A Connectionist Approach to Automatic Transcription of

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1
A Connectionist Approach to Automatic
Transcription of Polyphonic Piano Music
Matija Marolt, Member, IEEE
Abstract— In this paper, we present a connectionist approach
to automatic transcription of polyphonic piano music. We first
compare the performance of several neural network models on
the task of recognizing tones from time-frequency representation
of a musical signal. We then propose a new partial tracking
technique, based on a combination of an auditory model and
adaptive oscillator networks. We show how synchronization of
adaptive oscillators can be exploited to track partials in a musical
signal. We also present an extension of our technique for tracking
individual partials to a method for tracking groups of partials by
joining adaptive oscillators into networks. We show that oscillator
networks improve the accuracy of transcription with neural
networks. We also provide a short overview our entire
transcription system and present its performance on
transcriptions of several synthesized and real piano recordings.
Results show that our approach represents a viable alternative to
existing transcription systems.
Index Terms—adaptive oscillators, music transcription, neural
networks
M
I. INTRODUCTION
USIC transcription could be defined as an act of
listening to a piece of music and writing down music
notation for the piece. If we look at the traditional way of
making music, we can imagine a performer reading a score,
playing an instrument and thus producing music. Transcription
of polyphonic music (polyphonic pitch recognition) is the
reverse process; an acoustical waveform is converted into a
parametric representation, where notes, their pitches, starting
times and durations are extracted from the signal.
Transcription is a difficult cognitive task and is not inherent in
human perception of music, although it can be learned. It is
also a very difficult problem for current computer systems.
Separating notes from a mixture of other sounds, which may
include notes played by the same or different instruments or
simply background noise, requires robust algorithms with
performance that should degrade gracefully when noise
increases.
Applications of a music transcription system are versatile.
Transcription produces a compact and standardized parametric
Manuscript received October 23, 2001.
M. Marolt is with Faculty of Computer and Information Science,
University of Ljubljana, Trzaska 25, 1000 Ljubljana, Slovenia (phone:+386 1
4768483; fax: +386 1 4264647; e-mail: [email protected]).
representation of music. Such representation is needed for
content-based retrieval of music in most current musical
databases. It is useful in music analysis systems for tasks such
as melody extraction, music segmentation and rhythm tracking.
Transcription aids musicologists in analyzing music that has
never been written down, such as improvised or ethnical
music. The conversion of an acoustical waveform into a
parametric description is also useful in the process of making
music, as well as in newer coding standards, such as MPEG-4,
which may include such descriptions.
First attempts of transcribing polyphonic music have been
made by Moorer [1]. His system was limited to two voices of
different timbres and frequency ranges and had limits on
allowable intervals. In recent years, several systems have been
developed. Some of them are targeted to transcription of music
played on specific instruments [2-4], while others are general
transcription systems [5-6]. All of them share several common
characteristics. In the beginning, they calculate a timefrequency representation of the musical signal. Authors use
various representations ranging from Fourier analysis to
bilinear distributions. In the next step, the time-frequency
representation is refined by locating partials in the signal. To
track partials, most systems use ad hoc algorithms such as peak
picking and peak connecting. Partial tracks are then grouped
into notes with different algorithms relying on cues such as
common onset time and harmonicity. Some authors use
templates of instrument tones in this process [3-6], as well as
higher-level knowledge of music, such as probabilities of
chord transitions [6].
Recognizing notes in a signal is a typical pattern recognition
task and we were surprised to that few current systems use
machine learning algorithms in the transcription process.
Therefore, our motivation was to develop a transcription
system based on connectionist algorithms, such as neural
networks, which have proved to be useful in a variety of
pattern recognition tasks. We tried to avoid using explicit
symbolic algorithms, and employed connectionist approaches
in different parts of our system instead.
Music transcription is a difficult task, and we therefore put
one major constraint on our transcription system: it only
transcribes piano music, so piano should be the only
instrument in the analyzed musical signal. We didn't make any
other assumptions about the signal, such as maximal
polyphony, minimal note length, style of transcribed music or
the type of piano used. The system takes an acoustical
2
waveform of a piano recording (44.1 kHz sampling rate, 16 bit
resolution) as its input. Stereo recordings are converted to
mono. The output of the system is a MIDI file containing the
transcription. Notes, their starting times, durations and
loudness' are extracted from the signal.
The organization of this paper is as follows. In Section II we
propose a new model for tracking partials in a polyphonic
audio signal, based on networks of adaptive oscillators.
Section III presents a comparison of several neural network
models for recognizing piano notes in outputs of the partial
tracking model. Section IV presents a quick overview of our
complete transcription system and in section V we present
performance statistics of the system on transcriptions of
several synthesized and real recordings of piano music. We
also provide a comparison of our results to results of some
other authors. Section VI concludes this paper.
II. PARTIAL TRACKING WITH NETWORKS OF ADAPTIVE
OSCILLATORS
Most current transcription systems (including ours) are
composed of two main parts: a partial tracking module, which
calculates a clear and compact time-frequency representation
of the input audio signal, and a note recognition module, which
groups the found partials into notes. In contrast to most other
current transcription approaches, we use connectionist
methods for solving both problems. In this section, we propose
a new model for tracking groups of partials in an audio signal
with networks of adaptive oscillators. We describe how neural
networks can be used for note recognition in section III, where
we also provide a comparison of several neural network
models for this task.
