| Title:
|
Matematika hudebních nástrojů (Czech) |
| Title:
|
The mathematics of musical instruments (English) |
| Author:
|
Hall, Rachel W. |
| Author:
|
Josić, Krešimir |
| Language:
|
Czech |
| Journal:
|
Pokroky matematiky, fyziky a astronomie |
| ISSN:
|
0032-2423 |
| Volume:
|
47 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
37-49 |
| . |
| Category:
|
math |
| . |
| MSC:
|
00A69 |
| MSC:
|
00A99 |
| MSC:
|
11A55 |
| MSC:
|
35L05 |
| MSC:
|
74J05 |
| idZBL:
|
Zbl 1055.00522 |
| Note:
|
From The Amer. Math. Monthly 108, April 2001, 347-357, translated by J. Obdržálek. (English) |
| Note:
|
Z Amer. Math. Monthly 108, duben 2001, 347-357, přeložil J. Obdržálek. (Czech) |
| . |
| Date available:
|
2010-12-11T19:07:16Z |
| Last updated:
|
2012-08-26 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141111 |
| . |
| Reference:
|
[1] Arnol’d, V. I.: Geometrical methods in the theory of ordinary differential equations.($2^{\rm nd}$ ed.). Springer-Verlag, New York 1988. Z ruštiny přeložil József M. Szücs. MR 0947141 |
| Reference:
|
[2] Barbour, J. M.: Music and ternary continued fractions.Amer. Math. Monthly 55 (1948), 545–555. MR 0027293 |
| Reference:
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[3] Barbour, J. M.: Tuning and Temperament.Michigan State College Press, East Lansing 1953. |
| Reference:
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[4] Barbour, J. M.: A geometrical approximation to the roots of numbers.Amer. Math. Monthly 64 (1957), 1–9. Zbl 0078.13204, MR 0086098 |
| Reference:
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[5] Benson, D.: Mathematics and Music.V tisku, dosažitelné na ftp://byrd.math.uga.edu/pub/html/index.html (2000). |
| Reference:
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[6] Blackwood, E.: Microtonal Etudes.Cedille Records. CDR 90000 018. |
| Reference:
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[7] Boyce, W. E., DiPrima, R. C.: Elementary Differential Equations and Boundary Value Problems.($4^{\rm nd}$ ed.). John Wiley & Sons, Inc., New York 1986. Zbl 0652.34001, MR 0179403 |
| Reference:
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[8] Brimi, H.: “Willow Dance, 1994,” in The Sweet Sunny North.Shanachie Records64057. |
| Reference:
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[9] Chapman, S. J.: Drums that sound the same.Amer. Math. Monthly 102 (1955), 124–138. MR 1315592 |
| Reference:
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[10] Ctuistian, R. S., Davis, R. E., Tubis, A., Anderson, C. A., Mills, R. I., Rossing, T. D.: Effect of Air Loading on Timpani Membrane Vibrations.J. Acoust. Soc. Am. 76 (1984), 1336–1345. |
| Reference:
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[11] Devaney, R. L.: An introduction to chaotic dynamical systems.($2^{\rm nd}$ ed.). AddisonW̄esley Publishing Company Advanced Book Program, Redwood City, CA 1989. Zbl 0695.58002, MR 1046376 |
| Reference:
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[12] Fletcher, N. H., Rossing, T. D.: The physics of musical instruments.($2^{\rm nd}$ ed.). Springer-Verlag, New York 1998. Zbl 0898.00008, MR 1675659 |
| Reference:
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[13] Gordon, C., Webb, D. L., Wolpert, S.: One cannot hear the shape of a drum.Bull. Amer. Math. Soc. 27 (1992), 134–138. Zbl 0756.58049, MR 1136137 |
| Reference:
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[14] Hardy, G. H., Wright, E. M.: An Introduction to the Theory of Numbers.($5^{\rm nd}$ ed.). Oxford University Press, Oxford 1980. |
| Reference:
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[15] Helmholtz, H. v.: On thc sensations of tone as a physiological basis for the theory of music.Dover Publications, New York 1954. Originally published 1870, English translation by A. J. Ellis, 1875. |
| Reference:
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[16] Jorgensen, O.: Tuning.Michigan State University Press, East Lansing 1991. |
| Reference:
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[17] Kac, M.: Can one hear the shape of a drum?.Amer. Math. Monthly 73 (1966), 1–23. Zbl 0139.05603, MR 0201237 |
| Reference:
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[18] Kent, J. T.: Ternary continued fractions and the evenly-tempeted musical scale.CWI Newsletter 13 (1986), 21–33. MR 0898086 |
| Reference:
|
[19] Mersenne, M.: Harmonie universelle, contenant la théorie et la pratique de la musique.Centre national de la recherche stientifique, Paris, facsimile edition 1963. Původně vydáno v r. 1636. |
| Reference:
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[20] Pinsky, M. A.: Partial differential equations and boundary value problems with applications.(2$^{\rm nd}$ ed.). McGraw-Hill Inc., New York 1991. MR 1233559 |
| Reference:
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[21] Rayleigh, J. W. S.: The theory of sound.($2^{\rm nd}$ ed.). Dover Books, New York 1945. Původně vydáno v r. 1877. Zbl 0061.45904, MR 0016009 |
| Reference:
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[22] Rossing, T. D.: Acoustics of Percussion Instruments—part i.Phys. Teach. 14 (1976) 546–556. |
| Reference:
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[23] Rossing, T. D.: Acoustics of Percussion Instruments—part ii.Phys. Teach. 15 (1977), 278–288. |
| Reference:
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[24] Rossing, T. D.: The science of sound.($2^{\rm nd}$ ed.) Addison-Wesley, New York 1990. |
| Reference:
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[25] Sethares, W. A.: Tuning, timbre, spectrum, scale.Springer-Verlag, New York 1999. |
| Reference:
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[26] Varberg, D. E.: Pick’s theorem revisited.Amer. Math. Monthly 92 (1985) 584–587. Zbl 0578.52012, MR 0812105 |
| . |
