In ear training, we call an interval “harmonic” if its two tones are played simultaneously.
One way to hear harmonic intervals successfully is to imagine them as parts of chords that commonly appear in diatonic harmony.
We have already learned that all the simple intervals may be found between various tones of the diatonic scale. By extension, we can find all the simply intervals through commonly used chords.
These piano workouts stress the intervallic properties of familiar chords. Practice them on the piano and sing through the tones melodically for additional familiarization.
The perfect consonances (perfect fourths, perfect fifths, perfect octaves) and the imperfect consonances (major thirds, minor sixths, minor thirds, major sixths) can all be found within the tones of the major triad and its inversions.
The major-minor 7 chord (V7 in diatonic harmony) contains two dissonances: the diminished fifth and the minor seventh. In inversions, we can hear the major second (which is the inversion of the minor seventh) and the augmented fourth (which is the inversion of the diminished fifth).
The major-major 7 chord (MM7) provides the extreme dissonance of the major seventh and its inverse, the minor second. (Notice, too, the way perfect consonances appear in this workout.)