Music Theory: The 12 Notes...
The 12


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



A
A#
B
C
C#
D
D#
E
F
F#
G
G#
 
Geeks Note: The information in this page is not necessary for you to be able to play the guitar. However, it will help you understand how we tune guitars, it will help you understand why there are only 12 notes and it will help you understand why the notes repeat where they repeat.


Learning Objectives
By the end of this lesson, here is what you should have learned:
  1. Why there are twelve notes in the musical scale.
  2. What a Chromatic Scale is.
  3. What "Standard Tuning" or "A440" tuning is.
  4. The mathematical and physical difference between notes in different Octaves.
  5. Why it is imperative you put your finger as close to the Fret as possible.


No matter what musical instrument you play, there are only twelve (12) notes that you can choose from. It is the combination and relations of these notes that make "music". These twelve notes, in order, are called the Chromatic Scale and if you play the notes or any portion of the scale in order (i.e. playing C,D,E,F) then you are said to be playing a Chromatic Progression.

When man first experimented with and started playing music, the system was called "Just Intonation". While this sufficed for simple intruments as music became more complex, the disonance became more pronounced and music just sounded bad. In the late 1500's, the "Equal Temperment" system came into being. It is the Equal Temperment system that you and I play with today. Most western music, the stuff you and I play on the guitar utilize the "12 Tone Equal Temperment" scale.

What makes the notes we play sound good is the consonance of those notes (as opposed to the dissonance). The 12 Tone Equal Temperment scale is the only Equal Temperment scale that contains all seven intervals and more consonant intervals than disonant intervals.

What makes the notes what they are? It is the ratio of the notes pitch to the first note of the scale. In our case, A is the first note.

Before I go on, you will have heard the term "tuned to 440" or "tuned to A440". What this means is that the A note we play is tuned to 440Hz (speed at which the note vibrates or oscillates). It is a fact that Human perception of pitch is logarithmic. This means that humans perceive equivalent pitches when they are separated by a factor of two. Therefore, humans would recognize the resonance of sound pitches oscillating at 220Hz, 440Hz and 880Hz (as an example).

12 Note Chromatic Scale Relative Ratios
# Semi TonesInterval Name2RatioEqual Temperment
0Unison20/12=1.000
1Minor 2nd21/12=1.059
2Major 2nd22/12=1.122
3Minor 3rd23/12=1.189
4Major 3rd24/12=1.260
5Perfect 4th25/12=1.335
6Tritone26/12=1.414
7Perfect 5th27/12=1.498
8Minor 6th28/12=1.587
9Major 6th29/12=1.682
10Minor 7th210/12=1.782
11Major 7th211/12=1.888
12Octave212/12=2.000
Now what I said about western tuning standard being A440 because we tune A to 440Hz. Look at your guitar. Play the open A string. That is 440 Hz. If you play the low E string 5th fret, that is the exact same note or the same Octave as the open A string. They both oscillate at 440Hz. If you play the twelfth fret of the A string, also an A note, that is an Octave higher and is vibrating at 880 Hz. Play the A note on the D string (7th fret) and it is oscillating at 1760 Hz (a factor of 2 above the preceeding octave).

Okay, so in the Equal Temperment scale the first note is a logarithmic progression (up or down) from 440Hz and we can move up and down octaves from that position based on ratios. Yes, the notes of the Chromatic scale are based on ratios that are relative to the first note. The exact formulas are shown in the table above.

For example, the 7th tone, the perfect 5th is obtained by multiplying the 12th root of 2 by itself, seven times. This gives us a ratio of 1.498. This means that a perfect fifth above A (the E note) is vibrating/oscilating at 659Hz. If you looked at the A note an Octave BELOW A440, then that A notes perfect 5th (also the E note) would be vibrating/oscilating at 330Hz.

Now, remember people (music teachers mostly) whining and complaining that you aren't playing the note close enough to the fret? If you play the note with your finger on the string right against the fret, you are applying the tension needed for that string to resonate at the proper frequency to form the note relative to it's ratio of vibration compared to the Unison. If you fret a string way back from the fret, you will change how fast that string vibrates (albeit slightly) and you won't be playing the exact note (not to mention the string buzz).










© Aaron Gallagher