The borrowed name points at a real medieval system, and the mismatch between the two is exact enough to be worth setting out. Solmisation is the method of sight singing associated with Guido of Arezzo in the eleventh century, whose syllables ut, re, mi, fa, sol and la are taken from the opening words of successive lines of the hymn Ut queant laxis, each of which begins a step higher than the last.
What that system names are relative degrees within a hexachord. Ut is wherever the singer begins; the syllables describe the intervals between notes, not the notes themselves, and the whole point of the method is that the same pattern can be started anywhere. It fixes no absolute pitch and could not, because there was no standard of absolute pitch to fix. Pitch standards varied by region and by instrument for centuries afterward, and an international standard for concert A was not agreed until the twentieth century.
Measuring a tone as a number of cycles per second belongs to nineteenth century physics, and the unit itself is named after Heinrich Hertz, who died in 1894. Assigning a specific frequency in hertz to a medieval solmisation syllable is therefore not a recovery of anything: the two systems share six syllables and nothing else. The atlas states this because the historical claim is checkable, unlike the therapeutic ones, and because stating it is the most useful thing a reference work can do here.