## 4 Discussion and Conclusions  
A novel MIDI steganography method, called Velody 2, is presented. Its capacity turns out to be on par with the highest capacity methods available in the literature while still leaving few traces of manipulation, such as small values of Mean Absolute Error (MAE) and Peak Signal-to-Noise Ratio (PSNR). It also has no inflation and an experiment was carried out verifying that there are no signs of audible traces. Regarding many methods suggested in the literature, the MIDI code shows artificial patterns that would not be likely, or even possible, to produce by generating the MIDI file merely by automatic sequencing from sheet music or input of a MIDI song by playing on a keyboard and possibly modifying it slightly afterwards. Examples of such artefacts are extra data not occurring normally in a MIDI song (as is the case with the padding in [PERSON] and [PERSON] [7]), simultaneous note events (so-called simulnotes) that may occur in any order without sounding different and neither causing inflation but where the sequencer always put these events in a certain order and deviance from that pattern should arouse suspicion (in [PERSON], [PERSON] and [PERSON] [3]), and only two values of velocities (as in [PERSON], Wecksten and Jarpe [15]). Such artificial giveaways are perfect signals to a steganalyst searching for indications of suspect MIDI steganography. In the suggested method, velocities are scattered randomly within a narrow interval to be specified. This would have been the result of having played a piece on a keyboard or humanized using a midi software that supports randomization of the velocities. Of course, the mean level is constant and not drifting as is the case in a majority of MIDI music. Still, for harpsichord and organ music this poses no problem at all, and even if this is a strong restriction MIDI music is abundant within this subgroup. An audibility hypothesis test was carried out to see if there were audible traces in the stego MIDI files compared to the carrier files. However, the \(p\)-values here were 0.3431 (binomial test) and 0.8171 (chi-square test) meaning that no signs of steganography could be detected. If the music is entered by playing the piece on a keyboard this is also likely to cause starting time and duration of notes to be slightly fluctuating. Thus, if the velocities are scattered while starting times and duration are not this might be considered as an unrealistic artefact of the method. However, this is not at all unrealistic taking into account that the composer could well have \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **Notes** & **Available** & \(\mathbf{N_{b}}\) & \(\mathbf{N_{e}}\) & \(\mathbf{E_{r}}\) \\ \hline Velody 2, 4 bits & 2267 (474) & 2267 (474) & 9067 (1896) & 4.00 (0.00) & 6.43\% (0.30\%) \\ Velody 2, 5 bits & 2267 (474) & 2267 (474) & 11,333 (2370) & 5.00 (0.00) & 8.03\% (0.37\%) \\ Velody 2, 6 bits & 2267 (474) & 2227 (467) & 13,364 (2804) & 5.91 (0.05) & 9.48\% (0.40\%) \\ \hline [PERSON], [PERSON] and [PERSON] [8] & 4536 (1999) & 753 (371) & 919 (387) & 0.55 (0.12) & 1.11\% (0.22\%) \\ \hline [PERSON] and [PERSON] [7] & unknown & unknown & 492 & 1.95 (0.01) & 7.29\% 1  \\ \hline [PERSON], [PERSON] and [PERSON] [3] & unknown & unknown & 3120 (274) & unknown & 4.01\% 2  \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Table of averages of capacity properties: the number of embedded secret bits \(N_{b}\), number of bits per event \(N_{e}\) and embedding rate \(E_{r}\) as defined by [PERSON] and [PERSON] [7] and briefly explained in the text. Values within parentheses are standard errors. quantized the notes after having made the keyboard recording, a very common kind of facility in many MIDI sequencer programs. Thus, the notes would be perfectly according to the measures and bars but velocity differences would remain. Another aspect of footprint is the file-size change-rate (\(F_{r}\)). For Velody 2 this is 0, i.e., there is no change of the file-size at all.