Correction to: A rational framework for dynamic homogenization at finite wavelengths and frequencies (Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (2019) 475 (20180547) DOI: 10.1098/rspa.2018.0547)

Figure 4 is revised as follows: replace the reference number '[11]' with '[24]' Figure 6 is revised as follows: replace the equation number '(6.20)' with '(6.19)' replace the equation number '(6.21)' with '(6.20)' Equation (6.1) is revised as follows: replace the '+' sign on the right-hand side with the '−' sign Equation (6.2) is revised as follows: replace the '+' sign on the right-hand side with the '−' sign Equation (6.4) is revised as follows: replace the '+' sign on the right-hand side with the '−' sign. References [8,13,19] are revised as follows: 8. Meng S, Guzina B. 2018 On the dynamic homogenization of periodic media: Willis’ approach versus two-scale paradigm. Proc. R. Soc. A 474, 20170638. (doi:10.1098/rspa. 2017.0638) 13. Santosa F, Symes WW. 1991 A dispersive effective medium for wave propagation in periodic composites. SIAM J. Appl. Math. 51, 98401005. (doi:10.1137/0151049) 19. Craster RV, Kaplunov J, Pichugin AV. 2010 Highfrequency homogenization for periodic media. Proc. R. Soc. A 466, 234102362. (doi:10.1098/rspa.2009.0612).