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Inferring Communities of Medieval Music Manuscripts Using Stochastic Block Models Cover

Inferring Communities of Medieval Music Manuscripts Using Stochastic Block Models

By: Tim Eipert and  Fabian C. Moss  
Open Access
|Feb 2026

Figures & Tables

tismir-9-1-298-g1.png
Figure 1

Excerpt from a transcription of a trope to the antiphon Dominus Dixit with indicated structural elements. Trope elements have a numerical ID; primary chant cues are indicated by letters. Source: Tropus Hodie Cantandus Est, transcribed by David Catalunya, Corpus Monodicum Online Edition, https://corpus-monodicum.de/d/bdeea6d3-3c3f-4314-9f92-0ec8950535d6.

Table 1

Occurrences of trope elements for the incipit Puer Natus est.

Primary Chant IncipitFeastGenreManuscriptTrope Elements (Sequential Order)
Puer Natus estNat IIIintrBa 525 31 32 35 18 19 36 14 1 2 3 4 5 34 37 33
Puer Natus estNat IIIintrSG 37625 2 3 4 11 12 30 13 1 7 8 9 10 5 26
tismir-9-1-298-g2.png
Figure 2

Degree distributions of manuscript nodes (top) and trope element nodes (bottom). A base‑10 logarithmic scale is used for both y‑axes. On average, a manuscript node contains around 112 trope elements, and a trope element is contained in around four manuscripts.

Table 2

The 10 most‑connected manuscripts in the dataset. The degree of a manuscript represents the overall number of trope elements included in that manuscript.

#ManuscriptDegree
1Pa 1118784
2Apt 17727
3Pa 909688
4Pa 1871613
5Pa 887610
6Pa 1120603
7Pa 1119595
8Lo 14556
9Pa 1121534
10Ox 775506
tismir-9-1-298-g3.png
Figure 3

Posterior odds ratios represented as log10Λ. Colored points represent 10 independent runs per model, normalized so the log10Λ of the best‑performing model is 1 (right). All other points show each alternative model's odds ratio relative to this winner.

Table 3

Number of inferred blocks in the NDC‑SBM at each hierarchical level, reported for its manuscript and trope–element projections.

b0b1b2
Manuscripts39114
Trope elements34134
tismir-9-1-298-g4.png
Figure 4

Dendrogram of the inferred hierarchical blocks of the manuscript side, with terminals representing manuscripts. The shaded circles represent the manuscript level (M) as well as community assignments on increasing levels (b0,b1,b2). Branch colors represent the block assignment bi2 of the highest block level for manuscripts.

tismir-9-1-298-g5.png
Figure 5

Geographical distribution of inferred partitions at b2, b1, and b0. Each manuscript's provenance is indicated by a point colored by its b2 group; blocks at different levels are represented by the concave hull between the inherent manuscripts.

DOI: https://doi.org/10.5334/tismir.298 | Journal eISSN: 2514-3298
Language: English
Submitted on: Jun 26, 2025
|
Accepted on: Jan 31, 2026
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Published on: Feb 26, 2026
Published by: Ubiquity Press
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2026 Tim Eipert, Fabian C. Moss, published by Ubiquity Press
This work is licensed under the Creative Commons Attribution 4.0 License.