Fugue,
made spatial.

Read the sequence. Each note retains its onset in the complete work, duration, voice and measure. Ties become one sounding event, so a note held across a barline does not create a new attack. This separates musical succession from page layout: music21’s hierarchical representation supports following a voice and retrieving simultaneous events, but the extraction still needs musical checking (Cuthbert and Ariza 2010, 638, 641).

Place it in space. Rule R1 divides onset by the work’s complete notated duration and places that proportion along a 48-unit route. Thus the tenor’s first entry lies at 16/336, or 4.76%, in Bach’s m.5; Shostakovich’s tenor begins at 34/428, or 7.94%, in the second half of m.9. Their corresponding portals preserve this difference in entry pacing. Four-measure groups define the building’s bays; the final shorter group is retained. These are sampling windows, not automatically detected formal sections. The comparison aligns a musical function—an entering tenor—rather than pretending that equal bar numbers or clock times mean the same thing (Bach, ed. Moroney, n.d.; Shostakovich 1980).

Keep the distinction. A common route length preserves order and relative spacing while suppressing absolute length: Bach has 336 quarter lengths, Shostakovich 428. Audio retains its own tempo map. The route’s curvature and gradual 2.4-unit ascent are design choices prompted by the Great Wall experience; neither is evidence that the melody continuously rises. The route makes succession available to exploration, without reproducing a performance. Structural analogy can be useful without claiming a common origin (Dong, Yin, and Yu 2024, 354–359). Here, what is compared is explicit: order, proportional spacing and contrapuntal role. The shared 48-unit convention is our design choice, not a discovery that both pieces have equal dimensions.

Follow identities, not rankings. Soprano, alto, tenor and bass retain their score or track identity even when their pitches cross. For each bay, the analysis averages the number of sounding voices over time. Bach’s mm.1–4 contain one active voice; mm.5–8 contain two, as the bass continues beneath the tenor answer. Shostakovich’s mm.1–4 average 0.875 voices because the opening half-bar rest is retained. These are measurements of participation, not a scale of contrapuntal complexity (Bach, ed. Moroney, n.d.; Shostakovich 1980).

Give participation room. R2 sets a bay’s base half-span to 3.5 + 0.65 × mean active voices. Width gives concurrent participation more spatial capacity: an explicit design convention, not an acoustic law. Bach’s first two bays therefore change from 4.15 to 4.80 units; Shostakovich’s first is 4.06875. R3 separately maps duration-weighted mean pitch to column or arcade spring height on the common MIDI 35–84 scale. Optional voice ribbons preserve individual event pitches and gaps, while the existing overview chart shows each voice’s mean pitch per measure. That overview necessarily smooths motion within a bar.

Recognize the convention. Pitch-to-height is a chosen cross-domain correspondence. Zbikowski links such spatial concepts to embodied experience while describing alternative ways of conceptualizing pitch (1997, 199–202). Here, higher register consistently produces a higher local control value; it does not establish a universal equivalence between frequency and architecture. Bach’s central 18% expansion, interpolated vault boundaries, and Shostakovich’s five aggregate chambers are authored elaborations. Their finished silhouettes cannot be read as unmodified plots of voice occupancy. Recent crossmodal research distinguishes elementary correspondences from the interpretation of whole artworks (Spence and Di Stefano 2025, §§2–3); pitch-height alone cannot justify a church plan. Consistent voice identities and optional visual cues also take a design lesson from exploratory music visualization (Shell and Smith 2026, §§6–7), without claiming that its VR findings validate this browser experience.

Test recognition. Repeated notes are not automatically a subject, answer or meaningful return. Meredith, Lemström and Wiggins distinguish computational repetitions from those that matter analytically (2002, introduction). Recent BPS-Motif research makes annotation review explicit because motif boundaries and variants require judgment (Hsiao et al. 2023, §§3.2–3.3). Our simpler matcher proposes candidates, and score reading accepts selected entries. We do not implement either paper’s discovery algorithm or claim their independent review protocol. The result is a documented selection, not an exhaustive formal analysis.

Make an entrance recognizable. R6 places a member of the portal family at an accepted thematic onset and retains its voice and source identifier. Bach’s D-based bass return in m.31 begins at quarter position 120: its portal stands at 35.71% of the route. Shostakovich’s ornamented alto entry at m.80 begins at position 316, or 73.83%. The literal matcher missed that entry because of the added attacks, but reading the printed score restored it to the accepted set and therefore to the architecture (Bach, ed. Moroney, n.d.; Shostakovich 1980, 5).

Compare functions carefully. The repeated architectural vocabulary proposes an experience of recognition; its shape is designed. A pair of numbered portals may share a contrapuntal role without sharing melody, key, duration or formal location. The accepted set contains six Bach and twelve Shostakovich entrances, not every thematic event in either fugue. Missing markers therefore mean “not represented by this checked set,” not “no theme occurs here.”

Separate motion from participation. In Bach’s mm.1–4, eleven attacks across sixteen quarter lengths give a density of 0.6875; mm.5–8 rise to 2.4375. R4 converts these values into three and six articulation divisions in the gallery detailing. More frequent attacks prompt more frequent spatial articulations; sustained participation is handled separately by R2. The reason is the rate of new attacks, not simply that two voices sound. Rounding and the cap of eight divisions sacrifice exact rhythmic durations. A controlled study of short tone sequences and shapes found that different complexity measures behaved differently (Hayashi, Kato, and Yanagisawa 2024, §§3–4). Our attack count is therefore called activity, not perceived complexity; that study does not validate our railing formula.

Read harmony before naming a metric. Shostakovich’s diatonic collection does not make its vertical relations uniform. At m.34 the four voices sound G2–A3–A4–C5; at m.35 they sound C3–F3–A4–B4. Dineen’s original score excerpts and discussion distinguish changing dissonance treatment within this passage (2013, §§72–78, Examples 14a and 15a). This supports examining the moving relationships between voices. It does not license treating every change as tension or assigning automatic chord functions.

Expose the implemented proxy. R5 compares successive sounding pitch-class sets, measures the fraction of their combined content that is not shared, then averages it by duration. For Shostakovich’s mm.33–36, the result is 0.59778, producing a 14.9444° control angle for the bay’s diagonal joint articulation. Bach uses the same statistic to rotate tracery. This is a reproducible design proxy for pitch-class turnover, not a harmonic analysis in itself: even one unaccompanied line can score highly when its notes change. It discards octave, voice-leading direction and chord function. Recent score visualization also uses pitch-class set overlap, but with a different sampling definition (Heyen, Ngo, and Sedlmair 2023, §3.2). Our weighting is a separate authored definition, not their tested method. The shared rule makes its consequences comparable; it does not prove the music is the same.