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 (or if not pleasing, then at least intriguing). In order to better understand music, let's start at the beginning: "What is sound?"
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 (Hz, oscillations per second) and 15,000 Hz. We cannot hear sounds below 20 Hertz or above 15,000 Hertz.
A tone is a sound that repeats at a certain specific frequency.
This 440-Hz tone can be pictured as a sine wave, like this:
- Click here to hear a 440-Hz tone. (At the dialog select, click "Open.")
A tone is made up of one frequency or a 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 nonexistent station, you are hearing noise.
Noise not only sounds random but also presents itself graphically as randomness:
- Click here to hear noise. (At the dialog select, click "Open")
Note: This is an unpleasant sound -- turn down your speakers before playing it.
A musical note is a tone. However, a musical-note tone 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:
This particular collection of tones is known as the major scale. Each tone in the scale is multiplied by a certain fraction to come up with the next tone in the scale. Here's how the major scale works:
- 264 Hz
- 297 Hz
- 330 Hz
- 352 Hz
- 396 Hz
- 440 Hz
- 495 Hz
- 528 Hz
Why are these particular fractions chosen in the major scale? Simply because they sound pleasing. Listen:
- 264 Hz * 9/8 = 297 Hz
- 297 Hz * 10/9 = 330 Hz
- 330 Hz * 16/15 = 352 Hz
- 352 Hz * 9/8 = 396 Hz
- 396 Hz * 10/9 = 440 Hz
- 440 Hz * 9/8 = 495 Hz
- 495 Hz * 16/15 = 528 Hz
These particular tones have been given letter names, and also word names, like this:
- Click here to hear the major scale. (At the dialog select, click "Open.")
And the sequence repeats.
- 264 Hz - C, do (multiply by 9/8 to get:)
- 297 Hz - D, re (multiply by 10/9 to get:)
- 330 Hz - E, me (multiply by 16/15 to get:)
- 352 Hz - F, fa (multiply by 9/8 to get:)
- 396 Hz - G, so (multiply by 10/9 to get:)
- 440 Hz - A, la (multiply by 9/8 to get:)
- 495 Hz - B, ti (multiply by 16/15 to get:)
- 528 Hz - C, do (multiply by 9/8 to get:)
The names are totally arbitrary, as with the fractions. It just turns out that they have a pleasing sound to human ears.
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:
And the sequence repeats.
- 297 Hz, D, do (multiply by 9/8 to get:)
- 334.1 Hz, E, re (multiply by 10/9 to get:)
- 371.3 Hz, F, me (multiply by 16/15 to get:)
- 396 Hz, G, fa (multiply by 9/8 to get:)
- 445.5 Hz, A, so (multiply by 10/9 to get:)
- 495 Hz, B, la (multiply by 9/8 to get:)
- 556.9 Hz, C, ti (multiply by 16/15 to get:)
- 594 Hz, D, do (multiply by 9/8 to get:)
The notes at 297 Hz (D), 396 Hz (G) and 495 Hz (B) in the key of D match the same notes in the key of C exactly. The E note in the key of D (at 334.1 Hz) is pretty close to the E note in the key of C (330 Hz). The same applies for the A note. F and C, however, are distinct in the two keys. F and C in the key of D are therefore referred to as F# (F sharp) and C# (C sharp) in the key of C. (Note that F sharp is also known as G flat, and C sharp is also known as D flat.) If you apply the fractions to several different keys, merge together all the identical and pretty-close notes and then look at the unique sharps that fall out, you realize that you need A#, C#, D#, F# and G# to handle all the keys.
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... 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 Hz 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 scale:
As you can see in this table, we have finally been able to get the discussion back to guitars! This is how a guitar is tuned. A guitar with 12 clear frets has a range of three octaves, as shown above. The open sixth string is the lowest note, and the 12th fret on the first string is the highest. Here is the actual layout of all of the notes on a guitar.
- 82.4 E - open 6th string
- 87.3 F
- 92.5 F#
- 98.0 G
- 103.8 G#
- 110.0 A - open 5th string
- 116.5 A#
- 123.5 B
- 130.8 C
- 138.6 C#
- 146.8 D - open 4th string
- 155.6 D#
- 164.8 E
- 174.6 F
- 185.0 F#
- 196.0 G - open 3rd string
- 207.6 G#
- 220.0 A
- 233.1 A#
- 246.9 B - open 2nd string
- 261.6 C - "middle C"
- 277.2 C#
- 293.6 D
- 311.1 D#
- 329.6 E - open 1st string
- 349.2 F
- 370.0 F#
- 392.0 G
- 415.3 G#
- 440.0 A - 5th fret on 1st string
- 466.1 A#
- 493.8 B
- 523.2 C
- 554.3 C#
- 587.3 D
- 622.2 D#
- 659.2 E - 12th fret on 1st string
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 Hz. Then you know that E at the 5th fret on the second string is the same as the open first string, so you match those two notes up by tuning the second string. Similarly:
Once you have all of the strings on a guitar perfectly tuned, using 440 Hz for A as the primary note, then the guitar will have notes with the frequencies shown in the table above, and it is said to be tuned to "concert pitch."
- The 4th fret on the 3rd string (B) is the same as the B on the open 2nd string.
- The 5th fret on the 4th string (G) is the same as the G on the open 3rd string.
- The 5th fret on the 5th string (D) is the same as the D on the open 4th string.
- The 5th fret on the 6th string (A) is the same as the A on the open 5th string.