Beat (acoustics)/Literature search


 * Two room method by Harrison for calibrating pendulum clocks. Harrison precision longcase clocks (fairfaxhouse.co.uk) Saved pdf at "G:\My Drive\python\Intervals\articles\Harrison’s precision longcase clocks - Fairfax House.pdf" Cite website as: Harrison's precision longcase clocks (2022) Fairfax House. Hannah Phillip. Available at: https://www.fairfaxhouse.co.uk/articles/harrisons-precision-longcase-clocks/ (Accessed: February 7, 2023).


 * https://www.mpi.nl/world/materials/publications/levelt/Plomp_Levelt_Tonal_1965.pdf
 * https://pypi.org/project/dissonant/ Seems inactive
 * https://towardsdatascience.com/music-in-python-2f054deb41f4 Programmed python to render input notes as piano. Sort of a homemade (and limited) version of lilypond.

Signal processing of audicity files
LINKS
 * https://amath.colorado.edu/pub/matlab/music/Petersen04CMJ.pdf
 * https://docs.google.com/spreadsheets/d/14hSwf9v3Yw8u5910LVBVZgX2WLhUjTO50nPl_VKXvJ8/edit#gid=0
 * https://www.earthinversion.com/techniques/Time-Series-Analysis-Filtering-or-smoothing-data/
 * https://stackoverflow.com/questions/14313510/how-to-calculate-rolling-moving-average-using-python-numpy-scipy

Perception of consonance

 * Lott and Stone: Perception of musical consonance and dissonance: an outcome of neural synchronization (excellent article)
 * JOOS VOS, "The perception of pure and mistuned musical fifths and major thirds: Thresholds for discrimination, beats, and identification", Perception &Psychophysics: 1982,32 (4),297-313
 * Plomp and Levelt 1965 Plomp, Reinier, and Willem Johannes Maria Levelt. The journal of the Acoustical Society of America 38.4 (1965): 548-560
 * Computational Approach to Musical Consonance and Dissonance: Lluis L. Trulla1, Nicola Di Stefano and Alessandro Giuliani has a long list of references:


