The Sample Rate Pitch Transposer & Tape Speed Sizer provides an interactive three-parameter algebraic interface for exploring relative pitch alteration, sample playback frequencies, and tape motor transport ratios.

### Algebraic Ratio Formulation The component evaluates input values using three generalized algebraic equations: - Primary Metric: $(val_1 \times val_2) / \max(0.01, val_3)$. In audio resampling and tape speed modeling, this represents scaled frequency throughput relative to anti-aliasing filter dampening. - Geometric Mean (Secondary Index): $\sqrt{\max(0, val_1 \times val_2)}$, modeling harmonic resonance or geometric center frequencies. - Efficiency Ratio (%): $\min(100, \max(0, (val_1 / (val_1 + val_2)) \times 100))$, modeling proportional transport speed variation.

### Note on Acoustic Resampling & Analog Tape Physics This tool executes a three-variable algebraic proxy for comparative evaluation. In physical studio acoustics, exact digital pitch shifting follows logarithmic semitone ratios ($f_{\text{new}} = f_{\text{orig}} \times 2^{\Delta s / 12}$), and analog varispeed tape machines follow linear motor speed velocity ratios ($v_2 / v_1 = f_2 / f_1$). Detailed DSP sample rate conversion additionally requires polyphase sinc interpolation filtering.

### Worked Numeric Example Using default component parameter values: - Primary Dimension / Load ($val_1$): 100 - Operating Coefficient ($val_2$): 20 - Safety Factor / Loss Ratio ($val_3$): 5 - Evaluated Outputs: - Primary Metric: $(100 \times 20) / 5 = 400.00$ - Geometric Mean: $\sqrt{100 \times 20} = \sqrt{2000} \approx 44.72$ - Efficiency Ratio: $(100 / (100 + 20)) \times 100 = 83.33\%$

### Client-Side Execution Note All algebraic ratios evaluate locally within your browser JavaScript runtime with zero external server transit.