Tones of melodic music instruments can be roughly
described as a sum of frequency components (sinusoids) with
time-varying amplitudes and almost constant frequencies.
These frequency components are called partials and can be
recognized as prominent horizontal structures in the timefrequency representation of a musical signal. By finding
partials, one can obtain a clearer and more compact
representation of the signal, and partial tracking is therefore
used in all current transcription systems. Although partial
tracking algorithms play an important role in transcription
systems, because they provide data to the note recognition
module, little attention has been paid to the development of
these algorithms. Most systems use a procedure similar to that
of a tracking phase vocoder [13]. After the calculation of a
time-frequency representation, peaks are computed in each
frequency image. Only peaks with amplitude that is larger than
a chosen (possibly adaptive) threshold are kept as candidate
partials. Detected peaks are then linked over time according to
intuitive criteria such as proximity in frequency and amplitude,
and partial tracks are formed in the process. Such approach is
quite susceptible to errors in the peak peaking procedure,
where missed or spurious peaks can lead to fragmented or
spurious partial tracks. Some systems therefore use additional
heuristics for merging fragmented partial tracks. The second
main shortcoming of the “peak picking-peak connecting”
approach is detection of frequency modulated partials. Here,
the peak connecting algorithm can fail if it is not designed to
tolerate frequency modulation. An innovative approach to
partial tracking has been proposed by Sterian [3], who still
uses a peak picking procedure in the first phase of his system,
but later uses Kalman filters, trained on examples of
instrument tones, to link peaks into partial tracks. His system
still suffers due to errors in the peak picking stage, but its main
drawback is that partials have to be at least 150 ms long to be
discovered. For our system, this is a very serious limitation,
because tones in piano music are frequently shorter than 100
ms.
The shortcomings of most current partial tracking
approaches have led us to the development of a new partial
tracking model. In this section, we propose a partial tracking
model based on a connectionist paradigm. It is composed of
two parts: an auditory model, which emulates the functionality
of human ear, and adaptive oscillators that extract partials
from outputs of the auditory model. We also present an
extension of the model for tracking individual partials to a
model for tracking groups of harmonically related partials by
joining adaptive oscillators into networks.
A. Auditory Model
The first stage of our partial tracking algorithm transforms
the acoustical waveform into time-frequency space with an
auditory model, which emulates the functionality of human
ear. The auditory model consists of two parts. A filterbank is
first used to split the signal into several frequency channels,
modeling the movement of basilar membrane in the inner ear.
The filterbank consists of an array of bandpass IIR filters,
called gammatone filters. The implementation we use is
described in [14-16]. We are using 200 filters with center
frequencies logarithmically spaced between 70 and 6000 Hz.
Fig. 1. Analysis of three partials of piano tone F3 with the auditory model.
Subsequently, the output of each gammatone filter is
processed by the Meddis’ model of hair cell transduction [17].
The hair cell model converts each gammatone filter output into
a probabilistic representation of firing activity in the auditory
nerve. Its operations are based on a biological model of the
hair cell and it simulates several of the cell's characteristics,
most notably half-wave rectification, saturation and adaptation.
Saturation and adaptation are very important to our model, as
3
they reduce the dynamic range of the signal, and in turn enable
our partial tracking system to track partials with low
amplitude. These characteristics can be observed in Fig. 1,
displaying outputs of three gammatone filters and the hair cell
model on the 1., 2., and 4. partial of piano tone F3 (pitch 174
Hz).
B. Partial Tracking with Adaptive Oscillators
The auditory model outputs a set of frequency channels
containing quasi-periodic firing activities of inner hair cells
(see Fig. 1). Temporal models of pitch perception are based on
the assumption that periodicity detection in these channels
forms the basis of human pitch perception. Periodicity is
usually calculated with autocorrelation. This produces a threedimensional time-frequency representation of the signal
(autocorrelogram), with time, channel center frequency and
autocorrelation lag represented on orthogonal axes. A
summary autocorrelogram (summed across frequency
channels) can be computed to give a total estimate of
periodicity of the signal at a given time. Meddis and Hewitt
[18] have demonstrated that the summary autocorrelogram
explains the perception of pitch in a wide variety of stimuli.
We decided to use a different approach for calculating
periodicity in frequency channels. It is based on adaptive
oscillators that try to synchronize to signals in output
frequency channels of the auditory model. A synchronized
oscillator indicates that the signal in a channel is periodic,
which in turn indicates that a partial with frequency similar to
that of the oscillator is present in the analyzed signal.
An oscillator is a system with periodic behavior. It oscillates
in time according to its two internal parameters: phase and
frequency. An adaptive oscillator adapts its phase and
frequency in response to its input (driving) signal. When a
periodic signal is presented to an adaptive oscillator, it
synchronizes to the signal by adjusting its phase and frequency
to match that of the driving signal. By observing the frequency
of a synchronized oscillator, we can make an accurate estimate
of the frequency its driving signal.
