Mathematical model of melody perception

A. V. Glasko

Matematičeskoe modelirovanie, Tome 26 (2014) no. 9, pp. 65-82.

Résumé

On the basis of earlier offered theory of perception of individual stimulus (in particular, a sound), the model of melody perception, as sequences of sounds is developed. The basic mechanism of influence of melody on mentality of the person, named by flirtation, and leading formation and long existence (growth) of the convergent (peak) of attention is revealed. In view of overtone structures of a musical sound, flirtation can be carried out not only is obvious (due to the basic frequencies of sounds), but also indirectly (due to their harmonics), that allows "to deceive" effect fading reactions on repeatedly repeating stimulus. As examples, results of computer modelling of processes of two melody perception are resulted.

Détail

Keywords: melody, music, overtones, tonic triad, perception, flirtation
Mots-clés : attention, impression, convergent.

Bibliographie

[1] Evin I. A., Chto takoe iskusstvo s tochki zreniya fiziki?, Voentekhizdat, M., 2000, 144 pp.

[2] Detskaya entsiklopediya, v. 10, Literatura i iskusstvo, Izd-vo Akademii pedagogicheskikh nauk RSFSR, M., 1961, 710 pp.

[3] Manfred Clynes, Sentics: The Touch of The Emotions, DoubleDay, New York, 1977

[4] Koblyakov A. A., “Transmernye otnosheniya v muzyke, matematike i estestvoznanii”, Pervaya mezhdunarodnaya nauchno-tvorcheskaya konferentsiya «Muzyka-matematika-estestvoznanie», MGK im. P. I. Chaikovskogo, M., 2013

[5] Tangian A. S., “Evaluating melodies by the complexity of polyrhythm”, Actes des Journees d'Informatique Musicale (Bourges, 7–9 juin 2001, Institut international de musique electroacoustique de Bourges (IMEB) and Ecole nationale superieure d'ingenieurs de Bourges (ENSIB)), 183–194

[6] Tangian A., “Evaluating Melodies with regard to their polyrhythmic complexity”, Proceedings of the $7^{\mathrm{th}}$ Intern. Conf. on Music Perception and Cognition (17–21 July, 2002, Sydney, Australia), 232–235

[7] Petukhov S. V., Matrichnaya genetika, algebry geneticheskogo koda, pomekhoustoichivost, NITs «Regulyarnaya i khaoticheskaya dinamika», M.–Izhevsk, 2008, 316 pp.

[8] Glasko A. V., “O vospriyatii muzykalnoi melodii”, Obozr. prikl. i promyshl. matem., 15:2 (2008), 278–279

[9] Glasko A. V., “Vozmozhnyi mekhanizm vospriyatiya muzyki”, Matematika, informatika, ikh prilozheniya i rol v obrazovanii, Tezisy dokladov Rossiiskoi Shkoly-konferentsii, RUDN, M., 2009, 173–175 | Zbl

[10] Kulikova T. G., Issledovanie dinamiki vnimaniya v protsesse vospriyatiya muzykalnoi melodii, diplomnaya rabota. Nauch. ruk. Glasko A. V., MGTU im. N. E. Baumana, M., 2010

[11] Tarasova N. S., Modelirovanie vospriyatiya muzykalnykh kompozitsii s uchetom akkordov i melizmov, diplomnaya rabota. Nauch. ruk. Glasko A. V., MGTU im. N. E. Baumana, M., 2013

[12] Naatanen R., Vnimanie i funktsii mozga, Izd-vo MGU, M., 1998, 600 pp.

[13] Zabrodin Yu. M., Osnovy psikhofizicheskoi teorii sensornykh protsessov (Teoreticheskaya i eksperimentalnaya psikhofizika, avtoref. dis. dokt. psikhol. nauk, Leningr. un-t im. A. A. Zhdanova, L., 1977, 46 pp.

[14] Izmailov Ch. A., Sfericheskaya model tsvetorazlicheniya, MGU, M., 1980, 171 pp.

[15] Glasko A. V., “Sintez zakona induktsii Pavlova i psikhofizicheskogo zakona Stivensa v dinamicheskom uravnenii protsessa vospriyatiya”, Intellektualnye sistemy, Trudy mezhdunarodnoi konferentsii, v. 2, 2005, 166–174

[16] Glasko A. V., “Model dinamiki vnimaniya v protsesse vospriyatiya”, Zhurn. vyssh. nervn. deyat. im. I. P. Pavlova, 58:6 (2008)

[17] Glasko A. V., “Vnimanie kak dinamicheskii invariant”, Obozr. prikl. i promyshl. matem., 13:4 (2006), 624–625

[18] Glasko A. V., “Psikhofizicheskii zakon Stivensa, amplituda vyzvannogo potentsiala i dinamika vnimaniya”, Psikhofizika segodnya, eds. V. N. Nosulenko, I. G. Skotnikova, IP RAN, M., 2007

[19] Stivens S. S., Psikhofizika sensornoi funktsii. Psikhologiya oschuschenii i vospriyatiya, eds. Gippenreiter Yu. B., Lyubimov V. V., Mikhalevskaya M. B., «Che Ro», M., 1999, 283–290

[20] Zabrodin Yu. M., Lebedev A. N., Psikhofiziologiya i psikhofizika, Nauka, M., 1977, 286 pp.

[21] Kovalkin S. S., K eksperimentalnomu obosnovaniyu nekotoroi modeli vospriyatiya, diplomnaya rabota. Nauchn. ruk. Glasko A. V., MGTU im. N. E. Baumana, M., 2007, 104 pp.

[22] Mizyak V. G., Dinamika amplitudy slukhovykh i zritelnykh vyzvannykh potentsialov kak sledstvie dinamiki vnimaniya v protsesse vospriyatiya vneshnego stimula, diplomnaya rabota. Nauchn. ruk. Glasko A. V., MGTU im. N. E. Baumana, M., 2007, 102 pp.

[23] Glasko A. V., “O vospriyatii khudozhestvennoi kompozitsii”, Obozr. prikl. i promyshl. matem., 15:2 (2008), 279–280

[24] Shagas Ch., Vyzvannye potentsialy mozga v norme i patalogii, Mir, M., 1975, 314 pp.

[25] Tikhonov A. N., Samarskii A. A., Uravneniya matematicheskoi fiziki, Gosudarstvennoe izd-vo tekhniko-teoreticheskoi literatury, M.–L., 1951, 659 pp.

[26] Sokolov E. N., Teoreticheskaya psikhofiziologiya, Izd-vo MGU, M., 1986, 107 pp.

[27] Danilova N. N., Krylova A. L., Fiziologiya vysshei nervnoi deyatelnosti, Uchebnaya Literatura, M., 1997

[28] A. M. Prokhorov (gl. red.), Fizicheskii entsiklopedicheskii slovar, «Sovetskaya entsiklopediya», M., 1983

[29] Sposobin I. V., Elementarnaya teoriya muzyki, Kifara, M., 1996, 208 pp.

[30] Glasko A. V., Tarasova N. S., “Rezultaty modelirovaniya vospriyatiya muzyki s melizmami i akkordami”, Muzyka-matematika-estestvoznanie, Pervaya mezhdunarodnaya nauchno-tvorcheskaya konferentsiya, MGK im. P. I. Chaikovskogo, M., 2013