how do each measure made of rhythmic pattern?
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Answer:
with a measuring tape5~{MMS~™÷5=5
Answer:
Pre-processing
An optional preprocessing step in the system is preprocessing with a sinusoidal model [11]. When analyzing percussive rhythms in real-world musical signals, it is advantageous to suppress the other (pitched) musical instruments prior to rhythm processing. Drum sounds in Western music typically have a clear stochastic noise component [10]. In addition, some drums have strong harmonic vibration modes and they have to be tuned. In the case of tom toms, for example, approximately half of the spectral energy is harmonic. Nevertheless, these sounds are still recognizable based on the stochastic component only. A sinusoids plus noise spectrum model was used to extract the stochastic parts of acoustic musical signals. The model, described in [12], estimates the harmonic parts of the signal and subtracts them in time domain to obtain a noise residual. Even though some nondrum parts of signal end up to the noise residuals y1(k) and y2(k), the level of drums in relation to other instruments is considerably enhanced. The amount of non-drum sounds in the residual does not complicate the distance measuring too much since we are not interested in individual events, but in the entire rhythmic sensation.
Pattern Segmenting
An essential step before similarity measurements is to segment the continuous time domain signal into chunks that represent patterns. A brute force matching of all possible patterns of all lengths would be computationally too demanding. Pattern segmenting is a part of a rather complicated musical meter estimation process, which is more or less independent of the subsequent similarity measurements. Earlier algorithms for automatic meter extraction have been developed e.g. by Brown and Temperley [13,14]. The estimator proposed here has not been previously published and is therefore now briefly introduced. The module takes the acoustic musical signal without preprocessing as input, and outputs the lengths of the tactus (beat) and the musical measure. The latter is interpreted as the rhythmic pattern length. Also, pattern phase is estimated, in order to be able to list a vector of pattern boundary candidates b1(p) and b2(p).
Mid-level Representation
A signal model is used which retains the metric percept of most musical signals while significantly reducing the amount of parameters needed to describe the signal. Only amplitude envelopes of the signal at eight sub-bands are stored. The general idea that rhythmic ercept is preserved with this signal model has been earlier motivated by Scheirer in [15]. First, a bank of sixth-order Butterworth filters is applied to divide the input signal into eight non-overlapping bands. The lowest band is obtained by lowpass filtering at 100 Hz cutoff, and the seven higher bands are distributed uniformly on a logarithmic frequency scale between 100 Hz and half the sampling rate. Magnitude responses of the filters sum approximately to unity, and group delays of the filters are compensated for. At each subband, the signal is half-wave rectified, squared, and decimated by factor 45 to 980 Hz sampling rate. Then a fourthorder Butterworth lowpass filter with 20 Hz cutoff frequency is applied to obtain the amplitude envelope of the signal at each frequency channel. Finally, dynamic compression is applied to obtain compressed amplitude envelopes vc(k) at channels c at time k: , (1) where zc(k) is the signal before compression and J=1000 is a constant. The value of J is not critical, but merely determines the dynamic range after compression and ensures that numerical problems do not arise. The amplitude of the original wideband input signal x(k) is controlled by normalizing it to have zero mean and unity standard deviation before any of the described processing takes place.
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