When two or more pitches are sounded simultaneously, they are said to be in harmony. There are two kinds of harmonies expressed in the Muzoracle deck: Dyads and Triads. Their definitions combine with those of the Suits, together forming the basis of the individual Harmony Cards.
Dyads. Within an octave -- a frequency and another frequency at twice its rate -- there are twelve possible two-note combinations within the twelve-note chromatic scale; thirteen, if we include the Unison, which is the exact same note played twice. These combinations are called dyads. They are defined by the frequency relationships between their notes, expressed as a ratio.
The 13 Dyads and their Ratios as they arise in the Harmonic Series
Inversions. If we double the frequency of the bottom note of a dyad -- raise it an octave -- or cut the frequency of the top note in half -- lower it an octave -- we obtain a new dyad, which is an inversion of the former. A Perfect Fifth inverted, for example, is a Perfect Fourth, and vice versa; a Major Third inverted is a Minor Sixth, and vice versa.
The two dyads given on each Dyad Card are inversions of one another, one at each end of the card; in a casting, which end of the card lands up determines which of the two dyads is in play. In each of the five suits of the Muzoracle, there are seven Dyad Cards, with the thirteen dyads distributed among them. (Note that the Tritone cards are the same on either end. The interval of a Tritone falls at the exact center of an octave; inverting a Tritone creates another Tritone, a mirror image of the first.)
Dyads and their Inversions as they appear on the Harmony Cards
Major Triads. In addition to the Dyad Cards, there is one Major Triad Card per suit, each determinable by its three suit icons and no text.