Thermal tides are atmospheric planetary‐scale waves with periods that are harmonics of the solar day. In the Martian atmosphere thermal tides are known to be especially significant compared to any other known planet. Based on the data set of pressure timeseries produced by the InSight lander, which is unprecedented in terms of accuracy and temporal coverage, we investigate thermal tides on Mars and we find harmonics even beyond the number 24, which exceeds significantly the number of harmonics previously reported by other works. We explore comparatively the characteristics and seasonal evolution of tidal harmonics and find that even and odd harmonics exhibit some clearly differentiated trends that evolve seasonally and respond to dust events. High‐order tidal harmonics with small amplitudes could transiently interfere constructively to produce meteorologically relevant patterns. Plain Language Summary In analogy to the string of a guitar, which can oscillate in integer harmonics, planetary atmospheres exhibit oscillations that are harmonics of the solar day (Harmonic 1 with a period of 24 hr; harmonic 2, 12 hr; harmonic 3, 8 hr; etc.). These oscillations are part of the so‐called “atmospheric thermal tides”, which retain a complex global structure. They are conceptually related to ocean gravitational tides, and they have been observed in atmospheres of the solar system whose main source of energy is the light from the sun: Earth, Mars, Venus, and Titan. On Mars, thermal tides are particularly strong and they play a key role in atmospheric dynamics, presenting interactions with meteorological phenomena such as dust storms. Most studies on thermal tides focus on low‐order harmonics (1, 2, 3, and sometimes 4). In this study, we use a particularly sensitive pressure sensor that landed on Mars with the InSight mission to explore the existence of high‐order harmonics, and we find clear harmonics with very small amplitudes even beyond harmonic 24, which corresponds to 24 oscillations per solar day. We compare the characteristics of those harmonics and analyze their seasonal behavior, and we find that even and odd harmonics exhibit clearly different behaviors. Key Points Analysis of an unprecedented data set of pressure obtained by InSight suggests that tidal harmonics beyond 24 are present on Mars Even and odd modes exhibit distinct patterns with a seasonal dependency centered on equinoxes and solstices, and response to dust events