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EnglishWhat the 2D, 3D, Torus, Leading Tones and Chords Options Show in Z-Tonnetz
Updated
Z-Tonnetz is a browser-based, beta-stage visualization of a neo-Riemannian Tonnetz: a map of harmonic space in which chords and keys sit at fixed positions and voice leading appears as movement between them. The five options in its toolbar change how that map is drawn and what is layered on top of it. 2D and 3D choose between a flat and a spatial view of the same harmonic space; Torus wraps the space into a continuous surface so that edges join; Leading Tones highlights semitone motion between chords; and Chords overlays chord shapes on the visualization. The page also lists a Clear control and Free Mode, and the visualization runs alongside MIDI playback and a playable on-screen keyboard.
What each option changes
| Option | What it shows | When it helps |
|---|---|---|
| 2D | A flat view of the Tonnetz, with chord and key positions laid out on a plane | Reading exact positions, comparing chord shapes side by side, and following a progression step by step |
| 3D | The same harmonic space rendered spatially, so relationships can be seen in depth | Getting a sense of how distant regions of harmonic space relate, and watching motion that a flat view flattens out |
| Torus | The harmonic space wrapped into a continuous surface, so opposite edges meet | Seeing that the space repeats rather than ends, and following progressions that would otherwise run off the edge of the view |
| Leading Tones | Semitone motion between chords highlighted | Studying voice leading: which single note moves by a half step when one chord gives way to another |
| Chords | Chord shapes drawn on the visualization | Identifying which chords the current notes form, and seeing how those shapes sit relative to each other |
The page evidence shows these as toggle-style controls grouped with Clear, Free Mode, and the 2D / 3D / Torus / Leading Tones / Chords set, so they are display settings rather than separate tools. Clear resets the current selection or highlighting; Free Mode is listed alongside them but the page evidence does not describe its behavior, so treat it as an option to try rather than a documented feature.
How the views relate to each other
The 2D and 3D views are two renderings of one underlying harmonic space, not two different analyses. Switching between them should not change which chords are highlighted for a given passage; it changes only how you see their positions. Torus is best understood as a property of that space rather than a third view: in a Tonnetz, the harmonic space is periodic, so wrapping it into a torus makes the repetition visible instead of hiding it at the edges. In practice, use 2D when you want to read positions precisely, 3D when you want to see the overall shape of a progression, and Torus when a progression keeps moving toward the edge of the flat view.
Leading Tones and Chords are overlays that can be combined with any of these views. Leading Tones answers "which note moved by a semitone here?" and Chords answers "what chord is this, and where does its shape sit?" Together they let you check a progression twice: once as chord identities, once as the small motions that connect them.
A concrete way to use them
Take a short progression you already know, such as the opening of Pachelbel's Canon, which appears in the page's demo file list. Load it, then:
- Start in 2D with Chords on, and follow the chord shapes as the music plays.
- Turn on Leading Tones and replay the same passage, watching which notes move by a half step between chords.
- Switch to 3D to see the progression's path through the space rather than a sequence of separate shapes.
- Enable Torus if the progression keeps heading toward the edge of the flat view.
The expected result is the same harmony seen three ways: as chord identities, as voice-leading motions, and as a path through a repeating space. If a toggle appears to do nothing, check that playback is running or that notes are being played, since overlays depend on there being active notes to highlight.
Limits worth knowing
Z-Tonnetz is labeled beta on the page, so controls and behavior may change. The page evidence does not document what Free Mode does, whether settings persist between sessions, or how the options interact with imported MIDI files beyond the visible Import MIDI control. The demo list is described as "highly e…" in the captured excerpt, so treat the file list as a starting point rather than a complete catalog. None of the page evidence indicates pricing or login requirements for these display options.