We would know nothing of music were it not that somewhere, between the ear and our perceptions, what we actually hear (the differences between different frequencies of sound, that is, different tones) is heard as equivalent musical intervals (such as fifths, thirds, tones, semitones, etc), of the same size, even when the pitch range of the tones are different. This is not how musical strings work, where intervals of the same size get smaller as the pitch at which tones occur, grows larger. On the frets of a guitar for instance, if one plays the same intervals in a different key, the same musical structure, melodic and harmonic, is perfectly transposed, but the frets are spaced differently.
The key is that human hearing is logarithmic and is based upon the number two {2}, the “first” interval of all, of doubling. This can only mean that the whole of the possibilities for music are integral to human nature. But this miraculous gift of music, in our very being, is rarely seen to be that but, rather, because of the ubiquity of music, especially in the modern world, the perception of music is not appreciated as, effectively, a spiritual gift.
Music is often received as a product like cheese, in that it is to be eaten but, to see how this cheese is made from milk requires us to see, from its appearance as a phenomenon, what music perception is made up of . Where does music come from?
Normally a part of musicology, that subject is full of logical ambiguities, confusing terminology, unresolved opinions, and so on. Those who don’t fully understand the role of number in making music work, concentrate on musical structures without seeing that numbers must be the only origin of music.
The ancient explanation of music was that everything comes out of the number one {1}, so that octaves appear with the number two {2/1}, fifths from three {3/2}, fourths from four {4/3}, thirds from five {5/4} and minor thirds from six {6/5}. Note that, (a) the interval names refer to the order of resulting note within an octave, (b) that intervals are whole number ratios differing by one and that, (c) the musical phenomenon comes out of one {1}, and not out of zero {0}, which is a non-number invented for base ten arithmetic where ten {10} is one ten and no units.
Another miracle appears, in that the ordinal numbers {1 2 3 4 5 6 7 8 9 etc.} naturally create, through their successiveness, all the larger intervals before the seventh number {1 2 3 4 5 6 7} leaving the next three {8 9 10} to create two types of tone {9/8 10/9} and a semitone {16/15} thereafter {11 12 13 14 15 16}: by avoiding all those numbers whose factors are not the first three primes {2 3 5}. Almost the whole potential of western music is therefore built out of the smallest numbers!
This simplicity in numbers has now been obscured, though the structure of music remains in the Equal Temperament form of tuning evolved in the last millennium. By having twelve equal semitones that sum to the number two, we can now transpose melodies between keys (of the keyboard) but we have pretty much lost the idea of scales. Instead, each key is the major diatonic {T T S T T T S} (where T = tone and S = semitone intervals) starting from a different key. The fifth is called dominant and fourth subdominant and the black notes (someway fiendish to learn) required to achieve the major key in all keys but C which is all white keys.
The old church scales are achievable by over ruling the clef with accidental notes, and the reason for different keys sounding different is that they contain aspects of what were the scales. So a pop song, for example, is usually in a scale. “Bus Stop” by the Hollies was in the Locrian scale.
Equal Temperament enabled the Western tradition to create its Classical repertoire but it has made ancient musical theory very distant and has abandoned the exact ratios it used to use since every semitone is identical and irrational. Plato described this kind of solution as the best compromise, where every social class of musical numbers has sacrificed some thing of their former self in order to achieve the riches versatility bestows upon modern musical composition.
To be continued.
