This blog series draws from the work and calculations discovered and laid out by Hans Cousto in his seminal 1978 tome "The Cosmic Octave." If you find the info below to be resonant with you, we highly encourage you to purchase his book wherever you can find it...
Here's a fast link if you can't wait. The Cosmic Octave by Hans Cousto
Merci beaucoup, Hans Cousto!
In 1978, Swiss mathematician and musicologist Hans Cousto released his groundbreaking work, The Cosmic Octave. With it, he shared a formula to calculate the relative audible frequencies of the planets, colors, and other natural phenomena as they relate to the Law of Octaves in music. This work has since allowed instrument-makers to explore the audible frequencies of other stellar bodies as well, such as asteroids, planetoids, stars, and more.
Using this universal language of the cosmos, we can to tap into the energetic power of the planets, weather, visible light colors, and more, harnessing powerful healing energies for sound baths and musical compositions, aligning our creative efforts with the divine rhythms of the cosmos.
If you've had the joy and wonder of playing a Planetary Tuned Gong or other instrument, you have experienced this divine, cosmic math at work. Maybe you've felt the fundamental tone and the harmonics of the planet Mercury zip-zap-zopping through you at 141.27 cycles per second (Hz), or maybe you want to understand how the color Red relates to the note F#, creating a composition in the key of Red.
In this first part to this blog series I'll briefly break down the concept of the Cosmic Octave. In the next installment of this series, I'll explore the actual calculations and lay out the different musical and planetary correspondences along with examples of some of the cosmic instruments we offer (so after you read below, check back later for more on this topic).
The Cosmic Octave uses the natural musical phenomenon of Harmonics as its basis. Harmonics mark the relationship between a fundamental tone (the root note) and its overtones, where the wavelength of the overtone is a whole number multiple of the fundamental tone's wavelength.
Example - If the fundamental wavelength is 1 (a single peak and trough), and one of its harmonic overtone wavelengths is 4 (four peaks and troughs), that overtone is the 4th harmonic, a ratio of 1:4. In this case, this particular ratio also corresponds to the 2nd octave of the original note.
This diagram shows the Law of the Octave and the relationships between the fundamental octave tone (1:1), the 1st octave (1:2), the 2nd octave (1:4) and the 3rd octave (1:8).
Between fundamental and harmonic octaves are what are called intervals. Intervals are the notes in a major or minor scale that correspond to a harmonic relationship with the fundamental tone. These harmonic intervals are divided evenly by 64 Hz (cycles or wavelengths per second).
(Note: There are tones in each scale which are not harmonic, but they are still within the scale. These notes represent a dissonant timbre and relationship to the fundamental note. For this discussion however, we're only covering harmonic intervals, which represent a consonant timbre and experience).
A single harmonic octave represents a doubling of the frequency of the prior octave. In musical notation, for example, this represents the distance between one C on a piano to the next C on a piano.
So if the fundamental note we're playing is C at 64 Hz, the next interval is a C at 128 Hz. This is double the fundamental, so it is also the First Octave (representing a 1:2 relationship to the fundamental frequency).
The next interval after 128 Hz is another 64 Hz higher, so 192 Hz. This is NOT the double of the prior octave, so it is actually just a harmonic interval, not an octave. It represents a 1:3 relationship. One wavelength at 64 Hz will fit THREE wavelengths inside of it at 192 Hz, which is why it is a harmonic THIRD.
The next interval after 192 Hz is 256 Hz. 256 Hz IS the double of 128 Hz (the prior octave), so it represents the C in the Second Octave (and a 1:4 relationship to the fundamental frequency of 64 Hz, with FOUR wavelengths at 256 Hz fitting inside of ONE at 64 Hz).
This pattern continues, outlining all of the octaves in the audible range, as well as the Major Thirds, Natural Sevenths, and other harmonic intervals and relationships to the fundamental note of C at 64 Hz.
This chart shows the relationships between the fundamental tone and all of the harmonic intervals through the 4th octave.
The most important relationship to understand within this context is that of the Octave, the relationship between a fundamental tone and the repeated doubling (or halving) of that tone to find the higher or lower octaves. Look at the table above to assimilate that math and concept.
The other partial intervals (Fifth, Major Third, etc.) are not as important in terms of understanding how the calculations work when finding the “audible frequencies” of planets and other natural phenomena, though they are relevant to a deeper understanding of music theory, consonance, dissonance, and harmonics.
If you are new to this, grab onto this basic concept: Octaves represent a doubling at each level. So on a piano, the distance between each C and the next C has an exponential jump in frequency by a power of 2. (64 Hz, 128 Hz, 256 Hz, 512 Hz, 1024 Hz, etc.) as visualized by the chart below.
Using the Law of Octaves and the understanding of intervals laid out here, we can begin to look at each of the calculations that take us from an inaudible frequency (like the orbit of Mercury Mars, or the Moon) and convert them into frequencies we can hear, and thus, notes we can create on musical instruments, like a gong or sound plate or chime and thus be able to utilize them in cosmic compositions and sound healing.
In our next post in this series, we're going to get into a little bit of a philosophical discussion about energy and information. We'll explore the intricacies and differences between physical, grounded, quantitative information and emotive, virtual, qualitative information. And we'll see how these concepts relate to the use of symbols in sound healing and therapy.