픽업 위치의 공간 샘플링 가설을 반복 가능한 스펙트럼 측정과 불확도 분석으로 검증하는 방법
A02에서 정리한 pickup-position spatial sampling을 실제 측정 프로토콜로 전환한다. C01은 sin(nπd/L)를 완성된 pickup output으로 취급하지 않고, excitation·finite sensing aperture·magnetic transduction·string non-ideality·electrical load를 분리해 위치 signature가 실제 modal spectrum에서 반복되는지 검증한다.
1. 연구 질문과 측정 경계
이상적인 fixed-end string에서 point sensor의 공간 위치계수는 Hpos(n)=sin(nπd/L)이다. 이는 geometric spatial factor이며 실제 pickup output 전체가 아니다. 실제 출력에는 pluck point, sensing aperture, magnetic field, electrical transfer와 time-dependent decay가 함께 개입한다.
기하 좌표 모델
Bridgesensing centernut / fret
d = bridge → sensing center→r = d/L
Figure 1. Bridge 기준 d, speaking length L, normalized coordinate r=d/L. Multiscale/slanted pickup은 현마다 dᵢ와 Lᵢ를 기록한다.
2. 이상적 spatial weighting과 node
Ideal node condition은 r=m/n이다. 다만 real pickup의 finite magnetic aperture와 비대칭 field 때문에 실제 출력이 완전한 0이 된다고 단정하지 않는다. 아래 도표는 |sin(nπr)|의 계산값이며 RavenForge 실측값이 아니다.
공간 가중 구조
Geometry r=d/L→Mode sin(nπr)→Weight |sin(nπr)|
이상적 공간 가중치 계산 · 실측 데이터 아님
3. Pluck point와 pickup point는 분리한다
Ideal triangular-displacement pluck에서는 excitation coefficient가 pluck coordinate q에 의존한다. linearized velocity-sensitive pickup 근사에서는 Vₙ ∝ sin(nπq/L)·sin(nπd/L)/n 형태가 baseline이 된다. 따라서 pickup 위치만 시험하려면 pluck coordinate와 release condition을 고정해야 한다.
일반적인 sensitivity kernel g(u)에 대해 H_g(n)=∫g(u)sin[nπ(d+u)/L]du로 쓸 수 있다. 대칭 rectangular kernel에서는 고차 mode에 sinc형 attenuation이 생기지만 중앙 ideal node가 자동으로 이동하지는 않는다. Physical housing/pole width를 effective sensing width와 동일시하지 않는다.
유한 감지 폭 모델
Point sensor g(u)=δ(u)→Finite kernel g(u)→Spatial average
유한 감지 폭 응답 · 예시 비율
5. Fretting과 multiscale
F fret에서 L_F=L₀·2^(−F/12), r_F=d/L_F로 normalized coordinate가 이동한다. Multiscale에서는 각 현마다 rᵢ=dᵢ/Lᵢ를 계산한다. Pickup slant는 dᵢ를 바꿀 뿐 scale 차이를 자동 보정하지 않는다.
프렛·멀티스케일 좌표 변환
Fret F L_F ↓→r_F=d/L_F ↑+Per string rᵢ=dᵢ/Lᵢ
6. Spectral analysis audit
Exact n·f₀ FFT bin을 그대로 읽는 대신 실제 modal peak를 추적한다. Leakage, finite record, inharmonicity 때문에 peak가 bin center와 다를 수 있다. Zero-padding은 interpolation density를 높일 뿐 physical frequency resolution을 늘리지 않는다.
스펙트럼 분석 절차
Raw WAV→Onset + window→Local peak search→Amplitude / phase
FFT bin과 modal peak 비교 · 예시 스펙트럼
7. C01 bench protocol
C01-A는 가능하면 동일 pickup을 이동시켜 position effect만 분리한다. C01-B는 동일 pickup에서 fret을 바꾸며 r_F migration을 확인한다. A04의 electrical load는 C01에서 연구변수가 아니라 고정 boundary condition으로 기록한다.
반복 횟수나 ±dB 합격선을 임의로 고정하지 않는다. pilot variance를 먼저 구하고 geometry, pluck coordinate, pickup gap, tuning/speaking length, electrical load/gain, onset/window placement, spectral estimator를 uncertainty budget에 포함한다.
9. Myth audit
Claim
Verdict
Bridge pickup은 항상 더 많은 고조파를 낸다
Needs correction
sin(nπd/L)가 실제 pickup output 전체다
Ideal-model only
Ideal node에서는 실제 출력도 반드시 0이다
Not guaranteed
Housing width = sensing width
Unsupported
Finite width는 node 위치를 항상 이동시킨다
Incorrect for symmetric baseline
Fretting해도 weighting은 같다
Incorrect
Multiscale slant가 자동 보정한다
Unsupported
Exact n·f₀ bin만 읽으면 된다
Incorrect
Zero-padding이 true resolution을 높인다
Incorrect
96 kHz가 항상 더 정확하다
Unsupported as universal claim
Hₙ/H₁이면 항상 충분하다
Conditional
한 번의 pluck이면 검증 가능하다
Insufficient
Mohamad의 3.53 mm는 제작 허용오차다
Incorrect use of evidence
10. 현재 RavenForge design position
Pickup placement를 “neck/bridge라서 이 소리”가 아니라 per-string/per-fret normalized coordinate와 measured modal response의 관계로 기록한다. C01은 pass/fail보다 model validation / parameter estimation에 가깝고, consistent residual은 finite aperture·magnetic field·boundary condition의 후속 연구 대상으로 넘긴다.
