HEARING
GREEK MICROTONES
John Curtis Franklin
Forthcoming, with audio CD, in Hagel, S./Harrauer, Ch. (eds.), Ancient
Greek Music in Performance. Wiener Studien Beiheft 29 (Vienna, 2005).
(Note that 'microtone'
is a modern term, and should be used advisedly of Greek music: see
further here.)
Microtonal intervals occupy an important place in ancient Greek music theory,
beginning with Archytas and Aristoxenus, our earliest witnesses (early and late
fourth century B.C. respectively). It
is certain that their treatments reflect an important dimension of practice.
Yet most performances today render the ancient Greek fragments with uniformly
diatonic intonation. To be sure, many of the late pieces are in fact in the
diatonic genus. And even for those which do exhibit the non-diatonic pykna—the
‘close set’ pitches at the bottom of a tetrachord—the notation
system does not distinguish between enharmonic and chromatic, much less specify
which ‘shade’ (chroa) is to be used. Furthermore, these microtonal
shadings surely rank among the more culturally peculiar, and therefore elusive
to the modern performer, elements of Greek practice. Nevertheless, Archytas,
Eratosthenes (third century B.C.), Didymus (first century A.D.) and Ptolemy
(second century A.D.) propose exact ratios for the intervals of non-diatonic
systems, and even versions of the diatonic with microtonal modifications. It
would be unfortunate if, in the current renaissance of performing Greek music,
re-enactors continued to overlook this important material, which could bring
greater life both to the fragments and to new music based on ancient principles.
That the practical and theoretical position of microtones in ancient Greek music
may be understood as concretely as possible, this paper includes, in addition
to the essential philological arguments, a number of audio demonstrations featuring
the Virtual Lyre. It is therefore both about
performance, and a sort of performance itself.
First I explain and demonstrate the basic acoustic phenomena which bear on the
Greek use of microtonal intervals—namely the harmonic series, harmonic
‘refraction’, and resonance between musical tones. It is to be hoped
that most researchers of ancient Greek music are already familiar with the physical
laws involved. Yet probably even some of these scholars—alongside perhaps
the majority of those philologists who have recently recognized the importance
of music for the anthropology of ancient Greece, but are still daunted by the
technical material of the ancient theorists—have never heard these phenomena
demonstrated. And yet they are basic to the entire history of Greek tonality,
which, though a ‘technical’ subject in the first instance, is often
crucial for a proper understanding of the social and political dimensions of
ancient Greek music.
I then discuss two distinct customs in the Greeks’ use of resonance. The
perfect fifth and fourth, the most audible resonances after the octave, characterized
the diatonic, chromatic and enharmonic genera in their classical, textbook form.
By the late fifth century, however, the lesser resonances were frequently used
in some genres (especially citharody and the dithyramb) to give microtonal ‘shadings’
to all three genera, and this practice continued to grow for several centuries
thereafter. Many of the tunings preserved by the theorists, and expressed as
ratios between successive degrees, are commonly supposed to owe as much to mathematical
fantasy as musical reality. An analysis of their internal relations, however,
reveals how their scalar presentation conceals an extensive basis in lesser
resonant relations. Since such intervals are easily audible even to us, one
may be all the more certain that, if the ancient authors took the trouble to
record them, they reflect ancient musical practice quite faithfully. Some true
mathematical fictions remain, but these exceptions mark the rule. Finally, there
is a distinct tendency for these lesser resonances to be arranged in reference
to the central string mesê, which was of great practical importance
for the ‘classical’, i.e. Archaic, seven-stringed kithara,
both in tuning and performance. I conclude therefore with an étude employing
mesê in accord with allusions in ancient sources, thereby highlighting
these intervals and the character they impart to the harmonia.
The rest of this article may be downloaded
here in PDF format. The audio examples which accompany the paper are also
available here in MP3 format:
Example
1 harmonic series demonstrated with lowpass filter
Example 2 kithara overtones
Example 3 oscillators resonating from 1:1 to 3:2, then
4:3, 5:4 and so on to 12:11
Example 4 'Pythagorean' diatonic
Example 5 experiment from Aristoxenus Elementa Harmonica
56-57
Example 6 ditone (81:64), a result of 'Pythagorean'
tuning, compared with 5:4 third
Example 7 5:4 and 6:5 in the enharmonic of Archytas
Example 8 enharmonic of Archytas established from 'Pythagorean'
diatonic
Example 9 chromatic of Archytas
Example 10 diatonic of Archytas
Example 11 7:7 and 8:7 in diatonic of Archytas (8:7
as 'secondary epimoric')
Example 12 chromatic of Didymus
Example 13 6 brief études demonstrating 'epicentric'
tonality (intervals tuned to and emphasizing central string mesê)
Example 14 Eratosthenes enharmonic
Example 15 Eratosthenes chromatic
Example 16 Didymus enharmonic
Example 17 Didymus diatonic
Example 18 Ptolemy enharmonic
Example 19 Ptolemy soft chromatic
Example 20 Ptolemy tense chromatic
Example 21 Ptolemy soft diatonic
Example 22 Ptolemy tense diatonic
Example 23 Ptolemy even diatonic