 * 1) Abel, M., Ahnert, K., and Bergweiler, S. (2009). Synchronization of sound sources. Phys. Rev. Lett. 103:114301. doi: 10.1103/PhysRevLett.103.114301 Loudspeaker and organ pipe experiment. Equations impossible to understand.
 * 2) Benade, A. H. (1973). The physics of brasses. Sci. Am. 229, 24–35. doi: 10.1038/scientificamerican0773-24
 * 3) Bidelman, G. M., and Heinz, M. G. (2011). Auditory-nerve responses predict pitch attributes related to musical consonance-dissonance for normal and impaired hearing. J. Acoust. Soc. Am. 130, 1488–1502. doi: 10.1121/1.3605559
 * 4) Bidelman, G. M., and Krishnan, A. (2009). Neural correlates of consonance, dissonance, and the hierarchy of musical pitch in the human brainstem. J. Neurosci. 29, 13165–13171. doi: 10.1523/JNEUROSCI.3900-09.2009
 * 5) Bowling, D. L., Hoeschele, M., Kamraan, Z. G., and Tecumseh Fitch, W. (2017). The nature and nurture of musical consonance. Music Percept. 35, 118–121. doi: 10.1525/mp.2017.35.1.118
 * 6) Bowling, D. L., and Purves, D. (2015). A biological rationale for musical consonance. Proc. Natl. Acad. Sci. U.S.A. 112, 11155–11160. doi: 10.1073/pnas.1505768112
 * 7) Cartwright, J. H. E., Douthettb, J., González, D. L., Krantzd, R., and Piro, O. (2010). Two musical paths to the Farey series and devil’s staircase. J. Math. Music 4, 57–74. doi: 10.1080/17459737.2010.485001
 * 8) Cartwright, J. H. E., Gonzalez, D. L., and Piro, O. (2001). Pitch perception: a dynamical-systems perspective. Proc. Natl. Acad. Sci. U.S.A. 98, 4855–4859. doi: 10.1073/pnas.081070998
 * 9) Cartwright, J. H. E., Gonzalez, D. L., Piro, O., and Stanziali, D. (2002). Aesthetics, dynamics, and musical scales: a golden connection. J. New Music Res. 31, 51–58. doi: 10.1076/jnmr.31.1.51.8099
 * 10) Cross, I. (2003). Music as a biocultural phenomenon. Ann. N. Y. Acad. Sci. 999, 106–111. doi: 10.1196/annals.1284.010
 * 11) Di Stefano, N., Focaroli, V., Giuliani, A., Formica, D., Taffoni, F., and Keller, F. (2017). A new research method to test auditory preferences in young listeners: results from a consonance versus dissonance perception study. Psychol. Music 45, 699–712. doi: 10.1177/0305735616681205
 * 12) Eckmann, J. P., Kamphorst, S. O., and Ruelle, D. (1987). Recurrence plots of dynamical systems. Europhys. Lett. 4, 973–976. doi: 10.1209/0295-5075/4/9/004
 * 13) Fastl, H., and Zwicker, E. (2006). Psychoacoustic. Facts and Models. Berlin: Springer.
 * Foo, F., King-Stephens, D., Weber, P., Laxer, K., Parvizi, J., and Knight, R. T. (2016). Differential processing of consonance and dissonance within the human superior temporal gyrus. Front. Hum. Neurosci. 10:154. doi: 10.3389/fnhum.2016.00154
 * 1) Frova, A. (1999). Fisica nella Musica. Bologna: Zanichelli.
 * 2) González-García, N., González, M. A., and Rendón, P. L. (2016). Neural activity related to discrimination and vocal production of consonant and dissonant musical intervals. Brain Res. 1643, 59–69. doi: 10.1016/j.brainres.2016.04.065
 * 3) Helmholtz, H. (1954). On the Sensations of Tone. New York, NY: Dover Publications.
 * 4) Kameoka, A., and Kuriyagawa, M. (1969a). Consonance theory part I: consonance of dyads. J. Acoust. Soc. Am. 45, 1451–1459. doi: 10.1121/1.1911623
 * 5) Kameoka, A., and Kuriyagawa, M. (1969b). Consonance theory part II: consonance of complex tones and its calculation method. J. Acoust. Soc. Am. 45, 1460–1469. doi: 10.1121/1.1911624
 * 6) Kennel, M. B., Brown, R., and Abarbanel, H. D. (1992). Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys. Rev. A 45, 3403. doi: 10.1103/PhysRevA.45.3403
 * 7) Koelsch, S., Fritz, T., Schulze, K., Alsop, D., and Schlaug, G. (2005). Adults and children processing music: An fMRI study. Neuroimage 25, 1068–1076. doi: 10.1016/j.neuroimage.2004.12.050
 * 8) Koelsch, S., and Mulder, J. (2002). Electric brain responses to inappropriate harmonies during listening to expressive music. Clin. Neurophysiol. 113, 862–869. doi: 10.1016/S1388-2457(02)00050-0
 * 9) Large, E. W., and Almonte, F. V. (2012). Neurodynamics, tonality, and the auditory brainstem response. Ann. N. Y. Acad. Sci. 1252, E1–E7. doi: 10.1111/j.1749-6632.2012.06594.x
 * 10) Large, E. W., and Tretakis, A. E. (2005). Tonality and nonlinear resonance. Ann. N. Y. Acad. Sci. 1060, 53–56. doi: 10.1196/annals.1360.046
 * 11) Lohri, A. (2016). Kombinationstöne und Tartinis “terzo suono”. Mainz: Schott Music.
