Visualization of Multi - Part
Music
(Acoustics and Perception)
Werner A. Deutsch (Austrian Academy of Sciences, Acoustics
Research Laboratory) and
Franz Födermayr (Institute of
Musicology, University of Vienna)
Introduction
Frequency analysis of musical sounds came up to practical
applications with the development of the Sound Spectrograph
(Koenig, Dunn and Lacey, 1946). From the beginning much care
has been taken to choice the frequency resolution and the time
window properly in order to highlite important acoustical features
as well as perceptual ones. It has been demonstrated by several
studies (i.e. Potter, Kopp and Green, 1947) that the aural
presentation of speech (and music) and its simultaneous graphic
representation produces significantly deeper insight into the
generation of acoustical signals and the ongoing perception as
listening alone can provide.
Graf (1963) recognized the enormous potential of spectrographic
analysis for applications in ethnomusicology. His theoretical
concept assumes the acoustical signal to be the primary stimulus
which is processed by the human psychophysiological system
very much in the same way, even in different ethnic populations.
What makes the various differences in interpretation, reception
and perception under very similar acoustical stimulus
representations prominent, is due to the influence of the so called
social-cultural context in which music plays an important role.
Production Models
The pertinent acoustic analysis of musical signals with acoustic
laboratory methods (which today can be performed by using a
specially equipped laptop computer.) produces basically a
complete set of acoustical parameters which can be displayed as
graphical images of the spectral content, i.e. the physics of the
musical signal in real time or of those performances which have
been recorded in advance. The analysis data can be used as input
to comprehensive production models of voice( see: Fant, G.
(1970) Acoustic theory of speech production. Mouton, The
Hague; 2nd edition), musical instruments and musical ensembles.
Sound source characteristics, tuning, musical scales, timbre,
agogics, free field and room acoustics etc. can be observed on the
analysis parameters extracted directly from the musical signal.
Musical scales, vibrato, pulsato, beats are measured and detected
on the basis of the fundamental frequency analysis data and their
related spectral components, timbre is very much determined by
the spectral envelope of the signals, duration and rhythms are
mainly derived from the energy contour etc.
Perception Models
Whereas production models of the singing voice and musical
instruments describe the acoustics of musical sound sources only,
perception models deal with the signal processing of the listeners
auditory periphery, its associated central pathways and cortical
functions. It has to be admitted that psychoacoustics first started
from an acoustical engineering approach in order to collect all
technical basic data of the human auditory system, as selectivity
measured in terms of absolute thresholds, difference limens in
frequency, sound pressure level, signal duration and many other
psychophysical functions. Most of the early psychoacoustical
research was launched by telephone technical laboratories
( Fletcher, H. 1929, 1953), by the need to avoid noise and
distortions on the telephone lines or for compensation of the
hearing loss of listeners. Engineers, physiologists and
neurologists have described the mechanics of the outer and
middle ear, the hydromechanics of the inner ear ( Bekesy, G.v.
1960), the hair cell system and the resulting neural response up to
the brainstem ganglions as well as acoustical evoked responses on
the cortex. For technical and methodological limitations this early
research has been done in most cases applying musically less
relevant sinusoids, which could be controlled in experimental
procedures with sufficient accuracy. This has been critisized
frequently by musicologists for dealing rather with musicological
non relevant aspects of sound and arbitrary functions of the
auditory system instead of referring to the cognitive concepts of
music.
Nevertheless, as the work in psychoacoustics progressed, the
basic data obtained from the human auditory system contributed
to a comprehensive theory of hearing, which today is capable to
include highly relevant aspects of auditory localization, speech
and music perception. Today psychoacoustical models explain
complex perceptual functions, as musical pitch of complex tones,
melody contours, consonance-dissonance, simultaneous masking,
forward
and
backward
masking,
figure-background
discrimination as well as Gestalt of musical rhythms etc.
