Ancient Chinese musical scales: Best approximations, but why?

International Journal of Nonlinear Sciences and Numerical Simulation

Volumn 10, Issue 2, 2009, Pages 161-166

  Zhong, Ting ^a  

^a JISHOU UNIVERSITY   (China)

Author keywords

Ancient Chinese mathematics; Best approximation; Continued fraction; Farey sequence; Musical equation; Musical equations

Indexed keywords

EID: 65349107977     PISSN: 15651339     EISSN: None     Source Type: Journal    
DOI: 10.1515/IJNSNS.2009.10.2.161     Document Type: Article

References (21)

1. J.W. Dauben, Ancient Chinese mathematics: the (Jiu Zhang SuanShu) vs Euclids Elements. Aspects of proof and the linguistic limits of knowledge, International Journal of Engineering Science, 36(1998): 1339-1359
2. J.H.He, Solution of nonlinear equations by an ancient Chinese algorithm, Applied Mathematics and Computation, 151 (2004) : 293-297
3. J.H.He, Ancient Chinese algorithm: the Ying Buzu Shu (method of surplus and deficiency) vs Newton iteration method, Applied Mathematics and Mechanics, 23 (12) (2002) : 1407-1412
4. J.H. He, Comment on 'He's frequency formulation for nonlinear oscillators', European Journal of Physics, 29(2008): 19-22
5. J.H.He, Some interpolation formulas in Chinese ancient mathematics, Applied Mathematic and Computation, 152 (2004): 367-371
6. J.H.He, An elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering, Int. J. Mod. Phys. B, 22(2008): 3487-3578
7. J.H.He, Some asymptotic methods for strongly nonlinear equations, Int. J. Mod Phys. B, 20(2006)1141-1199
8. J.H.He, Max-min approach to nonlinear oscillators, Int. J. Nonlin. Sci. Num., 9(2008) 207-210
9. He JH. An improved amplitude-frequency formulation for nonlinear oscillators, Int. J. Nonlin. Sci. Num., 9(2008) 211-212
10. J.H.He, J. Tang, Rebuild of King Fang 40 BC musical scales by Hes inequality, Applied Mathematics and Computation, 168 (2005) : 909-914
11. E.Dunne, M. Mc Connell, Pianos and continued fractions, Mathematics Magazine 72(2)( 1999): 104-115
12. J.H.He, He Chengtians inequality and its applications, Applied Mathematics and Computation 151 (2004) : 887-891
13. Z. F. Ren, B.Z. Liu, Z.Y. Shao, et al. Allo-metric scaling law between average polymer molecular weight and electrospun nanofiber diameter, J. Polym. Eng. , 28 (2008) 19-26
14. J.H. He, Resistance in cell membrane and nerve fiber, Neuroscience Letters, 373(2005) 48-50
15. J.H. He, Allometric scaling law in conductive polymer, Polymer, 45(2004): 9067-9070
16. H.L. Zhang, Application of He's frequency-amplitude formulation to an x(l/3) force Nonlinear oscillator ,Int. J. Nonlin. Sci. Num., 9( 3) (2008 ): 297-300
17. J. Fan, Application of He's frequency- amplitude formulation to the Duffing- harmonic oscillator , Topological Methods in Nonlinear Analysis, 31(2008) 389-394
18. T. Zhong, Continued fraction for E-infinity theory, Chaos Soliton. Fract., in press
19. T. Zhong, Metrical properties for a class of continued fractions with increasing digits, J. Number Theory, 128(2008)1506-1515
20. A.Ya. Khintchine, Continued Fractions. P.Noordh off, Groningen, The Netherlands, 1963.
21. J.L. Lagrange,Additions au meoire sur la resolution des equations numeriques, Mem.Berl.,24(1770)