핵심 근거: Paiva, Pakarinen & Välimäki, JAES 60(10), 768–782 (2012); Mohamad, Dixon & Harte, JASA 142(6), 3530–3540 (2017), DOI 10.1121/1.5016815; Horton & Moore, AJP 77(2), 144–150 (2009); Lemarquand & Lemarquand, IEEE Trans. Magn. 43(9), 3573–3578 (2007); Harris, Proc. IEEE 66(1), 51–83 (1978). Mohamad의 3.53 mm는 estimation error이며 제작 공차가 아니다.
참고문헌
[1] Paiva, R. C. D.; Pakarinen, J.; Välimäki, V. “Acoustics and Modeling of Pickups.” Journal of the Audio Engineering Society 60(10), 768–782 (2012). Peer-reviewed.
[2] Mohamad, Z.; Dixon, S.; Harte, C. “Pickup position and plucking point estimation on an electric guitar via autocorrelation.” Journal of the Acoustical Society of America 142(6), 3530–3540 (2017). DOI: 10.1121/1.5016815. Peer-reviewed.
[3] Mohamad, Z.; Dixon, S.; Harte, C. “Estimating Pickup and Plucking Positions of Guitar Tones and Chords with Audio Effects.” Proc. DAFx-17, Edinburgh (2017). Conference paper; used as supporting evidence for persistence of spatial signatures through processed chains.
[4] Horton, N. G.; Moore, T. R. “Modeling the magnetic pickup of an electric guitar.” American Journal of Physics 77(2), 144–150 (2009). DOI: 10.1119/1.2990663.
[5] Lemarquand, G.; Lemarquand, V. “Calculation Method of Permanent-Magnet Pickups for Electric Guitars.” IEEE Transactions on Magnetics 43(9), 3573–3578 (2007). DOI: 10.1109/TMAG.2007.891671.
[6] Harris, F. J. “On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform.” Proceedings of the IEEE 66(1), 51–83 (1978). DOI: 10.1109/PROC.1978.10837.
[7] Murray, C. J.; Whitfield, S. B. “Inharmonicity in plucked guitar strings.” American Journal of Physics 90, 487–493 (2022). DOI: 10.1119/5.0064373.
[8] “Performance of Acoustic, Electro-Acoustic and Optical Sensors in Precise Waveform Analysis of a Plucked and Struck Guitar String.” Sensors 25(21), 6514 (2025). DOI: 10.3390/s25216514. Peer-reviewed; used for controlled excitation/sensor methodology.
[9] Gràcia, X.; Sanz-Perela, T. “The wave equation for stiff strings and piano tuning.” Reports@SCM 3(1), 1–16 (2017). Mathematical stiff-string reference.
[R1] RavenForge / Signal & Transduction Research Log A02. “Pickup Position and Harmonic Sampling.” Verified revision, 2026.
[R2] RavenForge / Signal & Transduction Research Log A04. “Electrical Loading of Passive Pickups.” Verified revision, 2026.
[R3] RavenForge / Signal & Transduction Research Log A03. “Magnetic Pickups as RLC Systems.” Figure-corrected revision, 2026.
출처 상태 및 해석 범위
[1,2,4–8]은 peer-reviewed journal literature, [3]은 conference proceedings, [9]는 mathematical technical reference다. Figure 2·4·5·6은 문헌에 근거한 RavenForge analytical/illustrative diagrams이며 실측값이 아니다. C01 acceptance threshold와 ASKR/EMBLA/EDDA의 실제 effect size는 prototype measurement 전까지 미확정 상태로 둔다.
References
[1] Paiva, R. C. D.; Pakarinen, J.; Välimäki, V. “Acoustics and Modeling of Pickups.” Journal of the Audio Engineering Society 60(10), 768–782 (2012). Peer-reviewed.
[2] Mohamad, Z.; Dixon, S.; Harte, C. “Pickup position and plucking point estimation on an electric guitar via autocorrelation.” Journal of the Acoustical Society of America 142(6), 3530–3540 (2017). DOI: 10.1121/1.5016815. Peer-reviewed.
[3] Mohamad, Z.; Dixon, S.; Harte, C. “Estimating Pickup and Plucking Positions of Guitar Tones and Chords with Audio Effects.” Proc. DAFx-17, Edinburgh (2017). Conference paper; supporting evidence for persistence of spatial signatures through processed chains.
[4] Horton, N. G.; Moore, T. R. “Modeling the magnetic pickup of an electric guitar.” American Journal of Physics 77(2), 144–150 (2009). DOI: 10.1119/1.2990663.
