PrimeComposer: Algorithmic Composition Systems

• PrimeComposer is an umbrella framework that integrates training-free image composition with attention steering and region-constrained editing for seamless object blending.
• Its symbolic music generation system leverages large-scale pre-training and targeted adapter fine-tuning to achieve high-fidelity composer-style outputs even with limited data.
• The microtonal notation component employs a rational comma assignment algorithm for precise Just Intonation adjustments, supporting interactive retuning and real-time notation conversion.

PrimeComposer is an umbrella term denoting advanced algorithmic systems for compositional tasks in both visual and symbolic music domains, as well as compact representation frameworks for microtonal music. Notably, it refers to: (1) a state-of-the-art training-free image composition framework focused on attention steering and region-constrained editing (Wang et al., 8 Mar 2024); (2) a large-scale composer-style symbolic music generator leveraging general corpus pre-training and targeted adapter-based fine-tuning (Yao et al., 20 Jun 2025); and (3) an algorithmic system for Just Intonation prime comma assignment facilitating universal Rational Comma Notation in microtonal composition (Ryan, 2016). These systems share principles of modularity, local control, precision in conditioning, and algorithmic notation, and are often implemented as interactive, extensible digital environments.

1. Image Composition: Training-Free Diffusion with Attention Steering

In the visual domain, PrimeComposer (Wang et al., 8 Mar 2024) addresses the challenge of seamlessly embedding arbitrary objects within specified backgrounds under minimal training constraints. Distinct from prior multi-sampler approaches that combine disparate attention maps—frequently leading to coherence confusion, inadequate appearance blending, and transition artifacts—PrimeComposer formulates image composition as a local subject-based editing process, emphasizing foreground generation and contextual consistency.

The composition pipeline consists of:

1. VAE encoding background $(I^{bg})$ and object images $(I^{obj})$ to latent representations $(z_{0}^{bg*}, z_{0}^{obj*})$ within a pre-trained Latent Diffusion Model (LDM).
2. Inverting latents to high noise $(z_{T}^{bg*}, z_{T}^{obj*})$ using DPM-Solver++.
3. Initializing $z_{T}^{init}$ via foreground mask $M^{fg}$, object mask $M^{obj}$, and additive noise:

$$z_{T}^{init} = z_{T}^{obj*} \odot M^{fg} + z_{T}^{bg*} \odot (1 - M^{fg}) + \epsilon \odot (M^{obj} \oplus M^{fg})$$

where $\epsilon \sim \mathcal{N}(0, I)$ and $\oplus$ denotes logical XOR.

1. Progressive denoising for $t = T \ldots 1$:
   • For $t \leq \alpha T$ (where $\alpha \in (0, 1)$ controls attention steering window):
     • Compute pixel-level composite latent, segment the object, extract self-attention maps $(A_{l,t}^{cross}, A_{l,t}^{obj})$ via Correlation Diffuser (CD), infuse attention maps into LDM, combine decoded foreground and background.
   • For $t > \alpha T$: perform standard LDM denoising and recombination.
2. Decode final $z_{0}$ to yield the composite image $I^*$.

The CD module performs multi-level self-attention extraction:

• For each layer $\ell$ and step $t$, query ($q_{\ell,t}$) and key ($k_{\ell,t}$) vectors are derived from the composite and segmented object features, forming:

$$A_{\ell, t} = \text{Softmax}\left(\frac{q_{\ell, t}\,k_{\ell, t}^T}{\sqrt{d}}\right) \in \mathbb{R}^{(h \cdot w) \times n}$$

where $d$ is attention head dimension, $n$ is object token count.

• $A_{\ell, t}$ is split into cross-object/background ($A_{\ell, t}^{cross}$) and intra-object ($A_{\ell, t}^{obj}$) correlations, guiding LDM denoising with tailored spatial focus.

