The Solfeggio set is not ancient, and its own literature is fairly open about where it comes from. The nine tones were put into circulation by Joseph Puleo and Leonard Horowitz in Healing Codes for the Biological Apocalypse, published in 1999, where they are presented as recovered from the medieval Latin hymn Ut queant laxis by a numerological procedure. The hymn is real and important: Guido of Arezzo took the first syllable of each of its lines in the eleventh century to name the notes of the hexachord, which is why the syllables ut, re, mi, fa, sol and la exist at all.
The structure of the set is arithmetic, and 639 Hz shows it clearly. Its digits sum to 18, and reducing that gives 9; every tone in the nine reduces to three, six or nine, and no other value appears. The tones also fall into triads a hundred and eleven apart: 417, 528 and 639. That pattern is the reason the set has the members it has. It was chosen for its numerology, which the source is explicit about, and not derived from any measurement.
Two problems sit under the ancient claim, and neither is a matter of opinion. The hymn carries no frequencies: medieval music had no absolute pitch standard, singers pitched to a comfortable range, and the idea of tuning a note to a fixed number of cycles per second is a later development. The hertz itself is a nineteenth century unit, named for a physicist born in 1857, so a number in hertz cannot have been handed down from an eleventh century source. The therapeutic effects attributed to this tone belong to the 1999 book and to the literature that followed it. The atlas records the claim, and records who makes it.
Sources Healing Codes for the Biological ApocalypseLeonard G. Horowitz and Joseph S. Puleo with Western Plainchant: A HandbookDavid Hiley, ISO 16:1975, Acoustics, Standard tuning frequency (Standard musical pitch)International Organization for Standardization