Visualization of polyphony
FFTs and Spectrograms
Applying the psychoacoustic knowledge to spectrographic
analysis of polyphony, the visualization of musical signals
represents both, the graphical output of psychoacoustic perception
models and the physics of sound. The spectral analysis of any
arbitrary acoustical signal at a given instant is obtained by its
Fourier Transform which produces a pair of real-valued functions
of frequency, called the amplitude (or magnitude) spectrum and
the phase spectrum. The amplitude spectrum stays moreover as a
first approximation for the (neuro-) physiological representation
of the signal in the human auditory system, the phase spectrum
can be neglected for spectrographical purposes:
As the time variant signal goes on, many closely time windowed
overlapping Fourier Transforms have to be computed at short
successive intervals (< 30 ms) in order to produce a pseudo3dimensional continuous graphic display of the sound, the
spectrogram. In general narrow band frequency components with
slow variations in frequency are detectable as horizontal
frequency lines, whereas very fast changes or signal envelopes of
a transient nature appear as vertical broad band bars in the
spectrogram. Many musical instrument sounds (plucked strings,
striked bars etc.) have a very short broad band attack and a
narrow band slowly decreasing decay. Thus the onset of a note is
easily identified, not so the end of the decay especially in
reverberant environments).
Beats: From left to right: simple tone 220 Hz, simple tone 227 Hz, two tone
complex 220 Hz + 227 Hz with beating, two tone complex 220 Hz + 240 Hz
(light roughness), two tone complex 220 + 260 Hz (roughness), two tone
complex (musical fifth).
Interference, Beats and Roughness
Usually directly incident or reflected waves from many sources,
sounding simultaneously (musical instruments, singing voices
etc.), are superposed at the listeners ear position, producing
interference when components of equal frequency appear.
Constructive interference takes place when the crests of two
waves coincide, resulting the amplitude will be twice that of
either wave. Destructive interference occurs when the crests of
one wave fall on the troughs of the second and cancellation will
be obtained. In case of interference of components slightly
different in frequency beats can be perceived. The beat frequency
is given by difference between the frequencies sounding together;
beats can be detected on the spectrogram as periodic rise and fall
in amplitude on a single (horizontal) frequency line. Whenever
the frequency difference exceeds a certain value of 20 Hz no
beating can be heard anymore and the perception of roughness is
raised which has its maximum between 40 and 70 Hz. Increasing
the frequency difference further on (see: critical bandwidth)
produces two tone perception.
Masking
One of the most difficult phases in the investigation of
spectrograms is the decision wether or not a spectral component
of a signal which physically exists can be perceived by the
auditory system and to what extent. The phenomenon that spectral
components of a complex tone are not audible, despite their
considerable amplitude measured, is described by the human
auditory masking function. Masking is (1) the process by which
the threshold of audibility for one sound is raised by the presence
of another (masking) sound and (2) the amount by which the
threshold of audibility of a sound is raised by the presence of
another (masking) sound. The unit customarily used is the decibel
(ANSI S3.20-1973). Masking may be seen as a general loss of
information or as an undesired decrease of sensitivity of the
auditory system but in contrary it is one of the most important
auditory functions in order to perform the frequency analysis of
the ear. Masking helps to process the sound into perceptual
relevant components either belonging to the same or different
sounds; it determines which components are resolved by the ear
as audible harmonics with spectral pitch as well as it fuses higher
harmonics according to the auditory critical bandwidth.
Critical Bands
The critical band in hearing can roughly be described as that
frequency band of sound, in between that two spectral
components influence one another. This influence can be
expressed in terms of masking, loudness summation, roughness,
consonance, dissonance etc. The bandwidth of the critical bands
remains constant with 100 Hz up to a frequency of 500 Hz and
increases up to 17\% of the midfrequency value beyond 500 Hz.