Region-Constrained Cross-Attention (RCA) rectifies generic LDM cross-attention by masking object-token attention to user-specified regions, minimizing semantic leakage and boundary artifacts:

• For each token $k$, RCA applies:

$$\hat{A}_{ij}^k = \begin{cases} A_{ij}^k, & M^{obj}_{i, j} = 1\ -\infty, & M^{obj}_{i, j} = 0 \end{cases}$$

leading to region-restricted token influence.

Experimental evaluation on 332 diverse cases—photorealism, sketch, oil painting, cartoon—demonstrates PrimeComposer's superiority, e.g., in photorealism: LPIPS$_{(BG)}$ = 0.08, LPIPS$_{(FG)}$ = 0.48, CLIP$_{(Image)}$ = 84.71, CLIP$_{(Text)}$ = 30.26, with inference speed nearly twice that of TF-ICON. User studies confirm perceptual improvements in fidelity and blending. This suggests direct applicability to fast interactive editing platforms where precise object insertion is paramount.

2. Symbolic Music Generation: Modular Pre-training and Adapter-based Style Conditioning

PrimeComposer in symbolic music (Yao et al., 20 Jun 2025) denotes a two-stage system for high-fidelity composer-style generation via domain generalization and targeted mastery. The architectural foundation combines extended REMI encoding (with scalar, structural, and content tokens including explicit composer/style indicators) and a 12-layer, 512-dimensional Transformer decoder.

Stage 1 involves large-scale corpus pre-training (pop, folk, classical, $\sim$64.8M tokens), optimizing next-token cross-entropy with Adam, context length 2400, gradient clipping, and cosine decay learning rate. Stage 2 freezes base parameters, fine-tuning lightweight adapters (bottleneck $r=64$) and composer embeddings on $\sim$1,000 human-verified works by Bach, Mozart, Beethoven, Chopin.

Adapter mechanics:

$$a = \mathrm{GELU}\Big(\big[h; e_s\big] W_{\mathrm{down}} + b_{\mathrm{down}}\Big) W_{\mathrm{up}} + b_{\mathrm{up}}, \qquad h' = h + a$$

where $e_s$ is the style embedding.

Generation employs composer/tempo token conditioning, top-$p$ sampling ($p=0.99$, $\tau=1.1$). Evaluation protocols include perplexity, pitch-class entropy $\mathcal{H}$, groove-pattern similarity $\mathrm{GS}$, and fitness scape plot structureness $\mathcal{SI}_l^u$. Results (e.g., $\mathcal{H}$ = 3.17, $\mathrm{GS}$ = 0.96 for “Mastery”) denote both enhanced general musicality and precise style rendering compared to ablation and contemporary baselines (NotaGen, Emo-Disentangler). Subjective listening tests (54 participants, 2AFC protocol, musicality MOS 3.82 ± 0.21) substantiate objective style mastery. A plausible implication is robustness in low-data composer style transfer, especially for interactive authoring or scoring environments.

Ablation studies show pre-training is essential for broad musical diversity, while fine-tuning adapters drives stylistic precision. Direct fine-tuning without pre-training yields overfit, repetitive outputs.

3. Rational Comma Notation: Prime Comma Assignment for Free Just Intonation

PrimeComposer also refers to algorithmic assignment of prime commas for microtonal frequency encoding in Just Intonation (JI) (Ryan, 2016). Here, the DR algorithm assigns to each prime $p \geq 5$ a unique comma $\delta_p = 2^{a_p} 3^{b_p} p^{-1}$, constructed to be both microtonally minimal (under 1 semitone) and notationally compact (low numerator/denominator).

The assignment minimizes “Comma Measure”:

$CM_p = AO_p \cdot LCY_p,$

where $AO_p = |\log_2 (2^{a_p} 3^{b_p} / p)|$ (octaves from unison), $LCY_p$ the binary complexity.

For each $p$, possible $b_p$ are sampled near $b_{\text{mid}} = -\tfrac{1}{2} \log_3 p$, and $a_p = \text{round}(-\log_2 p - b \log_2 3)$. Constraints ensure $|1200 \cdot \log_2 \delta_p| < 100$ cents.

