Music and the Making of Modern Science

36 Chapter 3

AB

mode, and assigned it the middle position in their diagrams. Though practical music was

still notated according to hexachords (spanning six notes), the cosmos spanned a full

octave from Earth to the fixed stars, according to the ancient diatonic pattern S T T (each

semitone followed by two whole tones).

This same solar primality appears in Henrich Glarean ’ s Dodecachordon (1547), which

summarized and reformulated the theory of the modes and their usage in contemporary

composition. To the eight standard church modes Glarean added four more, thereby includ-

ing the modern major (Ionian) and natural minor (Aeolian) scales on an equal footing with

the older modes (see figure 3.4). His cosmological diagram displays the two rival celestial

pitch-orderings side by side, but again the sun appears in a central position among the

planetary notes, whichever alternative one chooses to order the spheres of the outer planets

( figure 3.2a ). Glarean was an innovative geographer who drew one of the first polar pro-

jections of the northern hemisphere, but his views were completely geocentric, as shown

in his cosmological diagram centering the universe on his hometown ( figure 3.2b ), nor did

Figure 3.1

Cosmological diagrams from (a) Giorgio Valla, De expetendis et fugiendis rebus opus , “ De musica ” (1501);

(b) Franchino Gaffurius, Practica Musicae (1596).