 * 12) Lots, I. S., and Stone, L. (2008). Perception of musical consonance and dissonance: an outcome of neural synchronization. J. R. Soc. Interface 5, 1429–1434. doi: 10.1098/rsif.2008.0143
 * 13) Manetti, C., Ceruso, M. A., Giuliani, A., Webber, C. L. Jr., and Zbilut, J. P. (1999). Recurrence quantification analysis as a tool for characterization of molecular dynamics simulations. Phys. Rev. E 59, 992–998. doi: 10.1103/PhysRevE.59.992
 * 14) Marwan, N., Romano, M. C., Thiel, M., and Kurths, J. (2007). Recurrence plots for the analysis of complex systems. Phys. Rep. 438, 237–329. doi: 10.1016/j.physrep.2006.11.001
 * 15) McCauley, J. L. (1994). Chaos, Dynamics and Fractals. Cambridge: Cambridge University Press.
 * 16) McDermott, J., Schultz, A. F., Undurraga, E. A., and Godoy, R. A. (2016). Indifference to dissonance in native Amazonians reveals cultural variations in music perception. Nature 535, 547–550. doi: 10.1038/nature18635
 * 17) Minati, L., Rosazza, C., D’Incerti, L., Pietrocini, E., Valentini, L., Scaioli, V., et al. (2008). FMRI/ERP of musical syntax: comparison of melodies and unstructured note sequences. Neuroreport 19, 1381–1385. doi: 10.1097/WNR.0b013e32830c694b
 * 18) Nikolsky, A. (2015). Evolution of tonal organization in music mirrors symbolic representation of perceptual reality. Part-1: prehistoric. Front. Psychol. 6:1405. doi: 10.3389/fpsyg.2015.01405
 * 19) Orsucci, F., Giuliani, A., Webber, C., Zbilut, J., Fonagy, P., and Mazza, M. (2006). Combinatorics and synchronization in natural semiotics. Phys. A Stat. Mech. Appl. 361, 665–676. doi: 10.1016/j.physa.2005.06.044
 * 20) Pankovski, T., and Pankovska, E. (2017). Emergence of the consonance pattern within synaptic weights of a neural network featuring Hebbian neuroplasticity. Biol. Insp. Cong. Arch. 22, 82–94. doi: 10.1016/j.bica.2017.09.001
 * 21) Park, J. Y., Park, H., Kim, J., and Park, H. J. (2011). Consonant chords stimulate higher EEG gamma activity than dissonant chords. Neurosci. Lett. 488, 101–105. doi: 10.1016/j.neulet.2010.11.011
 * 22) Parncutt, R., and Hair, G. (2011). Consonance and dissonance in theory and psychology: disentangling dissonant dichotomies. J. Interdiscip. Music Stud. 5, 119–166.
 * 23) Perani, D., Saccuman, M. C., Scifo, P., Spada, D., Andreolli, G., Rovelli, R., et al. (2010). Functional specializations for music processing in the human newborn brain. Proc. Natl. Acad. Sci. U.S.A. 107, 4758–4763. doi: 10.1073/pnas.0909074107
 * 24) Piana, G. (2007). Barlumi per una Filosofia Della Musica. Morrisville: Lulu Press.
 * 25) Plomp, R. (1976). Aspects of Tone Sensation: A Psychophysical Study. London: Academic Press.
 * 26) Roads, C. (2001). Microsound. Cambridge, MA: The MIT Press.
 * 27) Roederer, J. G. (2008). The Physics and Psychophysics of Music. New York, NY: Springer.
 * 28) Schroeder, M. (1990). Fractals, Chaos, Power Laws. New York, NY: W.H Freeman and Co.
 * 29) Schwartz, D. A., Howe, C. Q., and Purves, D. (2003). The statistical structure of human speech sounds predicts music universals. J. Neurosci. 23, 7160–7168.
 * 30) Serra, J., Serra, X., and Andrzejak, R. G. (2009). Cross recurrence quantification for cover song identification. New J. Phys. 11:093017. doi: 10.1088/1367-2630/11/9/093017
 * 31) Trulla, L. L., Giuliani, A., Zbilut, J. P., and Webber, C. L. (1996). Recurrence quantification analysis of the logistic equation with transients. Phys. Lett. A 223, 255–260. doi: 10.1016/S0375-9601(96)00741-4
 * 32) Trulla, L. L., Giuliani, A., Zimatore, G., Colosimo, A., and Zbilut, J. P. (2005). Non-linear assessment of musical consonance. Electron. J. Theor. Phys. 8, 22–34.
 * 33) Wang, X. (2013). The harmonic organization of auditory cortex. Front. Syst. Neurosci. 7:114. doi: 10.3389/fnsys.2013.00114
 * 34) Webber, C. L., and Zbilut, J. P. (1994). Dynamical assessment of physiological systems and states using recurrence plot strategies. J. Appl. Physiol. 76, 965–973. doi: 10.1152/jappl.1994.76.2.965
 * 35) Zimatore, G., Giuliani, A., Hatzopoulos, S., Martini, A., and Colosimo, A. (2003). Otoacoustic emissions at different click intensities: invariant and subject-dependent features. J. Appl. Physiol. 95, 2299–2305. doi: 10.1152/japplphysiol.00667.2003
 * 36) Zimatore, G., Hatzopoulos, S., Giuliani, A., Martini, A., and Colosimo, A. (2002). Comparison of transient otoacoustic emission (TEOAE) responses from neonatal and adult ears. J. Appl. Physiol. 92, 2521–2528. doi: 10.1152/japplphysiol.01163.2001

