J Comp Physiol A (1997) 181: 665±676
Ó Springer-Verlag 1997
ORIGINAL PAPER
G. Langner á M. Sams á P. Heil á H. Schulze
Frequency and periodicity are represented in orthogonal maps
in the human auditory cortex: evidence from magnetoencephalography
Accepted: 25 July 1997
Abstract Timbre and pitch are two independent perceptual qualities of sounds closely related to the spectral
envelope and to the fundamental frequency of periodic
temporal envelope ¯uctuations, respectively. To a ®rst
approximation, the spectral and temporal tuning properties of neurons in the auditory midbrain of various
animals are independent, with layouts of these tuning
properties in approximately orthogonal tonotopic and
periodotopic maps. For the ®rst time we demonstrate by
means of magnetoencephalography a periodotopic organization of the human auditory cortex and analyse its
spatial relationship to the tonotopic organization by
using a range of stimuli with di€erent temporal envelope
¯uctuations and spectra and a magnetometer providing
high spatial resolution. We demonstrate an orthogonal
arrangement of tonotopic and periodotopic gradients.
Our results are in line with the organization of such
maps in animals and closely match the perceptual orthogonality of timbre and pitch in humans.
Key words Periodicity pitch á Tonotopy á Auditory
cortex á Magnetoencephalography á Neuronal map
Abbreviations AC auditory cortex á BMF best
modulation frequency á CF characteristic
frequency á ECD equivalent current dipole á
f0 fundamental frequency á MEG
magnetoencephalography á SF sustained ®eld
G. Langner (&) á P. Heil á H. Schulze
Institute of Zoology, Technical University Darmstadt,
Schnittspahnstr. 3, D-64287 Darmstadt, Germany
Fax: +49-6151/164808,
e-mail: [email protected]
M. Sams
Low Temperature Laboratory,
Helsinki University of Technology, Finland
Introduction
The relationships between frequency, periodicity,
pitch, and timbre
Acoustic signals used by humans and animals for
communication are often harmonic in structure. A
harmonic signal is characterized by a temporal envelope
which ¯uctuates periodically with a period given by the
reciprocal of the fundamental frequency (f0), and a
spectrum composed of frequencies which are integer
multiples of f0. Any portion of the spectrum which
contains at least two adjacent harmonics has the same
temporal envelope period and, in a human listener,
elicits the same pitch as the fundamental component
alone. This percept is referred to as Ôperiodicity pitch'
or, because the fundamental component is not required
to elicit that pitch, the percept of the Ômissing fundamental' (Schouten 1970).
The pitch of a harmonic signal can be varied, by
varying its temporal envelope period without varying its
spectral envelope or bandwidth ± two parameters essential for the timbre of a sound (Fig. 1). Conversely,
timbre can be varied by varying the spectral envelope
without varying the temporal envelope period, i.e.
without varying pitch (Fig. 1). For example, the timbre
of a pure tone di€ers from the timbre of a harmonic
sound, but it elicits the same pitch provided it has the
same period as the temporal envelope of the harmonic
sound (Fig. 1). Likewise, di€erent musical instruments
(or voices) can di€er in timbre when producing the same
note. In that sense pitch and timbre are largely independent and may be considered as orthogonal perceptual parameters related to temporal envelope periodicity
and spectral content, respectively. The independence of
pitch and timbre was demonstrated in psychophysical
experiments (Plomp and Steeneken 1971; Krumhansl
and Iverson 1992), and pitch and timbre were shown to
compete in streaming experiments (Singh 1987).
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coincidence units are activated (Langner 1981, 1983,
1992). Moreover, as found in the midbrain of cat and
chinchilla, neurons with di€erent BMFs are spatially
mapped in an orderly fashion, such that the gradients of
BMF (periodotopy) and CF (tonotopy) are roughly
orthogonal to each other (Schreiner and Langner 1988;
Langner et al. 1992).
Representation of frequency and periodicity
in the auditory cortex
Fig. 1 Pitch and timbre are largely independent percepts. Signals with
the same temporal envelope period have the same pitch, but they may
have di€erent spectral envelopes and therefore di€erent timbres.
Signals with di€erent periods elicit a di€erent pitch, while their spectral
envelopes (and their timbre) may be similar
Representation of frequency and periodicity
in the auditory brainstem
The independence of pitch and timbre is in line with
response properties of neurons in the brainstem of various animals. In addition to their frequency tuning
neurons are often tuned to particular modulation frequencies of temporal envelopes (for review see Langner
1992). Neurons which are tuned to a certain characteristic frequency (CF) may prefer di€erent temporal envelope modulations, e.g. they may have di€erent best
modulation frequency (BMF). To a ®rst approximation
their spectral and temporal tuning properties are independent. In the cochlear nucleus of various animals, the
tuning of neurons to temporal envelope modulations is
evident mainly with respect to the synchronization of
their discharges to the modulation (Frisina et al. 1990;
Rhode and Greenberg 1994). In the auditory midbrain,
synchronization is relatively poor, especially to high
modulation frequencies (>100 Hz, corresponding to
modulation periods<10 ms). However, neurons can be
tuned to such high modulation frequencies with respect
to their average discharge rate (Langner 1981, 1983,
1992; Rees and Mùller 1983; Rose and Capranica 1985;
Langner and Schreiner 1988; Heil et al. 1995).
In a theory of temporal correlation analysis neurons
in the auditory midbrain are considered as coincidence
detectors. Action potentials at their inputs represent
delayed and undelayed neuronal responses to the envelope of periodic signals. When these di€erent neuronal
delays are compensated by the period of the signal the
Orthogonality of neuronal representations of frequency
and envelope periodicity has been described in the auditory cortex (AC) analogue of the Mynah bird (Hose
et al. 1987). In contrast, Pantev et al. (1989), using
magnetoencephalography (MEG) in humans, found that
the locations of the magnetic ®eld generators within the
supratemporal cortex that were activated with a harmonic sound of missing fundamental and with a pure
tone of a frequency corresponding to that fundamental
were in close register. These authors concluded that ``...
the tonotopic organization of the primary auditory
cortex re¯ects the pitch rather than the frequency of the
stimulus''. This conclusion appears unsatisfactory, as it
is dicult to reconcile such an organization with the
perceptual orthogonality of pitch and timbre, as outlined above. Such an organization would also be at
variance with the quasiorthogonal arrangement of periodotopy and tonotopy found in animals.
