🎵 Music — TFT_3Pack Example Suite

Problem 1 — Harmonic Resonance Energy

H = D₆ T_f²

If \( T_f \) doubles, what happens to H?

Problem 2 — Tempo Drift

ΔT = F₃ / (ΛΘ)

If Λ increases by 25%, how does ΔT change?

Problem 3 — Beat Synchronization Time

t_s = τ_r D₃

If τ_r decreases by 15%, how does t_s change?

Solution 1 — Harmonic Energy

Doubling T_f → H becomes 4H.

Solution 2 — Tempo Drift

Drift decreases by 20%.

Solution 3 — Synchronization Time

t_s decreases by 15%.

Problem 4 — Resonant Chord Progression

R = X (D₃ + D₆ τ_r + √(D₉ τ_r))

Describe how increasing τ_r affects each term.

Problem 5 — Triadic Mixing in Synthesis

S(t) = D₃ sin(T_f t)
     + D₆ sin(2T_f t)
     + D₉ sin(3T_f t)
        

Describe how increasing T_f shifts the spectrum.

Problem 6 — Tempo Modulation

T(t) = T₀ + X e^{-D₃ t / τ_r}

Describe how increasing τ_r affects modulation decay.

Problem 7 — Overtone Decay

Aₙ = F₃ / (n² + ΛΘ τ_r)

Describe how increasing τ_r affects overtone amplitude.

Problem 8 — Ensemble Synchronization

S_sync = (T_f + D₆) / (1 + e^{-τ_r})

Describe how increasing τ_r affects synchronization.

Diagram 1 — Harmonic Energy

T_f → T_f² × D₆ → H
        

Diagram 2 — Tempo Drift

F₃ ÷ (ΛΘ) → ΔT
        

Diagram 3 — Beat Synchronization

τ_r × D₃ → t_s