PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Reconsidering the method of evaluation
for tempo estimation
Madoka OKEMOTO1; Masanobu MIURA2
1

Graduate School of Engineering, Hachinohe Institute of Technology
2

Faculty of Music, Kunitachi College of Music, Japan

ABSTRACT
Tempo estimation for musical audio has been intensively conducted in the field of MIR(Musical InformationRetrieval). Most popular methods for tempo estimation uses frequency analysis for envelope of the audio toobtain tempo from power spectrum of the Fourier transform of the envelope. A method is implemented toestimate local tempo for the audio of tempo-variated music. To estimate it, the authors’ former study employs
conventional Zero-padding, in order to obtain high resolution of tempo estimation. The resultant accuracy oftempo estimation is, however, not so high (37.6%) compared to their global tempo estimation’s result (83%).
Possible reason of it is the difficulty to have appropriate length of time window, since the desired length of thewindow depends on the cycle of beats. Thus, this report proposes a novel method for local tempo estimation
for tempo-variated musical audio. The authors propose to use a certain set of time window length for themusical audio, to obtain frequencies from power spectrum, and then estimate tempo by integrating the resultsof the Fourier analysis for the signals from different time windows.
Keywords: Tempo estimation, FFT, FFT window, Beat

1. BACKGROUND
Tempo is an index of the speed in music calculated by intervals between two beats, whichusually have large acoustic energy in musical signal. The envelope of the musical signalincludes large energy corresponding to the musical beats. Conventional methods [1,2] for theestimation of tempo utilize the frequency analysis for the envelope. The frequency analysis ispossible to analyze periodic feature of current waveform and describing it as constant periodic
signal. However, if the waveform is aperiodic signal is analyzed, the resultant power spectrum
is complex due to the aperiodic feature of signal. The beats of musical audio of tempo-variatedmusic appears aperiodically. Thus, tempo estimation for tempo-variated music is said asdifficult to obtain correct tempi.
2. MANUSCRIPT FORMAT
2.1 Aims
This report proposes a novel method for local tempo estimation for tempo variated musical audio.
2.2 Theory
Including several beats on tempo variated music in time window on frequency analysis may provide
a difficult result. Thus, designing a time window that includes only two distinct beats is desirable. On
other hand, estimation of the length of time window means the estimation of the tempo so that it is not
be conducted easily. At this point, considering window length, used by one pattern window length isn’t
suitable method. An alternative to cope with the problem is to utilize a certain set of length of timewindow.
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unkomgn@gmail.com
miura.masanobu@kunitachi.ac.jp

2.3 Method
This report tries to employ two length of time window for 1sec and 2sec, to obtain frequencies frompower spectrum and then estimate tempo by integrating the results of the Fourier analysis for thesignals from different time windows. Integrating method compare to two calculated by two windowsof rate is 2:1 (1sec and 2sec), and employ having high power.
2.4 Results
Figure 1 shows the result of tempo estimation by two type of time windows for the signal withaperiodic click sounds. Figure 2 shows the result of tempo estimation by proposed method, byintegrating the results of the two windows. Correct tempo is represented as a stepwise function. As thefigures shows the effectivity of use of the two windows to estimate tempo for interval variated clicksound.

Figure 1 Result of tempo estimation by two type of time window

Figure 2 Result of tempo estimation by proposed method6457

3. CONCLUSIONS
Here we newly proposed a method to employ several windows on the FFT, to preserve both time
resolution and frequency (at here, the bpm) resolution. Preliminary experiment was conducted to
examine the effectiveness of the proposed method. The efficiency of the method was confirmed. At
future work, we discuss the number of windows and the length on each window, so that the precisionof tempo estimation will be better than current result.

REFERENCES
1. Hiroshi Kuwabara and Masanobu Miura, “Tempo estimation from musical audio by solving thehalf/double tempo error problem,” In Proc. of meeting of the Acoustic Society of Japan, 3-3-4,
pp.929-932, 2013 (in Japanese).
2. Sota Okada and Masanobu Miura, "Tempo estimation for acoustic signal of tempo variation music",
Proc. of 5th Joint Meeting Acoustic Society of America and Acoustic Society of Japan, 5pMU17,p.3427 , 2016

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