Sound examples of an Impulse Pattern Formulation model synchronizing to different click tracks

<p>In the publication, supplemented by these sound examples, the Impulse Pattern Formulation is used to model the synchronization of musicians to a collective tempo. Several click tracks are numerically created, representing eighth notes played by a musician or a metronome for different tempo changes.<br> &nbsp;By replacing every beat with a sound sample, audio files are created for a more musical evaluation of the results. The IPF is represented by a cowbell and the underlying click track with claves. Those sound files are in stereo, whereby the click track is at the left channel, and the IPF&#39;s signal is at the right channel. Thus, e.g., the balance potentiometer of a stereo system can be used to blend both sounds freely. The practical examples are:</p> <p><strong>Fig.2:</strong><br> IPF reacts to four different step changes in tempo.</p> <p><strong>Fig.5:</strong><br> The IPF reacting to the same changes in tempo as shown in Figure 2, when changing the tempo linear during 24 beats instead of step changes.</p> <p><strong>Fig.8:</strong><br> IPF adapting to a noisy click track: the upper line (a) and b)) shows white noise, and the lower line (c) and d)) Brownian noise. On the left (a) and c)), the fluctuation is <span class="math-tex">\(\pm1~\%\)</span>, and on the right (b) and d)) <span class="math-tex">\(\pm 5~\%\)</span>.</p> <p><strong>Fig.9:</strong><br> IPF adapting to a sinusoidally modulated click track: the upper line (a) and b)) shows a modulation period of 32 eighth notes, and the lower line (c) and d)) shows a modulation period of 8 eighth notes. On the left (a) and c)), the amplitude is 36 bpm, and on the right (b) and d)) 6 bpm, both centered around 113 bpm.</p> <p><strong>Fig.12:</strong><br> Several scenarios shown in Figures 2, 5, 8, and 9 applied to an extended IPF which&nbsp;considers phase differences: a) step change from 120 to 100 bpm, b) linear change from 120 to 130 bpm, c)&nbsp;<span class="math-tex">\(\pm 5~\%\)</span> Brownian noise added to a 120 bpm click track and d) sinusoidal modulation with a period length of 32 eight notes varied&nbsp;<span class="math-tex">\(\pm 6~bpm\)</span> around 113 bpm.</p> <p><strong>Fig.13:</strong><br> Several scenarios shown in Figures 2, 5, 8, and 9 applied to an extended IPF optimized for polyrhythms: a) step change from 120 to 140 bpm, b) linear change from 100 to 120 bpm, c)&nbsp;<span class="math-tex">\(\pm 5~\%\)</span> Brownian noise added to a 90 bpm click track and d) sinusoidal modulation with a period length of 32 eight notes varied&nbsp;<span class="math-tex">\(\pm 6~bpm\)</span> around 113 bpm.</p> <p>In all Figures, blue lines refer to the tempo of the click track, and red lines correspond to the tempo of the IPF. The single crosses represent single beats.</p> <p>A more in-depth description of how these sounds were synthesized can be found in the publication supplemented by these examples:</p> <p>Linke,&nbsp;S., Bader,&nbsp;R., &amp; Mores,&nbsp;R. (2021). Modeling synchronization in human musical rhythms using Impulse Pattern Formulation (IPF). http://arxiv.org/pdf/2112.03218v1</p>