Various models of adaptive oscillators have been proposed,
some have also found use in computer music researches for
modeling rhythm perception [19-20] and for simulation of
various psychoacoustic phenomena [21]. After reviewing
several models, we decided to use a modified version of the
Large-Kolen adaptive oscillator [19] in our system.
The Large-Kolen oscillator oscillates in time according to
its period (frequency) and phase. The input of the oscillator
consists of a series of discrete impulses, representing events.
After each oscillation cycle, the oscillator adjusts its phase and
period, trying to match its oscillations to events in the input
signal. If input events occur in regular intervals (are periodic),
the final effect of synchronization is alignment of oscillations
with input events. Phase and period of the Large-Kolen
oscillator are updated according to the modified gradient
descent rule, minimizing an error function that describes the
difference between input events and beginnings of oscillation
cycles. The speed of synchronization can be controlled by two
oscillator parameters.
Our partial tracking model uses adaptive oscillators to
detect periodicity in output channels of the auditory model.
Each output channel is routed to the input of one adaptive
oscillator. The initial frequency of the oscillator is equal to the
center frequency of its input channel. When an oscillator
synchronizes to its input, this indicates that the input signal is
periodic and consequently that a partial with frequency similar
to that of the oscillator is present in the input signal. A
synchronized oscillator therefore represents (tracks) a partial
in the input signal.
To improve partial tracking, we made a few minor changes
to the Large-Kolen oscillator model. Most notably, we added a
new measure of successfulness of synchronization that is used
as the oscillator's output value. The measure is related to the
amount of phase corrections made in the synchronization
process; less phase corrections signify better synchronization.
Oscillator's output therefore indicates how successfully the
oscillator managed to synchronize to its input signal.
Fig. 2. Partial tracking with adaptive oscillators.
The modified Large-Kolen oscillator can successfully track
partials with diverse characteristics. Four examples are given
in Fig. 2. Example A presents a simple case of tracking a 440
Hz sinusoid. The oscillator (initial frequency 440 Hz)
synchronizes successfully, as can be seen from its output, and
after an initial 1 Hz rise, its frequency settles at 440 Hz.
Example B shows how two oscillators with initial frequencies
set to 440 and 445 Hz synchronize to a sum of 440 and 445 Hz
sinusoids (5 Hz beating). Both oscillators synchronize
successfully at 442.5 Hz, as can be seen from their outputs and
frequencies. The behavior is consistent to human perception of
the signal. Example C is shows the tracking of a frequency
modulated 440 Hz sinusoid. The oscillator synchronizes
successfully, its frequency follows that of the sinusoid. The
last example (D) shows how two oscillators track two
frequency components that rise/fall from 440 to 880 Hz.
4
Tracking is successful; each oscillator tracks the component
closest to its input frequency channel.
C. Tracking Groups of Partials with Networks of Adaptive
Oscillators
In the previous section we demonstrated how adaptive
oscillators can be used to track partials in a musical signal. We
extended the model of tracking individual partials to a model
of tracking groups of harmonically related partials by joining
adaptive oscillators into networks.
Networks consist of up to ten interconnected oscillators.
Their initial frequencies are set to integer multiples of the
frequency of the first oscillator (see Fig. 3). As each oscillator
in the network tracks a single partial close to its initial
frequency, a network of oscillators tracks a group of up to ten
harmonically related partials, which may belong to one tone
with pitch equal to the frequency of the first oscillator. Output
of the network is related to the number of partials found by its
oscillators and therefore represents the strength of a group of
partials that may belong to tone with pitch f (Fig. 3).
d is the number of the destination (non-synchronized)
oscillator in the network (1 to 10), while s represents the
number of the source (synchronized) oscillator. The period of
the destination oscillator pd and its output value cd change
according to two factors: rp and rc (Fig. 4). These are two
gaussians, representing the ratio of periods of the two
oscillators (pd - period of the destination oscillator, ps - period
of the source oscillator) and the ratio of outputs of the two
oscillators (cd - output of the destination oscillator, cs output of
the source oscillator). Factor rp is a gaussian with maximum
value, when periods of both oscillators are in a perfect
harmonic relationship (dpd/sps = 1). The value falls as periods
drift away from this perfect ratio and approaches zero, when
the ratio is larger than a semitone. rc has the largest value,
when a synchronized oscillator influences the behavior of a
non-synchronized oscillator (cs is large, cd is small) and falls as
cd increases. Connection weights wsd are calculated according
to amplitudes of partials in piano tones; the first few partials
are considered to be more important and consequently the
influence of lower-numbered oscillators in the network is
stronger than the influence of higher-numbered oscillators
(w1n>wn1).
Fig. 3. A network of adaptive oscillators.
Fig. 4. Plot of factors used for updating periods and output values of
oscillators in a network.
Our system uses 88 oscillator networks to track partial
groups corresponding to all 88 piano tones (A0-C8). The
initial frequency of the first oscillator in each network is set to
the pitch of one of 88 piano tones. Initial frequencies of other
oscillators are integer multiples of the first oscillator's
frequency (see Fig. 3). Networks consist of up to ten
oscillators. This number decreases as the frequency of the first
oscillator in the network increases, because the highest tracked
partial lies at 6000 Hz; i.e. network corresponding to tone A6
only has three oscillators with initial frequencies set to 1760
Hz, 3520 Hz and 5280 Hz.
