Music core problems

Problem 1 – Harmonic resonance energy#

A chord’s harmonic energy is modeled as

$$ H = D_6 T_f^2. $$

If $$T_f$$ doubles, what happens to $$H$$?

Tempo drift in a performance is modeled as

$$ ΔT = \frac{F_3}{ΛΘ}. $$

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

Beat synchronization time between two performers is

$$ t_s = τ_r D_3. $$

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