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Fig.1. Simply put, an Interval is the difference in Pitch between 2 notes.

4 Types of Intervals:

-When you change to the next fret higher (ascending) OR the next fret lower (descending) the Interval is a Half Step.
-A two fret change is an interval of a Whole Step.

-If two notes are sounded one after the other the interval is Melodic.
-If two notes are sounded at the same time the interval is Harmonic.

Using the Half & Whole Steps, Intervals are used to derive the “Major Scale Intervals” from the Chromatic 12 note Octave.
-The Major Scale Intervals are: W-W-H-W-W-W-H  (where W=Whole and H=Half).
-This is the Do-Re-Me-Fa-So-La-Si-Do we all learned in grade schoool.
Here is an example in the Key of C:

Fig.2. Major Scale Intervals for the Key of C.

-Intervals are also named by Degree.  In Fig.2. above, if C is the 1st Degree then D is the 2nd and E is the 3rd etc. up to B which is the 7th (see Interval chart below).  These are used in Chord naming. For example: C7 Chord. Or the Power 5th Chord which contains the Root and the 5th.

The Interval Chart

Fig.3. The Names and Abbreviations for Half Step Intervals (the Chromatic Scale)
& Major Scale Degrees.
Note: The Major Scale Degrees follow the W-W-H-W-W-W-H “Major Scale Pattern” 

-Any Interval within the Octave (1st through 7th) is known as a Simple Interval.
-Intervals outside the Octave (above or below) are known as Compound Intervals.

-Intervals can move down the scale also.  If so it is Lowered.  From Fig.2. the Lower Second of C is B.

-Furthermore, An Interval complements another if their sum is 8 (one octave).

Naming Convention of the Two Categories of Intervals:

-If an Interval is described with two words then the Interval is in Half Steps (the Chromatic scale) &
If the Interval is described in one word then the Interval is in Major scale degrees (W-W-H-W-W-W-H).

FOR EXAMPLE: the Second of C is D (refers to the Major Scale Interval) &
the Major Second of C is D (refers to the Half-Step Interval) while the Minor Second of C is C#.
Use the above Chart for reference.

Of Course this applies to any Key.  “The Key of C” was randomly chosen for the above example.

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