Barium sodium niobate (Ba2NaNb5O15) is a tungsten bronze structure that exhibits a complicated sequence ofsix structural phase transitions, including three incommensurate (IC)phases. The phases are unusual in that all but the highest temperatureP4/mbm structure are ferroelectric. Unlike the situation for most incommensurate insulators, inwhich ferroelectricity develops at low temperatures along the modulationdirection, the polarization direction in barium sodium niobate is orthogonal tothe modulation(s), permitting some unusual phenomena. In the present studywe analyse the thermal and dielectric behaviour at the Curie temperatureTC near 830 K as wellas that at the Ccm 21–IC(1q) transitionnear 543 K, the IC(1q)–IC(2q) transition near565 K and the IC(2q)–P4bm transition at 582 K. The entropy change at 565 K is related to the wallroughening model of Rice et al (1981 Phys. Rev. B 24 2751). Data nearTC = 830 K indicate close proximity to a tricritical point, and discussions of criticalexponents are presented, all of which are found to be mean field. Because ofNa vacancies, transition temperature variation is found among specimensBa2Na1−xNb5O15 (830 K<TC(x)<865 K), and the system appears to be describable by the disordered exclusion model as a slightlyfirst-order intrinsic system whose dynamics are suppressed by weak disorder. NearTC the specificheat C(T) is compared with the random bond prediction of Harris (1974 J. Phys. C: Solid State Phys. 7 1671):C(T) = C0(T)/[1+bx2C0(T)],where C0(T) is the intrinsic specific heat of the vacancy-free crystal varying as(TC−T)−1/2 and x is the sodium vacancy concentration. In agreement with Harris’s model, the shifts inTC(x) are to lowerT with increasingx and scale asx; the broadeningscales as x2; and the effective critical exponent remains unchanged atα = 1/2.