Six Degrees of Unification

To implement what was described in the last blog post deterministically, ADR 0028, on the hierarchical rendering pipeline, and ADR 0037, about measure distribution, both have been updated. The rendering pipeline now has six stages rather than five.

The additional stage enables the behaviour discussed in the previous post, but also allows slurs, lyrics, dynamics, and other elements that require vertical space to adapt dynamically without introducing layout jitter.

What follows is a brief tour of the six pipeline stages. Each has a clearly defined role, a fixed direction of information flow, and no hidden feedback paths. Together, they transform musical structure into pages without iteration.

If you are a musician, you should be able to follow how the music moves from essential meaning to visual expression. If you are a developer, the architectural choices should be readable between the lines. In both cases, the ADRs contain the full technical detail.

Stage 1: Atoms

Each measure is processed independently and turned into engraving atoms: indivisible musical units that already contain noteheads, augmentation dots, accidentals, stems, articulations: everything that belongs together. A note or a chord is an atom, including everything at a fixed distance from that note or chord. Once an atom is computed, its constituent parts never move relative to each other, though they can be adjusted manually or converted by the user to pure graphics for Illustrator-like manipulation.
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From these atoms, the system derives three facts about the measure stack: a minimum width, where atoms are simply lined up after one another (guaranteeing that nothing ever collides); an ideal width, based on proportional spacing from rhythmic density; and a gutter width – extra space required only if the measure begins a system. Courtesy accidentals caused by system breaks are accounted for here as space requirements, not as symbols. Ordinary courtesy accidentals are already part of the atom.

​Stage 2: Rhythmical Alignment

All measures in a stack contribute a rhythmic raster: the sequence of atom positions implied by their rhythmic content at ideal spacing. Stage 2 takes these per-staff rasters and aligns them into a single, stack-wide rhythmic grid, so that 'the beat structure' is shared across staves rather than each staff carrying its own local spacing. Because the system has both the rasters and the atom extents from Stage 1, it can adjust the aligned positions so that collisions are avoided while still preserving the intended proportional structure.

​Stage 3: System Formation

With rhythmical alignment complete, the score collapses to a one-dimensional sequence of measure stacks, each described only by stack minimum width, stack ideal width, and possible stack system-start gutter. System breaks are chosen using dynamic programming, and a scale factor is computed for each system so that ideal proportions are preserved as well as possible within the available width. At the same time, system preambles (clefs, key signatures) are fully determined. Apart from these, the stage produces only break decisions and scale factors; no measure content is positioned yet.

​Stage 4: Atom Positioning

The abstract decisions from system formation are applied. Each atom is positioned horizontally by scaling its ideal spacing according to the scale factor of its system. Because atoms were defined with purely relative internal geometry, they can be moved without recomputation. This stage is a pure projection from musical proportions to absolute coordinates.

​Stage 5: Spanners

All connecting elements are resolved against the fixed atom positions: ties, slurs, hairpins, ottavas, lyric extenders. They adapt to the horizontal geometry they are given and never influence spacing upstream. System-start decorations live here as well: courtesy accidentals now appear in the gutter space that was explicitly reserved earlier.

​Actual system heights emerge at this stage as a consequence of what must be drawn – slurs, ties, lyrics, pedalling indications, hairpins – each claiming vertical space as required to avoid collisions. In this stage, braces, brackets, and instrument name indications are also computed for the left margin, as all information required to determine system grouping and extent is now available.

​Stage 6: Page Formation

Systems are distributed across pages using dynamic programming, this time over the actual system heights produced by the previous stage. As in Stage 3, the distribution is optimal with respect to the available space. Once page breaks are chosen, layout is locked and no earlier stage is revisited. At this point, all rendering decisions have been made. The score can now be drawn directly from the cached paintlists.