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Piano chord theory is the same as guitar chord theory, you're just dealing with a different instrument.
Visit C Major Chord and Chord Theory to get a strong foundation of basic music theory.
It's very similar to what I will lay out here. Music theory is the same across all instruments. You can discover easy song chords and a variety of piano chords that can spark some songwriting!
The easiest place to begin is in the key of C because you're dealing with all white keys and it's easy to see how chords are built.
You create triads (three note chords) by skipping letters or numbers, however you want to think of it. Use the images above to make sense of what's below.
1) In piano chord theory and all music we use roman numerals to label chord names in a key: I II III IV V VI VII (or I ii iii IV V vi vii). Often the capital numerals indicate a major chord and the lower case numerals indicate a minor chord.
2) The distance in semitones (or half steps) from the 1st note to the 3rd note in the chord determines the quality of the chord (ie., major or minor). 4 semitones from the root is a major 3rd. 3 semitones from the root is a minor 3rd.
3) The distance in semitones (or half steps) from the 1st note to the 5th note in the chord determines if it is diminished or not. Chords I-vi have a perfect 5th or a distance of 7 semitones from 1st note to 5th note. The VII chord has a diminished 5th or a distance of 6 semitones between notes 1 and 5.
Here are the 7 diatonic chords in C Major. They are built off the 7 notes in a C Major scale. This pattern is the same for all piano chord theory, no matter what key you're in.
C-E-G (C Major triad)
1-3-5 (This is the I (one) chord in C major)
From C to E is 4 semitones, that's why it is a major chord
D-F-A (D minor triad)
2-4-6 (This is the II (two) chord in C major)
From D to F is 3 semitones, that's why it is a minor chord
E-G-B (E minor triad)
3-5-7 (This is the III (three) chord in C major)
From E to G is 3 semitones, that's why it is a minor chord
F-A-C (F Major triad)
4-6-1 (This is the IV (four) chord in C major)
From F to A is 4 semitones, that's why it is a major chord
G-B-D (G Major triad)
5-7-2 (This is the V (five) chord in C major)
From G to B is 4 semitones, that's why it is a major chord
A-C-E (A minor triad)
6-1-3 (This is the VI (six) chord in C major)
From A to C is 3 semitones, that's why it is a minor chord
B-D-F (B diminished triad)
7-2-4 (This is the VII (seven) chord in C major)
From B to D is 3 semitones and from B to F is 6 semitones making this a diminished chord
*Pick a key and follow the major scale pattern of WWHWWWH (whole step, whole step, half step, whole step, whole step, whole step, half step). This is how black keys (sharps and flats) are forced into the equation.
For deep analysis visit music theory...