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contrast to ordinal scale—it should be possible to map a proportional and
measurable discrimination (
mapping issue
);
• Effective and efficient perceptibility of sound variables (
physiological and
cognitive issue
);
• Simple design and implementation of the respective sound variable (
implemen-
tation issue
).
Concerning the
mapping issue
we know from the graphical domain that the
variables form, filling (except for hatching), hue and direction (except for the
indirect angle specification) are not or hardly suited for the representation of
quantitative data. In analogy to this we can state for an acoustic coding that the
following variables are not suited: timbre (i.e. the dominant characteristic or quality
of a sound), register (i.e. the relative position of a pitch in a given range of pitches),
sequence of sounds, location (like sound coming from right hand side) as well as
attack and decay of sounds.
Considering the
physiological and cognitive issue
we can rely on studies and
empirical values that have mainly been derived in the domains of psycho-acoustics
and music psychology. Focusing only on the remaining variables after applying the
mapping criterion from above, we have to look at
•
the
total interval
, as well as
•
the
resolution
that can be perceived by humans. In this context, the following can be stated
concerning their perceptibility for humans:
•
Loudness
: Expressing loudness by the sound level, a human is able to distinguish
differences of 2 to 5 dB in optimal settings, while differences between 5 and
10 dB are recognized as clear, and differences between 10 and 20 dB as quite
large (Lercher
1998
). Considering the well perceivable range between the
thresholds of hearing and pain (e.g. between 45 and 65 dB), we end up with a
rather small number of classes (e.g. with five classes at a level width of 5 dB).
While this is generally sufficient for data an ordinal scale representing a limited
number of classes, this range is generally not suited for a generally larger
number of quantitative values or levels.
•
Pitch
: The human being is able to recognize frequencies between 20 and
20,000 Hz. The frequency resolution is proportional to the frequency of the
standard sound; for example a 1,000 Hz tone allows for a perceivable resolution
of about 3 Hz. Cutting off extreme values, we are typically able to differentiate
between 48 and 60 pitches (which corresponds to four to five octaves; Yeung
1980
). For comparison purposes: Transferring this number to the graphical
counterpart, we would need for example a combination of eight to ten different
color hues and six intensities for each hue. While the human ear is quite well
suited for the description of
relative
pitches, an exact acquisition of
absolute
frequencies is only possible for quite a few musical people.
•
Duration
: Depending on the total interval and the required resolution an acoustic
coding that maps a value to the length of a sound might last very long. For
