The 3-6-9 algorithm is a mathematical formula attributed to Nikola Tesla that suggests the existence of a universal pattern of energy that governs the universe.

In the context of solfeggio frequencies, the 3-6-9 algorithm is often used as a way to derive the frequencies of the main Solfeggio tones. Here’s how it works:

1. Start with the frequency of 3 Hz.

2. Multiply 3 by 2 to get 6 Hz.

3. Multiply 6 by 2 to get 12 Hz, but then reduce the sum of the digits (1+2) to get 3 Hz again.

4. Multiply 12 by 2 to get 24 Hz, but then reduce the sum of the digits (2+4) to get 6 Hz again.

5. Multiply 24 by 2 to get 48 Hz, but then reduce the sum of the digits (4+8) to get 3 Hz again.

6. Repeat the pattern: 96 Hz (9+6=15, 1+5=6), 192 Hz (1+9+2=12, 1+2=3), 384 Hz (3+8+4=15, 1+5=6), and so on.

Using this algorithm, we can derive the frequencies of the Solfeggio tones as follows:

- 174 Hz (3×58)
- 285 Hz (6×47.5)
- 396 Hz (9×44)
- 417 Hz (3×139)
- 528 Hz (6×88)
- 639 Hz (9×71)
- 741 Hz (3×247)
- 852 Hz (6×142)
- 963 Hz (9×107)

It’s worth noting that not all of these frequencies are universally accepted as the “correct” frequencies for the Solfeggio tones. Some practitioners use slightly different frequencies for some of the tones, and there is ongoing debate and research about the origins and effects of the Solfeggio frequencies.