Educational Profiling of Guitar Tablature: Tools to Foster Self-Guided Learning

Educational Profiling of Guitar Tablature: Tools to Foster Self-Guided Learning Marcelo Rodríguez and Anssi Klapuri Yousician, Helsinki, Finland [email protected] http://www.yousician.com Abstract. Digital education platforms attract learners with a wide range of ages and interests. Platforms are hence required to accommodate guidance accordingly. For music education, showing learners what it is about that phrase or transition that is challenging, being able to tell them which skills they have improved or are lacking, suggest ways of practising, are sought-after features. That level of nuance puts significant pressure on manual curation, calling for tools to assist or automate courseware production. To meet that need, this paper introduces a system to enrich annotation of guitar courseware. More concretely, a means to automatically profile guitar tablature, annotating it with educationally relevant tags and difficulty estimates, down to the note level. We validate the resulting descriptors on the task of predicting expert-assigned song syllabus levels. We report a 0.94 Mean Squared Error, on a dataset of 5000 songs, each categorised into one of ten levels. We also show how the descriptors can be used to visualise skill demands, and are interpretable as psychomotor constraints, opening the possibility to offer nuanced, personalised instruction and feedback. 1Introduction Characteristic to the many services operating in the EdTech domain, is the vast range of learner ages and goals. More importantly, people that gravitate towards these services typically express a desire for autonomy [24,30,42]. The learner is hence expected to define, at least partially, how deep is deep enough, how hard is hard enough, and how good is good enough. In that context, progress and goal communication need to be not just transparent, but intuitive. Relying only on manual curation to support systems able to offer guidance, with that level of nuance, has shown monetarily unsustainable [10], making tools to assist or automate courseware production indispensable. In this paper we address that need. We focus on guitar learning, given its popularity and widespread demand [43,56], and propose a system to automate description of guitar courseware. More concretely, a means to automatically profile guitar tablature, annotating it with educationally-relevant tags and difficulty estimates, down to the note level. A profiled tablature can then express (1) a vocabulary of learning outcomes, flexible enough to serve the communication Proc. of the 17th International Symposium on CMMR, London, UK, Nov. 3-7, 2025 11 2 M. Rodríguez, A. Klapuri needs of learners of different abilities and interests, and (2) challenges in terms of instrumental technique and psychomotor difficulty. 2RelatedWork The field of music EdTech research is vast, ranging from machine-driven performance evaluation [19,20,25] and educational ontologies [3,16,46], to difficulty estimation [2,36–40,52,56]. From the latter, the works of Vélez et al. [56], and Ramoneda et al. [36], are closest to ours. We have two ways in which this work complements theirs. First, the type of music notation encoding: [56] focus on chord-based reductions for guitar, and [36] focus on public-domain collections for piano. We add to that the space of tablature arrangements for guitar, which dominates the courseware of platforms like Simply Guitar1and Yousician2. The second is the pursuit of interpretability. Representation learning is by now a well-performing, mature technology. Neural Network (NN) approaches are the top performers in that domain. Unfortunately, it is not straightforward, or in some cases even feasible, to interpret what each dimension in a learnt representation is describing [15,51,58,61]. Much less summarize it in way that is intuitive to students. For educational applications that is a major obstacle. It hinders the ability to communicate progress, provide error diagnosis, et cetera. Vélez et al. address this issue by proposing and validating a difficulty annotation rubric. They show RNNs can successfully predict the aggregate difficulty, as well as the difficulty of each rubric component. An elegant solution, pairing an opaque yet high-performing predictor, with a method of manual annotation that is both rich (multi-dimensional) and easy to grasp. Extending their approach beyond chord-based notation is, however, not scalable. The myriad of music textures and time spans require rubrics of higher dimensionality, which in turn make training data production expensive. We need additional automation that either operates below the rubric level, or can suggest rubrics. In [36] Ramoneda et al. pursue the latter for piano. The rubric components are annotated automatically, and an ordinal NN regressor is used to first combine the components into an aggregate of difficulty, and then predict suitable level classes. The model is not only transparent, but it also outperforms the end-to-end system they pursue in [39,40]. This paper extends that line of experimentation to guitar, expanding both on the number of descriptors, and their affordance. 