The overtone series affects the level of consonance and dissonance. When a note sounds it reverberates at several higher inaudible pitches, creating overtones. We don't hear the pitches in the series of overtones, but they do exist. When a note doesn't match the notes in the overtone series, we perceive it as dissonance. Use a piano to experience overtones. Depress the notes C-E-G on the piano gently, without making sound. Forcefully hit the C an octave lower. Listen, and you will hear the depressed notes sound because they are part of the overtone series. Try holding down an F-sharp, and you will not hear this effect.
Chordal dissonance in general, when not viewed from the standpoint of counterpoint, refers to the degree of dissonance within a chord. For instance, we classify major chords as consonant chords because they fit naturally with the overtone series. The C-E-G of a C major chord occurs within the first two octaves of the overtone series. Any chords that do not fit within the overtone series have a degree of dissonance. The more notes that do not fit the overtone series, the more chordal dissonance exists.
16th and 18th century counterpoint deals with a very specific definition of chordal dissonance. Rather than using the traditional definition of dissonant chords, in counterpoint, chordal dissonance refers to the relationship between intervals. Dissonant intervals include a minor seventh, major seventh, the tritone, and major and minor seconds. Any time you have one of these intervals in counterpoint, you must resolve them to a tonic chord. To determine intervals, use the chromatic scale and count the notes between the two pitches. A minor second has one half step, a major second has two, the tritone has seven, while the minor and major sevenths have 10 and 11 half steps, respectively.
Traditional triads provide a prime example of chordal dissonance when used in a modern sense. As stated earlier, the major chord does not have any dissonance. The minor chord includes a third, which is flat from the major chord, so it has more dissonance than a major chord. Next in line falls the augmented chord, which has the most chordal dissonance, since the third does not fit the overtone series and the fifth gets augmented, making it aurally a minor sixth. The diminished chord has the most dissonance since the third and the fifth of the chord are flat, creating a tritone between the first and fifth note of the chord.