Sound, Tones and Notes
The guitar is a musical instrument, so its goal in life is to make music. Music is the arrangement of tones into patterns that the human brain finds pleasing. Let's start at the beginning with the question, "What is sound?" in order to better understand music.
Sound is any change in air pressure that our ears are able to detect and process. For our ears to detect it, a change in pressure has to be strong enough to move the eardrums in our ears. The more strongly the pressure changes, the "louder" we perceive the sound to be.
For our ears to be able to perceive a sound, the sound has to occur in a certain frequency range. For most people, the range of perceivable sounds falls between 20 hertz (oscillations per second) and 15,000 hertz (oscillations per second). We cannot hear sounds below 20 hertz and above 15,000 hertz.
A tone is a sound that repeats at a certain, specific frequency. This 440 hertz tone can be pictured as a sine wave, like this:
A tone is made up of one frequency or very small number of related frequencies. The alternative to a tone is a combination of hundreds or thousands of random frequencies. We refer to these random-combination sounds as noise. When you hear the sound of a river, or the sound of wind rustling through leaves, or the sound of paper tearing, or the sound made when you tune your TV to a non-existent station, you are hearing noise.
Click here (and at the dialog select, "Open") to hear noise. [This is an unpleasant
sound - turn down your speakers before playing it.]
A musical note is a tone. However, a musical note is a tone that comes
from a small collection of tones that are pleasing to the human brain when used
together. For example, you might pick a set of tones at the following frequencies:
Click here (and at the dialog select, "Open") to hear the major scale.
- 264 hertz, C, do, multiply by 9/8 to get:
- 297 hertz, D, re, multiply by 10/9 to get:
- 330 hertz, E, me, multiply by 16/15 to get:
- 352 hertz, F, fa, multiply by 9/8 to get:
- 396 hertz, G, so, multiply by 10/9 to get:
- 440 hertz, A, la, multiply by 9/8 to get:
- 495 hertz, B, ti, multiply by 16/15 to get:
- 528 hertz, C, do, multiply by 9/8 to get... (and the sequence repeats)
One thing to notice is that the two C notes are separated by exactly a factor of two. 264 is one half of 528. This is the basis of octaves. Any note's frequency can be doubled to "go up an octave", and any note's frequency can be halved to "go down an octave".
You may have heard of "sharps" and "flats". Where do they come from? The scale of tones shown above
is "in the key of C" because the fractions were applied with C as the starting note. If we were to start
the fractions at D, with a frequency of 297, then we would be "tuned to the key of D" and
the frequencies would look like this:
You can see that, with all of these mergings of keys, the major scale can leave you with some pretty arbitrary decisions to make when you tune an instrument. For example, you can tune the major notes to the key of C, and then the sharps for F and C to the key of D, and the sharps for D and G to..., or you could..., or.... It can get pretty messy.
Therefore, over time, most
of the musical world came to agree on a scale called the tempered scale, with the A note set at 440
hertz and all of the other notes tuned off of that. In the tempered scale, all of the notes are offset by
the 12th root of 2 (roughly 1.0595) instead of the fractions we saw above. That is, if you take any note's
frequency and multiply it by 1.0595, you get the frequency for the next note.
Here are three octaves of the tempered
You can see in this diagram that there are 72 fret positions, but the table above shows only 37 unique notes. Therefore you have multiple ways to finger identical notes on a guitar. This fact is frequently used to get all of a guitar's strings tuned. For example, you can tune A on the first string (5th fret) to 440 hertz. Then it is a fact that E at the 5th fret on the second string is the same as the open first string, so you you match those two notes up by tuning the second string. Similarly:
- The 4th fret on the third string (B) is the same as the B on the open second string.
- The 5th fret on the fourth string (G) is the same as the G on the open third string.
- The 5th fret on the fifth string (D) is the same as the D on the open fourth string.
- The 5th fret on the sixth string (A) is the same as the A on the open fifth string.
[Fun fact: a piano has 88 keys stretching through more than 7 octaves. The lowest note on a piano vibrates at 27.5 hertz and the highest vibrates at 4,186 hertz.]