Consequently the distribution of the spectral components of any
acoustical signal along the basilar membrane of the inner ear is
best approximated by the Bark\footnote{according to the
acoustician Barkhausen (1926). scale which corresponds to the
frequency spacing of the critical bands. A formal expression for
the computation of the Bark scale has been given by Zwicker and
Terhardt (1980). The unit of frequency (f) is assumed to be in
kHz, arctan in radiants:
◦
z_c /Bark = 13 arctan (0.76 f/kHz) + 3.5 arctan (f /7.5
kHz)2
As a result of the Bark transformation a much better frequency
resolution in the linear low frequency range up to 500 Hz is
obtained. The resolution is progressively reduced at higher
frequencies. Spectrograms using the Bark scale represent the
psychoacoustical frequency spacing of the inner ear and can be
interpreted in terms of perceptual relevant spectral frequency
distribution.
Relevance-Spectrography
The transformation of the frequency axis into Bark scale and the
extraction of irrelevant spectral components from the signal
creates a so-called Relevance-Spectrogram which contains those
frequency components only which evoke neurophysiological
activity (SPL-Ecxess). It represents the signal associated to the
neural excitation pattern in the auditory nerve, containing the
relevant information parameters for the processing at higher
neural levels. Thus the musical interpretation of spectrograms is
highly facilitated as irrelevant signal parts can not show up.
Moreover by applying an categorized intensity detection
procedure (a concept of overmasking) the most prominent spectral
peaks of the signal are extracted and figure-background
discrimination can be obtained ( Deutsch \& Noll, 1993). This
enables the listener to follow the leading voice without
interference of the background signal in many cases.
Pitch
The perception of pitch of complex tones has been a topic
discussed extensively in psychoacoustics since the well known
controversy beween Hermann von Helholtz and Georg Simon
Ohm on one side and August Seebeck on the other. The problem,
which is still an important question in hearing theories, started
from Seebecks observation that the pitch of a complex tone with a
missing fundamental still remains at the pitch level of the
fundamental frequency. Ohms acoustic law followed Fouriers
theorem and stated in contrary, pitches of frequencies which
existe objectively (as components of a complex tone) can be
heard only. Ohms acoustical law strongly supported Helmholtzs
hearing theory according to which the partials of a complex tone
are distributed along the basilar membrane (place theory) and
resonance is responsible {Note: Helmholtzs experimental setup
consisted mainly in resonators, he invented). His acoustical
sources have been tuning folks. Seebeck used an acoustic siren,
blowing air against the holes of a turning disk. By proper spacing
of the holes a complex tone is produced without its fundamental
frequency. for the mechanical stimulation of the hair cells. He
explained Seebecks missing fundamental phenomenon by arguing
nonlinearities in the inner ear would evoke the low frequency
pitch, creating an objective product of nonlinearity (difference
tone or combination tone between the higher harmonics) at the
place of the fundamental frequency.
Modern pitch theory is based on the results of Georg von Bekesys
and J. F. Schoutens work. Both have stimulated the research on
pitch perception for about 50 years. Bekesys travelling wave
theory is strongly supported by physiological experiments
(Bekesy, 1960) and Schoutens (1940) observations on the residue
pitch made evident, that the ear works in both domains
simultaneously: in the frequency domain by means of
hydromechanics with a far then perfect result of a Fourier
Transform and in the time domain where any onset or even a
slight change in the regular vibration of the basilar membrane is
detected.
Fianlly pitch has been defined as that attribute of an auditory
sensation in terms of which sounds may be ordered on a scale
extending from low to high. The unit of pitch was assigned the
mel (ANSI S3.20-1973). Thus pitch depends primarily upon the
frequency of the sound stimulus, but it also depends upon the
sound pressure and the waveform on the stimulus. The pitch of a
sound may be described by the frequency or frequency level of
that pure tone having a specified sound pressure level that is
judged by subjects to have the same pitch.
The discussion on pitch perception came to an premature end
when Terhardt (1974) published a model of pitch perception
which includes both, the virtual pitch and the spectral pitch. He
applied the concept of Gestalt perception, which in musicology
frequently is understood to describe sequential melody contours
only, on simultaneous sounding partials of a single complex tone.