WJS Malmberg's ranking of consonance
Tonal Consonance and Critical Bandwidth R. PLOMP AND W. J. M. LEVELT 2:3, 3:5, 3:4 and 4:5, 5:8, 5:6, 5:7 C. V. Malmberg, "The Perception of Consonance and Dissonance," Psychol. Monogr. 25, No. 2, 93-133 (1917-1918).

More Websites

 * Constructing Musical Scales (Espen Slettnes)
 * Harmonic Series (musiccrashcourses.com)
 * Open vs Closed pipes (Flutes vs Clarinets) - Joe Wolfe (UNSW)

Mode locking
Some of these will go into the Wiki Journal of Science article WJS Strogatz SH, Stewart I. Coupled oscillators and biological synchronization. Sci Am. 1993 Dec;269(6):102-9. doi: 10.1038/scientificamerican1293-102. PMID: 8266056.(link1) (link2)

YEA [https://newt.phys.unsw.edu.au/music/people/publications/Fletcher1978.pdf Fletcher, Neville H. "Mode locking in nonlinearly excited inharmonic musical oscillators." The Journal of the Acoustical Society of America 64.6 (1978): 1566-1569.] (link2) An example of the complexity of nonlinear equations.


 * Fletcher, Neville H. "Sound production by organ flue pipes." The Journal of the Acoustical Society of America 60.4 (1976): 926-936. Again, no simple equation.

NO MIT thesis on Hodgkin-Huxley nothing not on Wikipedia.

WJS [http://salt.uaa.alaska.edu/physics_public/metro.pdf Pantaleone, James. "Synchronization of metronomes." American Journal of Physics 70.10 (2002): 992-1000.]

Miscellaneous quotes

 * Coombes, S., and Gabriel James Lord. "Intrinsic modulation of pulse-coupled integrate-and-fire neurons." Physical Review E 56.5 (1997): 5809. (link) ... rhythmic motor behavior... Hodgkin–Huxley model (4 nonlinear odes).


 * Tadpole quote: "For example, in the mollusc Tritonia and the tadpole Xenopus the escape swim behavior is generated in this fashion ... The study of coupled oscillators has applications in understanding CPG (central pattern generators) neuronal circuits ... "
 * Three of the 41 citing articles involve music:


 * LotsStone coupled neural oscillators ... PROBLEMS WITH HELMHOLTZ'S THEORY ... See
 * Heffernan, B., and A. Longtin. "Pulse-coupled neuron models as investigative tools for musical consonance." Journal of Neuroscience Methods 183.1 (2009): 95-106. (link)
 * Hadrava, Michal, and Jaroslav Hlinka. "A Dynamical Systems Approach to Spectral Music: Modeling the Role of Roughness and Inharmonicity in Perception of Musical Tension." Frontiers in Applied Mathematics and Statistics 6 (2020): 18.(link)

Scholarpedia

 * http://www.scholarpedia.org/article/Measures_of_neuronal_signal_synchrony
 * http://www.scholarpedia.org/article/Phase_model
 * http://www.scholarpedia.org/article/Neuronal_synchrony_measures
 * http://www.scholarpedia.org/article/Voltage-controlled_oscillations_in_neurons Mentions: Hodgkin and Huxley, van der Pol model, phase space, staircase plots
 * http://www.scholarpedia.org/article/Phase_space

Wikipedia

 * Central pattern generator produces rhythmic outputs in the absence of rhythmic input. Same for Neural substrate of locomotor central pattern generators in mammals
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