However, the stimulus set used by Pantev et al.
(1989), viz. only two pure tones and one harmonic
sound, may have been too restricted to reveal the spatial
representation of frequency and temporal envelope period. We therefore attempted to reinvestigate this issue
using a more extensive set of stimuli, viz. up to six pure
tones and six harmonic sounds, and a magnetometer
with high spatial resolution, hoping that these conditions would be suited to resolve the discrepancy between
the nearly orthogonal arrangement of tonotopy and
periodotopy in the auditory midbrain and forebrain of
animals and their proposed parallel arrangement in the
human AC.
Materials and methods
Acoustic stimuli
Acoustic stimuli were pure tones and harmonic sounds. Their
spectra are schematically illustrated in Fig. 2. Pure-tone frequencies were 50 Hz, 100 Hz, 200 Hz, 400 Hz, and, in some experiments, also 800 Hz and 1600 Hz. In the ®gures they are referred to
as s50, s100, etc. (Fig. 2, left column). Harmonic sounds (Fig. 2,
centre and right columns) were composed of harmonics of 50 Hz,
100 Hz, 200 Hz, and 400 Hz and thus elicited a pitch corresponding to these fundamental frequencies. All harmonic sounds
had an upper cut-o€ frequency of 5 kHz, but the lower cut-o€
frequency was either 400 Hz (Fig. 2, centre) or 800 Hz (Fig. 2,
right). Signals with 400 Hz cut-o€ are referred to as p50, p100, etc.,
and those with 800 Hz cut-o€ as h100 and h200 (h50 and h400 were
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Fig. 2 Schematic spectra of
pure tones and harmonic signals used as stimuli. The high
cut-o€ frequency was 5000 Hz
for all harmonic sounds, while
the low cut-o€ frequency was
400 Hz for p50, p100, p200, and
p400 and 800 Hz for h100 and
h200. The only harmonic stimulus of this set which includes
its fundamental frequency is
p400. The spectra do not show
the roll-o€ of the sound transmission
not used). Signals with the same cut-o€ frequency have very similar
spectral envelopes. Thus, pure tones and harmonic signals labelled
with the same number (signals within a given row in Fig. 2) have
the same temporal envelope period and elicit the same pitch. Signals labelled with the same letter (signals within a given column in
Fig. 2) have the same spectral envelope and elicit a similar timbre.
All stimuli had durations of 500 ms, including linear rise and fall
times of 10 ms, and were presented with interstimulus intervals of
1.2 s.
Stimulus presentation
Six subjects (one female, ®ve males) participated in the experiments. In early experiments, pure tones (four subjects) and harmonic sounds (six subjects) were presented in separate experimental
sessions. Within each session stimuli were presented in random
order. In later experiments (four subjects), each harmonic sound
was followed by a pure tone with the same pitch, and stimulus pairs
of di€erent pitch were presented in random order. The sounds were
produced by equipment located outside the magnetically shielded
room inside which the subjects were seated during the measurements. Sounds were led to the subjects' ears via plastic tubes of
several meters in length and specially designed ear pieces. The
transfer function of this system was ¯at from 1 kHz to 2 kHz and
fell o€ by 15 dB/octave below 1 kHz and by 20 dB/octave above
2 kHz. Before an experiment, each subject adjusted loudness levels
of all stimuli to be equal (60 dB HL). Prior to magnetoencephalographic recording subjects were asked to remember the highest
number of consecutive signals (or signal pairs) with the same pitch
in order to keep their attention high during the recording session.
One to ®ve independent measurements were performed per subject
and within each session each stimulus was repeated about 200
times. The duration of a session was about 45 min.
Magnetoencephalographic recording
Auditory-evoked magnetic ®elds were recorded with a 122-channel
magnetometer, covering the whole head (Ahonen et al. 1993; HaÈmaÈlaÈinen et al. 1993; MaÈkelaÈ et al. 1993). Location of the head with
respect to the SQUID sensors was determined by measuring the
magnetic ®elds produced by small currents delivered to three coils
attached to the scalp. The location of the coils on the preauricular
points and the nasion was measured with a 3D-digitizer. The recording bandpass was 0.03±100 Hz (3-dB points; high-pass roll-o€
35 dB/decade, low-pass over 80 dB/decade) with a sampling rate of
0.4 kHz. Trials contaminated by eye blinks were rejected.
Data analysis
After digital low-pass ®ltering at 40 Hz equivalent current dipoles
(ECDs) that best described the measured magnetic ®eld at a given
latency were found by least-squares ®t in a spherical volume conductor (Kaukoranta et al. 1986). We used a one-dipole model,
separately for the left and right hemisphere, with a subset of
channels over each hemisphere. Such a one-dipole approximation is
only a ®rst approximation, since in each hemisphere multiple
sources may be expected to be active at most times (for example in
di€erent cytoarchitectonic areas of the supratemporal AC). However, there is no reasonable estimate of how many sources should
be assumed to be active at a given time. Because it has previously
been shown that the one-dipole model provides a very good approximation of the measured magnetic ®eld during short time
segments (for review see Hari 1990), we concentrated our analysis
of ECD locations on those short-time segments during which the
measured magnetic ®eld was best approximated by the one-dipole
model.
In order to make our interpretation of the data as demonstrated
in the ®gures more comprehensible we added ellipses (Fig. 5),
polygons (Fig. 6) and arrows or dotted lines (Figs. 5±10), all of
them matched by eye.
Results
Basic observations
Typically, the computed time-course of the ECD magnitude and the corresponding goodness-of-®t of the onedipole model showed peaks around 100 ms and 200 ms
after stimulus onset followed by sustained plateaus.
These de¯ections are referred to as M100, M200, and SF
(sustained ®eld), respectively. Figure 3 illustrates an
example with additional peaks around 60 ms (M60) and
150 ms (M150) which were seen in some subjects.