3TablatureProfilingSystem The context of this paper is a guitar learning platform. The platform provides students with access to songs, arranged at different difficulty levels and oriented towards different styles (e.g. melodic playing, accompaniment). The arrangement’s notation can be assumed to specify, at least, the notes to be played, their musical timing, and the string, fret, and finger with which to articulate them. 1https://www.hellosimply.com/simply-guitar 2https://yousician.com/ Proc. of the 17th International Symposium on CMMR, London, UK, Nov. 3-7, 2025 12 Educational Profiling of Guitar Tablature 3 Figure. 1: Tablature profiling example, for 'Under The Bridge'by the Red Hot Chili Peppers. Figure 1 depicts our profiling system in action. The representation is dual. On the one hand, we have music vocabulary and instrumental technique (tags). On the other, psychomotor demands (difficulties). The former is expressed categorically, as either nominal data (e.g. "barre chords") or ordinal data (e.g. "small jump", "big jump"). The latter is a multidimensional vector. All descriptors are time-stamped, making a tablature profile a tabular, time-series hybrid. Vocabulary Tagging: Each tag is defined in collaboration with our team of educators. Tagging automation needs to support tag terms exclusive to the platform, and scale to both new tag definitions, as well as tag definition changes. We sided for a rule-based system, as it provided a clean way to address closedworld terminology and its updates. The rules and tags are defined so as to match the concepts and wording used in our instructional videos. The complete tag set has ⇠650 unique tags, which includes, among others, instrumental technique (e.g. 'slide','thick strings','partial barre'), rhythm (e.g. '16ths', 'off-beat','shuffles'), and ASCII renditions of notation symbols (e.g. 'xx0232', which is an open D chord vocing, in standard-tuning). Psychomotor Difficulty:Theplatformfocusesonscore-guidedmusicperformance. For analytical purposes we can reduce that to a sequential task, involving three fundamental steps: read symbols, translate symbols to movements, execute movements. We discuss how to describe challenges in that task chain, from a mental and physical perspective, in Section 4. 4 Describing Psychomotor Difficulty 4.1 Motor Control Motor control is responsible for planning and synchronizing movement. We tackle two control-related factors: predictability (e.g. how often do you need to refer Proc. of the 17th International Symposium on CMMR, London, UK, Nov. 3-7, 2025 13 4 M. Rodríguez, A. Klapuri to the notation), and counting (e.g. how to best entrain to the meter and/or backing-track). We scope out readability, which involves mapping notation to playing action, as it requires not only knowledge of the tablature, but also of how the tablature is presented to the student (engraving, user interface). We implement machines for next-token prediction, down-beat prediction, and syncopation prediction. Our strategy is to leverage the internal state of these machines for difficulty description. Importantly, we aim to develop them without the the need for student data (e.g. playing histories), in order to free the description from cold-start noise. Motor Control Difficulty Based On What’s Estimated [1,32] chord shape surprise neck position surprise fingering + articulation surprise rhythmic surprise [12,27] offbeatness [35] counting Table 1: List difficulty descriptors related to motor control. Table 1 summarises the descriptors. For next-token prediction we use an unsupervised, variable-length N-gram model, implemented through PPM-C, with interpolated smoothing [32]. Our modelling choice has been empirically validated in a wide range of music cognition tasks [33]. We use it for surprisal profiling: log(p(x|z)) with xcurrent token, and zpreceding tokens. Information-theoretic surprisal has shown a strong causal link to music complexity ratings [44]. It also ranks amongst the most relevant descriptors when predicting reading lags in language [14,47]. Parameters are tuned to minimise cross-entropy in our catalogue. We use [12,27] and [35] for syncopation prediction, and downbeat prediction, respectively. [35] finds the best pulse stream that subsumes an input rhythm. We use its internal representation to profile the degree of decorrelation between notated meter and rhythm. [12,27] provide (flat and hierarchical) ways to estimate saliency in beat-to-note distances. We use these machines to profile offbeatness. As before, our modelling choices have extensive validation in perception experiments [11,12]. Parameters proposed in [49,50] work best in our validation datasets. 