# Solfeggio Frequencies: hey music theorists, I did the math (and whooo is it weird)

I have a piece coming out in Real Life about pseudoscientific wellness trends like solfeggio frequencies. In researching that piece I did the math to figure out if and how the 9 frequencies identified by this theory have any connection to any of the Western harmonic systems adherents claim it is derived from. Since that info is a bit of a…niche interest, it got cut from the piece. But I know some of my music theory colleagues were interested in just this niche info, so I’ve posted it below.

There are usually 9 frequencies identified as having healing powers:

• 174Hz “relieve[s] pain and stress”;
• 285Hz “Heals tissues and organs”;
•  396Hz “eliminates fear”;
• 417Hz “wipes out negativity”;
• 528Hz “repairs DNA, brings positive transformation”;
• 639Hz “brings love and compassion in life”;
• 741Hz “detoxifies cells & organs”;
• 852Hz “awakens intuition, raises energy at cellular level;
• 963Hz “connects to higher self.”

Since these frequencies are often assigned the solfege syllables Western musicians assign to each of the scale degrees in the diatonic scale, I first looked to see if this series of frequencies mapped out the same sorts of intervals that compose that sort of scale. Musicians use solfege syllables to identify a set of 8 pitches that are in predetermined intervallic relationships to one another: “sol” is always a fifth above the root “do,” for example. However, in the solfeggio frequencies system, the syllables are assigned to a set of 6 or 9 frequencies that don’t fit into this interval pattern. For example, even though 528Hz is commonly identified as the most functionally significant frequency–e.g., the “frequency of love”–much in the same way tonal harmony treats the fifth as the most functionally significant scale degree, 528:174 reduces to 88:29 (which is close to 90:30, or 3:1), not 3:2, as a perfect fifth does. (Some guides list 396 as “ut” or “do” and 741 as “sol,” but that reduces to 274:132, which is close to 11:5.) The “solfeggio frequencies” are quite different from the ones contemporary western musicians and music theorists use solfege to identify.

Second, they are often claimed to be derived using Pythagorean methods…which is possible because Pythagoras’s series of harmonic ratios are well-known examples of ancient Greek music theory. As one of the more detailed accounts explains, Puello “discovered that the Old Testament’s Book of Numbers, specifically verses 12 through 83 of Chapter 7, contained a repeating pattern when looked at through the Pythagorean method of number reduction,” and then identifies the actual Pythagorean theorem, a² + b² = c², as that method of number reduction. (Which, notably, is not what Pythagoras himself used to calculate musical harmonies.) However, their examples sneakily use a technique that only resembles the Pythagorean theorem: “The Pythagorean method used by Dr. Puleo requires one to add all of the digits of a larger number together. For instance, the number 18 would become 9. But if the result is still a multi-digit number, the process is repeated. 184 is reduced to 13, which is reduced to 4.” Similarly,  the “Attuned Vibrations” website explains it thusly: “528 resolves to a 6, the icon for physical manifestation. That is, 5+2+8=15; and 1+5=6 (using Pythagorean math).” The actual Pythagorean theorem is a formula that can be variously permuted to figure out the measurements of a given triangle’s interior angles. Though they do add two numbers together, these example calculations have nothing to do with triangles, nor do they bother to square each variable. (They do, however, identify which sorts of numbers are reducible to 3, 6, or 9, which are numerologically significant.) The adding of two variables may resemble the standard expression of the Pythagorean theorem, but Pythagoras’s formula for calculating triangle angles is not what Puello & other believers use to calculate the solfeggio frequencies.