When two or more pitches sound simultaneously, they are said to be in harmony. Within an octave there are twelve possible two-note combinations within the twelve-note chromatic scale; thirteen, if we include the Unison (which is technically not a harmony, but two instances of the exact same note.) These combinations are called dyads. The dyads are formed from the harmonics that arise organically in the Harmonic Series, and are expressed as ratios.
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, with one at each end. In a casting, the dyad at the top of the card is the one 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; in the chromatic scale, tritones are at the center of an octave, and inverting one creates a mirror image of itself.)
A Note on Tuning: On the following pages, the ratios listed under each of the Harmonies correspond with their first appearance in the Harmonic Series, as shown on the diagrams running down the right of each page. The actual ratios heard in a Muzoracle casting, however, vary depending on which Solfège Die the Harmony appears above or under. An understanding of the pages under Mechanics to Metaphor, in the Table of Contents at left, will lead you to the hows and whys.