A Major Key is nothing more than a collection of 7 notes, or pitches, that sound good together. When played in series, they are called a Major Scale.
So, how did we decide on those 7 notes and why did we choose them? A lot of teachers tend to assume students will take the terms "Major Scale" and "Major Key" for granted and jump directly into performing songs with some vague explanation of why this particular key has more sharps or flats than the others.
Why does the Key of G Major have just an F# and the Key of C Major have no sharps or flats at all?
Why does the Key of F Major have a Bb? Why is there a F#, C#, and G# in the A Major?
I think a good place to start is with a note. Where the heck do these notes come from anyway?
Notes are nothing more than frequencies that exist in physics. When you puck a the string on the guitar, that string vibrates at a certain frequency based on the gauge, the force of the tension exerted onto it and the length of the string.
When you fret the guitar with your left hand, you are adjusting the length variable above and changing the frequency at which the string vibrates. As you fret up the neck, the energy of the vibrating string is confined into a smaller and smaller surface area. This forces the string to vibrate faster, producing a higher-pitched note.
The fundamental frequency we call A4 is 440Hz. Hz is a unit of measure for frequency and it's measured in cycles/second. That means the guitar string moves back and forth 440 times every second as the string vibrates and the note produced is an A at the 4th octave.
The 4 in A4 simply refers to the octave, or the doubling for halving of the frequency. For example, if A4 = 440Hz, than A3 = 220Hz and A5 = 880Hz. It's the same note with its frequency just doubled or halved to sound higher or lower in pitch.
In Western Music Theory, the smallest distances between two notes is a half-step - such as from A to A#. In Asia and other places in the world they play smaller intervals than the European half-step. Today, the majority of people study Western Music Theory because of its simplification, utility and commitment to 12 distinct pitches. Therefore, the half-step is the smallest interval distance between 2 notes in our everyday music.
If you are ascending the scale, you use a # symbol, or sharp, to describe the half-step.
For Example: A A# BC C# D D# EF F# G G# A
If you're descending the scale, you use a b symbol, or flat, to describe the half-step.
For Example: G Gb FE Eb D Db CB Bb A Ab G
If we were to create a scale (a collection of notes played in series) going up from A4 (a 440z A) to A5 (a 880Hz A) with only half-steps, we would play every possible note that exists in Western Music Theory within 1 octave range.
The A Chromatic Scale:
440Hz A A# BC C# D D# EF F# G G# A 880Hz
(Chromatic = a scale made up of half-steps.)
Notice, how there is no B# or E#? That is because the distances between B & C and E & F are naturally half-steps and we call these natural half-steps.
The distance between A & B is called a whole-step. The half-step in-between A & B can be called either an A# or Bb depending on if you were ascending or descending the scale. Thus, a half-step is in the middle of a whole-step.
If you played the A Chromatic Scale above, you would hear that this scale sounds very dissonant, or harsh on the ears, because the intervals between each note are short half-steps.
Therefore, the ancient Europeans cut 5 of the 12 available notes down to 7, also referred to as pitches or frequencies, and created a better sounding fundamental scale that consists of just 7 notes.
By doing so, they added more whole-steps and removed a lot of half-steps - increasing the size of the intervals to make a more pleasant sounding fundamental scale to the human ear.
A Whole-Step is the distance from A to B, you would skip over the A#/Bb in the middle. A half-step is called a half-step because it’s perfectly in the center of the whole-step. A whole-step is a fundamental interval distance, just like the half-step.
This fundamental scale is called the Major Scale. The Major Scale derives the notes that belong to any given Major Key.
Major Keys are the fundamental collections of notes that sound good together. There is nothing more fundamental than a Major Key and its Major Scale.
If you've heard the phrase "you sound out-of-key", it means you sound bad because you're incorporating notes that do not belong to the fundamental key the song is written in.
In other words, the Major Scale sets the rules for what notes sound good together within any Major Key.
