Harmony is when more than two or more notes are struck together at the same time.  Chords usually have three notes or more.  I like to look at chords in their most basic three note structure, triads.   To begin to understand chords let’s look at the “harmonized” major scale. In harmonizing the major scale you take groups of three notes by taking a succession of thirds, for example for the triad built on the C, you take the C, the E, and the G.  Let’s look at the chart below.

The Harmonized Major Scale

Let's also view this chart as scale steps:

The next step in analysis of triads is to determine what kind of triad it is. There are four basic triads major, minor, diminished, and augmented.  Since all triads consists of two ‘stacked thirds” determining the relationship of these notes is how to determine the quality of the triad.

There are two ways to analyze the triads, one is relationship to the two notes back to the root of the chord and the other is the notes relationship to each other.  Using the first method with the C triad you would take the relationship of the C to the E interval which is a major third, and the relationship of the C to the G interval which is a perfect fifth.  This is a major triad.  Major triads have the tonic, a major third and a perfect fifth.

Using the second method we would first analyze the root to the third, and then analyze the distance from the third to the fifth (or second two intervals).  In a  C major triad we see that  the distance of the first two notes is a major third and the distance between the second two intervals is a minor third.  So major triads consist of the first two intervals a major third from each other and the second two intervals a minor third a way from each other.

Major are triads above are indicated with the capital roman numerals while minor triads are indicated by the lower case roman numerals.  The diminished triad usually has a small circle from the lower case roman numeral, while the augmented triad would have a small plus sign.  Using the above method see if you can determine the relationships of the minor (ii, iii, vi) and diminished (vii dim) triads.

Let's also view this chart as scale steps:

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