**The Sine/Triangle Phi Wave**

One of the most fundamental ways that harmonic law manifests in reality is via the Golden Ratio…a relationship that’s fundamental to the way things grow and maintain balance and symmetry in structure. Pythagoras thought that mathematics and music were interchangeable expressions of the same divine language. Linked closely to the Fibonacci mathematical sequence, the golden ratio reveals the harmony in patterns between related parts of structures like buildings or facial features and even the distance ratios between the planets.

The Golden Ratio, also known as Phi, is a sacred and divine mathematical relationship (ratio) that is found all over nature in plants, flowers, humans, trees, coast lines mountains and in the architecture of building. The Greeks were able to utilize Phi to create the ideal acoustical environment because it minimizes acoustic resonance and imparts a unique musical quality to the listening environment based on its wave shape. Phi has also been found to provide superior acoustics in speaker wire and studio design It’s even used to project market swings based on investor psychology. This sacred geometry appears many times and in many different forms to remind us of our unity, wholeness and connection to the universe, reality and the circle of life.

The Fibonacci sequence leads to the golden ratio. The sequence is given by starting with 0 and adding the next number to the previous. The sequence then is 0,1,1,2,3,5,8,13,21,34….When you divide the larger digit by the former smaller digit, it approximates 1.618…the golden ratio or Phi as the ancient Greeks called it.

The Golden Ratio also plays heavily into the sound and music healing fields where it’s used to balance the autonomic nervous system. Listening to resonant sounds, moving in specific patterns or harmonizing with the voice while using tuning forks, crystal bowls, frequency generators and sacred geometry balances the body and aligns it with the brain for a calmer and more productive state of mind.

The time domain consists of frequency, magnitude, phase and wave shape. Waveshape is the most basic element of vibration before it becomes projected through a medium like air and manifests as sound. The listening environment shapes the wave without changing any of the frequencies. So, it’s possible, with the right amplitude adjustments to change the shape of any complex frequency without interfering with its spectral signature.

The only waveshape that conforms to the golden ratio of Phi is a triangle wave shifted 90˚ out of phase back to a spherical-like wave as shown below as a fundamental of 1 Hz. Combined with 5 of its first odd overtone harmonics (1-3-5-7-9-11).

A more accurate representative of this waveform can be made with the Sensorium™ LSV III Sensory Interface. Starting with any fundamental frequency or mode and adding at least five of its odd overtones will create this waveshape.

Starting with any fundamental frequency or mode and adding at least five of its odd overtones will create this waveshape. Extracting a person’s fundamental frequency and converting it to this waveshape is the equivalent of creating a personalized golden ratio wave that can potentially effect true and lasting positive change.

The image above shows a complex waveform of a human voice. The true fundamental frequency is determined for each word spoken and transferred to the Tone Bank of a Sensorium LSV III or IV. Then the magnitudes of its harmonics are adjusted to those of the golden ratio wave. Sound, music and color therapists can utilize this wave in their sessions to bring about the harmony invested in the **Golden Ratio**.