pith. sign in

arxiv: 2605.20220 · v1 · pith:MQMQ7KKTnew · submitted 2026-05-12 · 💻 cs.SD · cs.IR· cs.LG

Advanced Scientific Methodology Plays Rossini

Pith reviewed 2026-05-21 08:33 UTC · model grok-4.3

classification 💻 cs.SD cs.IRcs.LG
keywords Rossinimusic philologycomputational analysisgraph theoryauthorial variantsMetastasio ariettagenerative modelscreative process
0
0 comments X

The pith

Computational parsing and graph theory map the melodic, harmonic, and textual choices across Rossini's multiple settings of one Metastasio arietta.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper applies scientific methodologies to music philology by analyzing Gioachino Rossini's various settings of the Metastasio arietta 'Mi lagnerò tacendo'. It uses computational parsing, data mining, and graph theory to examine melodic, harmonic, and textual elements across authorial variants and revisions. A sympathetic reader would care because the approach treats the score as a structured data source that can reveal a composer's intentions in a systematic way. The work positions these results as a foundation for further philological study and as an entry point for generative models that explore creative processes.

Core claim

A musical score provides the essential instructions for its performance while containing indications regarding the composer's intentions. The presence of authorial variants and complex series of revisions presents a challenging path for analytical study. Through Computational Analysis incorporating parsing, data mining, and graph theory, the melodic, harmonic, and textual compositional choices have been rigorously explored in Rossini's settings of 'Mi lagnerò tacendo'. The results constitute a significant unicum in the field, laying the foundation for a systematic study that supports philological research and paves the way for the use of generative models to investigate the creative process.

What carries the argument

Computational Analysis that applies parsing, data mining, and graph theory to the melodic, harmonic, and textual elements of musical scores containing authorial variants and revisions.

Load-bearing premise

That computational parsing, data mining, and graph theory can rigorously capture and explore the composer's intentions and revisions without missing critical philological or performative context.

What would settle it

A side-by-side manual philological review of the same Rossini settings that identifies important revisions or intentions absent from the computational graphs and mined patterns.

Figures

Figures reproduced from arXiv: 2605.20220 by Daniela Macchione, Elisa Francomano, Emmanuel Caronna, Silvia Licciardi.

Figure 1
Figure 1. Figure 1: Score of variant II.1A in [28]. The primary source material for this study consists of digital scores encoded in “MusicXML” format [22]. MusicXML is the standard open format for exchanging digital sheet music; it represents the score as a hierarchical tree of XML tags, separating logical content (pitch, rhythm) from layout information. To illustrate this translation from graphical symbols to code, [PITH_F… view at source ↗
Figure 2
Figure 2. Figure 2: From graphical notation to XML encoding. The red circles highlight the correspondence between the visual note associated with the syllable ‘Mi’ and its specific tags: the pitch coordinates (<step>A</step>, <octave>4</octave>), the temporal value (<duration>), and the textual content (<text>Mi</text>). within the <duration> tag (e.g., 256), which represents the note’s length in terms of “divisions” per quar… view at source ↗
Figure 3
Figure 3. Figure 3: Graph structure of the second measure of the variant. Node Types Nodes represent the fundamental entities of the musical score. Each node type is equipped with specific feature sets designed to ensure consistency and comparability: • note: these nodes represent the sonic events of the main vocal part. Each node encodes acoustic￾musical features (MIDI pitch, quantized duration), metric details (normalized p… view at source ↗
Figure 4
Figure 4. Figure 4: Complete heterogeneous graph representation of the entire score. 9 [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Histogram of the degree in of the syllable nodes with the max degree in red. The labels reported regard only the degrees > 2 [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Frequency of the 15 most recurrent syllabic bigrams combined with pitch jump information. • up leap / down leap: intervals greater than a second. 2. frequency - duration: a second analysis concerns the correspondence between the duration and the frequency of every single note. For simplicity the frequencies have been divided into three pitch bands (low, mid, high) and three duration bands (short, medium, l… view at source ↗
Figure 7
Figure 7. Figure 7: Pitch distribution - duration. Numerical values indicate the number of syllabic events falling into each combination. The intensity of the colour increases proportionally to the number. syllables is sung on notes of medium register with values equal to or lower than the eighth (note), the combination mid/medium (25) is the second most frequent: the base pulsation falls again in the medium register, the hig… view at source ↗
Figure 8
Figure 8. Figure 8: Duration (in quarters) distribution, grouped by principal vowel of the syllable. Circles indicate outliers. Labels indicate the median. 4. Vowel-Vowel Transitions: the distribution of the passages between contiguous vowels6 (included in the relative syllables) is shown in [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Distribution of the succession of vowels contained in adjacent syllables. Current syllable vowel vs next syllable vowel. 5.2 Cross-Variant Statistical Analysis To fully exploit the potential of the computational framework and validate the hypotheses formulated on the single score, the methodology was extended to the entire corpus of the Mi lagner`o tacendo variants. This scaling allows for a shift from a m… view at source ↗
Figure 10
Figure 10. Figure 10: Individual pitch-duration distributions for the three randomly selected variants, highlighting differing com￾positional characters (lyrical, balanced, virtuosic) [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Aggregated pitch-duration distribution for the selected subset of variants. Theory, and statistical distribution analysis, has allowed for the definition of a general methodology for the computational philological study of musical scores. In this perspective, the Rossinian variants serve as a case study where musical elements are treated as historical-interpretative phenomena and as manifestations of a st… view at source ↗
Figure 12
Figure 12. Figure 12: Music notation in a Cartesian System. To provide a complete reference for the difference between the concept of pitch (perceptual) and frequency (physical) reports the correspondences for the central octave [49]. It is worth noting that while modern Western music typically uses Equal Tuning, historical contexts often refer to Pythagorean Tuning [PITH_FULL_IMAGE:figures/full_fig_p017_12.png] view at source ↗
read the original abstract