[5] Lemarquand, G.; Lemarquand, V. “Calculation Method of Permanent-Magnet Pickups for Electric Guitars.” IEEE Transactions on Magnetics 43(9), 3573–3578 (2007). DOI: 10.1109/TMAG.2007.891671.
[6] Harris, F. J. “On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform.” Proceedings of the IEEE 66(1), 51–83 (1978). DOI: 10.1109/PROC.1978.10837.
[7] Murray, C. J.; Whitfield, S. B. “Inharmonicity in plucked guitar strings.” American Journal of Physics 90, 487–493 (2022). DOI: 10.1119/5.0064373.
[8] “Performance of Acoustic, Electro-Acoustic and Optical Sensors in Precise Waveform Analysis of a Plucked and Struck Guitar String.” Sensors 25(21), 6514 (2025). DOI: 10.3390/s25216514. Peer-reviewed; controlled excitation/sensor methodology.
[9] Gràcia, X.; Sanz-Perela, T. “The wave equation for stiff strings and piano tuning.” Reports@SCM 3(1), 1–16 (2017). Mathematical stiff-string reference.
[R1] RavenForge / Signal & Transduction Research Log A02. “Pickup Position and Harmonic Sampling.” Verified revision, 2026.
[R2] RavenForge / Signal & Transduction Research Log A04. “Electrical Loading of Passive Pickups.” Verified revision, 2026.
[R3] RavenForge / Signal & Transduction Research Log A03. “Magnetic Pickups as RLC Systems.” Figure-corrected revision, 2026.
Source status / interpretation boundary
[1,2,4–8] are peer-reviewed journal literature; [3] is conference proceedings; [9] is a mathematical technical reference. Figures 2, 4, 5 and 6 are RavenForge analytical/illustrative diagrams grounded in the cited literature, not measured data. Acceptance thresholds and actual ASKR/EMBLA/EDDA effect sizes remain unresolved until prototype measurements exist.
Literatur
[1] Paiva, R. C. D.; Pakarinen, J.; Välimäki, V. “Acoustics and Modeling of Pickups.” Journal of the Audio Engineering Society 60(10), 768–782 (2012). Peer-reviewed.
[2] Mohamad, Z.; Dixon, S.; Harte, C. “Pickup position and plucking point estimation on an electric guitar via autocorrelation.” Journal of the Acoustical Society of America 142(6), 3530–3540 (2017). DOI: 10.1121/1.5016815. Peer-reviewed.
[3] Mohamad, Z.; Dixon, S.; Harte, C. “Estimating Pickup and Plucking Positions of Guitar Tones and Chords with Audio Effects.” Proc. DAFx-17, Edinburgh (2017). Konferenzbeitrag; ergänzende Evidenz für die Persistenz räumlicher Signaturen in bearbeiteten Signalketten.
[4] Horton, N. G.; Moore, T. R. “Modeling the magnetic pickup of an electric guitar.” American Journal of Physics 77(2), 144–150 (2009). DOI: 10.1119/1.2990663.
[5] Lemarquand, G.; Lemarquand, V. “Calculation Method of Permanent-Magnet Pickups for Electric Guitars.” IEEE Transactions on Magnetics 43(9), 3573–3578 (2007). DOI: 10.1109/TMAG.2007.891671.
[6] Harris, F. J. “On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform.” Proceedings of the IEEE 66(1), 51–83 (1978). DOI: 10.1109/PROC.1978.10837.
[7] Murray, C. J.; Whitfield, S. B. “Inharmonicity in plucked guitar strings.” American Journal of Physics 90, 487–493 (2022). DOI: 10.1119/5.0064373.
[8] “Performance of Acoustic, Electro-Acoustic and Optical Sensors in Precise Waveform Analysis of a Plucked and Struck Guitar String.” Sensors 25(21), 6514 (2025). DOI: 10.3390/s25216514. Peer-reviewed; kontrollierte Anregungs-/Sensormethodik.
[9] Gràcia, X.; Sanz-Perela, T. “The wave equation for stiff strings and piano tuning.” Reports@SCM 3(1), 1–16 (2017). Mathematische Referenz zur steifen Saite.
[R1] RavenForge / Signal & Transduction Research Log A02. “Pickup Position and Harmonic Sampling.” Verified revision, 2026.
[R2] RavenForge / Signal & Transduction Research Log A04. “Electrical Loading of Passive Pickups.” Verified revision, 2026.
[R3] RavenForge / Signal & Transduction Research Log A03. “Magnetic Pickups as RLC Systems.” Figure-corrected revision, 2026.
Quellenstatus / Interpretationsgrenze
[1,2,4–8] sind peer-reviewte Journalquellen, [3] Konferenz-Proceedings und [9] eine mathematisch-technische Referenz. Abbildungen 2, 4, 5 und 6 sind RavenForge-Analysen/Illustrationen auf Basis der Literatur und keine Messdaten. Akzeptanzgrenzen sowie reale Effektgrößen von ASKR/EMBLA/EDDA bleiben bis zu Prototypmessungen offen.