Our ears are very sensitive to sound. When regularly repeating sound waves occur around our ears, we perceive pitch. These sound waves are regularly repeated fluctuations of air pressure. For example, when a guitar string is set into motion by the pick of a guitar player, the string moves back and forth hundreds of times per second. With the aid of the guitar body or a guitar amplifier this motion is converted into sound waves that our ears perceive. The shorter or tighter the string, the faster it vibrates and the higher the pitch we perceive. The longer or looser the string, the slower it vibrates and the lower the pitch is that we perceive.
The rate of vibration is called frequency. For example, if a string vibrates at a rate of 110 times per second, its frequency is 110, and we perceive the pitch of A2 (the second A on the piano or the 5th string of the guitar). When this string is held down at the 12th fret, the vibrating length is one half of the original length and the frequency is doubled, 220. This ratio of 2:1 is called the interval 1) the distance between two pitches 2) two notes combine to form an interval of the octave an interval with the same note names but twelve half steps higher or lower.
Our notational system divides the octave into twelve parts. There are twelve notes within the octave and the distance between adjacent notes is called a half step a semitone, the octave is divided into twelve half steps or semitone one half of a tone, a half step. Two half steps make a whole step an interval of two half steps, a tone. On the guitar there are twelve frets within the octave. The thirteenth note is always one octave above the starting pitch.
A2 - Guitar 5th string
1 2 3 4 5 6 7 8 9 10 11 12 A3
Moving from the open string to the first fret (1 to 2 above) is a half step. There are twelve half steps in the octave.
You can also see this on the piano. There are twelve keys within an octave: count twelve half steps on the keyboard between C4 and C5:
A half step is the smallest interval and occurs between adjacent notes. Scales can be built starting on any note. Half steps and whole steps are the units of measurement used to build tetrachords and scales.
see also: Tetrachord and Scale, Interval Naming