Further reading & credits

PedalScope’s measurements are implementations of published research — none of the science here is ours. This page credits the ideas and points the curious at the sources. (The authoritative attribution record, with implementation and licensing notes, is ATTRIBUTION.md in the project repository; the citations below are the same list, written for reading.)

Credits — the ideas inside the app

The swept-sine measurement. The trick that powers the Harmonics measurement — playing one exponential sweep and unpicking each harmonic from the response — is Angelo Farina’s swept-sine technique, refined by Antonín Novák and colleagues into the synchronized swept sine, whose phase alignment makes the harmonic responses usable individually:

A. Farina, “Simultaneous Measurement of Impulse Response and Distortion With a Swept-Sine Technique,” AES 108th Convention, 2000.
A. Novák, P. Lotton, L. Simon, “Synchronized Swept-Sine: Theory, Application, and Implementation,” Journal of the Audio Engineering Society 63(10), 2015.
A. Novák, L. Simon, F. Kadlec, P. Lotton, “Nonlinear System Identification Using Exponential Swept-Sine Signal,” IEEE Transactions on Instrumentation and Measurement, 2010.

The playable models. When a Hear-it panel plays “your pedal”, it is rendering through a generalized Hammerstein model — parallel power branches fitted from the measured harmonics, per the same Novák group:

A. Novák et al., “Analysis, Synthesis, and Classification of Nonlinear Systems Using Synchronized Swept-Sine Method for Audio Effects,” EURASIP Journal on Advances in Signal Processing, 2010.

Loudness matching. Every comparison is matched with the broadcast loudness standard (the reason is the louder-sounds-better bias):

ITU-R BS.1770-4 / EBU R128 (K-weighting, gated integration).
B. De Man, “Evaluation of Implementations of the EBU R128 Loudness Measurement,” AES 137th Convention, 2014 — the arbitrary-sample-rate filter parameterization the app uses.

The plucked strings. The illustration notes are Karplus–Strong synthesis — a noise burst circulating in a tuned delay line, still the most guitar-per-CPU-cycle algorithm ever published:

K. Karplus, A. Strong, “Digital Synthesis of Plucked-String and Drum Timbres,” Computer Music Journal 7(2), 1983.
D. Jaffe, J. Smith, “Extensions of the Karplus–Strong Plucked-String Algorithm,” Computer Music Journal 7(2), 1983.

Two-tone protocols. The chord roughness measurement adapts the SMPTE and CCIF/ITU-R twin-tone intermodulation conventions to guitar-relevant intervals.

The perceptual words. When a summary says “brighter” or “smoother”, the underlying numbers are proxy implementations (openly simplified — see the honesty note on that page) of published psychoacoustic models:

E. Zwicker, E. Terhardt, “Analytical expressions for critical-band rate and critical bandwidth as a function of frequency,” Journal of the Acoustical Society of America 68(5), 1980.
DIN 45692:2009 (sharpness); H. Fastl, E. Zwicker, Psychoacoustics: Facts and Models, 3rd ed., Springer, 2007 (roughness).

Filters. Simulated-pedal tone stacks use Robert Bristow-Johnson’s “Audio EQ Cookbook” biquad formulas — the quiet workhorse of practically all digital audio EQ.

Independent cross-checking. The app’s analysis is validated against Stefan Gündert’s independent syncsweptsine Python implementation (github.com/SiggiGue/syncsweptsine) — at arm’s length, no code shared — with agreement to within thousandths of a dB on reference nonlinearities.