Fibonacci and the Golden Mean
What is the Golden Ratio?
The Golden Ratio is a unique number, approximately 1.618033989. It is also known as the Divine Ratio, the Golden Mean, the Golden Number, and the Golden Section. Its unique mathematical properties have resulted in a very long and influential history.
What is the Fibonacci Sequence of Numbers?
The Fibonacci numbers are a unique sequence of integers, starting with 1, where each element is the sum of the two previous numbers. For example: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, etc.
Relationship Between the Fibonacci Sequence and the Golden Ratio
The Fibonacci Sequence is an infinite sequence, which means it goes on for ever, and as it develops, the ratio of the consecutive terms converges (becomes closer) to the Golden Ratio, ~1.618. For example, to find the ratio of any two successive numbers, take the latter number and divide by the former. So, we will have: 1/1=1, 2/1=2, 3/2=1.5, 5/3=1.66, 8/5=1.6, 13/8=1.625, 21/13=1.615, 34/21=1.619
• Hold your tuning forks by the stems with moderate pressure, not to tight and not to loose. Do not hold your tuning forks by the prongs because the prongs need to vibrate in order to create a sound.
• Gently tap the flat side of the tuning fork on your knee cap. Do not hit your knee cap. All it takes is a gentle firm tap and your tuning fork will sound. It is best to tap the 1/1 Fibonacci Tuner on the knee and then the interval you want to explore on the other knee.
• Bring the forks slowly to your ears, about three to six inches from your ear canal, and listen to the sounds.
• The second way to sound the Fibonacci tuning forks is to tap them together. This method is to be used off the body. It is not to be used directly in the ears.
• Hold them by the stems and tap them together on their edges, not the flat side of the prongs. You do not have to use a lot of force to get the result and play with creating an easy sounding tap vs. a banging tap when too much force is used.
• When you tap them together the tuning forks will make sounds we call overtones. Move the tuning forks around, slow and fast, in the air and listen to the different tones as they get louder and softer.
• For practice, take the 2/3, 5/8, and 13/21 Fibonacci Tuners hold them in your left hand. Place the stems between your fingers. Allow them to stick out in different directions so that they do not touch. Hold the 1/1 tuning fork between your thumb and first finger in your right hand. Tap the three Fibonacci Tuners with the 1/1 tuning fork.
• Move the tuning forks around slow and fast and listen to the different overtones. Move them around and move the 1/1 tuning fork in circles underneath the 2/3, 5/8, and 13/21 tuning forks. The movement of the 1/1 tuning fork will bring out different overtones.
Our thanks to John Beaulieu of BioSonics for sharing this information and techniques.
Alternate Realities and the Fibonacci Tuners
- When we listen to the Fibonacci Tuners, like children going inside a seashell, we naturally seek out alternate realities within the sound.
- Each alternate reality is a location within a spiral revolving around a central vortex of stillness which connects with the Universal Energy Field.
- In many instances it may be more effective to work in an alternate reality to effect healing then in normal reality.
- This is no different than a psychotherapist using dreams or a reflexologist pressing points on the feet, hand, or ear to effect healing within the whole body.
- In cases of trauma and addiction people often times disassociate into alternate realities.
- The Fibonacci Tuners create a bridge between these realities which can promote a healing response.