4.2 Biomechanics We aim to describe five factors that may complicate guitar performance: fretting discomfort (e.g. when pressing strings), hand posture discomfort (e.g. when holding a chord), movement inefficiency (e.g. when transitioning from one point on the fretboard to another), positioning inefficiency (e.g. when rearranging fingers Proc. of the 17th International Symposium on CMMR, London, UK, Nov. 3-7, 2025 14 Educational Profiling of Guitar Tablature 5 so that they are placed on top of the strings that need to be pressed), and coordination inefficiency (e.g. when a picking pattern does not align with a metric subdivision pattern). Biomechanical Difficulty Based On What’s Estimated [13,18,55] [PD] elastic strain [PD] pressing force [MI] hand relocation speed [MI] finger relocation speed [PI] wrist repositioning speed [PI] finger repositioning speed [18,26] [MI] hand relocation speed [PI] pick repositioning speed [CI] meter-picking alignment Table 2: List of biomechanical difficulty descriptors. Stacks (top to bottom): fretting-hand, plucking-hand. Abbreviations: PD - Posture discomfort, MI - Movement inefficiency, PI - Positioning inefficiency, CI - Coordination inefficiency. To that end, we implement machines which, given an input tablature, can predict articulation symbols. We make one to predict fretting-hand fingering, based on [18], and another to predict plucking direction, based on [26]. Both frame articulation prediction as a search problem, where good fingers/plucking choices are those that minimize cumulative biomechanical cost. To solve the search problem efficiently, dynamic programming is used. Our references are instances of proof-of-principle work. In both cases we curated validation databases, so as to extend their processing capacity (e.g. have [18] support polyphonic input), and fine-tune their biomechanical interpretability. Table 2 gives a summary of the descriptors, and lists references to the models used to extend the representation capacity of our original sources. The reader can refer to Appendix A and B for a more detailed description. 5ExperimentalSetup Rating systems and rubrics are widely used in pedagogy, as a means to make learning goals and evaluation criteria explicit [4, 59]. When paired, they offer an efficient way to compress and chain pedagogical information, hence fostering discovery and choice (which in turn have strong links to positive engagement and motivation [9,60]). Our syllabus levelling system is an example of one of such tools, making level prediction both a suitable validation task, and a valuable addition to our software stack. Our objective is then exploring the relevance of different descriptor sets to level prediction. That includes the ones proposed in this paper, as well as descriptors proposed in previous research. In [31] we extend validation experiments to personalisation scenarios. Proc. of the 17th International Symposium on CMMR, London, UK, Nov. 3-7, 2025 15 6 M. Rodríguez, A. Klapuri 5.1 Level Annotated Dataset For our validation experiments, we use a dataset of guitar song arrangements, notated as tablature, and stored as MusicXML. The dataset consists of 5000 arrangements, randomly sampled from our platform’s catalogue. The ground-truth annotations consist of syllabus levels, annotated by expert educators. Levels are annotated on a scale from 1 to 10. Level Annotation Guidelines Level Chords RiffsMelodies 1E, Em, Am, strum down only Single notes, 1st pos, EAD strings 1st pos, GBE strings, no string skips 2C, G, basic down-up strumming Single notes, up to fret 5 (no pinky) Single notes, up to fret 5 (no pinky) 5Syncopation, arpeggios Faster, hammer-ons and pull-offs Hammer-ons, pulloffs 8 Full barre (maj, min, maj7, m7, dom7) Faster rhythms, more syncopation Bending introduced Table 3: Sample of guidelines used by experts to assign levels to song arrangements. Table 3 provides a sample of the annotation guidelines. The guidelines are clear cut for low levels, and get progressively more abstract for higher levels (e.g. "faster", "more syncopation"). While the guidelines represent a consensus, the annotations themselves do not: annotations are made by single experts. Due to the compactness and abstraction of the guidelines, we can expect a nonnegligible level of disagreement. We elaborate on the effects that that has on prediction performance in Section 6. 5.2 Descriptors, Predictors, and Figures Of Merit Preprocessing:Difficultiesarecontinuousvariables.Eachdifficultydimension has a different range and a different distribution. We quantise their range to integers in 1-10, based on sample quantiles. We quantise each dimension separately, using the entirety of our catalogue. Quantisation boundaries are chosen so that the data is distributed uniformly among the ten buckets. We also compute the ranking of each tag over the entirety of our catalogue. (The higher the rank, the more instances.) The reader can refer to Appendix A.3 for depictions. Descriptors: In a profiled song, each note/chord has 15 difficulty numbers, and between 5-20 tags. To summarise a song’s difficulty content, we take the cumulative sum over each dimension, and also compute the average over each