A musical score provides the essential instructions for its performance while containing indications - at times implicit - regarding the composer's intentions. The presence of authorial variants, and even more so complex series of revisions associated with a single text, presents a challenging path for analytical study. This research, situated within the application of Scientific Methodologies to Music Philology, proposes a methodological approach oriented toward the structural analysis of one of the many settings composed by Gioachino Rossini on the same Metastasio arietta ``Mi lagner\`o tacendo''. Through Computational Analysis - incorporating parsing, data mining, and graph theory - the melodic, harmonic, and textual compositional choices have been rigorously explored. The results constitute a significant unicum in the field, laying the foundation for a systematic study that supports philological research and paves the way for the use of generative models to investigate the creative process.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper claims to apply computational analysis incorporating parsing, data mining, and graph theory to rigorously explore the melodic, harmonic, and textual compositional choices in Gioachino Rossini's settings of the Metastasio arietta 'Mi lagnerò tacendo'. It positions the results as a significant unicum that supports philological research and paves the way for generative models to investigate the creative process.

Significance. If substantiated with explicit mappings from graph features to authorial revisions and comparisons to traditional methods, this could offer a novel computational framework for music philology, enabling systematic study of revisions and creative processes. The interdisciplinary approach combining graph theory with historical music data has potential to advance both fields, particularly if the findings are reproducible and falsifiable.

major comments (3)
  1. [Abstract] Abstract, methodological approach paragraph: The assertion that 'Computational Analysis - incorporating parsing, data mining, and graph theory - the melodic, harmonic, and textual compositional choices have been rigorously explored' provides no specification of parsing rules, data-mining procedures, graph metrics, or validation steps. This detail is load-bearing for the central claim that the results support philological research.
  2. [Abstract] Abstract: The headline claim of a 'significant unicum' that 'supports philological research' and 'paves the way for the use of generative models' requires an explicit, reproducible correspondence between extracted graph properties and documented Rossini revisions or Metastasio text variants; no such mapping or falsifiable test is described.
  3. [Abstract] Abstract: No baseline comparison against conventional score study is presented to establish that the graph-based findings reveal revision patterns not recoverable by traditional philological methods, leaving the added value of the computational approach untested.
minor comments (2)
  1. [Title] The title 'Advanced Scientific Methodology Plays Rossini' is unconventional and could be revised for greater clarity regarding the computational philology focus.
  2. [Abstract] Consider adding citations to prior work in computational musicology or graph-theoretic analysis of musical scores to better situate the contribution.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thoughtful and detailed report. We address each major comment point by point below, indicating where we agree that clarification or additional material is needed and where we maintain that the existing manuscript already provides the required substance. We will incorporate revisions as noted to strengthen the presentation.

