Edward W. Large and John F. Kolen. Resonance and the perception of musical meter. Connection Science, 6:177--208, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....to sync to the signal by adjusting its phase and period to that of the input signal. By observing the frequency of a synced oscillator, we can make a more accurate estimate of the frequency of the driving input signal. We are using a simplified version of the Large Kolen adaptive oscillator model [Large and Kolen, 1994] in our experiments. An oscillator has three variables that change with time: phase, period and output. Phase is defined as p t t t x ) # , 1) where t is time, p the period of oscillation and t x the time at which the oscillator expects an event to occur. When t reaches t x , phase ....

E.W. Large, J.F. Kolen, "Resonance and the perception of musical meter," Connection Science, 6(1), 1994.

.... oscillators have been introduced; some have also found use in computer music researches for modeling rhythm perception [1112 ] and for simulation of various psychoacoustic phenomena [13] After reviewing several models, we decided to use a modified version of the Large Kolen adaptive oscillator [11] 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 ....

E.W. Large, J.F. Kolen, "Resonance and the perception of musical meter," Connection Science, no. 6, vol. 2, 1994.

....deviations from metrical time were either not considered (e.g. 8] or treated as noise (e.g. 9, 2, 10, 1] and the systems processed symbolic data off line. More recently, several beat tracking systems have been developed which work with audio input (e.g. 11, 3] or run in real time (e.g. [7]) or both (e.g. 4, 5] Compared with the real time audio beat tracking work of [4, 5] our tempo tracking algorithm performs a simpler task, that of finding the tempo but not necessarily the beat. However, our work is not restricted to a particular musical style or tempo, whereas Goto s work is ....

E.W. Large and J.F. Kolen, `Resonance and the perception of musical meter', Connection Science, 6, 177--208, (1994).

....signals: Dixon [Dix01a] Foote Uchihashi [FU01] Laroche [Lar01] Muscle Fish [WBKW96] Sethares Staley [SS01] Tzanetakis Essl Cook [TEC01] and 3. models processing symbolic data: Allen Dannenberg [AD90] Brown [Bro93] Cemgil Kappen Desain Honing [CKDH01] Eck [Eck01] Large Kolen [LK94] Lee [Lee91] Parncutt [Par94] Povel Essens [PE85] Raphael [Rap01] Rosenthal [Ros92] Smith [Smi99] Temperley Sleator [TS99] and Toiviainen [Toi97] Above, I have not divided the non acoustic models according to causality, due to the fact that the publications do not usually consider ....

....responds with synchronized pulsation. When the oscillators are arranged into a bank of six oscillators in parallel and fed an identical pulse train, some of the oscillators synchronize with different metrical levels of the input, while others fail to synchronize at all. The model is symbolic. LK94] 8 Dixon remarks that the simplistic onset detector can be regarded as a filter of non accentuated events. 21 Toiviainen has developed an oscillator bank for the recognition of meter [Toi97] and applied it to automatic accompaniment of piano playing [Toi98] The nonlinear oscillators are ....

Edward W. Large and John F. Kolen. Resonance and the perception of musical meter. Connection Science, 6(2/3):177--208, 1994. 58

....the question of whether a simple model can find downbeats in patterns. Longuet Higgins Lee [10] and Povel Essens [15] o#er rules based symbolic models that find downbeats in symbolic patterns. Parncutt [14] considers the importance of presentation rate in beat induction. Large Kolen [8] and McAuley [12] provide oscillator models that work online to find downbeats in temporal signals. 2 Model Details The Fitzhugh Nagumo oscillator is a two variable caricature of the four variable Hodgkin Huxley model of neural action potential [6] It exhibits the integrate and fire spiking ....

....Given that these oscillators were designed to model the dynamics of neural action potential not rhythm cognition this is an interesting finding. This study is only preliminary, and clearly more work needs to be done. A comparison should be performed between this model and similar models (e.g. [8], 7] 12] Experimental data needs to be collected from listeners performing a similar task. Finally, a pattern set which does a better job of finding the breaking points of this model and others like it would be of great value. Though only 20 oscillators were used in these simulations, the ....

Edward W. Large and J. F. Kolen. Resonance and the perception of musical meter. Connection Science, 6:177--208, 1994.