This enables the listener to still perceive the complex tone as a
whole even when prominent components are missing (e.g. the
fundamental frequency) or when their amplitude is as low that
they can not contribute to pitch perception. Thus two general
modes of pitch perception have to be encountered: the holistic
mode integrating the partials of any complex tone to a good
Gestalt, evoking virtual pitches and the analytic mode, focussing
more on the spectral components of the sound and isolating
individual partials of the complex tone as it is described by the
concept of spectral pitch.
The following conclusions for the today work in pitch perception
and music transcription have to be drawn:
• the pitch of a complex tone very likely may be ambiguous,
• pitch matches have therefore to be done with sinusoids only,
• spectral pitch and virtual pitch may exist in between the same
individuum, responding to the same sound, dependent upon
subjective experiences,
• musical theories of melody and counterpart introduce
interpretative framework which not necessarily must
correspond with perception.
Example 1: Highland Bagpipe
In
the case of drone polyphony at least two psychoacoustical
phenomena are generally relevant: masking and interference; the
special characteristic of the drone sound is given by its relative
stationarity in pitch and timbre throughout the total duration of
the musical piece or a part of it, enabling melody tones to interfer
with related spectral components of the drone. The following
example is taken from a pibroch played on a Piob Mhor (highland
bagpipe, Vienna Phonogramm Archive, Tape 17979, J. Brune,
1973). The key of the pipe chanter is usually spoken as A. The
two tenor drones are tuned to the octave below the A of the
chanter and the bass drone sounds an octave lower still ( Mac
Neill, S. & Richardson, 1987). In our example the frequency
value of /A/ is 116 Hz. The drone pipes produce a harmonic
amplitude spectrum up to 7 kHz. Some partials show slow beats
appearantly according to the slight mistuning of both tenor pipes.
The ornamental sections of the sound probe are of equal overall
duration (820 ms), whereas the sustained melody tones vary in
duration from 1920 to 2830 ms. Interference is given mainly
between the 4th, 5th, 6th and 8th harmonic of the drone and 1st
harmonic of the sustained melody tones (/a3/, /c4 sharp/, /e4/,
/a5/) depending upon their amplitude relation.
• Spectrogram: Piob Mhor (highland bagpipe, Vienna Phonogramm Archive,
Tape B17979, J. Brune, 1973). Spectrogram unprocessed.
Piob Mhor: according to the irrelevance-threshold signal processed, all spectral
components below the masked threshold have been extracted. Approximately
67% of the weaker FFT-amplitudes have been set to zero. Piob Mhor: difference signal, 67\% of the weaker amplitudes represent the signal
below the masked threshold (irrelevance threshold). After being extracted from
the original signal these components can be made audible again. The
superposition of this spectrogram and the 2nd exactly produces
the first spectrogram as well as the difference signal + irrelevance
corrected signal = original.. Generally the sustained longer chanter (melody) pipe tones
interfere (11s to 16s) with higher harmonics of drone tones,
alternating with notes having no interference with the drone (see
8s to 11s) and short melody tones constituing the melismes (at 2s
to 8s, 14s). The occurence of beats at each 2nd harmonic of the
drone spectrum indicates beating between the two tenor drone
pipes with a frequency difference of 0.85 Hz. The beating
between the 2nd and the 4th harmonic of the drone with a rate of
approximately 1.7 Hz is not of most perceptual importance. This
beating does not effect the overall drone sound dominantely.
Perceptually more relevant is the beating between the partials of
the drone and sustained melody tones seen at 2.6s to 6s, 11s to
13s etc.
The interference of spectral components of both, the drone and
the melody tones can be observed already on the spectrogram (fig.