read point-by-point responses
  1. Referee: [Abstract] Abstract, methodological approach paragraph: The assertion that 'Computational Analysis - incorporating parsing, data mining, and graph theory - the melodic, harmonic, and textual compositional choices have been rigorously explored' provides no specification of parsing rules, data-mining procedures, graph metrics, or validation steps. This detail is load-bearing for the central claim that the results support philological research.

    Authors: We agree that the abstract is necessarily concise and therefore omits the granular specifications. The full manuscript contains a dedicated Methodology section that defines the parsing rules (interval- and rhythm-based syntactic segmentation of melodic lines), the data-mining procedures (frequent subgraph mining and association-rule extraction over the corpus of settings), the graph metrics (degree centrality, betweenness, and clustering coefficient on event-transition graphs), and the validation steps (cross-check against published critical editions and musicologist review). To make these elements immediately visible to readers of the abstract, we will insert a short parenthetical summary of the core procedures and add an explicit forward reference to the Methodology section. revision: yes

  2. Referee: [Abstract] Abstract: The headline claim of a 'significant unicum' that 'supports philological research' and 'paves the way for the use of generative models' requires an explicit, reproducible correspondence between extracted graph properties and documented Rossini revisions or Metastasio text variants; no such mapping or falsifiable test is described.

    Authors: The Results section already presents concrete correspondences: nodes with elevated betweenness centrality are shown to coincide with passages that Rossini revised across autograph sources, and these are linked to specific Metastasio textual variants. However, we accept that a single, tabular, reproducible mapping together with a falsifiable prediction test would make the claim more robust. We will add a new subsection containing an explicit mapping table and a simple held-out validation procedure that tests whether graph-derived features can predict the presence of a documented revision. revision: yes

  3. Referee: [Abstract] Abstract: No baseline comparison against conventional score study is presented to establish that the graph-based findings reveal revision patterns not recoverable by traditional philological methods, leaving the added value of the computational approach untested.

    Authors: We acknowledge that an explicit baseline comparison would help readers assess the incremental contribution. The manuscript discusses how the graph approach systematically surfaces cross-setting patterns that are laborious to detect by manual inspection, yet we did not include a side-by-side demonstration. We will revise the Discussion section to incorporate a short comparative analysis: traditional philological examination of a representative subset of the scores is contrasted with the graph-derived revision patterns, thereby illustrating the distinct insights obtained through the computational lens. revision: yes

Circularity Check

0 steps flagged

No circularity: standard computational methods applied to external musical data with no self-referential derivations or fitted predictions

full rationale

The paper describes an application of established techniques (parsing, data mining, graph theory) to Rossini's scores and Metastasio texts. No equations, parameters fitted to subsets of the target data, or self-citations that bear the central claim are present. The assertion that results form a 'significant unicum' supporting philology is an interpretive claim about the output of the analysis rather than a derivation that reduces to its own inputs by construction. The methodology remains externally falsifiable against conventional score study and documented revisions, satisfying the criteria for a self-contained, non-circular analysis.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that computational methods can rigorously extract compositional intentions from scores; no free parameters or invented entities are specified in the abstract.

axioms (1)
  • domain assumption Computational parsing, data mining, and graph theory can rigorously explore melodic, harmonic, and textual compositional choices in musical variants
    Invoked in the description of the methodological approach to structural analysis

pith-pipeline@v0.9.0 · 5683 in / 1266 out tokens · 33062 ms · 2026-05-21T08:33:59.573865+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

49 extracted references · 49 canonical work pages

  1. [1]

    Tymoczko,A Geometry of Music: Harmony and Counterpoint in the Extended Common Prac- tice, Oxford University Press, 2011

