Here is part of a packet I sent home to parents of new students this year:
Intervals
First of all, an interval is defined as a measure of distance between two pitches (notes, as in higher or lower notes). Two carpenters communicate to each other about how short or long they want a board to be cut by giving a measurement in inches (or feet and inches). The tool the carpenter uses for this is his/her tape measure. In music, the tape measure for telling the distances between pitches is called an interval.
Simple intervals
Half Steps
The smallest unit of distance in Western music is the half step. On a piano keyboard, a half step is the very next key. Usually this will involve going from a white key to a black key or visa versa. Occasionally, two white keys do not have a black key between them. Those two white keys are a half step apart. Frets on a guitar or bass guitar are in half steps.
Whole Steps
The next unit is the whole step which consists of two half steps. On a piano keyboard, the whole step skips one key and goes to the very next key after. In most cases, a white key will skip a black key and go to a white key, or a black key will skip a white key and go to a black key. The exceptions are in cases where two white keys have no black key in between. Then, a white skips a white key and goes to a black key, or a black key skips white and goes to another white key.
Octaves
The third unit is the octave. An octave is the next note that has the same name. In other words, an octave from F# is F#. On a piano keyboard, the octave is the next note that is found in the same pattern. In other words if the first note is the middle black key of the three black keys, then an octave would be the next middle note in the three black keys. On a guitar, if one plays an open string, then stops the string at the double dot fret it will form an octave.
Intervals of the octave (formal names)
These three units help describe other units in music. Within the octave, there are 12 half steps. Each half step has a name. I am going to make a list of those names below using abbreviations. "P" will stand for "perfect", "M" will stand for "major", "m" will stand for "minor", "U" will stand for "unison", "8" will be for "octave", and "TT" will stand for "tritone."
These intervals will be listed beside the number of half steps in the particular interval. Of course, the octave will be listed beside the number "12" since there are twelve half steps in an octave. The octave is called a "perfect octave." The perfect intervals are the only ones of their kind. The perfect octave is the only octave and the only representation for the number "8." A perfect fourth is the only interval with the number "4" in it. All other intervals have both a "major" and a "minor" interval. There are two intervals with "3" in them; the major third, and the minor third. Notice that the number "3" represents the word "third." The only interval that is neither a perfect, major or minor interval is the one called the "tritone."
The tritone has six half steps and falls in the very center of an octave. During Medieval times, the Roman church excommunicated anyone who sang or played a tritone because it was thought to be the "devil in music." I tell the children that no one believes the tritone to be evil today; and that much church music of all denominations uses it in many forms. The intervals of the octave are symmetrical on either side of the tritone. The perfect unison and perfect octaves are on the outsides, while the perfect fourth and perfect fifth are inside on either side of the tritone. A perfect unison is when the same note is played twice or when two or more voices or instruments sing or play the same note. A perfect unison has "0" half steps because it stays on the same note. Here is the list of intervals in the octave, and their corresponding half steps:
0- PU
1- m2
2- M2
3- m3
4- M3
5- P4
6- TT
7- P5
8- m6
9- M6
10- m7
11- M7
12- P8
Please point out that there are two sets of major-minor intervals between two perfect intervals. NOTE: "Minor" (m) always comes before "major" (M). Now that you have the list of intervals with half steps, the list can be used as a chart. If one wants to know how many half steps are in a minor sixth (m6) one can look at the chart and see the number "8" by "m6" and know that a minor sixth has eight half steps. If one counts five half steps, one can look at the chart and see that five half steps is a perfect fourth (P4).