C01 — Pickup Position FFT Mapping

1. Research question and measurement boundary

For an ideal fixed-end string, the point-sensor spatial factor is Hpos(n)=sin(nπd/L). It is a geometric factor, not the complete pickup output. Real measurements also contain plucking position, sensing aperture, magnetic field, electrical transfer and time-dependent decay.

Figure 1. d from bridge to sensing center, speaking length L, and normalized coordinate r=d/L. Record dᵢ and Lᵢ per string for slanted or multiscale layouts.

2. Ideal spatial weighting and nodes

The ideal node condition is r=m/n. A real pickup, however, has finite magnetic aperture and a potentially asymmetric field, so an exact zero output is not guaranteed. The plot below is calculated |sin(nπr)|, not measured RavenForge data.

3. Separate plucking point from pickup point

For ideal triangular initial displacement, the excitation coefficient depends on plucking coordinate q. Under a linearized velocity-sensitive pickup approximation, Vₙ ∝ sin(nπq/L)·sin(nπd/L)/n is a useful baseline. Therefore plucking coordinate and release conditions must be controlled when testing pickup position.

4. Finite sensing aperture

For a general sensitivity kernel g(u), H_g(n)=∫g(u)sin[nπ(d+u)/L]du. A symmetric rectangular kernel produces sinc-like attenuation of higher modes but does not automatically move the central ideal node. Physical housing or pole width must not be equated with effective sensing width.

5. Fretting and multiscale

At fret F, L_F=L₀·2^(−F/12) and r_F=d/L_F, so the normalized coordinate migrates. For multiscale instruments calculate rᵢ=dᵢ/Lᵢ for every string. Pickup slant changes dᵢ; it does not automatically compensate for scale-length differences.

6. Spectral-analysis audit

Do not read only the exact n·f₀ FFT bin. Track the actual local modal peak because leakage, finite records and inharmonicity can move the peak away from the bin center. Zero-padding increases interpolation density but not the physical resolving power of the observation window.

7. C01 bench protocol

C01-A should, where possible, move the same pickup so position is the primary changed variable. C01-B keeps the pickup fixed and changes fret to test r_F migration. The A04 electrical load is recorded as a fixed boundary condition rather than a C01 research variable.

8. Uncertainty and repeatability

Do not impose an arbitrary repeat count or ±dB acceptance limit before a pilot. Estimate pilot variance first and include geometry, pluck coordinate, pickup gap, tuning/speaking length, electrical load/gain, onset/window placement and spectral estimator in the uncertainty budget.

9. Myth audit

10. Current RavenForge design position

Record pickup placement as a relationship between per-string/per-fret normalized coordinate and measured modal response, not as “neck/bridge equals a tone adjective.” C01 is primarily model validation / parameter estimation; consistent residuals become candidates for later aperture, magnetic-field or boundary-condition studies.