dimension. A song difficulty vector then has 15 + 15 dimensions. To summarise a song’s tag content, we make Bag of Words (BoW) representations [54]. A BoW vector has over 600 dimensions. We use truncation, where we impose a rank limit (TopN tags), and dimensionality reduction (SVD, with TF-IDF weighting). Proc. of the 17th International Symposium on CMMR, London, UK, Nov. 3-7, 2025 16 Educational Profiling of Guitar Tablature 7 As benchmarks we use the descriptors proposed in [36, 56]. Table 4 provides asummary.Benchmarkdescriptorsarepreprocessedinthesamewayasour difficulty descriptors. Baseline Descriptors Vélez et al. [56] uncommonness of chord, chord finger positioning, chord fingering difficulty, song length in secs, righthand complexity. Ramoneda et al. [36] pitch entropy, pitch-set LZ, pitch range, average pitch, average IOI. Table 4: Benchmark Descriptors. The "repetitiveness" of [56], and "displacement rate" of [36] cannot be computed with our input data. The first requires phrase-level boundary annotations, which we lack. The second is piano specific. We also omit "beat difficulty", as suggested by [56]. Predictors:WeuseaMultivariateLinearRegressor(MLR)andaGradient Boosted Regressor (XGB). The former gives us an idea of how well a simple model does on the task at hand, and the latter is an established industry standard. These choices also allow a parallel with [31,39]. Figures of Merit:WeuseMeanAbsoluteError(MAE)andMeanSquared Error (MSE). Both measures are standard for regression. Performance aggregates are obtained by averaging over all predictions (micro-average). We also measure adjacent accuracy (ACC), where we count the number of predictions whose (absolute) class distance to the true class is no more than one. This score is [0,1] bounded, and unlike the other two, higher is better. 6ResultsAndDiscussion Table 5 shows our experiment results. Variant 1 presents the performance of regressors using the benchmark descriptors. Variants 2–4, stratify performances by tag and difficulty. Variants 5–6 present plateau performances for tags. Lastly, variants 7–11 present combination sets. For all experiments the regressors use factory defaults. We pair dimensionalities to mitigate imbalance effects. As a lower-bound, we present the results of two naive baselines: Constant5, which always predicts level 5, and Random which predicts levels by sampling from a N(µ, 2)distribution tuned to our dataset. We report a 0.94 MSE, obtained in variant 10, as the best result. The predictor consists of an XGB regressor, with an input of 15 SVD-encoded tag features, and 15 difficulty features (averages, computed using quadratic mean). We prefer variant 10 over similar performing variants on the grounds of parsimony (lower input dimensionality), and generalizability (both regressors perform well). This predictor is interpretable only through difficulties. If full interpretability is needed, variant 11 can be used. Proc. of the 17th International Symposium on CMMR, London, UK, Nov. 3-7, 2025 17 8 M. Rodríguez, A. Klapuri Naive Baselines MSE MAE ACC Random 10.7±0.38 2.67 ±0.05 0.22 ±0.02 Constant5 6.30 ±0.19 2.08 ±0.04 0.27 ±0.01 Id Descriptors MLR XGB MSE MAE ACC MSE MAE ACC 1Benchmark 1.97 ±0.09 1.02 ±0.03 0.68 ±0.01 1.56 ±0.07 0.96 ±0.02 0.73 ±0.02 2Tags [top15] 2.99 ±0.14 1.36 ±0.04 0.60 ±0.02 1.28 ±0.07 0.79 ±0.02 0.84 ±0.02 3Tags [svd15] 1.79 ±0.13 1.02 ±0.03 0.75 ±0.02 1.28 ±0.08 0.80 ±0.03 0.84 ±0.01 4Diffs [av15] 1.76 ±0.06 0.99 ±0.02 0.75 ±0.01 1.36 ±0.08 0.82 ±0.03 0.83 ±0.02 5Tags [top100] 2.43 ±0.12 1.19 ±0.04 0.69 ±0.02 0.92 ±0.05 0.64 ±0.01 0.89 ±0.01 6Tags [svd100] 1.55 ±0.10 0.93 ±0.03 0.80 ±0.02 1.22 ±0.07 0.85 ±0.01 0.90 ±0.01 7top30+all30 1.30 ±0.05 0.83 ±0.02 0.82 ±0.02 1.01 ±0.06 0.67 ±0.03 0.88 ±0.01 8svd30+all30 0.99 ±0.05 0.71 ±0.02 0.89 ±0.01 0.90 ±0.06 0.63 ±0.02 0.90 ±0.01 9top15+av15 1.44 ±0.07 0.87 ±0.02 0.81 ±0.02 1.09 ±0.05 0.72 ±0.02 0.87 ±0.01 10 svd15+av15 1.07 ±0.07 0.74 ±0.03 0.87 ±0.01 0.94 ±0.04 0.66 ±0.02 0.90 ±0.01 11 top75+av15 1.31 ±0.07 0.83 ±0.03 0.83 ±0.01 0.88 ±0.05 0.62 ±0.02 0.90 ±0.01 Table 5: Performances as µ±between folds of 10-fold cross-validation. Descriptor Importance: In our experiments, tag data has a primary role. Asophisticatedpredictorcanuseiteffectively.Wecanseethatinvariants2– 4, where tags show more explanatory power than difficulties, and in variant 5, where the XGB regressor reaches 0.92 MSE. That said, using a combination of tags and difficulty descriptors, we get competitive performance with lower input dimensionality (variants 7–10). Importantly, when using descriptor combinations, even the humble linear regressor can reach competitive level (variant 8). The latter also reveals that the difficulty space forms an orthogonal basis. (MLR machines are known to have performance issues when the input is correlated, visible in variants 2-3, 5-6.) Afewparametrisationaspectsworthnoting.First,thetagdescriptorspreferred by the XGB machine (TopX tags), are dominated by abstractions (e.g. 