaking the pattern.

2. Avoiding accidentals

You don't avoid accidentals. You use just as many as necessary, neither more, nor less. Even though G# and Ab sound the same in twelve-tone equal temperament, their functions are still different.

For instance in a C major context, G# is a raised fifth and tends to resolve to A, like when modulating to A minor. On the other hand Ab is a lowered sixth and tends to resolve to G, like when using an Italian sixth. They are notated differently to convey this information, not to use fewer accidentals (but see the next part for an exception).

If you look at it the other way, when you use the G#/Ab pitch as a modified version of the fifth degree (G), e.g. as an approach note to A, you notate it as a G#. When you use it as as a modified version of the sixth degree (A), e.g. as an approach note to G, you notate it as an Ab.

It doesn't matter that they sound the same in isolation, they don't sound (feel) the same in context and it's a useful information to convey.

3. Key signatures

At least half of the 30 theoretically possible key signatures are not used in practice. You will rarely encounter the ones with 7 accidentals and the ones with 8 (or more) are practically nonexistent. Enharmonic equivalents with 5 or 4 (or less) accidentals are used instead.

With little practice their distinctive shapes and orderings are actually pretty easy to remember.

4. Interval qualities

If I understand correctly, you imply that a system based on the number of chromatic steps would be more logical.

It's not so. Like I tried to explain in the second part, G# and Ab are not equivalent. In C major, the first is an augmented fifth and the second is a minor sixth. They have very different functions.

5. Interval numbers

Here, I mostly agree with you. But remember that the more mathematical system would have its problems too. Most people are not used to start counting from zero. It would still cause some confusion.

Conclusion

Having said all these, I have to agree that there are some shortcomings of the current musical notation. But it evolved to have its present form throughout centuries with compromises, trying to make some things easier while not making some other things unreasonably difficult. Like most compromises, it's probably not optimal but it works well in practice.

Answer 2

TL;DR: Backwards compatibility, and the predominance of seven-note scales.

We're going to take a musical walk through history...

Let's say you're inventing music, and you start out with a single string playing a single note. That gets boring after a while, but you realize that you can play more notes by shortening the string length, so with a bit of playing around, you come up with a scale that sounds good to you. That scale has only 7 notes in it, because the eighth one ("octave") sounds like the first, only higher. Now you decide to name these 7 notes based on the letters of the alphabet: A, B, C, D, E, F, G. After that, the pitches start to repeat at the octave, so you give them the same names.

Since the idea of zero being a number doesn't really exist yet, you decide to measure the distance between notes by counting them (in other words, you're using ordinal numbers rather than cardinal numbers). So the note you start on is the first note, the note above that is the second, and the note above that is the third, then the fourth, and so forth. For example, if you count to the third note above your starting note, and then, using that as a new first note, you count to the third note above that, you end up with the note that is the fifth note from your starting note. It's a real shame that zero hasn't been invented yet, because now you have 3 + 3 = 5.

Now fast forward a bit and you've decided that, using the same seven notes, C actually sounds like a better place to start and end the scale. Same notes, just a different convention for where you start. You decide to maintain the original naming convention, though, because that's what everyone is used to, and backwards-compatibility is important.

There's one problem with your scale, though. When you picked out the notes that sounded good, you actually picked an unequally-shaped scale. Some of the notes are closer together, and some of the notes are farther apart. This leads to the scale shape you may have seen before: WWHWWWH. As long as you're just playing a melody, you don't really need to worry about this shape (except that it determines how much shorter to make the string) -- everything just sounds good. The trouble comes when you start to get fancy, and play more than one note at a time.

Let's say that you have a simple melody that goes C-D-E-F. You know that notes "a fourth" apart sound good together, so you decide to harmonize this in fourths. When the melody plays a C, you play an F, and it sounds great. That's followed by a D and an G, great! Then comes E and A, still sounding good. But then the melody goes up one more note to F, so your harmony goes up one more note to B, and YUCK! B is the fourth note above F, so it should sound good... What happened?

The problem is that, because your scale is unequally shaped (because that's what sounded good), the distance between E and F is a smaller distance than the distance between A and B, so your nice perfect fourth got all messed up. In order to fix this, you have to kind of fudge your B a little bit, and make it lower. But don't worry, there's plenty of room between A and B to stick your new modified-B. But what are we to call this new note? We can't just go renaming all the notes of our scale every time we need to throw in a new note. So instead, we name it after the note it replaced. Instead of a "B", we have a "lowered B", aka, B-flat.