Within a network, each oscillator is connected to all other
oscillators with excitatory connections. These connections are
used to adjust the frequencies and outputs of non-synchronized
oscillators in the network with the goal of speeding up their
synchronization. Only a synchronized oscillator can change
frequencies and outputs of other oscillators in the network.
Adjustments are made according to the following rules:
rp = exp(−1000(dpd /( sps ) − 1) 2 )
rc = exp(−2.3cd2 / cs2 )
pd = pd + rp rc wsd ( sps − dpd ) / d
cd = cd + cd rp rc wsd
(1)
Adjustments push the period (frequency) of a nonsynchronized oscillator closer to frequency of the partial it
should track and also increase its output value. This results in
faster synchronization of all oscillators in the network and
consequently in faster discovery of a group of partials. The
output of a network is calculated as a weighted sum of outputs
of individual oscillators in the network and represents the
strength of a group of partials tracked by oscillators in the
network. Outputs of individual oscillators are weighted
according to their importance and deviation of their frequency
(fi) from ideal frequency if0; an oscillator with large deviation
has little influence on output of the network, as it probably
tracks a partial that does not belong to the network's group of
partials. Larger deviations are tolerated for higher-numbered
oscillators to account for frequency stretching. Because the
network's output only depends on outputs of its oscillators, it is
virtually independent of the amplitude of the tracked partials.
Connecting oscillators into networks has several advantages
for our transcription system. Output of a network represents
the strength of a group of harmonically related partials tracked
by oscillators in the network, which may belong to one tone.
Such output provides a better indication of presence of the
5
Fig. 5. Representations of piano tone A3 and chord C3E3B4.
tone in the input signal than do outputs of individual
oscillators. Noise doesn't usually appear in the form of
harmonically related frequency components, so networks of
oscillators are more resistant to noise and provide a clearer
time-frequency representation of the signal. Within the
network, each oscillator is connected to all other oscillators
with excitatory connections. Connections are used by
synchronized oscillators to speed up synchronization of nonsynchronized oscillators, leading to a faster network response
and faster discovery of a group of partials.
Fig. 5 displays slices taken from three time-frequency
representations of piano tone A3 (pitch 220 Hz –A-D) and
piano chord C3E3B4 (E-H), calculated 100 ms after the onset:
representation with uncoupled oscillators, representation with
networks of adaptive oscillators and short-time Fourier
transform. The representation with uncoupled oscillators was
calculated with 88 oscillators tuned to fundamental frequencies
of piano tones A0-C8. For tone A3, oscillator outputs
(independent of partial amplitudes) are presented in Fig. 5A.
Fig. 5B shows outputs of 88 oscillator networks, the
combination of these outputs with amplitudes of partials is
shown in Fig. 5C. Fig. 5D displays 440 frequency bins of the
Fourier transform calculated with a 100 ms Hamming window.
Individual oscillators have no difficulty in finding the first
eight partials of tone A3 (A). Not all of the higher partials are
found, because they are spaced too close together (we use only
one oscillator per semitone). Noisy partials found below 220
Hz are the consequence of noise caused by the hammer hitting
the strings. Oscillator networks (B) produce a clearer
representation of the signal; most notably the noisy partials
below 220 Hz are almost completely eliminated. Networks
coinciding with tones A3 and A4 produce the highest outputs,
because all partials in the networks are found. The output of
the network at 3154 Hz, representing the 14th partial, is also
very high, because it only has one oscillator that synchronizes
with the partial. The combination of outputs of networks with
partial amplitudes (C) produces the clearest representation,
with the first three A3 partials standing out.
For piano chord C3E3B4 (Figs. 5E-5H), oscillator networks
also produce the clearest representation. When amplitudes are
combined with networks' outputs (Fig. 5G), only four partials
stand out: first partials of all three tones (C3, E3, B4) and the
second partial of tone E3 (C2).
Both examples show that oscillator networks produce a
compact and clear representation of partial groups in a musical
signal. The main problem of this representation lies in
occasional slow synchronization of oscillators in networks,
which can lead to delayed discovery of partial groups. This is
especially true at lower frequencies, where delays of 40-50 ms
are quite common, because synchronization only occurs once
per cycle; an oscillator at 100 Hz synchronizes with the signal
every 10 ms, so several 10s of milliseconds are needed for
synchronization. Closely spaced partials may also slow down
synchronization, although it is quite rare for a group of partials
not to be found.
III. NEURAL NETWORKS FOR NOTE RECOGNITION IN
POLYPHONIC PIANO MUSIC
A note recognition module is the central part of every
transcription system. Its input usually consists of a set of
partials found by the partial tracking module and its task is to
associate the found partials with notes. Statistical methods are
frequently used to group partials into notes [3,5,6]; in our
transcription system the task is performed by neural networks.
We use a set of 76 neural networks to perform note
recognition. Inputs of each network are taken from outputs of
the partial tracking module presented in the previous section.