The precise latency of the prominent de¯ections was
stimulus dependent (see also Forss et al. 1993; Roberts
and Poeppel 1996). Figure 4 shows the latency of the
peak of M100 from the right hemisphere of all subjects
which were stimulated with harmonic sounds of 400 Hz
cut-o€ plotted against the envelope period. The contin-
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Fig. 3 Time-course of the
magnitude of an equivalent
current dipole (ECD), computed for consecutive 2-ms intervals from the magnetic ®elds
measured over the left hemisphere of one subject. The
stimulus was a harmonic signal
(p100) with a duration of
500 ms which started at
t = 10 ms. Acoustic delays
have been subtracted. The
goodness-of-®t (g) between the
®eld predicted by the one-dipole
model and the original data is
also shown. Typically, peaks of
the ECD magnitude and g were
observed at latencies corresponding to peak de¯ections of
the averaged original MEG
signal
uous line without symbols in Fig. 4 represents the result
of
a
linear
regression
analysis:
latencyM100 = (89 ‹ 3) ms + (1.38 ‹ 0.24) á period (ms);
r = 0.774 and P < 0.001.
The location of the ECD in each hemisphere was not
stable as a function of time. Two representative examples from di€erent hemispheres of two subjects are
shown in Fig. 5a, b. The data in this ®gure and most of
the following ®gures are presented as viewed from a
lateral perspective. Three-dimensional data analyses are
presented in Figs. 11, 12, and 13. During certain time
Fig. 4 Latency of the peak of M100 plotted as a function of temporal
envelope period of harmonic signals with a cut-o€ frequency of
400 Hz. Results were obtained from the right hemisphere of six
subjects stimulated through the contralateral ear. The results of a
linear regression analysis (continuous line without symbols) are also
shown
Fig. 5a, b ECD location as a function of time after stimulus onset
(stimulus: p400; time steps: 5 ms) and as seen from a lateral
perspective. Data are from the right (a) and left auditory cortices
(b) of two subjects. Note that di€erent regions (elliptical boundaries)
seem to be active at di€erent delays with the momentary maximum of
activity jumping rapidly between those regions (indicated by arrows)
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segments after stimulus onset the ECD is located within
rather restricted cortical areas (elliptical boundaries in
Fig. 5) and the ECD location changes relatively little as
a function of time. At other times, however, there appear
to be rapid (i.e. often within <5 ms) and pronounced
changes in ECD location from one restricted cortical
area to another or back and forth between two such
areas. However, the goodness-of-®t during such rapid
changes in ECD location was very small, preventing a
functional interpretation.
Figure 6 shows for the right hemisphere of one subject the ECD locations during short time segments
around M100 and M200 and during SF where the
goodness-of-®t was maximal (80±98%), i.e. around the
peaks of the ECD magnitude. Each data point represents 2 ms. The ECD trajectories are viewed from a
lateral perspective and their approximate position in
relation to the whole head is indicated by the inset in
Fig. 6a, b Lateral view of ECD trajectories in the right hemisphere of
one subject for stimulation with pure tones (a) and harmonic sounds
(b). The labels next to the trajectories identify the stimuli (see
Materials and methods and cf. Fig. 2). Each data point designates the
location of the ECD during a 2-ms interval within time segments of
maximal goodness-of-®t. The selected segments had durations of
10 ms for M100, of 20 ms for M200, and of 30 ms for SF. The arrows
indicate the systematic spatial progressions of the ECD trajectories
with frequency for pure tones and with fundamental frequency for
harmonic sounds during M100 and during SF. A systematic
progression during M200 is questionable. The positions of M100,
M200, and SF relative to one another were similar in most subjects
and in both hemispheres. For a better comprehension, their positions
in relation to a whole head are schematically indicated in the insert in a
Fig. 6a. The stimuli were four pure tones (a) and four
harmonic sounds (b). Note that the ECD trajectories of
M100, M200, and SF are spatially segregated. The ECD
trajectories of M200 are located most anteriorly, as has
been described earlier (e.g. Pantev et al. 1989; Hari
1990), and those of SF are located slightly more anterior
than those of M100, corroborating more recent results
of Pantev et al. (1994). Also note that for each de¯ection
(M100, M200, SF) the ECDs obtained with pure tones
and with harmonic sounds are localized in approximately equivalent cortical areas. However, there are
systematic detailed di€erences which are addressed further below.
Tonotopy
Previous MEG studies have demonstrated that the tonotopic gradient obtained for M100 and for SF runs
mainly along the lateromedial axis, thus approximately
perpendicular to the projection plane of Figs. 6±10, with
more lateral ECD locations for low frequencies and
more medial locations for high frequencies (e.g. Romani
et al. 1982; Pantev et al. 1988, 1989, 1994, 1995; Cansino
et al. 1994). However, the tonotopic gradient for M100
has a signi®cant component also in the tangential plane,
so that a gradient should also be visible from a lateral
perspective. Indeed, in several cases a tonotopic order of
ECD trajectories obtained with pure tones of di€erent
frequencies was evident in a lateral view. In the case
illustrated in Fig. 6a, for example, the ECD trajectories
during M100 shifted with increasing frequency from a
more posterior and superior location to a more anterior
and inferior location (arrow in M100 box in Fig. 6a; see
also Fig. 10), a shift in line with results of Pantev et al.
(1994, 1995). A similar shift of ECD trajectories with
frequency, in this case from posterior-inferior to anterior-superior, was seen during SF (arrow in SF box in
Fig. 6a). While during M200 the positional changes of
ECD locations for s100, s200, and s400 seem to indicate
a gradient mainly from superior to anterior, this gradient is not corroborated by the ECD position for s50.
