Symbolic Music Generation with Non-Differentiable Rule Guided Diffusion

1California Institute of Technology, 2Rensselaer Polytechnic Institute, 3NVIDIA, 4Dalhousie University, 5Vector Institute

Examples of Our System as a Compositional Tool

To demonstrate how our system can be used effectively as a compositional tool, we provide three example videos. A musician specifies musical characteristics characteristics in terms of the rules (e.g. fairly sparse excerpt, following a simple I-V chord progression in C major, etc), and the system generates 3-5 samples per request. The musician selects a favorite sample, loops it as accompaniment on a Disklavier piano, and improvises over it. The following three videos feature the musician's performance with the system-generated music.

Demo 1: I-V, Sparse (C Major)

In Demo 1, the model generated material that suggested a melody. Since the musician wanted to play the second track in the upper register, they first allowed the excerpt to play in full, as generated, and then removed the upper notes from the accompaniment to give room for themselves to play overtop. They chose to use the model’s generated melody as a motif, and further improvise based on it.

Demo 2: Triplet Ostinato (C minor)

In Demo 2, the model generates an excerpt with a steady accompanying triplet ostinato behind a slower-moving descending melody in C minor (that suggests a progression that moves between the I and the V).

Demo 3: Alternating Textures, Bb7 / Eb / Eb-

In Demo 3, the model generates a sample with a changing note density and texture, and a slightly ambiguous harmonic quality that allowed flexibility in the improvising over it.

Composite Rule Guidance

Rules

Pitch Histogram
Time Window 1 2 3 4 5 6 7 8
Vertical Note Density 1.89 1.89 2.70 2.13 1.74 1.84 1.77 1.90
Horizontal Note Density 8.00 7.00 5.00 10.00 14.00 14.00 15.00 14.00
Chord Progression I IV vi V I I I I

Rules

Pitch Histogram
Time Window 1 2 3 4 5 6 7 8
Vertical Note Density 1.65 1.36 2.09 1.67 2.31 2.01 2.56 2.96
Horizontal Note Density 16.00 11.00 13.00 11.00 13.00 189.00 17.00 13.00
Chord Progression IV vi I I I I V IV

Rules

Pitch Histogram
Time Window 1 2 3 4 5 6 7 8
Vertical Note Density 3.32 3.09 3.22 2.81 2.52 2.74 3.34 2.99
Horizontal Note Density 8.00 7.00 7.00 6.00 6.00 8.00 7.00 5.00
Chord Progression V I IV I iii vi IV vi

Rules

Pitch Histogram
Time Window 1 2 3 4 5 6 7 8
Vertical Note Density 1.89 1.89 2.70 2.13 1.74 1.84 1.77 1.90
Horizontal Note Density 8.00 7.00 5.00 10.00 14.00 14.00 15.00 14.00
Chord Progression I I V I ii ii ii ii

Unconditional Generation

Single Rule Guidance

Pitch Histogram

Pitch Histogram

Note Density

Time Window 1 2 3 4 5 6 7 8
Vertical Note Density 3.66 3.36 3.91 2.75 3.16 3.91 3.63 3.81
Horizontal Note Density 3.00 2.00 1.00 2.00 3.00 1.00 3.00 2.00

Chord Progression

Time Window 1 2 3 4 5 6 7 8
Chord Progression ii V V I ii I iii I