1). Its perceptual relevance as indicated above can be seen in the
relevance-spectrogram (fig. 2) from which the masked
components of the signal have been removed. What happens to
the signal when the masked threshold has been computed is
demonstrated in the difference signal (fig. 3). From the lower
harmonics of the drone sound, a2 and a3 are not affected by
masking, as well as the 6th harmonic (e5). This results in a
continous prominence of the fundamental and the fifth of the
drone, the first corresponding to the basic tone of the melody, the
second corresponding to the dominant tone of the melody. This
fact has been mentioned already by Collinson (1970:167); Brune
(1981:48) and MacNeill & Richardson (1987:32) but they all
explained it by focussing on a strong 3 rd harmonic of the bass
drone. In contrary the example currently under investigation
shows a very week 3rd harmonic of the bass drone and a strong,
almost unmasked 3rd harmonic of the tenor pipes.
Several harmonics of the chanter pipes are stroger than the drone
and consequently mask their neighbouring partials of the drone.
The first partial of a4 of the chanter masks e4 and c-sharp5 of the
drone sound and the first partial of e5 of the chanter masks csharp and g of the drone sound; whereas the sustained melody
tones c-sharp5 and f-sharp5 themselves are partially masked by
the harmonics of the drone sound. Taken together, the results of
these observations provide psychoacoustical evidence (1) for the
characteristic hierarchical structure given by the fifth a-e of the
melody, which is strongly supported by the masking phenomenon.
(2) The continuous sounding drone enlarges the overall frequency
range downward, anchoring the melody into the tonal space.
Example 2: Bulgarian Multi-Part Song
The next example (fig.4 to 6) shows the role of roughness and
frequency fluctuations (tremolo) as characteristics of a diaphonic
type of Bulgarian multi-part singing (Messner, 1980:passim;
Brandl, 1992; Födermayr & Deutsch, 1992:381-384). Masking
has no effect in the region of the fundamental frequencies, even at
the strongest partials (2 and 4) weak masking can be observed
only. It does not influence the constituting elements of the sounds.
Thus the partials of the individual voices interact with their full
objective existent amplitudes. Throughout the whole piece a
characteristic interval between two voices is produced, fairly
constant with a width of three quarters of a whole tone. The
resulting frequency differences between the fundamental
frequencies are in the range of 30 Hz, evoking the sensation of
roughness. Even when strong tremolo appears in Tressene figures,
the average frequency difference remains close to 150 cents.
Generally start and target points of exclamations fall on frequency
values of the characteristic interval. The rate of the tremolo
ranges between approximately 4 and 8 fluctuations /s which is
known close to the ears maximum of sensitivity to frequency
modulation.
Long term spectrogram of Bulgarian multi-part song: Balkanton BHA 2067, II 6.
The duration of the piece is 39s. The spectrogram shows the segmentation of the
song
in
3
x
3
parts
of
equal
duration.
Segment No. 3 (8s - 13s) of Bulgarian multi-part song: Balkanton BHA 2067, II
6. The spectrogram shows the characterstic interval of 150 Cents, several
exclamations and two tremolo of 8 and 4 Hz fluctuation rate
Example 3: Epic Chant, Gujarat
The sound of the drone instrument ( Tharisar, Födermayr, 1968)
is characterized by a single pitched (233 Hz) harmonic spectrum
with decreasing amplitudes. The recitation as well as the sung
parts follow the fundamental frequency of the drone sound with
distinct variations. Short quasi-stationary tones of the recitation
have an ambitus up to several whole tones using the fundamental
frequency of the drone as midfrequency value, those of the sung
parts are asymmetric and clother to the drone frequency with
intervals downwards to a semi tone and upwards to a third. The
drone implements a tonal function as finalis of the song.
Roughness is produced during the sung parts only due to the
interference of the drone and sustained voiced tones.
Long term spectrogram: Epic Chant of the Kunkana, Gujarat (PhA B 12125).