....3) 9) V ( 2 1 e z , where z = cos[ 0 ] 1) This equation represents a cosine shaped potential whose valleys have been flattened by the logistic squashing function, commonly used in connectionist computational models, in which defines the severity of squashing (Fig. 2; see [16] for a related use of squashing functions in a coupled oscillator framework) We chose this function for its relative simplicity. More elaborate functions would allow window width and flatness to be manipulated independently. As with Eq. 3, we use this potential function to define a 1 st order ....

Large, E.W. and Kolen, J.F. (1994). Resonance and the perception of musical meter. Connection Science, 6, 177-208.

....to non stationary temporal pattern structure in general. For these reasons it seems unlikely that a simple grammatical approach will capture all of the important details of beat induction, and we agree with Large and Jones (1999) that a process model such as a beat inducing nonlinear oscillator (Large and Kolen, 1994; McAuley, 1994; Gasser et al. 1999) is a more appropriate mechanism. See Eck (2001b,a) for our recent attempts. 8 Future Research 8.1 The relative importance of unaccented and accented onsets One important way in with NPOS TNPOS di ers from NEG, POS and HYBRID is that it pays no attention to ....

Large, E. W. and Kolen, J. F. (1994). Resonance and the perception of musical meter. Connection Science, 6:177-208.

....addressed the question of whether a simple model can nd downbeats in patterns. Longuet Higgins Lee [12] and Povel Essens [17] o er rules based symbolic models that nd downbeats in symbolic patterns. Parncutt [16] considers the importance of presentation rate in beat induction. Large Kolen [10] and McAuley [14] provide oscillator models that work online to nd downbeats in temporal signals. 2 Model Details The Fitzhugh Nagumo oscillator is a two variable caricature of the four variable Hodgkin Huxley model of neural action potential [8] It exhibits the integrate and re spiking ....

....Given that these oscillators were designed to model the dynamics of neural action potential not rhythm cognition this is an interesting nding. This study is only preliminary, and clearly more work needs to be done. A comparison should be performed between this model and similar models (e.g. [10], 9] 14] Experimental data needs to be collected from listeners performing a similar task. Finally, a pattern set which does a better job of nding the breaking points of this model and others like it would be of great value. Though only 20 oscillators were used in these simulations, the ....

Edward W. Large and J. F. Kolen. Resonance and the perception of musical meter. Connection Science, 6:177-208, 1994.

....rhythm, but is not a primary part of the system. For example, Todd et al. 1999) incorporates an oscillator model of musculoskeletal movement in a system that synchronizes body movements with temporal regularities in an input signal. Similar oscillator models by McAuley (McAuley, 1994) and Large (Large and Kolen, 1994; Large and Jones, 1999) are successful at nding downbeats in patterns even when non stationary noise (e.g. acceleration) is present in the patterns. McAuley used the term adaptive oscillator to describe a limit cycle oscillator that entrains both its phase and its period to recurring events in a ....

....aligns its zero phase with that of events in the input. The Large oscillator has a second variable that modi es the slope and width of the gradient descent function such that the oscillator can sharpen its receptive eld, allowing it to lock onto speci c periodic components in the signal. Large and Kolen (1994) show that such an oscillator can form the basis of small connectionist networks that nd salient events at multiple levels of the metrical hierarchy. 3 Research Goals It is clear, even with this cursory sampling of models, that many approaches to oscillator beat induction have already been ....

Large, E. W. and Kolen, J. F. (1994). Resonance and the perception of musical meter. Connection Science, 6:177-208.

....For the beat induction example, our modeling tool would presumably be taken from the class of dynamical systems with trajectories which exhibit limit cycle behavior. These mathematical tools are of course called oscillators and are popular mechanisms for modeling beat induction (McAuley, 1995; Large Kolen, 1994) 1994). Of particular relevance for rhythm cognition is the way dynamical systems handle time. The crucial observation is that a dynamical system is de ned at all points in time. The temporal resolution of a dynamical system is limited only by one s computational resources when running a simulation. ....

