The cantus firmus, literally 'fixed song,' is a pre-existing melody that serves as the structural foundation upon which additional voices are composed in a polyphonic musical work. In medieval and Renaissance counterpoint, the cantus firmus provided a slow-moving, stable melodic line, typically in long note values, around which one or more faster-moving voices wove their melodic lines in consonant and dissonant counterpoint. The technique was fundamental to sacred music for centuries: Gregorian chant melodies served as cantus firmus for the great polyphonic masses of the fifteenth and sixteenth centuries. The term translates the foundational role of this voice: it is the 'fixed' element against which the 'mobile' elements are set in motion.

In the Atalanta Fugiens, the cantus firmus takes on an extraordinary double function, serving simultaneously as a musical and an alchemical structural element. Each of the fifty emblems is accompanied by a three-voice fugue composed by Maier himself. The subtitle of the work describes these as 'fifty musical fugues for three voices, of which two correspond to a simple melody, which is suited to be sung in strophes of two lines.' The simple melody is the cantus firmus: the stable, fixed voice around which the two fleeing and pursuing voices weave their canonic lines. In Maier's musical structure, one voice flees (representing Atalanta), another pursues (representing Hippomenes), and the third voice, the cantus firmus, stands still, representing the golden apple that brings the chase to rest.

Maier makes this allegorical identification explicit in his preface to the reader. De Jong quotes the crucial passage: 'Just as this Atalanta flees, one voice flees time and again from the other one and the other voice pursues, like Hippomenes. In the third voice they are brought to a standstill; that third voice is simple and homogeneous in its value, like the golden apple.' The cantus firmus thus functions as the resolution principle in the musical structure, the stable element that harmonizes the volatile dynamic of pursuit and flight. In alchemical terms, it corresponds to the fixed principle (the philosophical gold, the philosopher's stone) that reconciles the opposition between volatile mercury (the fleeing voice) and active sulphur (the pursuing voice).

De Jong connects Maier's musical structure to the deep relationship between alchemy and music that had been expressed in the writings of Zosimos and Stephanos and that received its most elaborate visual expression in Heinrich Khunrath's Amphitheatrum Sapientiae Aeternae (1598). In Khunrath's famous engraving, a table of musical instruments occupies the center foreground, forming the connecting link between the oratorium (prayer) and the laboratorium (laboratory work). Maier's fugues literalize this connection, making audible music an integral component of the alchemical work rather than merely an accompaniment.

Wescott's modal analysis of Maier's fugues demonstrates that the musical structures encode alchemical correspondences beyond the simple pursuit-and-rest allegory. The modes, intervals, and voice-leading patterns of individual fugues relate to the specific alchemical processes depicted in their corresponding emblems. Hasler identifies the Atalanta Fugiens as an early form of multimedia, in which the cantus firmus serves as the structurally unifying element that links visual, verbal, and auditory channels into a single pedagogical experience.

For the modern reader, the cantus firmus in the Atalanta Fugiens is a key to understanding Maier's most radical innovation: the addition of music to the emblem book format. The fixed song represents stability, resolution, and the gold that the work pursues. When the two volatile voices of pursuit and flight are brought to rest upon the cantus firmus, the musical structure enacts the alchemical coniunctio: the union of opposites in the stable perfection of the golden apple.

Meanings Across Registers

De Jong shows that alchemical terms operate simultaneously across material, medical, spiritual, and cosmological dimensions.

Alchemical

The 'fixed song' of the soprano voice in Maier's three-voice fugues: the unchanging melodic line representing the fixed principle (philosophical Sulphur or the King) around which the volatile voices weave.

Medical

The body's steady underlying rhythm—pulse, breath, circadian cycle—on which fluctuating symptoms play; the diagnostic baseline against which deviation is measured.

Spiritual

The unchanging contemplative ground beneath the fluctuations of psychic life; the still center whose constancy enables the seeker to register and integrate the soul's mobile voices.

Cosmological

The fixed stars of the eighth sphere whose unchanging position anchors the whirling motions of the planets below; the celestial cantus firmus on which the cosmic polyphony sings.