The first 3s of the sound example show the drone isolated, followed by drone and
recitation (3s - 15.5s) and sung part segments (15.5s - 30s). This example
demonstrates the special kind of voicing during the parlando up to the first half
duration of the sound segment displayed (up to 15s) and the song section with
melodic lines closely related to the drone tones. The drone is given by a friction
idiophone (Tharisar).
Epic Chant of the Kunkana, sung part segment, duration 3.5 s. The asymetry of
the sung part in relation to the drone frequency can easily be detected from the
first and 2nd harmonic.
Example 4: Lullaby in Yodel-technic, Bangombe
Pygmies
The interdependence of pitch and timbre has been pointed out
already in the section on pitch perception. The Yodel-technique of
the Bangombe Pygmies elicitates both different modes of pitch
perception: virtual pitch and spectral pitch. Two female voices
exhibit the following variations:
• tone to tone change of voice register: chest - falsetto
• no isoparametric tone sequences with register change
• unisono with different register: upper voice chest, lower voice
falsetto
• tone to tone vowel quality change (first and second vowel
formant effect), upper voice: vowel /a/ chest, lower voice
vowel /i/ falsetto, vowels /a/, /ae/ chest voice
The interaction between pitch, vowel quality and register change
causes selective amplification of partials in the area of the vowel
formant peak frequency, in the range of the first or 2ndnd partial of
the female voices (633 Hz). The harmonics are sufficiently spaced
apart to be resolved by the ear, producing virtual as well as
spectral pitches. Whenever the fundamental frequency is
significantly weaker as the 2ndnd harmonic, spectral pitch can be
perceived by the analytic type of listeners. At will the perception
can be focussed on the fundamental again and a holistic type of
listening
occurs.
Lullaby of Bangombe pygmy women (PhA B10840 G. Kubik, 1965): the
peak amplitude contour of the solo part shows the A-B-A pattern of fundamental
/e5-flat/ - 2nd harmonic /b4-flat/ - fundamental /e5-flat/ and so on. Falsetto tones
are marked in diamonds. The inherent pattern of the upper voice is indicated,
starting at 114 s.
The perceptual pitch ambiguity can best be described on the basis
of the spectrogram: the peak amplitude of the beginning solo part
shows the A-B-A pattern of fundamental /e-flat/ - 2ndnd harmonic
/b-flat/ - fundamental /e-flat/ etc. According to the virtual pitch
perception /e5-flat/ /b4-flat/ /e5-flat/ has to be perceived whereas
subjects following the sepctral pitch hear /e5-flat/ /b5-flat/ /e5flat/. The spectrogramm clearly shows the fundamental frequency
contour. The phenomenon described has been addressed by a
number of investigators and in detail by Albrecht (1972). By
further analysing the spectrogram a melo-rhythmic pattern in the
upper voice (120s to 134s) can be identified; it is aready seen as
inherent pattern in the beginning of the solo part starting from the
third phrase. The perception of the inherent pattern can be
explained by the similarity of timbre of neighbouring tones, the
falsetto /f/ and /e-flat/ of phase 3 and the chest voice /c/ /b-flat/ as
well as /b-flat/ /g/ of phrase 4. Approximately at location 115s
(marked with an asterix) /b4-flat/ is perceived instead of /b5-flat/
which exists objectively. This octave error helps to obtain the
continuity of the melody in order to support the good Gestalt.
Finally even in parts both voices are in unisono the distinction
between the individual voices can easily maintained due to the
predominant difference ebtween the chest and falsetto register.
In conclusion and for further studies on that line the spectrogram
has been proved as an indespensible basis for the evaluation of
complex tonal patterns as represented by the example described.
Lullaby of Bangombe pygmy women: duet. The arrows pointing downward
indicate spectral components associated witjh the upper voice. Arrows pointing
upward indicate those belonging to lower voice.
continuation of previous spectrogram. Example 5: Overtone Singing: Tran Quang Hai
Overtone singing of the nature given by mongolian and turk
people (as well as by Tran Quang Hai's reproductive
performances) is characterized by (1) a sustained fundamental
frequency contour and (2) a melody which is composed from
harmonic overtones of that fundamental frequency. The overtone
phenomenon has been recognized to be an acoustical factor of the
special setting of resonances of the human vocal tract. It has been
sufficiently explained by the acoustic theory of voice production
(Fant, 1960). Moreover this example shows the coincidence of a
production model and the corresponding perception model.