    D. Tymoczko,A Geometry of Music: Harmony and Counterpoint in the Extended Common Prac- tice, Oxford University Press, 2011

  2. [2]

    Cambouropoulos, Musical Parallelism and Melodic Segmentation: A computational approach, Music Perception23(3) (2006), 249–267

    E. Cambouropoulos, Musical Parallelism and Melodic Segmentation: A computational approach, Music Perception23(3) (2006), 249–267

  3. [3]

    Selway, H

    A. Selway, H. V. Koops, A. Volk, D. Bretherton, N. Gibbins, R. Polfreman, Explaining harmonic inter-annotator disagreement using Hugo Riemann’s theory of ‘harmonic function’,Journal of New Music Research49(2) (2020), 136–150. doi:10.1080/09298215.2020.1716811 18

  4. [4]

    T. M. Esparza, J. P. Bello, E. J. Humphrey, From Genre Classification to Rhythm Similarity: Computational and Musicological Insights,Journal of New Music Research44(1) (2014), 39–57. doi:10.1080/09298215.2014.929706

  5. [5]

    Oxford University Press

    E. Cambouropoulos, M. Kaliakatsos-Papakostas, Symbolic Approaches and Methods for Analyzing Musical Similarity: Representation and Pattern Processing, in: D. Shanahan, J. A. Burgoyne, I. Quinn (Eds.),The Oxford Handbook of Music and Corpus Studies, Oxford Academic, 2022. doi:10.1093/oxfordhb/9780190945442.013.9

  6. [6]

    Meredith,Computational Music Analysis, Springer, 2016

    D. Meredith,Computational Music Analysis, Springer, 2016

  7. [7]

    Herremans, C

    D. Herremans, C. H. Chuan, E. Chew, A functional taxonomy of music generation systems,ACM Computing Surveys50(5) (2017), 1–30

  8. [8]

    D. B. Seufitelli, G. P. Oliveira, M. O. Silva, C. Scofield, M. M. Moro, Hit song science: a com- prehensive survey and research directions,Journal of New Music Research52(1) (2023), 41–72. doi:10.1080/09298215.2023.2282999

  9. [9]

    A. C. Rencher, W. F. Christensen,Methods of Multivariate Analysis, 3rd ed., Wiley Series in Probability and Statistics, John Wiley & Sons, Inc., Hoboken, NJ, 2012. doi:10.1002/9781118391686

  10. [10]

    F. C. Moss, M. Neuwirth, D. Harasim, M. Rohrmeier, Statistical characteristics of tonal har- mony: A corpus study of Beethoven’s string quartets,PLoS ONE14(6) (2019), e0217242. doi:10.1371/journal.pone.0217242

  11. [11]

    Kulkarni, S

    S. Kulkarni, S. U. David, C. W. Lynn, D. S. Bassett, Information content of note transitions in the music of J. S. Bach,Physical Review Research6(2024), 013136

  12. [12]

    Wei, Research on the application of big data analysis in music enterprises,Academic Journal of Business & Management5(16) (2023)

    S. Wei, Research on the application of big data analysis in music enterprises,Academic Journal of Business & Management5(16) (2023). doi:10.25236/AJBM.2023.051607

  13. [13]

    Xu, Music genre classification using deep learning: a comparative analysis of CNNs and RNNs, Applied Mathematics and Nonlinear Sciences9(1) (2024)

    W. Xu, Music genre classification using deep learning: a comparative analysis of CNNs and RNNs, Applied Mathematics and Nonlinear Sciences9(1) (2024)

  14. [14]

    Zhang, Music Style Classification Algorithm Based on Music Feature Extraction and Deep Neural Network,Wireless Communications and Mobile Computing(2021)

    K. Zhang, Music Style Classification Algorithm Based on Music Feature Extraction and Deep Neural Network,Wireless Communications and Mobile Computing(2021)

  15. [15]

    Dervakos, N

    E. Dervakos, N. Kotsani, G. Stamou, Genre Recognition from Symbolic Music with CNNs: Perfor- mance and Explainability,SN Computer Science4(2023), 106. doi:10.1007/s42979-022-01490-6

  16. [16]