The three-dimensional orientation of the tonotopic
gradient during M100 was analysed in the following way
and the results are demonstrated in Figs. 12 and 13: for
each 10-ms ECD trajectory with a maximal goodness-of®t the centre of gravity was ®rst computed. Then, the
distances in three-dimensional space of the centres for
pure-tone stimuli of neighbouring frequencies were
computed. Figure 12a shows, for all four subjects for
which data were available, cumulative distances of these
centres of gravity in the left hemisphere plotted against
pure-tone frequency. Note that the frequency axis in
Fig. 12a is logarithmic and that the cumulative distances
increase roughly linearly with the logarithm of stimulus
frequency. The thick solid line in Fig. 12a represents the
result of a linear regression analysis between the logarithm to the base 2 of stimulus frequency and the
cumulative distance. This function indicates an ap-
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proximately equal spacing of octaves in the human AC,
a result also in line with those of previous studies (e.g.
Romani et al. 1982; Pantev et al. 1989, 1994, 1995;
Cansino et al. 1994).
The thick broken line in Fig. 12a represents the
component of the average cumulative distance only
along the lateromedial or depth coordinate. The proximity of this line to the individual data and their ®t reveals that the depth coordinate is a major contributor to
the cumulative three-dimensional distances of the data.
The thin broken line in Fig. 12a represents the component of the average cumulative distance within the tangential or lateral surface plane. This line is not quite as
close to the data as the thick broken line. Nevertheless,
the contribution of the tangential plane to the cumulative three-dimensional distances is signi®cant. In other
words, frequency is represented along the depth coordinate, with low frequencies more lateral and high frequencies more medial, and also within the tangential
dimension, with low frequencies more superior and
posterior and high frequencies more anterior and inferior.
The average three-dimensional orientation of the tonotopic gradient, from low to high frequencies, and the
spatial frequency resolution that emerged from this
analysis, are represented by the orientation and length of
a vector in Fig. 13. The top and middle panels present a
lateral and a top view, respectively. The lateral view can
conveniently be compared with the raw data (e.g. Figs.
6a, 10).
Periodotopy
The ECD trajectories during M100 and during SF obtained with harmonic sounds of di€erent fundamental
frequency also showed a topographic order that was
evident in a lateral perspective. Examples of periodotopic organizations during M100 are illustrated in Figs.
6b, 8, and 10, and during SF in Fig. 7. In each case, the
approximate course of the periodotopic gradient is indicated by an arrow. The periodotopic gradients obtained in di€erent subjects di€er somewhat, but in
general seem to run along a posterior and inferior to
anterior and superior axis during M100 (Figs. 6b, 8, 10),
and along a posterior and more superior to anterior and
more inferior axis during SF (Fig. 7).
The reproducibility of the measurements is indicated
by Fig. 7a, b, which shows results from two measurements made on the same subject (PH) several months
apart. Note that the obtained periodotopic gradients
were quite similar, viz. were oriented from posteriorsuperior to anterior-inferior (see arrows). Furthermore,
absolute coordinates obtained in di€erent measurements
and subjects de®ned from external head coordinates are
quite similar. The average distance of the centres of
gravity of ECD trajectories for corresponding stimuli in
the three di€erent experiments illustrated in Fig. 7 is
12.0 ‹ 4.0 mm, only about twice the average distance
Fig. 7a±c Lateral view of the ECD locations during SF (~380 ms).
For each stimulus, the ECD trajectory represents a 20-ms segment
(time interval: 2 ms). The results were obtained from the right
hemisphere of two subjects with (a) being a repetition of (b) several
months later. The approximate orientations of the periodotopic
gradients are indicated by arrows
between centres of gravity for neighbouring stimuli obtained in the same experiment (viz., 6.3 ‹ 4.8 mm).
Orthogonality of periodotopy and tonotopy
In a given subject there are obvious di€erences in the
orientations of the tonotopic and periodotopic gradients
for corresponding de¯ections, as seen from the lateral
perspective (cf. Fig. 6a and 6b). To investigate this issue
further, ®ve subjects were stimulated with harmonic
signals di€ering in f0 (hence in pitch) and in the low cuto€ frequency of the spectrum. The lower cut-o€ frequency was 400 Hz for p50, p100, p200, and p400, and
800 Hz for h100 and h200 (Fig. 2). This di€erence in
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Fig. 9 Lateral view of ECD trajectories during M60 (10-ms segments;
time intervals of 2 ms) in the left hemisphere of subject HS. Note the
di€erent orientations of the tonotopic and periodotopic gradients
(dashed lines). Also note that the trajectories for the two harmonic
stimuli with a cut-o€ frequency of 800 Hz (viz. h100 and h200) are
displaced relative to those with a cut-o€ frequency of 400 Hz (viz.
p50, p100, p200, p400) in the direction of the tonotopic gradient. Note
the grid-like regular spacing of ECD trajectories, especially for
harmonic signals
Fig. 8a±c Lateral view of the ECD trajectories during M100 in the
left hemisphere of two subjects (a and c) and in the right hemisphere
of a third subject (b). Subjects were stimulated with six harmonic
sounds di€ering in fundamental frequency and in low cut-o€
frequency which was 400 Hz for p50, p100, p200, and p400, and
800 Hz for h100 and h200 (see also Fig. 2 for key to the stimuli). For
each stimulus, the ECD trajectory represents a 10-ms segment (time
interval: 2 ms). The approximate orientations of the periodotopic
gradients are indicated by arrows with continuous lines while the
approximate displacements of h100 and h200 (owing to their higher
cut-o€ frequency) are indicated by arrows with dotted lines
the lower spectral boundary also constitutes a shift of
the centre of gravity of the stimulus spectrum along the
frequency axis. We therefore expected to obtain di€erences in the ECD locations between p- and h-stimuli that
should indicate the tonotopic gradient. In addition,
stimuli with identical cut-o€ frequency, but with di€erent fundamental frequency, should reveal the periodotopic gradient.
Figure 8 shows the results obtained for M100 from the
left hemisphere of two subjects (Fig. 8a, c) and from the
right hemisphere of a third subject (Fig. 8b). As noted
above, the periodotopic gradients, revealed by stimuli of
di€erent fundamental frequency and similar spectral
envelope, are oriented roughly from posterior to anterior
(as suggested by the arrows with continuous lines). ECD
trajectories for stimuli of di€erent cut-o€ frequency are
displaced. In other words, stimuli eliciting the same pitch
are not colocalized. As suggested by the arrows with
dotted lines, the displacement is roughly along the superior to inferior axis and within, approximately orthogonal to the periodotopic gradient (see also Fig. 10).
