Harmonic Tierce is listed only by Wedgwood, who says: Mutation ranks are sometimes made of double length and harmonic intonation. The effect of this treatment is to increase their power without giving rise to concomitant development of their own upper partials. As a result they also stand better in tune and are less affected by fluctuation of wind pressure than the true-length varieties. The practice is not unknown abroad. See Harmonic Stopped Twelfth. Maynouth College, Ireland (Stahlhuth); Emmanual Church, Nottingham, Hucknall Torkard, Nottingham (Musson & Compton). Tierce Harmonique is not mentioned in the literature, but we assume it to be a synonym.
Osiris contains seven examples of Tierce Harmonique, all at 1-3/5' pitch, and all from the late 20th century.