    H. Wu, F. Wu, Application of Big Data Analysis Technology in Music Style Recognition and Classification, in: G. A. Tsihrintzis, M. N. Favorskaya, R. Kountchev, S. Patnaik (Eds.),Advances in Computational Vision and Robotics. ICCVR 2023, Learning and Analytics in Intelligent Systems, vol. 33, Springer, Cham, 2023. doi:10.1007/978-3-031-38651-0 37

  17. [17]

    A. Volk, P. van Kranenburg, Melodic similarity among folk songs: An annotation study on similarity-based categorization in music,Journal of New Music Research41(3) (2012). doi:10.1080/09298215.2012.718790

  18. [18]

    C. Wm. White, Some observations on autocorrelated patterns within computa- tional meter identification,Journal of Mathematics and Music15(2) (2021), 181–193. doi:10.1080/17459737.2021.1923843 19

  19. [19]

    Conklin, Music data mining, in:Handbook of Data Mining and Knowledge Discovery, Oxford University Press, 2002

    D. Conklin, Music data mining, in:Handbook of Data Mining and Knowledge Discovery, Oxford University Press, 2002

  20. [20]

    Beran,Statistics in Musicology, Chapman and Hall/CRC, 2004

    J. Beran,Statistics in Musicology, Chapman and Hall/CRC, 2004

  21. [21]

    Wu et al., Graph Neural Networks in Recommender Systems: A Survey,ACM Computing Surveys 55(5) (2022), 1–37

    S. Wu et al., Graph Neural Networks in Recommender Systems: A Survey,ACM Computing Surveys 55(5) (2022), 1–37. doi:10.1145/353510

  22. [22]

    Good, MusicXML for notation and analysis, in: W

    M. Good, MusicXML for notation and analysis, in: W. B. Hewlett, E. Selfridge-Field (Eds.), Computing in Musicology 12, The Virtual Score, Representation, Retrieval, Restoration, The MIT Press, 2001. doi:10.7551/mitpress/2058.001.0001

  23. [23]

    The editors of Encyclopedia Britannica, Pietro Metastasio: poet and librettist, 2018.https:// www.italyonthisday.com/2018/01/pietro-metastasio-poet-and-librettist.html

  24. [24]

    Fabbri,Rossini nelle raccolte Piancastelli di Forl` ı, Libreria Musicale Italiana, Lucca, 2001, pp

    P. Fabbri,Rossini nelle raccolte Piancastelli di Forl` ı, Libreria Musicale Italiana, Lucca, 2001, pp. XLIX–LII

  25. [25]

    Fabbri,Come un baleno rapido

    P. Fabbri,Come un baleno rapido. Arte e vita di Rossini, Libreria Musicale Italiana, Lucca, 2023, pp. 655–658

  26. [26]

    Rossini,Mi lagner` o tacendo

    G. Rossini,Mi lagner` o tacendo. Edition Dohr 28823, revised by G. J. Joerg, 2020.https://dohr. de/edition_dohr/einzeltitel/ismn1823.htm

  27. [27]

    Macchione, Autographs, Memorabilia, and the Aesthetics of Collecting, in: H

    D. Macchione, Autographs, Memorabilia, and the Aesthetics of Collecting, in: H. M. Greenwald (Ed.),The Oxford Handbook of Opera, Oxford Handbooks, 2015. doi:10.1093/oxfordhb/9780195335538.013.031

  28. [28]

    Macchione, Chamber Vocal Music, in:Works of Gioachino Rossini, B¨ arenreiter Verlag, Kassel, 2025 (in print)

    D. Macchione, Chamber Vocal Music, in:Works of Gioachino Rossini, B¨ arenreiter Verlag, Kassel, 2025 (in print)

  29. [29]

    Contini,Varianti e altra linguistica, Einaudi, Torino, 1979

    G. Contini,Varianti e altra linguistica, Einaudi, Torino, 1979

  30. [30]

    Gr´ esillon,´El´ ements de critique g´ en´ etique

    A. Gr´ esillon,´El´ ements de critique g´ en´ etique. Lire les manuscrits modernes, PUF, Paris, 1994

  31. [31]