A similar result was obtained for M60 in subjects
with a prominent de¯ection at this latency. Data from
one subject (HS) are illustrated in Fig. 9. Note the gridlike arrangement of ECDs suggesting a regular representation of signal parameters along two axes as well as
equal distances for ECDs elicited by harmonic stimuli
separated by octaves. Note also that during M60 the
periodotopic gradient and the displacement of p- and
h-stimuli are reversed compared to those during M100
(cf. Figs. 8 and 9).
The reliability of these measurements is again emphasized by the similarities in the absolute coordinates
of ECD trajectories. The average di€erences in threedimensional space between the centres of gravity of
ECD trajectories for corresponding stimuli in di€erent
subjects was 10.3 ‹ 6.3 mm, less than twice the average
distance between neighbouring stimuli in the same subject (viz., 6.5 ‹ 4.0 mm).
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It may be noteworthy that in some cases the ECD
trajectories for p400, the only harmonic stimulus whose
spectrum included the f0, showed peculiarities. For example, in subject GL (Fig. 8a) the position of the ECD
trajectory for p400 would seem more appropriate for
h400, a stimulus which was not tested. Since p400 is a
combination of h400 and the fundamental frequency of
400 Hz (see Materials and methods), p400 would be
expected to elicit the same response as h400, provided
the subject did not hear or was able to Ôignore or suppress' the fundamental component. In subject PH
(Fig. 7a, b; Fig. 6b) the orientation of the ECD trajectory for p400 is markedly di€erent from the orientation
of the trajectories for the other stimuli.
Evidence for orthogonality from experiments
using harmonic and pure tones in the same session
As noted above, the relative displacement of ECD trajectories for stimuli of di€erent cut-o€ frequency was
roughly orthogonal to the periodotopic gradient. More
direct evidence for an approximately orthogonal organization of tonotopy and periodotopy comes from the
analysis of the locations of ECD trajectories for harmonic and pure tone stimuli which were presented to
four subjects as stimulus pairs in the same experimental
session. Figure 9 presents such data for M60. In this
lateral view the tonotopic gradient, revealed by the ECD
trajectories for pure-tone stimuli of di€erent frequency,
runs approximately from inferior to superior, while the
periodotopic gradient, revealed by the ECD trajectories
for harmonic stimuli of di€erent f0 runs approximately
from anterior to posterior. While in this lateral view
tonotopic and periodotopic gradients (dotted lines in
Fig. 9) are not orthogonal to each other, it is important
to stress that they are clearly not parallel. The displacement to more superior loci of ECD trajectories for
harmonic stimuli of higher (h100, h200) relative to those
of lower cut-o€ frequency (p50, p100, etc.) is approximately in the direction that is expected from the orientation of the tonotopic gradient. Note that the ECD
trajectories for the harmonic stimuli with a cut-o€ frequency of 400 Hz (viz. p50, p100, etc.) are located between the ECD trajectories for pure-tone stimuli of 400
and 800 Hz, while harmonic stimuli with a cut-o€ frequency of 800 Hz (h100 and h200) are located between
pure tones of 800 and 1600 Hz. For harmonic stimuli of
di€erent fundamental frequencies the ECD trajectories
are regularly spaced with an average of 6 mm/octave
and for pure tones of di€erent frequencies with an average of 8 mm/octave. The cut-o€ frequencies of p100
and h100, as well as of p200 and h200 and h200 (400 Hz
and 800 Hz, respectively) are also separated by one octave, however, in this case along the frequency axis.
Accordingly, the corresponding ECDs are separated by
about 10 mm in the direction of the tonotopic gradient.
Corresponding data for M100, from a di€erent subject and hemisphere, are illustrated in Fig. 10. In this
case and in this lateral view, tonotopic and periodotopic
gradients are roughly orthogonal and, as during M60,
the displacement of ECD trajectories for harmonic
stimuli of higher (h100, h200) relative to those of lower
cut-o€ frequency (p50, p100, etc.) is again approximately in the direction expected from the orientation of
the tonotopic gradient. Note that the tonotopic and
periodotopic gradients run in directions opposite to
those of the corresponding gradients during M60 (cf.
Figs. 9 and 10).
Three-dimensional analysis of ECD positions
The most direct evidence for an orthogonal organization
of tonotopy and periodotopy comes from analysis of the
three-dimensional spatial relationships between ECD
trajectories for pure-tone and harmonic stimuli in all
four subjects which were stimulated with both types of
signals in the same experimental session. The analysis
was performed in the following way. We ®rst calculated
the centre of gravity of the ECD trajectory for each
stimulus in a given subject and hemisphere during M100
and, where possible, during M60. Next, we obtained the
vector between centres of gravity for pure-tone and for
harmonic stimuli that are neighbours along the dimen-
Fig. 10 Lateral view of ECD trajectories during M100 (10-ms
segments; time intervals of 2 ms) in the right hemisphere of subject
PH. Note the quasi-orthogonal orientations of the tonotopic and
periodotopic gradients (dashed lines). Also note that the trajectories
for the two harmonic stimuli with a cut-o€ frequency of 800 Hz (viz.
h100 and h200) are displaced relative to those with a cut-o€ frequency
of 400 Hz (viz. p50, p100, p200, p400) approximately in the direction
of the tonotopic gradient
673
sion of frequency and fundamental frequency, respectively, i.e. the vector between s50 and s100 (s50®s100),
between s100 and s200 (s100®s200), etc., between h100
and h200 (h100®h200), between p50 and p100
(p50®p100), between p100 and p200 (p100®p200), and
between p200 and p400 (p200®p400). Finally, we calculated the angles formed by all vectors between two
neighbouring pure-tone stimuli with all vectors between
two neighbouring harmonic stimuli (e.g. the angles
formed by s200®s400 with p50®p100, with
p100®p200, etc.). Figure 11 shows the frequency distributions of these angles, with a bin width of 15 degrees,
for M100 in the left and right hemispheres and for M60
in the left hemisphere. The number of M60 data with
sucient goodness of ®t for the right hemisphere was
too limited for an evaluation. The angles were not evenly
distributed. Rather, the distributions peak near 90 degrees, as identi®ed in Fig. 11. These values emphasize
that, on average, tonotopic and periodotopic gradients
are oriented nearly orthogonally to one other.