As we play around with different scales and harmonies, we find all kinds of places where we have to raise and lower notes in order to maintain the proper scale shape. We always name them based on the original note that they're replacing, plus whether it was raised or lowered. In fact, any of our original 7 notes can be raised or lowered. The staff notation still reflects that we are still basically using the same 7-note scale, but depending on where we start, some of those notes may have to be raised or lowered in order to maintain the same scale shape. It's a clever little hack that allows us to maintain backwards compatibility with previous music notation, while "patching" it to allow new pitches that didn't exist before.

Eventually, to simplify things, you decide that when two notes are closer together (like E and F), the raised version of the lower note (E#) is "close enough" to the higher note (F) to pretend like they're the same (and vice versa with the lowered version of the higher note). OTOH, for notes that are further apart, you decide that the raised version of the lower note is "close enough" to the lowered version of the higher note note. This rounding off prevents you from inventing wacky keyboards with gazillions of keys, or fretboards with a large number of impossibly close frets.

Since there are five of these wider gaps, this adds five new notes to our inventory of notes -- causing 12 notes in total. But we still generally tend to use only 7 note scales. As a result, the 5 new notes don't have any inherent name of their own -- they always replace one of the previous 7. By using these modified notes in place of the original, it allows us to play the same scale shape starting on any possible note (including one of the modified notes). Of course, now you have to specify up front which version of any modified notes you are using.

Answer 3

You are asking quite a few different questions here, and I'm not sure your main question (about C Major) is even the main question you ask in the main body of your question!

All of the questions you ask about accidentals, the relationship between keys, and so on, have information available either here, at music.SE, or elsewhere on the web (have a good look at the right hand side of this page for starters!)

So, sorry to not give you a definitive answer to your question.

However, as a guitarist myself, I can give you a little insight into why keys (and the "hierarchy" of keys) can seem confusing to guitarists. As a guitarist, we tend to think of keys and scales as being patterns which we can move up and down the neck, each being essentially the same, simply shifted by some number of semitones. However, you're right, on an instrument such as piano (but in a purely theoretical sense too) it is the changes of accidentals between keys that allow us to understand the relationships between keys. Unless you have perfect pitch, any one key in isolation may as well be written as C major (as long as you don't want any pitches which are chromatic within that key, and don't want to change key). But, once we want to write and play more complex music, the way accidentals, key signatures and changes to them work, gives us an insight into the relationships between keys, and the theory behind these relationships, which a system of equally spaced semitone pitch names (and some kind of stave that uses them) would not.

If one is only interested in using the stave as a guide for playing the correct notes, then guitarists already have a specific stave for our use, which takes no consideration of key, music theory or key relationships, it's called TAB! But, as I said earlier, this gives no insight into how the music works, with regard to key relationships (or even pitch relationships). As you are now studying theory, I assume you are keen to gain this knowledge. As you say, as you study more, the importance of key relationships, with C major given it's own specific prominence, will become clear.

Answer 4

One thing I didn't really pick up from anybody else's answers is about key signatures.

A key signature isn't a guess - they're built according to the progression of the circle of fifths, so there aren't that many possible key signatures and you learn to recognise them quite quickly as you gain experience playing different pieces. You said "instead of just writing the key at the start of the music" - well, sometimes it is, but it's actually not very helpful.

The key signature isn't really there to tell you what key it's in - saying it's in F major is all very well, but I want to know what that means for what notes I'm going to play. The key signature for F major tells me that all the notated Bs will, unless otherwise stated, be played as B flats, and all other notes will be naturals. This is useful information for the player, and helps keep the rest of the stave clean for easier reading. If you had to put a flat on every single B in the piece instead of using a key signature you'd be adding a lot of clutter, and it'd only get worse in keys like A major (three sharps) or B major (five sharps).

Now sure, there aren't key signatures for minor keys (they use the signature of their relative major), but there's a reason for that too - minor keys use more notes. You can't represent it accurately in a key signature because minors commonly use both flattened and sharpened sixths and sevenths, which would be difficult to convey clearly in the key signature (and would still need accidentals to tell you which one to use when anyway). So you just set off as if it's in the relative major, and take the accidentals as they come which mutate the music into the minor.

With some practice you soon learn to glance through the music and identify if it's in the major or the relative minor based on the key signature, which is handy because you can't really play it well until you've understood what key you're in - especially if you're playing with other musicians and thus need to accurately tune chords. A lot of instruments let you play notes slightly sharper or slightly flatter, or just make up new notes between the normal ones, so you've got the flexibility to make that distinction between G# and Ab if you need it, or to counteract the problem with an equally-tempered major triad where the major third is horribly sharp.

