## 4 Discussion  
The premises of this study, besides the presentation of the custom-made SYNTHPITCH dataset, were to implement an ultra-fast pitch detection algorithm for real-time applications and ease of hardware implementation. Our proposed algorithm, OneBitPitch (OBP), despite running on a software environment, confirms the premises by providing by far the fastest results in terms of time elapsed for pitch detection. On the other hand, as is expected due to its nature, SWIPE is the heaviest algorithm and takes an average of 256 ms to be executed, despite the \"large\" window frame selected and the SWIPEP variant. YIN, considered one of the fastest pitch detection algorithms, being based on a modified autocorrelation, was about nine times faster than SWIPE, with only a 38 ms average. NLS needs a special mention, as its accuracy values are outstanding, and, on synthetic signals, its time performances are too, with only a 27 ms average. However, OBP shows its real strength with an average elaboration time of only 4.6 ms. It is 50 times faster than SWIPE and even 9 times faster than YIN, which is considered a fast algorithm. Figure 7 displays an alternative visualization of the performance of the four algorithms in terms of speed, plotting the elapsed time, which immediately shows the differences in speed. Other works such as that by [PERSON] et al. [21] report speed as a multiplier of the \"realtime\", which is the duration of the audio segment to be evaluated. Their approach, based on leveraging the constant-Q Gabor Transform followed by harmonic shift algorithms and corrective heuristics, reaches a declared 0.29 \(\times\) realtime speed on a more powerful machine than what has been used in the present work; nonetheless, OBP reaches 0.046 \(\times\) realtime. The choice of the right algorithm for a specific application is mainly based on the latency and accuracy tradeoff required, and the computational power available, so it is safe to say that each of the proposed algorithms has a specific field and reason to be applied. Looking at the RAE and accuracies, the NLS appears as the best-performing algorithm, always providing less than 1% RAE on average, followed by SWIPE. It is, however, worth  
Figure 7: Average elapsed time (in seconds) for each algorithm. See Table 3 for numeric data. noting that the NLS was one of the algorithms suffering the most from octave errors, especially when processing noisy signals or square waves. Moreover, this test confirms the noise-robust nature of SWIPE, performing well even with harsh signals like square waves and/or noise. Looking at the accuracy tables for ACC-1, ACC-2 and ACC-10, NLS confirms its performances by always providing the highest accuracy, at 93%. However, this value stays the same for all three ranges, which indicates that all the errors reported by NLS within these tests were greater than 10% in RAE, which is a good indicator of a certain proneness to octave errors. Although OBP underperforms when it comes to 1% accuracy, that is to be expected: only 42% of the time was the error smaller than 1%. On the other hand, its performances become comparable to YIN and SWIP for ACC-2, which represents the acceptability range. The discrete nature of musical notes within the Western tempered system is so that a 2.5% error still leads to a discretized pitch being correct. For larger-scale errors, OBP actually brings better ACC-10 values than YIN and SWIPE, with more than 90% accuracy. TE can be considered as the most crucial metric for the present paper, due to the improvement that OBP aims to bring, which is specifically in terms of speed. Within this context, the differences between all of the algorithms considered, especially OBP, have been proven to be statistically significant with a Mann-Whitney test yielding a U close to 0, which brings \(p<0.00001\), which is much lower than the desired threshold of 0.05. A z-score \(<-4\) points to a confidence higher than 99.997%.