Another independent demonstration of the orthogonality of tonotopy and periodotopy comes from a
comparison of the average tonotopic and periodotopic
vectors in three-dimensional space. Figure 12b plots the
cumulative three-dimensional distances of the centres of
gravity of ECD trajectories during M100 for neighbouring harmonic stimuli, in a fashion analogous to that
described above for pure-tone stimuli (see Fig. 12a). The
periodotopic data in Fig. 12b are from the same subjects
and hemispheres that provided the tonotopic data in
Fig. 12a and the angle distribution of Fig. 11a, and, in
addition, from two subjects (SA and SL) who were
stimulated with harmonic signals only. Although the
cumulative distances of the centres of gravity for harmonic signals scatter more widely among subjects than
those for pure tones (cf. Figs. 12a and 12b), they also
increase roughly linearly with the logarithm of f0 (thick
solid line in Fig. 12b). Thus, octaves of f0 are approximately equally spaced in the human AC. However, the
spatial resolution for fundamental frequency (viz.
5.5 mm/octave) is less than that for pure tone frequency
(viz. 7.1 mm/octave).
The thick broken line in Fig. 12b represents the
component of the average cumulative distance along
the lateromedial or depth coordinate only. Note that this
line deviates considerably from the individual data, thus
the depth coordinate is not the major contributor to
the cumulative three-dimensional distances of the periodotopic data. In contrast, the thin broken line, which
represents the component of the average cumulative
distance within the tangential or lateral surface plane, is
in rather close register with the data. Thus, the tangential plane contributes most to the cumulative threedimensional distances of the ECD centres of gravity for
harmonic stimuli.
To allow the comparison with the tonotopic vector,
the average three-dimensional orientation of the periodotopic gradient, from low to high fundamental frequencies, and the spatial frequency resolution that
Fig. 11a±c Distributions of angles (binwidth: 15 degrees) formed by
tonotopic and periodotopic gradients during M100 in the left (a) and
right hemisphere (b) and during M60 in the left hemisphere (c). Each
entry is the angle formed by a vector between the centres of gravity of
ECD trajectories for two pure-tone stimuli of neighbouring frequency
and a vector between the centres of gravity of ECD trajectories for
two harmonic stimuli of neighbouring fundamental frequency, as
described in detail in the Results. The mean angles, the standard
deviations, the vector strengths, and the likelihoods of the distributions to be random, as obtained by circular statistics, are also
identi®ed
emerged from this analysis, are also represented by the
orientation and length of a vector in Fig. 13. The two
vectors form an angle of 95 degrees when viewed from
the lateral perspective (Fig. 13a), and an angle of 89
degrees when viewed from the top perspective
(Fig. 13b). However, to derive the average spatial organization, the two vectors should be viewed from an
674
Fig. 12a, b Cumulative three-dimensional distances in the left hemisphere between the centres of gravity of ECD trajectories during
M100 as a function of frequency for pure-tone stimuli (a) and of
fundamental frequency for harmonic stimuli (b). Di€erent symbols
represent di€erent subjects. The thick continuous lines represent the
results of linear regression analyses between cumulative distance (cd)
and the logarithm to the base 2 of frequency and fundamental
frequency (1d f). These results suggest a 30% greater spacing for
tonotopy than for periodotopy (7.1 versus 5.5 mm/octave). The thick
broken lines represent the components of the distances along the
lateromedial or depth coordinate and the thin broken lines within the
tangential or surface plane only
optimal perspective, i.e. by looking down onto that
plane in which both vectors have their maximal length.
In this plane, the tonotopic vector has a length corresponding to a frequency resolution of 7.1 mm/octave
and the periodotopic vector a length corresponding to a
resolution of 5.5 mm/octave, i.e. the values derived from
the cumulative three-dimensional distances of the ECD
centres of gravity (cf. Fig. 12). This optimal plane is
tilted relative to a horizontal plane and points downward in the anterior and medial directions. Figure 13c
shows that in this optimal plane, periodotopic and
tonotopic vectors form an angle of 85 degrees, i.e. an
angle again close to 90 degrees.
Fig. 13 Average orientation and spatial resolution of tonotopic and
periodotopic gradients during M100 represented by the orientation
and length of two vectors. The radius of each circle represents
7.1 mm/octave. The data are shown from a lateral view (top), the
same perspective as used for Figs. 5±10, from a top view (middle), and
from an optimal view (bottom), i.e. by looking down onto that plane
in which both vectors have their maximal length. This optimal plane is
tilted relative to a horizontal plane and points downward in the
anterior and medial directions. The angle formed by the average
tonotopic and periodotopic vectors is 85 degrees (bottom panel), but
appears slightly di€erent when viewed from a lateral or top
perspective, viz. 95 (top) and 89 degrees (middle), respectively
Discussion
The present study has demonstrated with the MEG
technique the existence of a tonotopic and a periodotopic organization of the human AC and, most importantly, an approximately orthogonal arrangement of
tonotopic and periodotopic gradients.
675
The tonotopic organization, which was analysed here
in most detail for the generators of M100 (Figs. 6a, 10,
12a, 13), compares well with that reported in previous
studies (e.g. Romani et al. 1982; Pantev et al. 1989, 1994,
1995; LieÂgeois-Chauvel et al. 1994; Cansino et al. 1994).
In agreement with our results, the tonotopic gradient
during M100 has been reported to be oriented along the
depth coordinate with low frequencies being represented
more laterally and high frequencies more medially
(Romani et al. 1982; Pantev et al. 1989, 1994, 1995).