'thick strings'). The dominance of abstractions in TopX sets consistently outperformed variants in which we injected high ranking tags that more closely represent the notation (e.g. 'xx0232','Amaj7'). Second, for the difficulty descriptors, kinematics drive performance. We attribute that to the fact that kinematics have a notational, quantifiable counterpart: tempo. Annotation guidelines that refer to kinematic aspects, e.g. "faster", have less room for interpretation than e.g. "more syncopation", leading to more consistent level annotations. Third, we found that, when summarising difficulty over a whole song, length descriptors (cumulative sum) are less relevant than means, which is in line with [56]. In our experiments the quadratic mean outperformed all classic Pythagorean means. Performance Upper-Bound:AgoodnumberofperformancesinTable5 show an MSE ⇠1. We argue that that is likely bordering human error. As mentioned in section 5.1, we can expect disagreement among annotators. DisagreeProc. of the 17th International Symposium on CMMR, London, UK, Nov. 3-7, 2025 18 Educational Profiling of Guitar Tablature 9 ment translates into inconsistent labelling: one annotator may think that X amount of, for instance, syncopation, makes an arrangement a level 5, while another may think it makes it a level 6. The compactness of the guidelines shown in Table 3 make it reasonable to expect a minimum of a ±1level of disagreement, more likely dominant in higher levels. Sustaining consistent agreement, over years, with teams that vary over time, is understandably complex. Vélez et al. discuss the negative effect it has in community lead annotation [56]. We hence consider the expected level of noise in our dataset is not exceptional, but common. While we can not say anything definitive, and much less speculate how our performances translate to other rubrics, guideline sets, or instruments, we hope that this discussion, however brief, inspires more research on this topic. Skill Demands:Lastly,weprovideanexampleofhowourdescriptorsenable educational visualisations, and granular skill diagnosis. Figure 2 shows a difficulty profile in contrast to a learner’s error plot. All overlaid on top of a song timeline. The error plot corresponds to the average number of errors learners made, over multiple trials, for each note/chord. We use a 1K sample of learner historicals to represent the population. In this example we can see the temporal structure of errors correlates with that of difficulties. One possible use of the profile is hence as a preview mechanism, highlighting which parts of the song are more complex. We aim to pursue experimental validation of these possibilities in future work. Another use is as a way to modulate experience accumulation. In other words, correctly playing something difficult grants more experience points than correctly playing something easy. In [31] we pursue prediction of prima vista performances based on that idea. We tested various ways of quantifying and accumulating experience. Results show that accumulating experience modulated by difficulty estimates performs best. Figure. 2: Fretting-Hand difficulty profile (bars) vs. learner error data (line). Proc. of the 17th International Symposium on CMMR, London, UK, Nov. 3-7, 2025 19 16 M. Rodríguez, A. Klapuri Figure. 5: Example difficulty dimension: raw values (bars) and quantisation cuts (lines). quantisation boundaries (discussed in section 5.2 of the parent document). Raw values correspond to relocation velocities, in centimetres per second, which involve moving the pick so that it is ready to pluck the next string. In most acoustic and electric guitars the distance between strings is roughly 1centimetre. So, lower quantised levels describe situations where either the pick is (mostly) plucking a single string, or when time is not a constraint. Appendix B Predicting Fretting-Hand Fingering B.1 Search Space Representation We use a trellis graph, depicted in Figure 6, as an abstraction of the search space. The trellis represents notation-guided performance. Each vertical layer corresponds to a note/chord, and each node to a candidate fingering, from a finite set. We use tto denote layer indexes, and i, j to denote the indexes of transitions from one candidate to another, over adjacent layers. Formally, we assume a set of nodes S,representingthespaceofperformerhandstates,sothateachs2Shas alayerl(s)2{1,...,T},andasetofarcsA✓{(si,s j):l(sj)=l(si)+1},for i, j 2[1,|S|).Acompletepaththroughthetrellisisanodesequence(s1,...,s n), such that l(s1)=1,n=T,andeverypair{(sk,s k+1)}n1 k=1 2A. If we then assume the cost of a complete path can be scored c(s1,...,s n)= Pn1 kc(sk,s k+1),searchingfortheoptimalpathS⇤can be approached as a cost minimization problem, efficiently solvable using the Viterbi algorithm [57]. Our trellis formulation presupposes a 1-1 correspondence between note/chords and action units. While that is not always the case, in this appendix we take it as true, for brevity. B.2 Starting Point: Melody-Only Fretter We base our modelling on the work of Hori and Sagayama [18]. They propose an approach to predict fretting-hand fingers, given a monophonic tablature. For monophony a fretting =hstring, fret, fingerispecifies the triplet needed to articulate a note. Triplet elements follow the definitions given in A.1. Openstring frettings are undefined, and hence discarded. It is assumed the tablature has tempo markings, so that onset time, in seconds, is computable throughout. Proc. of the 17th International Symposium on CMMR, London, UK, Nov. 3-7, 2025 26 Educational Profiling of Guitar Tablature 17 t i j Figure. 