They contain one or more time frames (sampled at every 10
ms) of output values of oscillator networks, amplitude
envelopes of signals in frequency channels of the auditory
6
model (calculated by half-wave rectification and smoothing)
and a combination of amplitude envelopes and oscillator
networks' outputs.
Each network is trained to recognize one piano note in its
input; i.e. one network is trained to recognize note A4, another
network recognizes note G4... Altogether 76 networks are used
to recognize notes from A1 to C8. This represents the entire
range of piano notes, except for the lowest octave from A0 to
Ab1. We decided to ignore the lowest octave, because of poor
recognition results. These notes are quite rare in piano pieces,
so their exclusion doesn't have a large impact on overall
performance of the system. Because each neural network
recognizes only one note (we call it the target note) in its input,
it only has one output neuron; a high output value indicates the
presence of the target note in the input signal, a low value
indicates that the note is not present.
A. Comparison of Neural Network Models for Note
Recognition
As we found no previous references to works that use neural
networks for transcription of polyphonic music, we made a
comparison of several neural network models for note
recognition. We tested multilayer perceptrons (MLPs) [8],
radial basis function (RBF) networks [11], time-delay neural
networks (TDNN) [10], Elman's partially recurrent networks
[9] and fuzzy-ARTMAP networks [12]. Supervised learning
was used to train all of the tested network models. Because no
standard database of music pieces that could be used to train or
test transcription systems currently exists, we first constructed
a database for training and testing our neural networks.
Supervised learning requires that pairs of input-output patterns
be presented to the network during training. We therefore
constructed the database from a set of synthesized piano pieces
and piano chords, which enabled us to collect pairs of inputoutput patterns for training. The database includes patterns
taken from a set of 120 MIDI piano pieces, rendered with 16
different piano samples obtained from commercially available
piano sample CD-ROMs (using a sampler with digital I/O).
The set contains pieces of various styles, including classical
from several periods, ragtime, jazz, blues and pop. To
diversify the distribution of notes in the training set and to
provide more training patterns for networks that recognize low
and high notes (these were not very frequent in the chosen
pieces), we complemented the song set with a set of
synthesized chords with polyphony from one to six. Notes in
each chord were chosen randomly. Altogether, the database
consists of around 300,000 pairs of input-output patterns.
The database was used to train a set of neural networks for
each of the tested neural network models. Each network in a
set recognizes one piano note (its target note) in its input. The
training set for each network included approx. 30000 patterns
with 1/3 of them containing the target note. Networks were
tested on a different database, constructed from 40 new MIDI
piano pieces and piano chords (not used in the training
database), rendered with over 20 piano samples. The database
contains approx. 60000 input-output patterns; each network
was tested on 6000 patterns. Average performance statistics on
the test database of the entire set of networks for each neural
network model are given in Table I.
TABLE I
PERFORMANCE STATISTICS OF NEURAL NETWORK MODELS FOR NOTE
RECOGNITION
neural network model
time-delay NNs
Elman's NNs
multilayer perceptrons
RBF NNs
fuzzy-ARTMAP
correct
spurious
96.8%
95.2%
96.4%
88.2%
84.1%
13.1%
13.5%
16.0%
14.6%
18.9%
The table lists average percentages of correctly found and
spurious notes (notes found, but not present in the input
pattern) for each network model. Time-delay neural networks
showed the best performance on the test set. Networks had a
single hidden layer with 18 neurons and two time delays.
Inputs of the network consisted of three consecutive time
frames (time step 10 ms) of outputs of the partial tracking
model. We used a modified backpropagation algorithm [9] for
training. The performance of TDNNs was superior in
comparison to other network models in the number of
correctly found notes, as well as in the number of spurious
notes found (most of them were octave errors). The largest
increase in performance was observed in networks recognizing
notes in the C4-A5 interval (261-880 Hz), where time delays
contributed to more accurate resolution of octave errors that
frequently occur in this interval, mostly because of a high
number of partials produced by the lower-pitched notes (A2C4).
B. Impact of Partial Tracking on the Accuracy of Note
Recognition with Time-Delay Neural Networks
To assess the impact that the proposed partial tracking
module has on the accuracy of note recognition (transcription)
with TDNNs, we compared the performance of TDNNs
trained on patterns that consisted of outputs of the partial
tracking module (as described previously) to the performance
of TDNNs trained on patterns that consisted of outputs of a
multiresolution time-frequency transform, similar to constantQ transform [7] with window sizes from 90 ms to 5 ms at
frequencies from 60 Hz to 9 kHz.
TABLE II
AVERAGE PERFORMANCE STATISTICS OF SYSTEMS WITH AND WITHOUT
PARTIAL TRACKING
No PT
With PT
correct
92.8
94.4
spurious
27.9
11.1
oct. err.