These studies also document a component of the tonotopic gradient in the tangential plane with low frequencies being represented more posteriorly and high
frequencies more anteriorly. Likewise, the above studies
and ours agree in that there is an approximately equal
spacing of octaves (Figs. 6a, 10, 12a). Our cumulative
distances suggest an average spatial resolution of
7.1 mm/octave. The values that can be derived from
other studies vary considerably. The data of Cansino
et al. (1994; their Fig. 9) reveal three-dimensional resolutions of about 4±7 mm/octave in di€erent individuals,
those of Romani et al. (1982; their Fig. 4) average resolutions of about 4 mm/octave, and those of Pantev
et al. (1994; their Fig. 5) some 2±3 mm/octave. Whatever the source of this variability, it is important to note
that these studies, while they disagree with respect to
absolute distances, do agree with respect to the relative
spatial relationships of ECD locations for di€erent
stimuli. Furthermore, they seem to agree with respect to
the relative spatial relationships of ECD locations for
di€erent de¯ections of the response, e.g. the anterior
location of M200 relative to M100, of SF relative to
M100, etc. (see e.g. Pantev et al. 1989; Hari 1990;
McEvoy et al. 1994).
The periodotopic organization of the human AC,
demonstrated here for M60 (Figs. 9, 13c) SF (Figs. 6a,
10, 12a), and in most detail for M100, con®rms our
preliminary results reported elsewhere (Langner et al.
1994). The nearly orthogonal arrangement of the tonotopic and the periodotopic gradients, again documented
here in most detail for M100 (Figs. 6, 8, 10, 12, 13),
constitutes the central ®nding of the present study. This
®nding is radically opposed to the conclusion drawn by
Pantev et al. (1989) from their MEG study in humans,
viz. that ``... the spatial arrangement of the generators of
the magnetic wave M100 re¯ects the pitch rather than
the spectral contents of the stimulus'', i.e. in e€ect the
conclusion that tonotopy and periodotopy are organized
in parallel.
We believe that these opposing conclusions originate
from the design and selection of stimuli. Pantev et al.
(1989) used only two pure-tone stimuli with frequencies
of 250 and 1000 Hz and only one harmonic signal,
composed of the fourth to eighth harmonic of the 250Hz f0, i.e. of 1000 Hz, 1250 Hz, 1500 Hz, and 1750 Hz.
Clearly, the selection of only a single harmonic stimulus
prevents the demonstration of any periodotopic gradient. Furthermore, this harmonic signal was presented
together with a (continuous) narrow-band noise centred
at the f0. This may explain why that the ECD evoked by
this stimulus was located closer to the ECD evoked by
the 250-Hz tone than to that evoked by the 1000-Hz
tone.
The demonstration of an orthogonal arrangement of
tonotopic and periodotopic gradients in the present
study was achieved by selecting stimuli that allowed the
variation of temporal envelope period without varying
the spectral envelope and vice versa (see Fig. 2). The
orthogonality could easily be missed by the use of
stimuli that are designed such that temporal envelope
period and spectral envelope vary concomitantly.
The orthogonal arrangement agrees well with results
of single- and multi-unit mapping studies of tonotopy
and periodotopy in the auditory midbrain and forebrain
of mammals and birds, which have demonstrated nearly
orthogonal maps of CF and BMF (Hose et al. 1987;
Schreiner and Langner 1988; Langner et al. 1992). It was
shown that a temporal analysis of periodicity analysis is
underlying the spatial representation of periodicity orthogonal to the tonotopic map in the midbrain (Langner
and Schreiner 1988). The similarity of representations in
the midbrain of animals and in the human cortex may
suggest also similar mechanisms of pitch perception. The
conclusion would be that one dimension of the cortical
map represents the result of the cochlear frequency
analysis and corresponds to the perceptual quality of
timbre, while the other dimension, orthogonal to the
frequency axis, represents the result of the temporal
periodicity analysis in the brainstem and corresponds to
the perceptual quality of pitch. As a result, signals with
the same timbre (e.g. two vowels [a:]) are represented at
di€erent locations in this map, provided they di€er in
pitch (e.g. when uttered by a male subject and a female
subject).
The orthogonality of tonotopy and periodotopy, as
well as their relative spatial resolutions, obtained from
our results in the human AC, are also in line with the
perceptual independence of pitch and timbre as described by Plomp and Steeneken (1971). In fact, the
correspondence is most remarkable. These authors presented subjects with stimuli of ®ltered periodic pulses.
Stimuli di€ered in repetition rate (200±640 Hz), i.e. in
pitch, and in the centre frequency of the 1/3-octave
bandpass ®lter (2000±6400 Hz). Subjects were asked to
judge and rank the similarity of signals presented in
triads. The multi-dimensional scaling analysis of their
data revealed an orthogonal organization of pulse repetition rate and centre frequency, i.e. a perceptual orthogonality of pitch and timbre. Furthermore, the
perceptual distances of stimuli di€ering in centre frequency were about 1.6 times as large as those of stimuli
di€ering in repetition rate. This compares remarkably
well with the ratio of 1.3 between the spatial resolutions
for frequency and fundamental frequency (viz. 7.1 mm/
octave divided by 5.5 mm/octave) obtained in the present study. This close correspondence may constitute
another example of the match of behavioural discriminability of a stimulus parameter and the scaling of its
676
cortical representation, well known from the somatosensory and visual systems, as well as from the auditory
system, particularly of echolocating bats (Suga et al.
1987).
Acknowledgements This study was supported by the Academy of
Finland, the Deutsche Forschungsgemeinschaft, and the Human
Frontier Science Program Organization. We are grateful to
Prof. R. Hari and many colleagues at the Low Temperature Laboratory of the Helsinki University of Technology for making these
experiments possible.
References
Ahonen A, HaÈmaÈlaÈinen M, Kajola MJ, Knuutila JET, Laine PP,
Lounasmaa OV, Parkkonen LT, Simola JT, Tesche CD (1993)
122-Channel SQUID instrument for investigating the magnetic
signals from the human brain. Physica Script T49: 198±205
Cansino S, Williamson SJ, Karron D (1994) Tonotopic organization of human auditory association cortex. Brain Res 663: 38±
50
Forss N, MaÈkelaÈ JP, McEvoy L, Hari R (1993) Temporal integration and oscillatory responses of the human auditory cortex
revealed by evoked magnetic ®elds to click trains. Hear Res 68:
89±96
Frisina RD, Smith RL, Chamberlain SC (1990) Encoding of amplitude modulation of the gerbil cochlear nucleus: I. A hierarchy of enhancement. Hear Res 44: 99±122
HaÈmaÈlaÈinen M, Hari R, Ilmoniemi RJ, Knuutila J, Lounasmaa OV
(1993) Magnetoencephalography ± theory, instrumentation,
and applications to noninvasive studies of the working human
brain. Rev Mod Phys 65: 413±497
Hari R (1990) The neuromagnetic method in the study of the human auditory cortex. In: Grandori F, Hoke M, Romani GL
(eds) Auditory-evoked magnetic ®elds and electric potentials.