The A Major Scale consist of: A B C#/D E F# G#/A
(Notes with a "/" in-between are half-step intervals, otherwise it's a whole-step.)
If we step-out these notes by numbering them we get:
Step 1 = A, Step 2 = B, Step 3 = C#, Step 4 = D, Step 5 = E, Step 6 = F#, Step 7 = G#, Step 8 = A
Let's analyze the sequence of notes and their whole-step & half-step intervals.
Notice the half-steps exist between the 3rd & 4th notes and the 7th and 8th notes? This is consistent for every Major Scale and by maintaining this sequence of whole-steps & half-steps we can create a Major Scale starting from any of the 12 available pitches we learned in the A Chromatic Scale. Thus, we can create 12 Major Scales, which are 12 collections of 7 notes, that make up all 12 Major Keys.
The Major Scale Interval Sequence is: WWHWWWH
(W = Whole-step & H = Half-Step).
If you didn't understand this, here's another breakdown of the A Major Scale above: From Step 1 = A to Step 2 = B is a whole-step, from Step 2 = B to Step 3 = C# is a whole-step, from Step 3 = C# to Step 4 = D is a half-step, from Step 4 = D to Step 5 = E is a whole-step, from Step 5 = E to Step 6 = F# is a whole-step, from Step 6 = F# to Step 7 = G# is a whole-step and from Step 7 = G# to Step 8 = A is another half-step.
See, the half-steps exist between the 3rd & 4th and 7th & 8th steps.
Now, let's look at the Key of C Major.
C Major Scale: C D E/F G A B/C = Notes that exist in the Key of C Major.
(Notes with a "/" in-between are half-step intervals, otherwise it's a whole-step.)
Just like like the A Major Scale, the half-steps naturally exist between the 3rd & 4th notes and 7th & 8th notes.
Below is a list of the 12 Major Scales and Major Keys that exist, period.
There are no more keys than this, just rearrangements of these Major Scales we'll explain in upcoming articles regarding the Major Modes. Even the Natural Minor Scales are just simple re-arrangements of these fundamental Major Scales.
As you can see, every Major Key contains the Major Scale Interval Sequence (WWHWWWH) with half-step intervals between the 3rd & 4th steps and 7th & 8th steps.
The ancient Europeans simply maintained this sequence of whole-steps & half-steps starting on each of the 12 available pitches you learned from the A Chromatic Scale above.
Notice how we introduce sharps # and flats b to simply maintain the Major Scale Sequence (WWHWWWH) for every Major Scale.
The Root Note WWHWWWH starts from determines what sharps and flats exist in each Major Scale & Major Key.
Below are the 12 Major Scales that make up all 12 Major Keys. Each scale is created from doing WWHWWWH from each of the 12 individual notes created by Western Music Theory.
(Notes with a "/" in-between are half-step intervals, otherwise it's a whole-step.)
1) Ab Major Scale: Ab Bb C/Db E F G/Ab = Every note that exist in Ab Major
2) A Major Scale: A B C#/D E F# G#/A = Every note that exist in A Major
3) Bb Major Scale: Bb C D/Eb G A B/C = Every note that exist in Bb Major
4) B Major Scale: B C# D#/E F# G# A#/B = Every note that exist in B Major
5) C Major Scale: C D E/F G A B/C = Every note that exist in C Major
6) Db Major Scale: Db Eb F/Gb Ab Bb C/Db = Every note that exist in Db Major
7) D Major Scale: D E F#/G A B C#/D = Every note that exist in D Major
8) Eb Major Scale: Eb F G/Ab Bb C D/Eb = Every note that exist in Eb Major
9) E Major Scale: E F# G#/A B C# D#/E = Every note that exist in E Major
10) F Major Scale: F, G, A/Bb, C D E/F = Every note that exist in F Major
11) Gb Major Scale: Gb Ab Bb/B Db Eb F/Gb = Every note that exist in Gb Major
12) G Major Scale: G A B/C D E F#/G = Every note that exist in G Major