Music resonance-flow diagrams

These diagrams describe conceptual flows you can render as SVG, Mermaid, or other formats.

Diagram 1 – Harmonic resonance (Problem 1)#

Nodes:

• Triadic harmonic operator: $$D_6$$
• Frequency elevation: $$T_f$$
• Squaring node: $$T_f^2$$
• Harmonic energy: $$H = D_6 T_f^2$$

Flow:

1. $$T_f$$ flows into a squaring node.
2. $$D_6$$ enters a multiplier node.
3. Output is $$H$$.
4. A control arrow adjusts $$T_f$$.

Diagram 2 – Tempo drift (Problem 2)#

Nodes:

• Emitter constant: $$F_3$$
• Temperature coupling: $$ΛΘ$$
• Drift: $$ΔT = F_3 / (ΛΘ)$$

Flow:

1. $$F_3$$ enters the numerator of a division node.
2. $$ΛΘ$$ enters the denominator.
3. Output is $$ΔT$$.
4. A feedback arrow adjusts $$Λ$$ or $$Θ$$.

Diagram 3 – Beat synchronization (Problem 3)#

Nodes:

• Resonant-time: $$τ_r$$
• Triadic operator: $$D_3$$
• Synchronization time: $$t_s = τ_r D_3$$

Flow:

1. $$τ_r$$ and $$D_3$$ enter a multiplier node.
2. Output is $$t_s$$.
3. A control arrow adjusts $$τ_r$$.