I got a bit rambly here, but the point really is that theory and notation evolved hand in hand, and the notation not only takes in the need to represent all possible pieces of music, but is also significantly influenced by the needs of musicians to actually use the notation. Written language would be pretty poor if you could never learn to read aloud at a reasonable pace, and music notation is much the same. The simplifications which are in the notation help us sight-read pieces at full speed (depending on our ability level and the difficulty of the music of course), something we might struggle with much more if we had a more 'logical' system of notation which would in turn have to take up space conveying a lot of information we mostly don't need.

Answer 5

It's a far reaching question, based on some theoretical knowledge, but some misconceptions. Initially, everything has to have its datum point, and the music system has Cmajor - which happens to be the white notes on a keyboard, as you state. It could have been called A, or 1, or i or alpha or just about anything you can think of. It was (and still is - convention and usage-) called C.

The accidentals at the beginning of a piece actually aren't. They're the key signature, and, yes, they can be memorised, like most other things.Key signatures numberless than 30. Each one could end up as a major or a minor, and for practical purposes, going up to 6 #s or 6bs will be sufficient. With an open key sig. for C/Am, that makes 13. A far cry from 30 ! They tell the reader which black notes are used instead of specific white notes. I realise on your guitar there are no black ,or white notes, and this makes it all confusing - I know, I play guitar and keys.On a keyboard, to make a white note go up by a semitone, you move to the nearest black to the right.Except, of course, B and E, which move to the next white - C and F respectively. Just another foible of the music system which can, and does, appear non-sensical to a lot of guitarists. On guitar, you just slide up one fret regardless !

Intervals - start at note one, move up two notes diatonically (as in a scale, maj/min) and you're on the third note. Call this 'a third' and the job's done. Start again at one, move up four and call it a fifth. That means it's the fifth note because it is ! Simple.

There are other points you make, but that'll do for now. Hope it helps !

Answer 6

Here's another way of looking at it, which has nothing to do with the historical development.

Suppose you had an instrument that was similar to a piano, but had no black keys. (So each of the 12 pitches that make up an octave had its own white key.) It would be more "elegant " mathematically, but (a) it would take up a ridiculous amount of space and (b) you wouldn't be able to tell which note was which (unless you wrote a special symbol on each key).

To address the first of these problems, you could have a piano in which white keys and black keys alternate. Then the piano would take up half as much space, and still be "elegant" mathematically. But you would still face the second problem.

The construction of the piano may seem a bit arbitrary, but at least you can easily tell which note is which. In fact, the very source of the mathematical "ugliness" --- the lack of complete symmetry --- is what makes it easy to identify the notes.

Answer 7

Only answering #3: You don't read the accidentals to figure out the key, you count them. And yes, it involves the Circle of Fourths and Fifths. You will learn, if you haven't already, that each note in the scale has an inverse: 4th up = 5th down, 6th down = 3rd up, and so forth. Each key can be thought of in the abstract as a major or minor key. Example: A minor and C have the same key signature, as do E minor and G.

Answer 8

In relation to your source of irritation about everything being in C, when I go shopping for music theory books, I specifically look for those that give examples in other keys.

Yes, many times laying out things in C makes it easier to explain, yet it's not the only key in the world. I've seen some books that will choose a different key because it makes a given instrument sound better (e.g., guitar.) Other times I've seen books that will show examples in C for sure and least 2 more keys, 1 with sharps and another with flats.

Answer 9

You don't actually have to guess the key or memorize all 30. 99 times out of a hundred the key is the last note. (But that could also pose a problem because A major and A minor both end on an A) I play flute, keyboard, mandolin and trumpet, and overall my favorite key is E minor (F♯ minor for trumpet because trumpets do not play in concert pitch). I find B minor / D major is easiest for piano because it fits well with the particular size and shape of my hands. C major is definitely easiest for flute because it simply lifting each finger up. G major is easiest for mandolin because the 3 most common chords (G, C, and D) are alll easy for mandolin. I don't have as much experience with the trumpet (because it confuses my ears) but my favourite scale is F major (concert E♭) because it doesn't use the third finger. I really don't have a preference for keys while singing, since depending on the song, the range is different, but with most songs with male vocalsists since I have a rather large vocal range, G1-B4 for so called "chest voice" I can either sing the lower octave or the actual octave.

But it seems most instruments are based on a C major scale, so I presume the reason a lot of music is in C major is because of this.