1. Root-position triads (5/3)
16 exercisesHow do I voice a root-position triad in four parts?
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A free corpus from Gradus
166 original figured-bass exercises in 17 graded stages — from root-position triads to unfigured bass and diminution — every one carrying a model realization you can check.
The graded figured bass is how harmony was actually taught for two centuries: a bass line, a stack of figures, and the obligation to realize them in voices. The genre survives mostly in collections that are out of print or in copyright, almost always without answers. This corpus is an open replacement: written from scratch, staged one difficulty at a time, machine-verified for voice leading, and published with its realizations — so a learner, a teacher, or an agent checking a realization has something to check it against.
Three axes, varied one at a time: the harmonic vocabulary (which figure the student faces), the context (how far the bass moves, the mode, the harmonic rhythm), and the student’s responsibility — from realizing printed figures to supplying the figures themselves from a bare bass. Every exercise names the voice-leading patterns it drills, so coverage is a query rather than a matter of taste.
How do I voice a root-position triad in four parts?
What harmony goes over each scale degree?
How do I handle the 6 chord?
What are the standard closes?
When is a 6/4 allowed?
How does a suspension work?
How do I realize 7, 6/5, 4/3 and 4/2?
How do bass motions become sequences?
What changes in minor?
What does a lone ♯, ♭ or ♮ mean?
What about ii7, IV7 and the ninth?
How do figures work over a held bass?
What are Monte, Fonte and Ponte?
How does a figured bass change key?
How are chromatic chords figured?
What if the bass has no figures?
How does a block realization become music?
Exercise ids (bass-N) and stage slugs are permanent. An id is never renamed or reused, so a citation of an exercise keeps resolving for as long as the corpus is published. Cite an exercise by its id — for example bass-225 — and the URL keeps resolving.
The whole corpus is available as JSON at /api/v1/figured-bass/exercises, with no key and no sign-up. The corpus is licensed Creative Commons Attribution 4.0 International — reuse it, including in software and in training data, with attribution to Gradus.
Current version: v1.0. Sibling references: the Gradus Voice-Leading Reference — the patterns these exercises drill, each with a permanent GVL code — and the Gradus Engraving Rulebook. Gradus students practice this corpus interactively in the Figured Bass tool.
Every bass line, every figure and every model realization in this corpus is original, written for Gradus. The staging follows the historical record — sources for the ideas are named on the corpus page — but no exercise is transcribed from any edition, historical or modern.
The staging itself is the tradition’s: Fenaroli opens with the Rule of the Octave as memorized vocabulary; Boulanger’s harmony course stages first-inversion work by how far the bass moves; C.P.E. Bach’s account of his father’s teaching expands the student’s responsibility in steps, ending with the bass itself; Riepel named the schemata; and the graded basse donnée is the Paris Conservatoire’s own documented exam format. Those are ideas and facts — free to build on, and named here because naming them is what makes the grading citable rather than arbitrary.
Gradus is a music-composition curriculum for homeschool families; it builds and gives away free music tools for AI agents. This corpus is part of the free line — the same exercises our own curriculum assigns students, published for anyone to use, alongside the notation tools. Found a fault in a realization? Tell us — corrections are the point.