6: Depiction of a trellis graph. The fingering problem is then finding good finger elements for each prescribed (string,fret)pair.HoriandSagayamamakeaprobabilisticformulation, modelling trellis nodes as states of a Markov process, with transition probabilities aij(dt)=P(Xt=frettingj|Xt1=frettingi,dt), where dt is the time available to transition from ito j,computedasonsettonsett1. Computing log(aij (dt)) yields a cost. A small cost value means moving from one posture to the next is easy, and a large value means it is difficult. Transition Model. At the time of writing, Hori and Sagayama reported a lack of available data to learn model parameters, and sought out a design that wouldn’t require it. To that end, they formulate transition probability as aij(dt)/L(dx;0,dt)⇥p'(fingerj).(1) In Eq. 1 /means proportional, and the left hand side is normalized so that the summation with respect to jequals 1for all i. The right hand side consists of two terms, modelling kinematic and physiological factors, respectively. The first term is the Laplace distribution, with dx denoting the length of hand displacement along the fretboard, and, as before, dt denoting the time available to transition. Due to its heavy tails, L(·)approximates the kind of zoned movement characteristic of guitar playing, where small distances are typical, but large ones (outliers) are not uncommon [17]. It also integrates dt as a scale parameter. As a result, the model accounts for a (widely validated) notion: time constraints make accurate movement less feasible [28, Ch. 7]. To compute position estimates, h(fretting)=fretfinger+1,(2) is used. Equation 2 estimates the index finger position, which in guitar playing dictates the position of the hand. The formula quantifies a posture guide, popular in guitar pedagogy, known by the mnemonic "one-fret-per-finger" [8]. With that, the density function for L(·)can be expressed as Proc. of the 17th International Symposium on CMMR, London, UK, Nov. 3-7, 2025 27 18 M. Rodríguez, A. Klapuri L(dx;0,dt)= 1 2dt exp ✓|h(frettingj)h(frettingi)| dt ◆.(3) The second term in Equation 1 is a physiological prior, aiming to account for finger length and mobility constraints at arrival point j. The prior is elicited subjectively, with p('=finger)obtained through {f(')|'2{1,2,3,4},f(1) = 0.4,f(2) = 0.3,f(3) = 0.2,f(4) = 0.1}. In that setting fretting candidates that use the index finger are the easiest, and those using the pinky finger are the hardest. The suggested setting agrees with findings in finger dexterity [5,22]. B.3 Generalizing: Polyphonic Fretter We extend [18], aiming towards polyphony, where a fretting =hhstring, fret, fingeri,...i, with |fretting|2[1,6].Asbefore,onsettimeisderivedfromtempo markings, and open-string frettings are discarded. For optimal path search we assume cost cij is decomposable into movement and posture components, as cij =↵c m(si,s j)+(1↵)cp(sj),(4) where ↵is a mixing weight. We address cmand cpin turn, using the same framework as before, with a model inferable from displacement, and one defined with tunable weights. We keep the probabilistic frame, but only as an abstraction. In practice that means we don’t normalize layers so that they add up to 1, and drop additive constants. Movement Difficulty We need to account for kinematic cases involving transitions from/to frettings with multiple pressed strings. Following A.1, we limit our scope to the movement of hand, fingers, and wrist. In order to accommodate the dimensionality increase (in anatomical space), we start by restating our representation, and continue with the approach to cost computation. Fretboard Space. We model the fretboard as a N2motion plane, with (string, fret)coordinates. The space is discrete, non-negative, and equidistant. We can then project our guitarist’s hand onto that plane as an ordered point set {qn}4 n=1, consisting of fingertip positions q2N2. The set is ordered index to pinky, so that n+1retrieves the finger corresponding to position qn. To fully specify a point set, we need the positions of both pressing and idle fingers. As with 2, we make use of the "one-fret-per-finger" guide to extrapolate positions. Let us assume a given fretting, containing candidate fingers for a prescribed set of (string, fret)positions, and represented in our search space by a given node s2S. In that setting, idle fingers, if any, are assigned (stringav,fret idle)positions. The stringav coordinate, constant for every