....with periodic signals. 4 4 Dynamical systems which synchronize 4.1 Adaptive oscillators There are exist dynamical models which achieve beat induction by modifying their frequencies and phases to match the characteristics of some input signal. These adaptive oscillators (McAuley, 1995; Large Kolen, 1994) are limit cycle oscillators which use a nonlinear phase dependent function to match the phase and frequency of the oscillator to that of the input signal. fullciteAmcauley:1995 used a particular adaptive oscillator to model human sensitivity to relative timing in auditory signals. Large and Kolen ....

[Article contains additional citation context not shown here]

Large, E. W., & Kolen, J. F. (1994). Resonance and the perception of musical meter. Connection Science, 6, 177-208.

....to non stationary temporal pattern structure in general. For these reasons it seems unlikely that a simple grammatical approach will capture all of the important details of beat induction, and we agree with Large and Jones (1999) that a process model such as a beat inducing nonlinear oscillator (Large Kolen, 1994; McAuley, 1995; Gasser, Eck, Port, 1999) is a more appropriate mechanism. See Eck (2001a, 2001b) for our most recent contributions. 3 Details of Four Matching Models All four of the matching models considered in this paper use the same underlying pattern classi cation algorithm. What di ers ....

Large, E. W., & Kolen, J. F. (1994). Resonance and the perception of musical meter. Connection Science, 6, 177-208.

....have addressed the question of whether a simple model can nd downbeats in patterns. Longuet Higgins and Lee (1982) and Povel and Essens (1985) o er rules based symbolic models that nd downbeats in symbolic patterns. Parncutt (1994) considers the importance of presentation rate in beat induction. Large and Kolen (1994) and McAuley (1995) provide oscillator models that work online to nd downbeats in temporal signals. 2 Model Details The Fitzhugh Nagumo oscillator is a two variable caricature of the four variable Hodgkin Huxley model of neural action potential (Hodgkin and Huxley, 1952) It exhibits the ....

....Given that these oscillators were designed to model the dynamics of neural action potential not rhythm cognition this is an interesting nding. This study is only preliminary, and clearly more work needs to be done. A comparison should be performed between this model and similar models (e.g. Large and Kolen (1994), Large and Jones (1999) McAuley (1995) Experimental data needs to be collected from listeners performing a similar task. Finally, a pattern set which does a better job of nding the breaking points of this model and others like it would be of great value. Though only 20 oscillators were used ....

Large, E. W. and Kolen, J. F. (1994). Resonance and the perception of musical meter. Connection Science, 6:177-208.

....oscillators are used to model a wider range of behaviors including predator prey relationships and synchrony in animal populations such as re ies. See Winfree (1980) for a review. Though nonlinear limit cycle oscillators have been successfully applied to beat induction (Large Jones, 1999; Large Kolen, 1994; McAuley, 1995; Gasser, Eck, Port, 1999) relaxation oscillators have received less attention. In this work we o er a novel and e ective relaxation oscillator model of beat induction. We outline the model in detail and provide a perturbation analysis of its response to external stimuli. In a ....

....and other beat tracking simulations are presented in the current study. 1. 1 Oscillator Approaches to Beat Induction The literature on oscillators and rhythm (e.g. Gasser, Eck, and Port (1999) Miller, Scarborough, and Jones (1992) Todd, O Boyle, and Lee (1999) Torras (1985) Dannenberg (1984) Large and Kolen (1994), Large and Jones (1999) McAuley (1995) is signi cant and, due to space considerations, is not summarized here. Readers are referred to Eck (2000a) for a review. For an excellent overview of nonlinear oscillation in general, see Winfree (1980) Two particularly relevant limitcycle oscillator ....

[Article contains additional citation context not shown here]

Large, E. W., & Kolen, J. F. (1994). Resonance and the perception of musical meter. Connection Science, 6, 177-208.

....nd downbeats in patterns. Longuet Higgins Lee (Longuet Higgins Lee, 1982) and Povel Essens (Povel Essens, 1985) o er rules based symbolic models that nd downbeats in symbolic patterns. Parncutt (Parncutt, 1994) considers the importance of presentation rate in beat induction. Large Kolen (Large Kolen, 1994) and McAuley (McAuley, 1995) provide oscillator models that work online to nd downbeats in temporal signals. 2 Model Details The Fitzhugh Nagumo oscillator is a two variable caricature of the four variable Hodgkin Huxley model of neural action potential (Hodgkin Huxley, 1952) It exhibits the ....