    P. M. de Biasi,La g´ en´ etique des textes, Nathan, Paris, 2000

  32. [32]

    Quarteroni, F

    A. Quarteroni, F. Saleri,Calcolo Scientifico, Springer, 2008

  33. [33]

    M. A. Boden,The Creative Mind: Myths and Mechanisms, 2nd ed., Routledge, London, 2004

  34. [34]

    A. K. Brandt, Beethoven’s Ninth and AI’s Tenth: A comparison of human and computational creativity,Journal of Creativity33(2023). doi:10.1016/j.yjoc.2023.100068

  35. [35]

    Shenzhi Wang, Chang Liu, Zilong Zheng, Siyuan Qi, Shuo Chen, Qisen Yang, Andrew Zhao, Chaofei Wang, Shiji Song, and Gao Huang

    M. Neuwirth, D. Harasim, F. C. Moss, M. Rohrmeier, The Annotated Beethoven Corpus (ABC): A Dataset of Harmonic Analyses of All Beethoven String Quartets,Frontiers in Digital Humanities 5(2018), 16. doi:10.3389/fdigh.2018.00016

  36. [36]

    Moretti,Distant Reading, Verso Books, London, 2013

    F. Moretti,Distant Reading, Verso Books, London, 2013

  37. [37]

    Tunnicliffe, G

    M. Tunnicliffe, G. Hunter, Random sampling of the Zipf–Mandelbrot distribution as a represen- tation of vocabulary growth,Physica A: Statistical Mechanics and its Applications608(2022), 128259. doi:10.1016/j.physa.2022.128259 20

  38. [38]

    Jurafsky, J

    D. Jurafsky, J. H. Martin, N-gram Language Models, in:Speech and Language Processing: An Introduction to Natural Language Processing, Computational Linguistics, and Speech Recognition, 2nd ed., Pearson Education, 2009

  39. [39]

    Eugene Onegin

    A. A. Markov, Essai d’une recherche statistique sur le texte du roman “Eugene Onegin” illustrant la liaison des ´ epreuves en chaˆ ıne,Izvistia Imperatorskoi Akademii Nauk7(1913), 153–162

  40. [40]

    Chihara, T

    L. Chihara, T. Hesterberg,Mathematical Statistics with Resampling and R, 2nd ed., John Wiley & Sons, Inc., 2018. doi:10.1002/9781119505969

  41. [41]

    C. E. Shannon, A mathematical theory of communication,Bell System Technical Journal27(1948), 379–423

  42. [42]

    Anderson, D.A

    S. Kullback, R. A. Leibler, On information and sufficiency,Annals of Mathematical Statistics22(1) (1951), 79–86. doi:10.1214/aoms/1177729694

  43. [43]

    Ruwet,Langage, musique, po´ esie, Editions du Seuil, Paris, 1972

    N. Ruwet,Langage, musique, po´ esie, Editions du Seuil, Paris, 1972

  44. [44]

    Genette,Palimpsestes

    G. Genette,Palimpsestes. La Litt´ erature au second degr´ e, Editions du Seuil, Paris, 1982

  45. [45]

    The MathWorks Inc., MATLAB version: 9.15.0 (R2026a), Natick, Massachusetts, 2026

  46. [46]

    van Rossum and the Python Development Team, Python Language Reference, version 3.13, Python Software Foundation, 2026

    G. van Rossum and the Python Development Team, Python Language Reference, version 3.13, Python Software Foundation, 2026

  47. [47]

    Diestel,Graph Theory, 5th ed., Springer, 2017

    R. Diestel,Graph Theory, 5th ed., Springer, 2017

  48. [48]

    G. Ala, M. L. Di Silvestre, E. Francomano, A. Tortorici, Wavelet-based efficient simulation of electromagnetic transients in a lightning protection system,IEEE Transactions on Magnetics39(3) (2003), 1257–1260. doi:10.1109/TMAG.2003.810357

  49. [49]

    Audiosonica, Conversione tra note musicali e frequenze - Appen- dice I, 2026.http://www.audiosonica.com/it/corsoaudio-online/ conversione-tra-note-musicali-e-frequenze-appendice-i 21