39.5
77.9
We tested the performance of both sets of TDNNs on
transcriptions of several synthesized piano pieces. Table II
lists average performance statistics of both sets of networks on
seven synthesized piano pieces of different complexities and
styles, containing over 20000 notes. Percentages of correctly
7
found notes, spurious notes and octave errors are given for
both sets of networks. The percentage of correctly found notes
is similar in both systems; partial tracking improves accuracy
by approximately 1.5%. Partial tracking significantly reduces
the number of spurious notes, as it more than halves. Just as
important is the change in the structure of errors. Almost 80%
of all errors in the system with partial tracking are octave
errors that occur when the system misses or finds a spurious
note, because of a note an octave, octave and a half or two
octaves apart. Octave errors are very hard to remove, but
because the missed or spurious notes are consonant with other
notes in the transcribed piece, they aren't very apparent if we
listen to the resynthesized transcription. Octave errors are
therefore not as critical as some other types of errors (i.e.
halftone errors), which make listening to the resynthesized
transcription unpleasant. We therefore consider the higher
percentage of octave errors in the system with partial tracking
to be a significant improvement. Overall, we can conclude that
the partial tracking model proposed in section II significantly
improves transcription accuracy with TDNNs.
IV. SYSTEM FOR TRANSCRIPTION OF PIANO MUSIC
The presented partial tracking model and time-delay neural
networks were incorporated into a system for transcription of
piano music, called SONIC. The system also includes an onset
detector, a module for detecting repeated notes and simple
algorithms for length and loudness estimation (see Fig. 6), all
of these parts are briefly presented in this section.
Fig. 6. Structure of SONIC.
A. Onset Detection
We added an onset detector to SONIC to improve the
accuracy of onset times of notes found by the system. We
based our onset detection algorithm on a model proposed by
Smith [22] for segmentation of speech signals. The algorithm
first splits the signal into several frequency bands with a bank
of gammatone filters. We are using the same set of filters as in
our partial tracking system. The signal is split into 22
overlapping frequency bands, each covering half an octave.
Channels are full-wave rectified and then processed with the
following filter:
t
t−x
t−x
O(t ) = (exp(−
− exp(−
)) s ( x)dx
(2)
f s ts
f s tl
0
s(x) represents the signal in each frequency channel, fs the
sample rate, ts and tl are two time constants. The filter
calculates the difference between two amplitude envelopes;
one calculated with a smoothing filter with short time constant
ts (6-20 ms), and the other with a smoothing filter with a longer
time constant (20-40 ms). The output of the filter has positive
values when the signal rises and negative otherwise. Outputs of
all 22 filters are fed into a fully connected network of
integrate-and-fire neurons. Each neuron in the network is
connected to the output of one filter. It accumulates its input
over time and if its internal activation exceeds a certain
threshold, the neuron fires (emits an output impulse). Firing of
a neuron provides indication of amplitude growth in its input
frequency channel. After firing, activity of the neuron is reset
and the neuron is not allowed to respond to its input for a
period of time (50 ms in our model). Neurons are connected to
all other neurons in the network with excitatory connections.
The firing of a neuron raises activations of all other neurons in
the network and accelerates their firing, if imminent. Such
mechanism clusters neuron firings, which may otherwise be
dispersed in time and improves the discovery of weak onsets.
A network of integrate-and-fire neurons outputs a series of
impulses indicating the presence of onsets in the signal. Not all
impulses represent onsets, because various noises and beating
can also cause amplitude oscillations in the signal. We use a
MLP neural network to decide which impulses represent
onsets. We trained the MLP on a set of piano pieces, the same
as we used for training note recognition networks.
We tested the algorithm on a mixture of synthesized and
real piano recordings. It correctly found over 98.5% of all
onsets and produced around 2% of spurious onsets. Most of
the missed notes were notes played in very fast passages, or
notes in ornamentations such as thrills; spurious notes mostly
occurred because of beating or other noises in the signal.
B. Repeated Note
Detecting repeated notes in a musical signal can be a
difficult problem, even if the played instrument has
pronounced onsets (such as piano). An illustration of the
problem is given in Fig. 7. The upper part of Fig. 7 shows
outputs of the onset detection network and five note
recognition networks on an unknown piece of music. Four
onsets and five notes were found; note C4 lasts through the
entire duration of the piece, while other notes appear for
shorter periods of time. Four transcription examples show four
possible interpretations of these outputs. Interpretations differ
in the way note C4 is handled; we could transcribe it as one
whole note, four quarter notes... Altogether eight combinations
are possible, and all of them are consistent with networks'
outputs.
It becomes apparent that the system needs an algorithm for
8
Fig. 7. Different interpretations of networks' outputs.
detecting repeated notes. At first, we used the most obvious
solution, which is to track the amplitude of the first harmonic
of a possible repeated note and produce a repetition if the
amplitude rises enough. Because of shared partials between
notes, this approach fails when a note that shares partials with
the repeated note occurs in the signal. We therefore decided to
entrust the decision on repeated notes to a MLP neural
network, trained on a set of piano pieces. Inputs of the MLP
consist of amplitude changes, as well as several other
parameters. This solution improves transcription accuracy for
approximately 2.5% over the "first harmonic" approach.
C. Tuning, Note Length and Loudness Estimation
Before transcription actually starts, a simple tuning
procedure is used to calculate tuning of the entire piano and
initialize frequencies of adaptive oscillators accordingly. The
procedure uses adaptive oscillators to find partials in the piano
piece and then compares partial frequencies to frequencies of
an ideally tuned piano. The tuning of the piano is calculated as
a weighted average of deviations of partial frequencies from
ideal tuning. Stretching of piano tuning is also taken into
consideration in the process. The tuning procedure guarantees
unchangeable transcription accuracy, when the piano is tuned
differently then the standard A4=440 Hz. The procedure only
calculates the tuning of the entire piano, not of individual
piano tones.