Tran Quang Hai: overtone singing, spectrogram.
The acoustic model of the speech production assumes the glottal
spectrum as the primary source for voiced sounds and the vocal
tract acting as a filter attached on it: the glottal spectrum consists
of a series of harmonics produced by glottal air pulses described
in a model according to the myoelastic theory of {Berg (1957)}
which has been accepted widely. The slope of the {\em source
spectrum} depends on the shape of the individual closing and
opening of the vocal folds during one fundamental period; a
glottal waveform with more sudden closures produces stronger
high frequency harmonics and a sharper timbre or voice quality.
The fundamental frequency of the voice is determined by the
repetition rate of the glottal pulses which is controlled (1) by the
laryngeal musculature affecting the tension and the mass
distribution of the vocal chords and (2) by changes of subglottal
pressure. Decreased subglottal pressure, reduced mass of the
vocal chords and increased tension raise the fundamental
frequency.
The tube of the human vocal tract with a length of approximately
17,5 cm is attached on top of the laryngeal section. Its cross
section can be changed to wider and narrower constrictions by the
walls of the pharynx, the tongue, the jaw opening and the lips.
The formant frequencies of vowels are related to the length of the
tube and its shape. They represent the resonance frequencies of
the vocal tract in non nasalized sounds. When the nasal tract is
coupled on, by lowering the soft palate, the amplitude of the
vowel
formants
decreases
and
a
more
complex
resonace/antiresonace behavior of the vocal tract can be observed.
The special setting of overtone singing suppresses the formant
frequencies of the normal voice and emphasizes a very small
frequency range, as narrow that one partial is amplified only. The
result is shown in the spectrograms (fig. 12,13); the fundamental
frequency is continuously sounding on one sustained low pitch
and the melody is controlled by proper changing of the main
resonace frequency. Thus overtone melodies can be played by
picking out individual harmonics from the complex tone of the
glottal pulse.
Tran Quang Hai: overtone singing. The output of the model of voice production
(Linear Prediction Coding, 24 coefficients) extracts the first overtone of the
fundamental frequency and the harmonics with the peak amplitude. The overtone
melody is produced by setting the vocal tract main resonances accordingly.
The point to be emphasized is that in this case a coincidence of a
(voice) production model and the associated perception model can
be stablished. Nevertheless it has to be examined from case to
case which aspects of the production model can be considered as
significant for the perception.
Conclusion
Although these examples are of demonstrative nature only they
are consistent with the general concept of introducing acoustics,
physiology and psychoacoustics into the process of musical
analysis. We have excluded for reasons not outranging the size of
this contribution only the very challenging approach of {\em
Analysis by Synthesis} as it has been applied in speech research
since the beginning of vocoder techniques. Resynthesis of
musical sounds can be extremly forceful when appropriate sound
analysis data are available. As long as the physical parameters of
musical sounds have not been evaluated upon their
psychoacoustical effects, the perceptual relevance of individual
components of complex sounds can be determined by trial and
error only. The introduction of perceptual concepts in the analysis
of music yields to results typically much better than would be
obtained from acoustics alone.
Aknowledgments
Our special thanks to Prof. Dr. Kreysig for reading the english
version of this paper and improving its style.
References
Albrecht, Erla M. (1972): Das akustische Residuum. Phil. Diss.
Univ. Wien.
ANSI
S3.20-1973}:
American
National
Psychoacoustical Terminology. New York.
Standard;
Bekesy, Georg von (1960): Experiments in Hearing. New York:
McGraw-Hill.
