The Universal Pattern and It’s Correlation to Musical Harmony
For some 25 years I have observed the accuracy of this pattern. For me, the question of why it works has been a burning one. My search for an answer has carried me in a lot of different directions. One of the most fruitful has been in seeing the analogy between the “rules” of this pattern and mathematical rules governing musical harmony. In modern western music, their can be said to be two primary scales that are utilized most universally, the 12 tone chromatic scale and the 7 tone diatonic.
In exploring the mathematical “whys” of the chromatic and diatonic scale, and their relationship to each other, I found an exact correlation or analogy, if you will, for the universal pattern of human growth that I have observed over these many years. This was a revelation to me, not having had any formal training in music or music theory.
As I continued my search I found that this discovery of a correlation between the laws of musical harmony and a set of observations about how a holistic system works is a very ancient one, and hardly unique to me. To state this another way, one of the earliest observations that man made about his world, and what you might term (as others have) the beginnings of science, was that the rules or mathematical laws governing musical harmony correlate with laws governing physical reality. In other words, the laws of harmony in what can be heard correlate to the laws of harmony in what can be seen or observed. This insight has driven the development of science from its earliest beginnings, and it is my assertion that it continues to do so.
Before moving to examples of how this paradigm has been at the core of science from ancient times, I want to show the correlation between the pattern of growth I have outlined in this web site and musical harmony. The following explanation is of course somewhat simplified in its musical theory, but serves the purpose. The dictionary definition of harmony is:
1. Agreement in feeling or opinion; accord
2. A pleasing combination of elements in a whole
In music this refers to how two notes or tones sound together, and the development of all the possible notes/tones that sounded well with a “neighboring” note/tone within the most basic “consonance” of an octave produced the scales referred to earlier. The octave in music is actually a ratio of frequency between two notes. The ratio is 1:2. This ratio is considered to be the most consonant or “harmonious” of all. The octave cosonance was recognized by many ancient civilizations as a basic construct and is why two notes/tones with this frequency ratio are considered the same note but an octave higher or lower in “the scale”.(3) The next ratio that produced the next most consonant or harmonious sound was 2:3 or 3:2, in musical terminology the ratio of the fifth. (Dont become confused with the terminology, as it is secondary). All the other primary scales, including the diatonic (7 tone) and chromatic (12 tone) were developed historically so that their notes/tones related to the frequency of the fundamental or beginning tone by the smallest possible interger ratios that would produce the most consonant sounds. These were 3/2 ,4/3, 5/3, 5/4, 6/5. Thus the scales in use today grew directly out of a long history, a very ancient history of exploration of the mathematical/auditory relationships between different tones based on these number ratios.
Consonance is a basic concept in music and is similar to harmony, in other words, tones that sound well together. As John Pierce stated: “It is these experiences of consonance and dissonance that underlie the evolution of the musical theory of harmony.”(19) In exploring what is perceived by the human ear as consonant or dissonant, John Pierce concludes that though custom and rules developed over millennia presently define what is and what isn’t consonant, these customs and rules “are based on experiences of consonance and dissonance that are inherent in normal hearing.” In music it is universally accepted that notes/tones that are most consonant together are those “whose fundamental frequencies have integer ratios, such as 3:2, 4:3, 5:4, 5:3, 6:5.” As John Pierce further states: “In a very real sense, perfect intervals, whose frequencies ratios are the ratios of small integers, are the very foundation of music. These intervals derive from the harmonics present in musical tones. They are important to the human ear.”(19)
In the observation of the existence and universality of the 7 tone diatonic and 12 tone chromatic scale, and in the exploration of the relationship between the two scales, I intuited that I might be on to some of the “whyness” for the universal pattern of growth I had uncovered. The rational for these scales lie in the fact they were built up from the most consonant ratios of frequencies, and this lies in the nature of what is perceived as harmonious by the ear. You cannot “fool” around with these “ratio laws” and have music still sound harmonious. So these scales take on an order of “law”, akin to a basic principal. As John Pierce concludes about the diatonic scale : “If either the diatonic scale or the harmonic partials essential to it is slightly tampered with, overall music or consonant effect is destroyed.”(19)
Now in looking at the correlation between these two scales , the diatonic and the chromatic, and the universal pattern of growth that I have outlined, the primary feature of this pattern of growth is that it consists of a seven year cycle of 12 phases, each of which consist of 7 months with their own unique lesson and characteristic flavor. The most obvious first thing to notice about musical harmony is that there does exist the two scales in music, the diatonic with 7 tones and the chromatic, with 12 tones, both of which are related to each other in a fashion that is very similar to the way the 12 phases relate to the 7 year cycle. This relationship in music is illustrated by what is referred to as the “cycle of fifths”. As we have said, the next most perfectly harmonious ratio that can exist between two tones after the octave ratio of 2:1, is 3:2. In multiplying this ratio, represented as 1.5, times a frequency of a fundamental tone, such as a “c” with a frequency of 16, we will return to a “c” of frequency 2076 seven octaves higher. In other words, we have 12 tones within 7 octaves, correlating in our growth pattern to having 12 phases within 7 years. In addition, each of the 7 octaves has 12 notes, corresponding to having 12 months during a year within each of the 7 years. Obvious arithmetic, but deserved of mention. (Actually, the frequency of 2076 overshoots exactly 7 octaves higher, which would have been a frequency of 2048. The amount that is overshot or the difference between these two frequencies is known as the “pythagorean comma” and was dealt with in music through the adoption of different tuning systems. As we will see, instead of this spoiling the idea that there is a correlation between music and this universal pattern of growth, it actually reinforces it.)
In summary, in finding that these two scales that are so fundamental to the development of musical harmony and their relationship to each other could serve as analogy for the universal pattern I had uncovered, I was spurred on to find other correlation’s between this “pattern of scales and harmony” and other systems of “knowledge” that man has developed. The following are some of these ‘findings’.