SONIC also calculates the length and loudness of each note.
Both are needed to produce the final MIDI file containing the
transcription. The length of a note is calculated by observing
activations of the note recognition network; note is terminated
when the network's activation falls below the training
threshold. Loudness is calculated from the amplitude envelope
of the note’s first harmonic.
V. PERFORMANCE ANALYSIS
A. Synthesized and Real Recordings
In this section, we present the performance of our system on
transcriptions of three synthesized and three real recordings of
piano music. Originals and transcriptions of all presented
pieces (and more) can be heard on http://lgm.fri.unilj.si/SONIC. Table III lists percentages of correctly found and
spurious notes in transcriptions, as well as the distribution of
errors into octave, repeated note and other errors. Separate
error distributions are given for missed and spurious notes. An
error can fall into several categories, so the sum of error
percentages may be greater than 100. The total number of
notes, as well as maximal and average polyphony of each piece
are also shown.
The transcribed synthesized recordings are: (1) J.S. Bach,
Partita no. 4, BWV828, Fazioli piano; (2) A. Dvo ak,
Humoresque no. 7, op. 101, Steinway D piano; (3) S. Joplin,
The Entertainer, Bösendorfer piano. Real recordings are: (4)
J.S. Bach, English suite no. 5, BWV810, 1st movement,
performer Murray Perahia, Sony Classical SK 60277; (5) F.
Chopin, Nocturne no. 2, Op. 9/2, performer Artur Rubinstein,
RCA 60822; (6) S. Joplin, The Entertainer, performer
unknown, MCA 11836.
The average number of correctly found notes in synthesized
recordings is around 90%. The average number of spurious
notes is 9%. Most of the missed notes are either octave errors
or misjudged repeated notes. Notes are also missed in very fast
passages, such as arpeggios or thrills (most missed notes in
Partita), when they are masked by louder notes (many notes in
Humoresque) or due to other factors such as missed onsets and
high polyphony. A majority of spurious notes are octave
errors, often combined with misjudged repeated notes. These
are especially common in pedaled music (Humoresque) or in
loud chords (The Entertainer). Other reasons for spurious
notes include missed and spurious onsets and errors due to
high polyphony.
Some common errors can be seen in a transcription example
taken from Humoresque and shown in Fig. 8A (table III/2).
Missed notes are marked with a - sign, spurious notes are
marked with a + sign. All three spurious notes are octave
errors. Out of the two missed notes, A5 was missed, because it
is masked by the louder E3C4 chord, while note E3 is a missed
repeated note.
Results on real recordings are not as good as those on
synthesized recordings. Poorer transcription accuracy is a
consequence of several factors. Recordings contain
reverberation and more noise, while the sound of real pianos
includes beating and sympathetic resonance. Furthermore,
performances of piano pieces are much more expressive, they
contain increased dynamics, more arpeggios and pedaling. All
of these factors make transcription more difficult.
9
TABLE III
PERFORMANCE STATISTICS OF TRANSCRIPTIONS OF 3 SYNTHESIZED AND 3 REAL PIANO RECORDINGS
1
2
3
4
5
6
corr.
notes
spur.
notes
98.1
92.3
86
88.5
68.3
85.9
7
10.6
9.5
15.5
13.6
15.2
octave
31.4
53.2
80.8
35.1
30.3
70.3
missed notes
repeat.
23.6
39.2
25.6
18.2
2.1
10.8
other
56.4
29.4
9
52.2
75.3
27
octave
84.4
95.3
96
80.5
79
87.4
spurious notes
repeat.
22.3
29.9
8.2
17.6
6.4
7.1
other
7.9
0
5.1
13.9
20.7
12.3
num.
notes
avg. poly
max.
poly
6680
1008
1564
1351
457
1564
2.7
4.1
3.4
2.6
4.4
3.4
6
12
9
6
11
9
Fig. 8. Transcription examples: A: Humoresque (III/2), B: BWV810 (III/4), C: The Entertainer (III/6).
The analysis of SONIC's performance on the real recording
of Bach's English Suite (table III/4, Fig. 8B) showed that
besides octave and repeated note errors, most of the missed
notes are either quiet low pitched notes (E3 in measure 2, Fig.
8B) or notes in arpeggios and thrills. Chopin's Nocturne (table
III/5) proved to be the greatest challenge for our system. The
recording is a good example of very expressive playing, where
a distinctive melody is accompanied by quiet, sometimes
barely audible left hand chords. The system misses over 30%
of all notes, but even so the resynthesized transcription sounds
very similar to the original (listen to the example on the
aforementioned URL address). We compared transcriptions of
the real and synthesized version of The Entertainer (table III/3
and III/6, Fig. 8C) and both turned out to be very similar.
Transcription of the real recording contains more spurious
notes, mostly occurring because of pedaling, which was not
used in the synthesized version. The number of correctly found
notes is almost the same in both pieces. Octave errors are the
main cause of both types of errors.
