Kepler and the Song of the Earth 77
Boethius had assigned complex (hence less consonant) ratios to those intervals, according
to the original Pythagorean tuning. Contemporary practice and theory (including Zarlino)
used simpler intervals for these intervals, known as just intonation (see box 4.1).^32 Kepler
sided with these contemporary musicians, critiquing the Pythagoreans for judging “ from
their numbers alone, doing violence to the natural prompting of hearing. ”^33 For his part,
Kepler combines musical practice with geometric arguments about the ratios between sides
of regular polygons.^34 For instance, though he used a pentagon to justify the major sixth
as 3:5, he refused to use a heptagon to allow such discordant ratios as 3:7.^35 Euclidean
geometry could disqualify the heptagon, which, unlike a pentagon, cannot be constructed
with ruler and compass, but Kepler notes that the nascent art of algebra would allow a
calculation of the heptagon ’ s side that, if accepted, would give the heptagon as much
validity as the pentagon.
Though he expressed admiration for the calculational powers of algebra, Kepler finally
did not allow it full legitimacy because it implies infinite processes (akin to Stifel ’ s “ cloud
of infinity ” ) and also for musical reasons. Algebra would allow intervals like 3:7, which
Kepler finds “ utterly abhorrent to the ears of all men and the usages of singing, even though
it may be possible for strings to be tuned in that way, seeing that as they are inanimate
they do not interpose their own judgment but follow the hand of the foolish theorist without
the least resistance. ”^36
Going past basic issues of tuning, Kepler discusses what constitutes “ naturally tuneful
and suitable melody. ”^37 He attempts a rhetorical analysis that encompasses fine details of
the melodic skeletons of two very different melodies, beginning with the Turkish chant
mentioned earlier ( figure 5.1 , top; ♪ sound example 5.1). He treats this as a kind of anti-
music, “ that grating [ stridulo ] style of song which the Turks and Hungarians customarily
use as their signal for battle, imitating the uncouth voices of brute beasts rather than human
nature. ”^38 As nearby fellow-subjects of the emperor, perhaps the Hungarians ’ use of such
signals might make their rudeness more intelligible or at least more familiar. Kepler specu-
lates that such songs arose because their “ original author absorbed uncouth melody of this
kind from an instrument which was rather unsuitably shaped, and from long familiarity
with the construction of the instrument transmitted such melody to his descendants and to
his whole nation. ” The problem is not a barbaric soul but the instrument ’ s disproportionate
body, whose physical shape gives rise to its sound.
Kepler ’ s transcription may attempt to capture the ululation of Muslim cantillation, as
of a muezzin ’ s call to prayer. Here he confronted the complex melody and pitch slides that
are an essential part of Middle Eastern music. Kepler took some pains to be faithful to
what he heard, though his notation and musical preconceptions were of little help. For
comparison, Kepler cites a famous Gregorian chant, the Easter sequence Victimae paschali
laudes ( figure 5.1 , middle; ♪ sound example 5.2). Perhaps not coincidentally, it too begins
and ends on G, its highest note the g an octave higher; Christians and Muslims both
acknowledge the overarching octave G as they worship the same God. In his commentary