References
- Resolution threshold for low-numbered harmonics (cochlear filter bandwidth and critical-band arguments). The “about the 10th harmonic” boundary is a useful rule of thumb, not a fixed physiological cutoff. Moore, B. C. J., & Gockel, H. E. (2011). “Resolvability of components in complex tones and implications for theories of pitch perception.” Hearing Research, 276(1-2), 88-97. https://doi.org/10.1016/j.heares.2011.01.003.
- Benade, A. H. (1976; 2nd rev. ed. reprinted 1990). Fundamentals of Musical Acoustics. Oxford University Press / Dover. Benade’s 1973 measurements of Duff’s timpano are reported and reproduced in “Defining a Standard,” The Quantum World of Timpani Pitch, Pauken, 2021: https://quantum.pauken.org/defining-a-standard/. The measurement record is also reproduced in WTT Chapter 3 (Missing Fundamental): https://wtt.pauken.org/chapter-3/missing-fundamental.
- Albera, R., Urbanelli, A., Lucisano, S., Aprigliano, A., Morando, L., Amoroso, A., Alexeev, M., & Albera, A. (2025). “Musical note recognition based on the upper adjacent harmonics without the presence of the fundamental frequency.” Scientific Reports, 2025. PMCID: PMC12022334; PMID: 40274804. https://pmc.ncbi.nlm.nih.gov/articles/PMC12022334/. https://doi.org/10.1038/s41598-025-89454-7.
- Preisler, A. (1993). “The influence of spectral composition of complex tones and of musical experience on the perceptibility of virtual pitch.” Perception & Psychophysics, 54(5), 589-603. PMID: 8290328. https://doi.org/10.3758/BF03211783.
- Terhardt, E. (1974). “Pitch, consonance, and harmony.” Journal of the Acoustical Society of America, 55(5), 1061-1069. https://doi.org/10.1121/1.1914648.
- Seebeck, A. (1841). “Ueber einige Bedingungen der Entstehung von Tönen” [On some conditions of the generation of tones]. Annalen der Physik und Chemie, 53, 417-436. For modern summary, see WTT Chapter 4-2: https://wtt.pauken.org/chapter-4-2/chapter-4.
- Saus, W., Seither-Preisler, A., & Schneider, P. (2025). “Harmonic vowels and neural dynamics: MEG evidence for auditory resonance integration in singing.” Frontiers in Neuroscience, 19, 1625403. PMID: 40880852. https://doi.org/10.3389/fnins.2025.1625403.
- Andermann, M., Reineke, A. L., Riedel, H., & Rupp, A. (2026). “The role of (missing) fundamentals, active listening, and musical expertise in cortical and subcortical correlates of consonance/dissonance.” European Journal of Neuroscience, 63(6), e70483. PMID: 41873637. https://doi.org/10.1111/ejn.70483.