idle finger, is the average over the strings in s,roundedtothenearest string. If sspecifies one pressed string, each fretidle is computed by recursing Proc. of the 17th International Symposium on CMMR, London, UK, Nov. 3-7, 2025 28 Educational Profiling of Guitar Tablature 19 fretnext fingeridle +fingernext,startingfromtheclosestprescribedposition. If it specifies many, we interpolate between prescribed fret positions, or cap to the nearest one, as applicable. Hand, wrist, and fingers are considered as separate moving components. The first is characterized using a single position (stringav,fret index). The latter subscript means the fret is that corresponding to the index finger. As a reminder: in guitar playing the index dictates the position of the hand. For the wrist we use a scalar angular position. We compute unit vectors for the index and pinky, derive a rotation matrix, and then the position angle. For the fingers we use the full point set. Movement Difficulty. We can generalise Equation 1 so that pm/Y c L(dc;0,dt)Y n p'(fingern),(5) calculates movement probability, where dcdenotes the length of displacement, for the cth moving component, bounded to 3 components, and fingerndenotes the nth (pressing) finger at arrival point, bounded to 6 (string) positions. Taking log(pm)we can express movement cost as cm=dx dt X n log(p'(fingern)) + Alog(dt)+B, (6) where A, B denote constants, and dx =dh+df+dwlinearises displacement length, as the aggregate for hand, fingers, and wrist, respectively. dhis modelled as taxicab distance, dfis modelled as the average of individual finger displacements, using euclidean distance and quadratic mean, and dwis modelled as normalised angular displacement. There is no theoretical underpinning for these choices, they were selected on the basis of experimental performance. Parametrizations and Practicalities 1. If the transition involves fretting pairs with only one pressed string, we set p'as Hori et al. If the transition involves moving from/to frettings with multiple pressed strings, altering the setting so that f(1) = f(3) = 0.3,andf(2) = f(4) = 0.2, performed best in our validation dataset. 2. We found log-compressing dhimproves generalisability. 3. For fingering prediction we use the aggregate computed in Equation 6. For the tasks explored in the parent paper each term is returned separately. That includes all displacement components, as well as the bias term. All are interpretable as speed constraints, with the latter referred to as "repositioning difficulty" in Figure 4. Posture Difficulty We model posture difficulty taking into account two factors, that of holding a posture, and that of pressing strings. We introduce our approach in stages, first defining a suitable representation space, then a model for finger-pairs, and lastly amodelforafullposture. Proc. of the 17th International Symposium on CMMR, London, UK, Nov. 3-7, 2025 29 20 M. Rodríguez, A. Klapuri Elastic Space. We use an elastic graph G=(V,E)to represent the space of posture-related elastics. We define Gto be undirected and simple. The graph is elastic in that edges represent ideal springs [53]. Let us then define a map :V7! R2to embed the graph onto the guitar fretboard, with (string, fret) dimensions, measurable in centimetres. Any fretting can hence be represented as a subgraph Fwith {vk}n=6 k=1 2Vand {(vk,v k+1)}n1 k=1 2E. Importantly, each v2Ftakes a label equal to the candidate finger considered for that position, and each e2Eadopts the equilibrium length of its corresponding finger pair. The equilibrium length is the spacing between fingers, when the hand is in resting position, which, for expository purposes, we assume to be known. Finger-Pair Discomfort. For any {v,u}✓F,wecancalculatethepair’s posture probability as ppair /N(d";0,1) ⇥p(v,u),(7) where Nis a Gaussian distribution, accounting for the probability of holding the posture, and pis a prior accounting for the probability of pressing the strings. In both cases a lower probability can be interpreted as higher discomfort, and consequently higher difficulty. The term d"=(kvukrvu)/rvu denotes displacement-related strain, with v,uas the position vectors associated with each node in fretboard space, and rvu the equilibrium distance for the fingers corresponding to the node pair, expressed as a radius. The unit Gaussian choice means the model assumes elastics under static equilibrium: displacements are not a function of time, and muscle stresses arise from deformation. Taking log(ppair)we get cpair =d(v,u|rvu)2+ log(p(v,u)) + C, (8) where the first term on the right expresses d"computation as a distance function, and Cdenotes a constant. Finger-Pair Strength. Let us assume a known prior p'defined for each finger '2{1,2,3,4}. A low probability means pressing a string, with the fingertip, is difficult, and a high probability means it is easy. On that grounding, we define the probability for finger-pairs as p(v,u)=(pavg(v,u)fingerv6=fingeru |1 stringvstringu|⇥pavg(v,u)fingerv=fingeru where