Advances in Audiology, vol 6. Karger, Basel, pp 222±282
Heil P, Schulze H, Langner G (1995) Ontogenetic development of
periodicity coding in the inferior colliculus of the mongolian
gerbil. Aud Neurosci 1: 363±383
Hose B, Langner G, Scheich H (1987) Topographic representation
of periodicities in the forebrain of the Mynah bird: one map for
pitch and rhythm? Brain Res 422: 367±373
Kaukoranta E, HaÈmaÈlaÈinen M, Sarvas J, Hari R (1986) Mixed and
sensory nerve stimulation activate di€erent cytoarchitectonic
areas in the human primary somatosensory cortex SI. Neuromagnetic recordings and statistical considerations. Exp Brain
Res 63: 60±66
Krumhansl CL, Iverson P (1992) Perceptual interactions between
musical pitch and timbre. J Exp Psychol 18: 739±751
Langner G (1981) Neuronal mechanisms for pitch analysis in the
time domain. Exp Brain Res 44: 450±454
Langner G (1983) Evidence for neuronal periodicity detection in
the auditory system of the guinea fowl: implications for pitch
analysis in the time domain. Exp Brain Res 52: 333±355
Langner G (1992) Periodicity coding in the auditory system. Hear
Res 60: 115±142
Langner G, Sams M, Heil P, Schulze H, Hari R (1994) Orthogonal
representation of frequency and periodicity in the human auditory cortex: evidence from magneto-encephalography. Soc
Neurosci 20 (part1): 325 (abstract)
Langner G, Schreiner CE (1988) Periodicity coding in the inferior
colliculus of the cat. I. Neuronal mechanisms. J Neurophysiol
60: 1799±1822
Langner G, Schreiner CE, Albert M (1992) Tonotopy and periodotopy in the auditory midbrain of cat and guinea fowl. In:
Cazals Y, Horner K, Demany L (eds) Auditory physiology and
perception. Pergamon Press, Oxford, pp: 241±248
LieÂgeois-Chauvel C, Musolini A, Badier JM, Marquis P, Chauvel P
(1994) Evoked potentials recorded form the auditory cortex in
man: evaluation and topography of the middle latency components. Electroencephalogr Clin Neurophysiol 92: 204±214
MaÈkelaÈ JP, Ahonen A, HaÈmaÈlaÈinen M, Hari R, Ilmoniemi R,
Kajola M, Knuutila J, Lounasmaa OV, McEvoy L, Salmelin R,
Salonen O, Sams M, Simola J, Tesche C, Vasama J-P (1993)
Functional di€erences between auditory cortices of the two
hemispheres revealed by whole-head neuromagnetic recordings.
Human Brain Mapping 1: 48±56
McEvoy L, Hari R, Imada T, Sams M (1994) Human auditory
cortical mechanisms of sound lateralization: I Interaural time
di€erences at sound onset. Hear Res 67: 98±109
Pantev C, Hoke M, Lehnertz K, LuÈtkenhoÈner B, Anogianakis G,
Wittkowski W (1988) Tonotopic organization of the human
auditory cortex revealed by transient auditory evoked magnetic
®elds. Electroencephalogr Clin Neurophysiol 69: 160±170
Pantev C, Hoke M, LuÈtkenhoÈner B, Lehnertz K (1989) Tonotopic
organization of the auditory cortex: pitch versus frequency
representation. Science 246: 486±488
Pantev C, Eulitz C, Elbert T, Hoke M (1994) The auditory evoked
sustained ®eld: origin and frequency dependence. Electroencephalogr Clin Neurophysiol 90: 82±90
Pantev C, Bertrand O, Eulitz C, Verkindt C, Hampson S, Schuierer G, Elbert T (1995) Speci®c tonotopic organizations of
di€erent areas of the human auditory cortex revealed by simultaneous magnetic and electric recordings. Electroencephalogr Clin Neurophysiol 94: 26±40
Plomp R, Steeneken HJM (1971) Pitch versus timbre. Seventh
International Congress on Acoustics, Budapest, pp 387±380
Rees A, Mùller AR (1983) Responses of neurons in the inferior
colliculus of the rat to AM and FM tones. Hear Res 10: 301±
330
Rhode WS, Greenberg S (1994) Encoding of amplitude modulation
in the cochlear nucleus of the cat. J Neurophysiol 71: 1797±1825
Roberts TPL, Poeppel D (1996) Latency of auditory evoked M100
as a function tone frequency. Neuroreport 7: 1138±1140
Romani GL, Williamson SJ, Kaufman L (1982) Tonotopic organization of the human auditory cortex. Science 216: 1339±1340
Rose GJ, Capranica RR (1985) Sensitivity to amplitude modulated
sounds in the anuran auditory nervous system. J Neurophysiol
53: 446±465
Schouten JF (1970) The residue revisited. In: Plomp R, Smoorenburg GF (eds) Frequency analysis and periodicity detection in
hearing. Sijthof, Leiden, pp 41±54
Schreiner CE, Langner G (1988) Periodicity coding in the inferior
colliculus of the cat. II. Topographical organization. J Neurophysiol 60: 1823±1840
Singh PG (1987) Perceptual organization of complex-tone sequences ± a tradeo€ between pitch and timber. J Acoust Soc
Am 82: 886±899
Suga N, Niwa H, Taniguchi I, Margoliash D (1987) The personalized auditory cortex of the mustached bat ± adaptation for
echolocation. J Neurophysiol 58: 643±654