B. Comparison to Other Approaches
The lack of a standard set of test examples makes
comparison of different transcription systems a difficult task,
at best. The task is further complicated by the fact that systems
put very different constraints on the type or style of music they
transcribe. In this section, we present the performance of our
system on examples other authors used to evaluate their
systems. Note however, that even though we used the same
examples as others, comparisons are to be taken with some
restraint, as the transcribed pieces were recorded or
synthesized under different conditions.
Klapuri [5] developed a system for transcription of
polyphonic music. He tested his system on three short passages
taken from two piano pieces: J.S. Bach, Inventio 8 and L.V.
Beethoven, Fur Elise. Both pieces were recorded on a real
piano in a controlled studio environment. Tones of the same
piano were previously analyzed and their spectral templates
were used in the transcription process. We compared Klapuri's
results to the performance of our system on synthesized
passages of the same pieces. Results were similar; our system
correctly found approximately 2% more notes, but also
produced approximately 4% more spurious notes. Most
spurious notes were octave errors, which Klapuri managed to
reduce by using spectral templates of piano tones in the
transcription process. Unfortunately, no results of
transcriptions of real piano recordings were published, which
would make the comparison of more valid. His system has
lately been improved [23], but as to our knowledge it has not
yet been evaluated on transcriptions of piano pieces.
Rossi [4] developed a system for transcription of polyphonic
piano music. Like Klapuri, Rossi first analyzed the tones of a
piano, and then used spectral templates of these tones for
transcribing music played on the same piano. She tested her
system on three 17th century chorales. SONIC's transcriptions
of these pieces contain more spurious notes, all of them octave
errors, and a similar number of correctly found notes. Octave
errors were removed effectively in Rossi's system by using
spectral templates of piano tones. No evaluations of
transcriptions of real piano recordings were published to make
the comparison more valid.
Sterian [3] developed a system for transcription of music
played on brass and woodwind instruments. He published
performance statistics of transcriptions of parts of a
synthesized and real recording of Bach's Contrapunctus I from
The Art of Fugue. Sterian used Kashino's recognition factor R
[6] to evaluate the performance of his system;
R=100*(0.5*(correct-spurious)/all_notes+0.5). The accuracy
of his system ranged from R=1 to R=0.8 on one to four-voice
parts of the synthesized version of Contrapunctus I and from
0.8 to 0.5 on the same parts of the real recording. SONIC's
10
accuracy is better; R ranges from 1 to 0.95 on the synthesized
recording and from 0.9 to 0.8 on the real recording of
Contrapunctus I (performer V. Feltsman, MusicMasters
67173).
Dixon published preliminary results of his system for
transcription of piano music [2]. He made an extensive
evaluation of his system on 13 piano sonatas composed by
W.A. Mozart. Pieces were played by a real performer, but the
recordings were synthesized with different piano samples.
When the system was not specifically tuned for the piano
sample used, it correctly found 90% of all notes and produced
30% of spurious notes. We were unable to obtain all 13
Mozart sonatas used by Dixon, but the average score of
SONIC on seven synthesized Mozart sonatas was significantly
better; 92% of notes were correctly found, together with 8% of
spurious notes.
ACKNOWLEDGMENT
The author would like to thank the reviewers for their
suggestions and comments.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
VI. CONCLUSION
[7]
In this paper, we presented a connectionist approach to
transcription of polyphonic piano music. We first proposed a
new model for tracking partials in polyphonic musical signals,
based on an auditory model for time-frequency representation
and adaptive oscillators for discovery and tracking of partials.
By using a connectionist approach, we avoided some of the
problems of classical partial tracking approaches, such as
missed or spurious peaks, which lead to fragmented or
spurious partial tracks, and also showed that our model
successfully tracks partials in the case of beating and
frequency modulation. An additional advantage of our partial
tracking model is that it can be extended to a model for
tracking groups of harmonically related partials by joining
oscillators into networks. Oscillator networks provide a clearer
time-frequency representation of a signal and are especially
suitable for transcription purposes. We showed partial tracking
with networks of adaptive oscillators significantly improves
the accuracy of transcription with time-delay neural networks.
We then presented a comparison of several neural network
models for note recognition; the best performance was
obtained by time-delay neural networks. We presented an
overview of our transcription system called SONIC and
presented performance statistics of transcriptions of several
synthesized and real piano recordings. We also provided a
rough comparison of the performance of our system to several
others, and showed that it achieves similar or better results.
Overall, results show that neural networks present a good
alternative in building transcription systems and should be
further studied. Further researches will include addition of
feedback mechanisms to the currently strictly feedforward
approach, with the intention of reducing some common types
of errors. Additionally, an extension of the system to
transcription of other instruments may be considered.
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11
Matija Marolt (M’96) received the B.S. and Ph.D. degrees, both in computer
science, from University of Ljubljana, Slovenia in 1995 and 2002
respectively.
From 1995, he has been working at Laboratory of Computer Graphics and
Multimedia, at Faculty of Computer and Information Science, University of
Ljubljana, where he is currently Assistant. His research interests include
music information retrieval, audio transcription and recognition and audiovisual interaction.

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