pavg(v,u)=pp('=fingerv)⇥p('=fingeru),andfingerv,u^stringv,u are, respectively, the finger label and string coordinate of the corresponding subscript. For fingerv=fingeruwe have a smoothing condition, to account for barre technique. The smoother evenly distributes fingertip probability mass over each pressed string. Proc. of the 17th International Symposium on CMMR, London, UK, Nov. 3-7, 2025 30 Educational Profiling of Guitar Tablature 21 Hand Discomfort. For each v2Fwe define a neighbourhood ⌘(v),containing all pairings of vto every vertex uon a thinner string. Formally, ⌘(v)={u2F| stringv>string u}.Withthat, cp=X n max ⌘(vn){Ue(vn,u) + log(p(vn,u))},(9) calculates the overall discomfort of holding a posture, while depressing multiple strings, as the maximum of individual finger-pair discomforts, where nis bounded to 6 pressing positions (strings). This formulation uses potential energy Ue,consideringthat Ue(v,u)/d(v,u|rvu)2=w1("fret)2+w2("string)2. In the right-most expression we focus on string and fret orientations separately, with "=(lL)/L denoting normal strain, Llength at rest, ldeformation length, and w1,w 2tunable weights. Parametrizations and Practicalities 1. Defining prior p'as {f(')|'2{1,2,3,4},f(1) = 0.4,f(2) = 0.2,f(3) = 0.2, f(4) = 0.2},aswellsettingw1,w 2=2, performed best in out validation dataset. 2. We model guitar fretboard dimensions using manufacturer averages. We settled for a middle ground between acoustic and electric guitar. The reader can refer to [41] for methods to calculate fret positions in centimetres, given fretboard dimensions. 3. We make a parametric model of resting position distances, for each finger pair. The model consists of 12 fret-wise distances, and 12 string-wise distances. All distances are specified in centimetres. The model takes into account orientation. That is, which finger presses the thicker string, and which the thinner, can make the same distance between strings comfortable in one case, and very uncomfortable in another. Rest distances were first calculated using publicly available data on physiological averages for hands, as well as adduction / abduction angle ranges, and then fine-tuned experimentally, on the basis of validation dataset performance. 4. For fingering prediction we use the aggregate computed in Equation 9, for the task explored in the parent paper, we return each component in the summation separately. The components are interpretable as posture discomfort and pressing discomfort, respectively. B.4 Outlook The approaches presented in this appendix answer to situations of data scarcity. We focus on domain-informed model design, and aim for low dimensionality. One area in which we (strongly) enforced that focus is on the representation of the hand-guitar interaction space, where we favoured planar approximations. In this last section we outline directions to extend the approaches presented. We centre on ways to enrich the representation space, while still assuming data to train/validate models is limited. Proc. of the 17th International Symposium on CMMR, London, UK, Nov. 3-7, 2025 31 22 M. Rodríguez, A. Klapuri Assuming enough data for validation, but not for training In our evaluation experiments, we saw planar approximations performed worse for posture difficulty modelling. In short, finger-pair flexibility thresholds change if a third (or fourth) finger is also pressing a string, and our model does not account for that. One way to extend the planar approach to tackle that problem, is to reformulate neighbourhood construction. That can be done, for instance, by framing it as a graph-partitioning problem, operating on vertex simplexes [23,62]. Adifferentalternativeistoallowforathree-dimensionalrepresentation.Forthat approaches of inverse kinematics [34], or inverse dynamics [29], can be tested. These alternatives come with a substantial increase in computation time, as well as a need for careful calibration (hand-guitar interaction is a niche application area, so it is not unreasonable to expect unsatisfactory off-the-shelf performance). Assuming enough data for validation, and limited data to train Two recent areas of research in machine learning lend themselves well to the problem at hand. One integrates knowledge of Physics, in the form of established governing equations, using them as a way to regularize Neural Networks. For instance, [7] train a model to reconstruct the Young’s modulus field of a heterogeneous object, based only on a partial measurement of the object’s axial displacement field. The other area focuses on dynamical systems, aiming to learn state-space representations. For instance, [6] proposed an approach to map non-linear dynamics to a high-dimensional space, where the dynamics of state and control are linearly separable. For training, these approaches would require music scores aligned to a recording of performance movement, or force dynamics (e.g. via motion capture data, or strain-gauge data, respectively). Proc. of the 17th International Symposium on CMMR, London, UK, Nov. 3-7, 2025 32