Berg, Jw.van den, J.T. Zantema, and P. Doorenbal, Jr. (1957): On
the Air Resistance and the Bernoulli Effect of the Human Larynx.
Journal of the Acoustical Society of America, Vol.29,
No.5,p626-631.
Brandl, Rudolf M. (1992): Die Schwebungsdiaphonie im Epiros
und verwandte Stile im Lichte der Psychoakustik, in: Schumacher,
R. (Hg): von der Vielfalt musikalischer Kultur. Anif 1992:43-79.
Brune, John A. (1981): Piob Mhor und andere britisch-irische
Sackpfeifen, in: Schriften zur Volksmusik (Wien, 1981) 41-58.
Collinson, Francis (1970): The traditional and national music of
Scotland. London.
Deutsch, W.A. & Anton Noll (1993): Simulation auditorischer
Signaltrennung in komplexen musikalischen Signalen durch
Übermaskierung. DAGA, Fortschritte der Akustik.
Fant, Gunnar (1970): Acoustic theory of speech production.
Mouton, The Hague; 2nd edition.
Fletcher, Harvey (1929): Speech and Hearing. D. van Nostrand
Company, Inc. New York.
Fletcher, Harvey (1953): Speech and Hearing in Communication.
D. van Nostrand Company, Inc. New York.
Födermayr Franz (1968): Über ein indisches Reibidiophon und
die Drone-Praxis, in: Mitteilungen der Anthropologischen
Gesellschaft in Wien, 98:75-79.
Födermayr Franz & Werner A. Deutsch (1992): Musik als
geistes- und naturwissenschaftliches Problem, in: Gratzer, W. &
A. Lindmayr (Hg.), De editione musices. Laaber, 377-389.
Graf, Walter (1963/64): Moderne Klanganalyse und
wissenschaftliche Anwendung, in: Schriften des Vereins zur
Verbreitung naturwissenschaftlicher Kenntnisse in Wien, 104:4366. Neudruck in Graf (1980).
Graf, Walter (1980): Vergleichende Musikwissenschaft.
Ausgewählte Aufsätze, hg. von F. Födermayr, Wien-Föhrenau.
Helmholtz, Hermann von L.F. (1863): Die Lehre von den
Tonempfindungen als physiologische Grundlage für die Theorie
der Musik. Vieweg & Sohn, Braunschweig; 6. Aufl. 1913.
Koenig, Walter K., H.K. Dunn, L.Y. Lacey (1946): The Sound
Spectrograph. Journal of the Acoustical Society of America, Vol.
18, p. 19-49.
Mac Neill, Seumas and Frank Richardson (1987): Piobreachd and
its interpretation. Edinburgh; p.32.
Messner, Gerald F. (1980): Die Schwebungsdiaphonie in Bistrica
Tutzing.
Ohm, Georg, Simon (1843): Über die Definition des Tones, nebst
daran geknüpfter Theorie der Sirene und ähnlicher tonbildender
Vorrichtungen. Annalen der Physik und Chemie, 59, pp. 513-565.
Potter Ralph K., George A. Kopp, Harriet C. Green (1947):
Visible Speech. D.van Nostrand Company Inc. New York.
Schouten, J.F. (1940): The perception of subjective tones Proc.
Kon. Nederl. Akad. Wetensch. 41, 1086-1093.
Seebeck, A. (1841): Beobachtungen über einige Bedingungen zur
Entstehung von Tönen. Annalen der Physik und Chemie, 53;
417-436.
Seebeck, A. (1843): Über die Sirene. Annalen der Physik und
Chemie, 60; 449-487.
Terhardt, Ernst (1972): Zur Tonhöhenwahrnehmung von Klängen.
II. Ein Funktionsschema. Acustica, Vol 26/4, 187-199.
Zwicker, Eberhard and E. Terhardt (1980): Analytical expression
for critical-band rate and critical bandwidth as a function of
frequency. JournaL of the.Acoust.Soc.Am. 68(5), Nov. 1980;
1523-1525.