Designing inharmonic strings

References

• Blackmore, Kim L., Robert C. Williamson, Ivan M. Y. Mareels, and William A. Sethares. 1997. “Online Learning via Congregational Gradient Descent.” Mathematics of Controls, Systems, and Signals 10 (4): 331–363. doi: 10.1007/BF01211551
   Web of Science ®Google Scholar
• Caldersmith, Graham. 1995. “Designing a Guitar Family.” Applied Acoustics 46 (1): 3–17. doi: 10.1016/0003-682X(95)93949-I
   Web of Science ®Google Scholar
• Chowning, John. 1988. “Phone/Turenas/Stria/Sabelithe.” CD 50.
   Google Scholar
• Cook, Perry R. 2018. “Sound Lab's Research in Physical Modeling.” http://soundlab.cs.princeton.edu/research/phymod/. Accessed: 16 May 2018.
   Google Scholar
• Dalmont, Jean-Pierre. 2017. “Harmonic Stepped Waveguides and Their Application to Music.” In 2017 International Symposium on Musical Acoustics, McGill University, Montreal, Quebec, Canada, edited by Gary Scavone, Esteban Maestre, Connor Kemp, and Song Wang.
   Google Scholar
• Dalmont, Jean Pierre, and Jean Kergomard. 1994. “Lattices of Sound Tubes with Harmonically Related Eigenfrequencies.” Acta Acoustica 2 (5): 421–430.
   Google Scholar
• Fletcher, Neville H. 1993. “Tuning a Pentangle – a New Musical Vibrating Element.” Applied Acoustics 39 (1): 145–163. doi: 10.1016/0003-682X(93)90001-M
   Google Scholar
• Fletcher, Neville H., and Thomas D. Rossing. 1991. The Physics of Musical Instruments. New York: Springer-Verlag.
   Google Scholar
• Hobby, Kevin, and William A. Sethares. 2016a. “Inharmonic Strings and the Hyperpiano.” Applied Acoustics 114 (1): 317–327. doi: 10.1016/j.apacoust.2016.07.029
   Google Scholar
• Hobby, Kevin, and William A. Sethares. 2016b. “Website for Inharmonic Strings and the Hyperpiano.” http://sethares.engr.wisc.edu/papers/hyperOctave.html. Accessed: 2018–5–16.
   Google Scholar
• Hobby, Kevin, William A. Sethares, and Zhenyu Zhang. 2017. “Using Inharmonic Strings in Musical Instruments.” In Mathematics and Computation in Music: 6th International Conference, MCM, Mexico City, Mexico, 26–29 June, 2017, Proceedings, edited by Octavio A. Agustín-Aquino, Emilio Lluis-Puebla, and Mariana Montiel, 104–116. Cham, Switzerland: Springer Nature.
   Google Scholar
• Hodges, C. H., and James Woodhouse. 1983. “Vibration Isolation from Irregularity in a Nearly Periodic Structure: Theory and Measurements.” Journal of the Acoustical Society of America 74 (3): 894–905. doi: 10.1121/1.389847
   Web of Science ®Google Scholar
• Kalotas, T. M., and A. R. Lee. 1992. “The Transverse Modes of a String with Variable Mass Density.” Acustica 76 (1): 20–26.
   Google Scholar
• Kiefer, Jack, and Jacob Wolfowitz. 1952. “Stochastic Estimation of a Regression Function.” Annals of Mathematical Statistics 23 (1): 462–466. doi: 10.1214/aoms/1177729392
   Google Scholar
• Kinsler, Lawrence E., Austin R. Frey, Alan B. Coppens, and James V. Sanders. 1999. Fundamentals of Acoustics. 4th ed. Hoboken, New Jersey: Wiley.
   Google Scholar
• McLachlan, Neil M. 2004. “The Design and Analysis of New Musical Bells.” Journal of the Acoustical Society of America 115 (1): 2565–2570. doi: 10.1121/1.4784017
   Google Scholar
• O'Connell, Walter. 1993. “The Tonality of the Golden Section.” Xenharmikon 15: 3–18.
   Google Scholar
• Partch, Harry. 1974. Genesis of a Music. New York: Da Capo Press.
   Google Scholar
• Sethares, William A. 1993. “Local Consonance and the Relationship between Timbre and Scale.” Journal of the Acoustical Society of America 94 (3): 1218–1228. doi: 10.1121/1.408175
   Web of Science ®Google Scholar
• Sethares, William A. 2004. Tuning, Timbre, Spectrum, Scale. 2nd ed. Berlin: Springer.
   Google Scholar
• Smethurst, Reilly. 2016. “Two Non-Octave Tunings by Heinz Bohlen: A Practical Proposal.” In Bridges 2016 Conference Proceedings, edited by Eve Torrence, Bruce Torrence, Carlo H. Séquin, Douglas McKenna, Kristóf Fenyvesi, and Reza Sarhangi.
   Google Scholar
• Smith, Julius O. 2010. Physical Audio Signal Processing for Virtual Musical Instruments and Digital Audio Effects. Stanford, CA: W3K Publishing.
   Google Scholar
• Spall, James C. 1992. “Multivariate Stochastic Approximation Using a Simultaneous Perturbation Gradient Approximation.” IEEE Transactions on Automatic Control 37 (4): 332–341. doi: 10.1109/9.119632
   Google Scholar
• Spall, James C. 1997. “A One-Measurement Form of Simultaneous Perturbation Stochastic Approximation.” Automatica 33 (2): 109–112. doi: 10.1016/S0005-1098(96)00149-5
   Google Scholar