# Populating the Mix Space: Parametric Methods for Generating Multitrack Audio Mixtures
## 3 Applications
### Testing the Robustness of Tempo Estimation Algorithms to Changes in the Mix  
In the absence of any time-stretching processes, the tempo of each mix should be identical for a given song. As a result, if the tempo of alternate mixes is estimated and any disagreement is found, this suggests limitations in the tempo-estimation algorithm. In this section, the process of estimating tempo across a large set of artificial mixes is presented as a means of assessing the performance of tempo-estimation algorithms. Two such algorithms are tested herein: the classic and metre-based [21] implementations of mirtempo in the MIRtoolbox. In short, the classic tempo estimation algorithm performs onset detection based on the amplitude envelope of the audio. Periodicities in the detected onsets are determined by finding peaks in the autocorrelation function. The metre method additionally takes into account the metrical hierarchy of the audio, allowing for a more consistent tempo-tracking. Whichever tempo-estimation is used, the resultant tempo is the mean value over the 30-second audio segment. Panning and equalisation were not considered here as tempo was estimated from a mono signal.  
Figures 13a and 14a show the results for \"Burning Bridges\", where it is clear that the classic method performs poorly. The correct tempo of 100 bpm is estimated for only a small percentage of the mixes while all others are estimated close to 133 ppm (see Figure 14a). This leads to a high mean squared error (MSE) as shown in Table 1. A similar flaw is evident for \"I'm Alright\" where the tempo is again overestimated by roughly 33% for both mix distributions (see Figures 13b and 14b). This indicates a consistent error in the tempo-estimation routine, which is being revealed by these mix distributions. The metre-based method performs much better, estimating the correct tempo in almost all cases and exhibiting a lower MSE, with only a small amount of absolute error (0.1-0.2 bpm). The performance of the classic tempo-estimation method is improved for \"What I Want\", where both methods are found to have a high level of accuracy, as shown in Figures 13c and 14c. For both distributions, the metre-based version produces clusters of solutions for \"What I Want\", although the tempo represented by largest cluster is consistent.  
It is conceivable that no tempo-estimation algorithm is able to obtain the correct result in all cases. What this experiment reveals is that there is also variation within the mixes of a given song, with some mixes providing the correct tempo and other mixes yielding error, with different estimation methods showing varying levels of robustness to mixing practice.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Audio** & **BPM** & **Mixes** & **Mirtempo (Classic)** & **Mirtempo (Metre)** \\ \hline Burning Bridges & 100 & Equation (7) & 998.54 & 13.05 \\  & & Equation (8) & 1082 & 0.0147 \\ \hline I’m Alright & 96 & Equation (7) & 738.4297 & 16.4854 \\  & & Equation (8) & 742.37 & 16.7442 \\ \hline What I Want & 99 & Equation (7) & 1.5110 & 0.3803 \\  & & Equation (8) & 0.8394 & 0.4251 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of tempo estimation accuracy results. Shown is the mean squared error (MSE) in each set of 500 mixes.  
Figure 14: _Cont._  
Figure 13: Estimated tempo for three songs, 500 mixes each using Equation (7). In each histogram, the data is split into 100 bins. Overall, performance is better for the metre-based method, as it demonstrates greater accuracy and improved robustness to changes in the mix. (**a**) “Burning Bridges”—The correct tempo is \(\approx\)100 bpm; (**b**) “I’m Alright”—The correct tempo is \(\approx\)96 bpm; (**c**) “What I Want”—The correct tempo is \(\approx\)99 bpm.