Equal Temperament
Please read the introduction first.
An equal temperament is a musical temperament, or a system of tuning, in which every pair of adjacent pitches is separated by the same interval. In other words, the pitches of an equal temperament can be produced by repeating a generating interval. Twelve tone equal temperament took hold for a variety of reasons. It conveniently fit the existing keyboard design, and permitted total harmonic freedom at the expense of just a little impurity in every interval.
Source: wikipedia.
Impact
This little impurity has a huge impact. We aren't happy to find out or admit that this is a fact and we're not the only ones. We love music just the way it is. We don't hear the impurity, so does it need our attention? Please continue, because the more you learn about this little fraction of dissonance, already recognized by Pythagoras, which he called 'the Comma', the more you realise what this means for our lives.
“The day science begins to study non-physical phenomena, it will make more progress in one decade than in all of the previous centuries of its existence.”
The passage below is taken from a valuable paper by Bo Constantinsen — What Music Really Is .com cited here with the author's permission. Italics by SOS.
"The effect of music on the ear is just the surface aspect of a much profound interaction between vibratory states of energy.
We are the physical manifestation of sound; every oscillating particle of our bodies moves according to the same harmonic laws found in music. These universal laws of energy, known for centuries to the mystics, have just recently been (re)discovered by modern science. Thus the vibratory harmony of natural music will resonate with the harmonic vibratory motion of our atomic structures, while equal temperament will induce dissonance.
Movement is harmonic when it repeats the same cycle in exactly the same time. Harmonic sound moves like waves of energy fitting perfectly into each other. In equal temperament harmonics never cycle, because this tuning's base is the twelfth root of two, replacing the harmonic progression of whole numbers from 1 to 12 with:
“If you want to find the secrets of the universe, think in terms of energy, frequency and vibration.”
1
2
2,9966141537534...
4
5,0396841995795...
5,9932283075067...
7,1271897451227...
8
8,9796963864750...
10,0793683991590...
10,6787188333603...
11,9864566150135...
These numbers are a close approximation to the natural harmonic series (built upon integer values), but cannot be found in nature. They do not define any other system, except this one. It grew out of the need of medieval musicians to “change key” and “transpose”, and was a convenient solution that facilitated the construction of musical instruments – thus it reflects the rigidity and limitations of Middle Age engineering.
Equal tempered music generates disharmony, because its waves of energy never meet and cannot support resonance. On a surface level, your mind enjoys the slight harmonic discrepancies tolerated by the ear – an ear which has been gradually accustomed to disregard these barely noticeable differences. But on a deeper level, your whole being is affected by the concealed dissonance, creating disruptive and nonharmonic states between your physical, mental and emotional bodies."
Continue with step 2: our web of relativity in the numeric realm of the 9-based tuning.