~ICMC 2015 - Sept. 25 - Oct. 1, 2015 - CEMI, University of North Texas
from which time the instrument could finally be constructed
locally. Modern chromatic instruments were only developed
in the past quarter of a century, notably by Hyung-gon Kim
in the 1990s.
One of the more interesting physical characteristics of the
pyeongyeong is the stone itself. In Korean, the stone is
called "gyeongseuk," and is composed of mixed geological
materials, including limestone, jade, and andesite. The combination of these different materials contributes to its unique
sound. It is worth noting that ceramic pyeongyeong chimes
have occasionally been made, however the sound of these
instruments is quite different from those made of stone, and
the instruments remain equally cumbersome due to their
large size and weight.
/ 305 mm
16 mm
160 mm
1 20mm
2.2 Virtual Instruments, Physical Modeling & Modalys
Virtual instruments can emulate a wide variety of instruments in addition to being used to create unusual sounds not
associated with real-world instruments. The ability to creatively modify the sound of a virtual instrument depends on
the synthesis technique used. Existing virtual instrument
sets that include traditional Korean percussion often make
use of sampling, thereby limiting the types of modification
that can be applied to them. Physical modeling synthesis, on
the other hand, is a viable alternative that results in seemingly "realistic" sounds that can be modified creatively at
the synthesis stage, as opposed to post-playback.
Modalys is a physical modeling synthesis application developed at Ircam for research and musical use. The advantages of Modalys over many other physical modeling toolkits and frameworks are that it is easy for both developers
and musicians to use, it has a large set of built-in tools, it is
extendable via user-created objects, and it has a real-time
playback engine compatible with Max/MSP. Furthermore,
Modalys also allows users to create 3D meshes (or import
3D mesh files created in other software2) which can be used
to calculate modal objects compatible with the rest of the
Modalys toolkit. This conversion uses the finite element
method (FEM)3 so these objects are, quite logically, known
as finite-element objects in the Modalys environment [2].
3. MODELS AND RESULTS
3.1 Analysis of the Original Instrument
As a first step towards making a model of a pyeongyeong,
its 16 chimes and the single chime of the teukgyeong were
individually recorded to serve as reference data. In the
sonogram of the teukgyeong sound shown in figure 4, we
can see that the instrument has an inharmonic spectrum
composed of closely-spaced pairs of frequencies (roughly a
fourth apart).
ssm
m
Figure 2. Pyeongyeong/teukgyeong: side view of a single chime.
Another important characteristic of the pyeongyeong is
the distinctive L-shape of its chimes. The instrument was
derived from the Chinese "bianqing," whose stone chimes
originally had a different shape: the chimes of the oldest
Chinese bianqing were almost square and evolved to be
more triangular. Over the years, the stone chimes became Lshaped (see figure 2), the practical result of which was a
longer vibration time. [1]
(mm) 27 28.5 30 33 33.9 35.6 37.5 40.3 42.3 44.1 51 52.5 55.5 60 64.5 54.2
Figure 3. The 16 notes of the modern pyeongyeong, the Korean
(and Chinese character) names of each pitch and the average
thickness of each chime (in mm).
The 16 chimes of the modern pyeongyeong range between 528Hz and 1262Hz (see figure 3). All of the chimes
are the same size when viewed from the side, but the thickness of each chime is different. The thickness of each stone
is the key feature for tuning all 16 notes of the pyeongyeong.
Seemingly paradoxically, thicker chimes sound higher in
pitch than thinner ones (this is also shown in figure 3).
Figure 4. Teukgyeong waveform and sonogram (3.7 sec.).
2 Modalys can currently only import "Mesh Version Formatted 2" files that
use "hexahedral" (i.e., cube-based) meshes.
The finite element method (FEM) is a mathematical technique for finding
approximate solutions for partial differential equations.
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