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Appendix E
Tuning Systems

 

There are 100’s of tuning systems, however there are only 3 main ones that are commonly used in the field of Sound Healing: Just Intonation (Just Tuning), Pythagorean (Ancient Egypt / Chinese) and Equal Tempered.

The whole subject of tuning systems gets really deep and mathematical very quickly. If you want to dive in to the math, you can go to the Wikipedia explanation of tuning systems. There is also a Yahoo group for Tuning Systems.

The reason it is important is that the ancient tuning systems are tuned to nature’s harmonic series instead of a construct of the mind like the Equal Tempered tuning system. Whenever using tuning forks, it is important they are not tuned to Equal Tempered tuning.

A tuning system is:

1. The number of notes in an Octave.

2. The frequency of each note in the Octave.

Number of Notes in an Octave
Nobody seems to know how we got 12 notes in our tuning system. I believe that it is more likely that someone got an inspiration from Source rather than actually figuring it out.

Here is an article I found on the web, that gives some possibilities:

Theory 1: Some have argued that the importance of the number 12 in music is thanks to the fact that the 12 equal tempered pitches approximate many simple ratios such as 4/3 or 5/4 very closely, but this surely isn’t the full story, since other numbers (such as 19 notes to the octave) are quite good at this too. Also, you can use progressively ever more complex ratios – thus theoretically producing an infinite amount of possible pitches (most of which do not approximate the 12 golden notes very well at all). Finally, there are even ‘rival’ ratios for certain intervals such as the minor seventh (which could be 9/5, 16/9, or 7/4). Actually, pure ratios in general are ideal for timbre (the basis behind the harmonic series), but I don’t think they should necessarily stretch to melody and chords.

Theory 2: Others have argued how successive powers of 3 will ‘complete’ the scale after 12 iterations (the basis behind Pythagorean tuning), but this can’t be the full story, since the twelfth iteration (312 or 3-12) – known infamously as the ‘wolf’ note – is a fraction over (or under) the octave. As a result, you could quite easily iterate further, and divide the octave nicely into 53 notes, 306 notes and beyond. Actually, even if 312 directly intersected the octave, this wouldn’t be 100% proof, but it would be a good sign of ‘mathematical evidence’.

Theory 3: Alternatively, the 12-note scale could just be an arbitrary cultural construct, with no special reason to choose 12 above 5 or 50 note scales.

Theory 4: It’s always a possibility that there may be no mathematical explanation why there are 12 notes. In the same way that science can’t explain what it ‘feels’ like to see the color ‘red’, perhaps the notes of the scale are beyond mathematics, and reach into the metaphysical or spiritual realm.

Theory 5: A neat honeycomb lattice appears to fit around the major/minor 12 note system. This seems an interesting coincidence until you realize a similar pattern can be achieved with the 16 note scale and beyond. There still might be something unique about the 12-lattice though.

Theory 6: You can surround a single sphere perfectly with 12 identically sized spheres – with each sphere perfectly touching its neighboring spheres (this forms the points of the cub octahedron, or the faces of its dual – the ‘rhombic dodecahedron’). Twelve also has the exclusive property of being the Gravitational Symmetry Limit – another sphere arrangement based on the icosahedron. While we’re in geometrical territory, there also appears to be an interesting relation to the 4 dimensional 24-cell.

Theory 7: A number of curious relationships exist between simple ratios and 12. For example, 37/213 * 5 is very close to the equal tempered perfect fourth (1.000000739402 off).

Theory 8: According to Schoenberg (who promoted the idea of atonal 12-tone style music), there are 12 notes because if you take the sum of its digits: 1 and 2, they make 3.

 

Frequency of Each Note in the Octave

Just Intonation
The easiest way to explain how the frequencies of Just Intonation are found is to simply play the harmonics on one string. If you lightly touch a string to divide it into 1/2, 1/3 and 2/3, 1/4 and 3/4, 1/5 and 4/5, and so forth you get each of the harmonics. You then tune the rest of the strings to these harmonics. It’s that simple.

On a guitar you would actually have to move the frets to be able to tune the guitar to these ancient tunings.

Here is a more detailed way of explaining it. Take a look at the chart at the bottom of the page.

Remember that a tuning system is the frequency of each note in the octave. We are using the harmonic series as the raw material to create the frequencies within one octave. Once we have one octave figured out, we can just double it or halve it to get the rest of the octaves.

The column labeled Just Intonation is simply the harmonic series (1x, 2x, 3x, 4x, etc.) based on A440. We then find the notes needed to create the tuning system (in color in the Just Intonation column). However, they are two high of a frequency to fit within the octave so we Octavize them down (1/2, 1/2, 1/2, etc.) until they fit within the one octave (far left column). When you do half the frequency it is still the same note.

Again, we are using the Harmonic Series as the raw material to create each of the frequencies within one octave.

Pythagorean Tuning
The only difference with the Pythagorean tuning system is that we are only using the Musical 5ths within the harmonic series as the raw material. Using only the 5ths creates a little more harmonious tuning system to our ear. Note that we have only shown the first 4 notes of the circle of 5ths (C, G, D, A). We would have to continue up much higher to get the rest of the 5ths to use in creating the one octave.

Equal Tempered Tuning
Equal tempered in tuning divides the Octave into 12 notes that are equal distance from each other. Again, this allows us to go from key to key without dissonance. However, it detunes us from the natural harmonic series of nature, which includes the distance between the planets, the distance of electron shells around the nucleus of an atom, and the weight of each vertebrae in our back, and possible the auras and chakras. There is not a bird on the planet that sings in Equal Tempered Tuning.

Just about all music on the radio is in Equal Tempered tuning. Symphonies that play without a piano or xylophone naturally tune to Just Intonation. Also, accapella sing groups, sing in just intonation.