Example assignments:

• $$p=5: (a_5, b_5) = (-4, -1), \delta_5 = 80/81, -21.51$$ cents
• $p=7: (-6, -1), 63/64, -27.26$ cents
• $p=11: (-5, -3), 33/32, +53.27$ cents
• $p=13: (-3, -2), 26/27, -65.34$ cents

Comparison of DR, SAG, KG2 algorithms for primes $2$–$29$ shows broad agreement for $p=5,7,11$, divergence for larger primes.

Notation proceeds by decomposing any free-JI frequency $q = 2^{x} 3^{y} \prod_{p\geq5} p^{e_p}$ into: (1) a Pythagorean note/octave $Lz$, (2) a rational comma $[x/y] = \prod_{p\geq5} \delta_p^{e_p}$, yielding final RCN symbol $Lz \cdot [x/y]_{\text{DR}}$. Shorthand, e.g., $[5] \equiv '$, $[7] \equiv \sim7$.

4. Interactive Composition Environment and Notation Translation

PrimeComposer operationalizes these frameworks in digital composition environments supporting algorithmic notation, parameterized compositional control, and interoperability between traditions.

Key subsystems:

• Global prime comma assignment (DR, SAG, KG2), lookup tables for $p \leq 10^6$.
• Entry via Scientific Pitch Notation and ASCII-bracketed comma syntax, supporting shortcuts for common intervals.
• Real-time conversion of RCN to Hz (A4=440 Hz), with microtonal synthesizer or live sample retuning.
• Pitch-class lattice visualization (2D/3D) for compositional navigation; interactive retuning by lattice node manipulation.
• One-click chord, tetrachord presets, normalize function for stable retuning across segments.
• Export capability to RCN or Sagittal/Kite plaintext, with automated translation via frequency equivalence.

This suggests substantial potential for algorithmic composition pedagogy, rapid notation translation, and microtonal performance.

5. Performance, Evaluation, and Empirical Findings

Across domains, PrimeComposer implementations are distinguished by quantifiable gains in both efficiency and quality.

Visual composition (Wang et al., 8 Mar 2024):

• LPIPS$_{(BG)}$ improved by 20%, CLIP$_{(Image)}$ by 1.85 over prior methods.
• Inference time per image halved compared to TF-ICON.
• Qualitative assessments confirm preservation of texture, seamless transitions, high semantic correspondence.
• User studies consistently rank foreground fidelity and background coherence highest.

Symbolic music (Yao et al., 20 Jun 2025):

• Strongest pitch-class entropy and groove similarity among evaluated models.
• Composer classifier accuracy highest on Mozart and Beethoven, confirmed by participant style discrimination.
• Fréchet Audio Distance lower for mastery-tuned outputs, indicating proximity to real composer distributions.

Microtonal JI (Ryan, 2016):

• DR algorithm produces microtonal shifts $<1$ semitone with minimal fraction complexity.
• RCN is algorithmically interoperable; translation between DR, SAG, KG2 is algorithmic rather than heuristic.

6. Contextual Significance and Prospective Developments

PrimeComposer systems epitomize modularity, algorithmic precision, and high-fidelity control in contemporary composition technologies. In image editing, the formulation as localized subject-based editing directly addresses coherence and speed bottlenecks in previous diffusion-based schemes. In symbolic generation, adapter-based specialization enables robust style transfer under data scarcity. For microtonal notation, the DR prime-comma framework underpins universal algorithmic notation across JI traditions.

A plausible implication is that further advances in attention steering, domain generalization, and symbolic-adapter architectures will integrate into broader creative AI environments. In microtonal music, the compactness and universality of RCN suggest wider adoption in notation software and real-time synthesis. These frameworks align with ongoing efforts in AI and algorithmic musicology to provide both analytic transparency and compositional agency.