When you want to harmonize a hymn in four parts (soprano, alto, tenor, and bass), one of the main things you have to discover is the 3 main chords of any given key or tonality: the tonic (notated T or I in the major key or i in the minor), the subdominant (S or IV in the major and iv in the minor), and the dominant (notated D or V - most of the times it will be a major chord).
These are three-note chords which consist of two thirds built on top of another (like the C major chord C-E-G is built from two thirds, one major (C-E) and another minor (E-G). The distance between the two outer notes is a perfect fifth.
So T, S, and D are the main chords that many other are derived from. Here we have to remember the basics of music theory for a moment. You probably know that any major or minor scale has 7 scale degrees.
The tonic is built on the 1st scale degree: I-III-V (C-E-G in C major). The dominant - on the 5th scale degree: V-VII-II (G-B-D in C major). And the subdominant is built on the 4th scale degree: IV-VI-I (F-A-C in C major).
If you keep these scale degrees in mind, you can easily find out these main chords in your hymn melody. The two remaining difficulties are:
1) Discovering the main key of the hymn.
2) Noticing any modulations (excursions to different keys) within the hymn.
So open any familiar hymn from your hymnal and try to put these tips in practice and notate T, S, or D below each note of the melody with pencil. Remember, sometimes hymns have eighth notes from which only the first one is a chordal note.
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