Since intervals are easy to recognize in Clairnote DN, it is easy to see the interval patterns that make up chords and to tell one type of chord from another.
The most basic chords are called triads and contain three notes. In their simplest form, known as "root position" (shown above), they are two thirds stacked on top of each other. A major triad is a major third (4 semitones) with a minor third (3 semitones) on top of it. In a minor triad it is the opposite, a minor third with a major third on top of it. In both cases the highest note, known as the fifth of the chord, is a perfect fifth (7 semitones) above the lowest note, known as the root note. The middle note is known as the third of the chord since it is a third above the root note.
These differences between chords are easy to see in Clairnote DN because the interval patterns that make up chords are readily apparent. In traditional notation all thirds look alike so major and minor triads look alike and it is difficult to determine which are major and which are minor.
Major Triads: Root Position, First Inversion, Second Inversion
In addition to root position, triads can appear in two other positions known as first inversion and second inversion. Moving the lowest note up an octave will change a triad from root position to first inversion. Doing it again will change it to second inversion.
Notes an octave apart look the same in Clairnote DN which makes it easy to see these patterns and recognize that the notes are the same three notes, just placed in different octaves. In traditional notation notes an octave apart do not resemble each other, making this more difficult.
Minor Triads: Root Position, First Inversion, Second Inversion
Since the notes in the inverted chords remain the same (except for their octave) the chords are still the same chords (e.g. still a "C major" chord). Only their position has changed.
The notes do not necessarily have to be in the exact positions shown in these illustrations. For example, some could be placed two or more octaves higher rather than just one. A triad's position is determined solely by which note is lowest. If the root note is the lowest then the chord is in root position. If the the third of the chord is lowest, then it is in first inversion. If the fifth of the chord is lowest, then it is in second inversion.
The name of a chord is based on the name of its root note, regardless of its position. To determine the name and position of a chord, mentally transpose the notes into root position (a stack of thirds) to identify which note is the root and which are the third and fifth of the chord.
More Complex Chords
Many more types of chords can be built by altering or adding notes to the basic triads. The following illustration shows 46 different variations on a C chord, many of which are used in jazz music. They are shown in Clairnote DN and in traditional music notation for comparison. (Thanks to Pierre Schneidy for sharing the original file illustrating these chords with the LilyPond user list.) Unlike the images above, which omit accidental signs for the sake of explanation, this illustration includes Clairnote DN's accidental signs.
It is easier to see the interval structures of these chords in Clairnote DN, than it is in traditional notation, which makes it easier to understand the chords and tell them apart.
You can also listen to what these chords sound like and/or check out a PDF version.