....Given that these oscillators were designed to model the dynamics of neural action potential not rhythm cognition this is an interesting nding. This study is only preliminary, and clearly more work needs to be done. A comparison should be performed between this model and similar models (e.g. (Large Kolen, 1994), Large Jones, 1999) McAuley, 1995) Experimental data needs to be collected from listeners performing a similar task. Finally, a pattern set which does a better job of nding the breaking points of this model and others like it would be of great value. Though only 20 oscillators were used in ....

Large, E. W., & Kolen, J. F. (1994). Resonance and the perception of musical meter. Connection Science, 6, 177-208.

....LSTM s ability to track slow oscillations in the chaotic signal is notable. In simple cases, synchronization with a periodic signal is easily achieved using mechanisms such as phaselocked loops (PLLs) But when noisy or complex signals are used, synchronization can be challenging (McAuley, 1994; Large Kolen, 1994). Systems like LSTM that can nd periodicity in complicated signals should be applicable to cognitive domains such as speech and music (Large Jones, 1999; Eck, 2000a) See (Gers Schmidhuber, 2000c) and (Eck, 2000b) for more on this topic. Iterated training yielded improved results for ....

Large, E. W., & Kolen, J. F. (1994). Resonance and the perception of musical meter. Connection Science, 6, 177-208.

....to non stationary temporal pattern structure in general. For these reasons it seems unlikely that a simple grammatical approach will capture all of the important details of beat induction, and we agree with Large and Jones (1999) that a process model such as a beat inducing nonlinear oscillator (Large Kolen, 1994; McAuley, 1995; Gasser, Eck, Port, 1999) is a more appropriate mechanism. See Eck (2000) for our most recent contribution. 3 Details of Four Matching Models All four of the matching models considered in this paper use the same underlying pattern classi cation algorithm. What di ers among ....

Large, E. W., & Kolen, J. F. (1994). Resonance and the perception of musical meter. Connection Science, 6, 177-208.

....pulse trains into twos, threes or fours. The first element of the group is perceived as accented, and the interval between last element and the first element of the next group is perceived as lengthened [41] In modern terminology, the term subjective metricality is now more appropriate [80]. Subjective rhythmisation evokes a sense of pulse whose period is longer than that of the stimulus [129, pp. 421] The relative length of a silent interval following a tone in equitone sequences is a determinant of the perceived accent on that tone. Povel and Okkerman [135, 41] varied both the ....

.... will be the one favoured for the tactus [103, pp. 1947] 2.3. 5 Connectionist Oscillator Models Neural oscillator entrainment models use a hierarchy of oscillators to e#ectively respond to periodicities in the rhythm within frequency bands defined by the dynamics of the phase locking behaviour [80, 113, 121, 47, 179]. Typical versions of such models are not actually interlocked between hierarchies [80, pp. 198] This suggests that independent stratified layers of rhythmic times produced by a time frequency analysis will equally reveal the signal on which the oscillators are adapting to and their behaviour. ....

[Article contains additional citation context not shown here]

E. W. Large and J. F. Kolen. Resonance and the perception of musical meter. Connection Science, 6(2+3):177--208, 1994.

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Edward W. Large and John F. Kolen. Resonance and the perception of musical meter. Connection Science, 6:177--208, 1994.

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Large E.W., Kolen, J.F. (1994). Resonance and the perception of musical meter. Connection Science, vol. 2, no. 6, 177-208.

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E.W. Large and J.F. Kolen, `Resonance and the perception of musical meter', Connection Science, 6, 177--208, (1994).

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E.W. Large and J.F. Kolen, `Resonance and the perception of musical meter', Connection Science, 6, 177--208, (1994).

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E. Large and J. Kolen, \Resonance and the perception of musical meter," Connection Science 6, pp. 177-208, 1994.

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Large, E. W. and Kolen, J. F. Resonance and the perception of musical meter. Connection Science. 6(2,3), 1994.

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E. Large and J. Kolen, "Resonance and the perception of musical meter," Connection Science 6, pp. 177--208, 1994.

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, 169-185. Large, E. W. & Kolen, J. F. (1994). Resonance and the perception of musical meter. Connection Science,

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