## 6 Results and Discussion  
The proposed methodology was validated by considering three different metrics: (i) accuracy of the leader-tape detector; (ii) accuracy of the overdub detector; (iii) comparison of the estimated phylogenetic tree with the ground-truth. The performance of the two detection modules are measured and presented here in terms of the probabilities of correct-detection and false-positive, as obtained from the employed dataset. Results are shown in Table 3, where \(p(A|A)\) denotes the correct-detection probability for alteration \(A\) and \(p(A|\
eg A)\) denotes the false-positive probability. \begin{table}
\begin{tabular}{c c c c} \hline
**30 ips** & **15 ips** & **7.5 ips** & **3.75 ips** \\ \hline
**AES: 17.5/\(\infty\)** & **CCIR: 35/\(\infty\)** & 70/\(\infty\)** & 90/3180 \\
**AES: 17.5/\(\infty\)** & **NAB: 50/3180** & 50/3180 & 90/3180 \\ \hline \end{tabular}
\end{table} 
Table 1: Equalization standards supported by the Studer A810 described by their time constants. Source: [39]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Samples**} & \multicolumn{3}{c}{**Recording Parameters**} \\ \hline
**\#** & **Composer** & **Title** & **Year(s)** & **Speed** & **Equation** & **D8X** \\ \hline
1 & [PERSON] & Differences & 1958–1959 & 7.5 & CCIR & yes \\
2 & [PERSON] & Dialogue de l’ombre double & 1985 & 7.5 & CCIR & yes \\
3 & [PERSON] & Mnemosyne & 1986 & 7.5 & CCIR & no \\
4 & [PERSON] & Mnemosyne & 1986 & 15 & CCIR & yes \\
5 & [PERSON] & Continua & 1958 & 15 & CCIR & no \\
6 & [PERSON] & Dimensioni II–invenzione su una voce & 1960 & 7.5 & NAB & yes \\
7 & [PERSON] & & 1956 & 7.5 & NAB & no \\
8 & [PERSON] &...sofferte ondereere... & 1976 & 15 & NAB & yes \\
9 & Gruppo NPS & Interferenze II & 1965–1968 & 15 & NAB & yes \\
10 & Gruppo NPS & Ricerca 4 & 1965–1968 & 15 & NAB & no \\ \hline \end{tabular}
\end{table} 
Table 2: Samples of electroacoustic music recorded on experimental tapes with the related configuration. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**Leader**} & \multicolumn{2}{c}{**Overdub**} \\ \hline \(p(L|L)\) & \(p(L|\
eg L)\) & \(p(O|O)\) & \(p(O|\
eg O)\) \\
90.0\% & 0.0\% & 75.0\% & 3.3\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Correct-detection and false-positive probabilities for leader-tapes and overdubs. Leader-tape detection turns out to be highly reliable, with a solid 90% rate of correct-detection and no false-positives at all. Overdub detection represents a more complex problem. On the one hand, in some cases, the detector is not able to correctly identify the presence of an overdub, as its spectral fingerprint does not appear sufficiently visible with respect to the background noise or the overdub interval limits are not sufficiently sharp in the difference of the spectrograms. On the other hand, it was observed that cases might occur in which different kinds of tape alterations (e.g., presence/absence of DBX or different equalizations) may produce artifacts that might be confused with those left by an overdub (false-positive). However, the estimation of the phylogenetic tree does not strictly require 100% accuracy of the detectors. In fact, the tree reconstruction process involves the dissimilarity matrix as a whole, which means that it is usually robust to local noise and errors, as long as the algorithm has gathered enough information. Since the validation dataset consisted of relatively small trees, results were obtained by qualitatively inspecting the estimated structures in comparison to the ground-truth. Three possible outcomes were observed. 1. In 50% of the cases, the estimated tree perfectly reproduces the ground-truth. Specifically, all the tracks sharing the same tape modifications (leader-tape and/or overdub) are collected in the same clique, and the resulting cliques are correctly ordered in the phylogeny sense. 2. In 40% of the cases, the estimated tree is not identical to the ground-truth, but still makes sense in phylogeny terms.