Octaves and Intervals
When one note vibrates at a frequency of double or half of another, we say that these two notes are octaves. These notes sound very similar to our ears, almost identical in fact.
Try it. Pick the 8th string without the bar; this is an E note. It vibrates at 164.81 hertz. Then pick the 8th string again with the bar at the 12th fret. This is an E note, one octave above the last E note. It vibrates at 329.63. It vibrates exactly twice as fast as the first E: 164.81 x 2 = 329.63. These are E octaves.
There's another way to play E octaves. Play the 8th string with no bar. Then play the 4th string with no bar. These are the same two notes. Play them together, then separately. They sound similar, don't they?
Now play the other strings with the 8th string E. First try string 7 and string 8 together. Doesn't sound too pleasant, does it? Then try string 6 and string 8. That sounds better, but still not like the octave interval.
Then try combining the other strings with string 8. They don't sound as similar, do they? That's because they are not octaves. Octaves are more closely related harmonically than any other notes and this is because their frequencies are so closely related mathematically.
A scale is any set of notes between two octaves. The most common scales are comprised of 7 (heptatonic), 5 (pentatonic), or 6 (hexatonic) notes between the octaves.
Tones and Semitones
In European and American musical culture, each octave is divided into twelve semitones. These are all the white and black keys on the piano. On the guitar or steel guitar, each fret makes up one semitone. Every two frets make a tone (also called a whole tone).
All scales are different combinations of these twelve semitones.
Each one of the twelve semitones has a name based on its distance from the root note.
Intervals are spaces between notes. They are measured in semitones and each interval has a name. For example, the interval of one semitone is called a minor 2nd (m2). The interval of two semitones (one tone), is a Major second (M2). Three semitones is a minor third (m3).
Here are all the intervals with their symbols and their names:
If we continue into the next octave, we will get the following intervals:
Sometimes musicians use flat (b) or sharp (#) symbols to talk about intervals. For example you will often see me call a m3 interval a b3 interval. My meaning is the same only the terminology is different.