Judged simply as a number, 1.0594631... is hardly likely to set
the pulses racing. Yet it lies at the heart of that which
possesses this peculiar quality in abundance. I refer, of course,
to the twelfth root of two - the common ratio in the geometrical
progression that defines musicās Īchromatic scaleā.
It was Pythagoras (c600BC) who first realised that music is
essentially mathematical in nature - and derives from the mapping
of certain definite proportions onto the indefinite continuum of
musical pitch (itself a function of the frequency of vibration of
its source). Until the late sixteenth century, the so-called
Īnatural scaleā was the basis of all music, and the definite
proportions referred to were proper fractions like 9/8, 3/2, 4/3,
and so on. In effect, working with a keyboard without the Īblack
notesā it is little wonder that such Īmodalā music sounds strange
to the modern ear.
The development of a proper basis for harmony and modulation, and
for the freeing of melody from the bondage of the natural scale
required the frequency ratios between successive semitones to be
equalised. This was achieved by making slight adjustments (the
largest, a mere 0.9%) - to the frequencies occurring in the
natural scale. In this process, the 2:1 interval of the octave
was preserved. The result was the scale of Īequal temperamentā,
the familiar keyboard layout of twelve notes to the octave, and
the flowering of a new genre - typified by the music of Bach, Mozart and
Beethoven.
My purpose in painting this concise background is to draw the
readerās attention to some close links between these features of
music as it is practised today and the Creator, Jesus Christ, and
the Act of Creation. To demonstrate this, all we need is access
to a standard keyboard - or to a simple picture of one - and
proceed as follows:
1) Select any key toward the lower (left) end and mark it Ī1ā;
let us assume that the musical note associated with it has the
frequency Īfā.
2) Proceeding stepwise up the keyboard, mark the keys Ī2ā, Ī3ā,
and so on; we shall then find the octave above our starting point
numbered Ī13ā (there being 12 semitones to the octave) with an
associated note frequency, Ī2fā.
3) Continuing this process (and extending the keyboard in our
mindās eye, if necessary) we arrive at the following table of
coincidences:
Octave: 0 1 2 3 4 5 6 7
Frequency: f 2f 4f 8f 16f 32f 64f 128f
Key No (semitone): 1 13 25 37 49 61 73 85
Key Pair (tone): 1 7 13 19 25 31 37 43
Observe that at the 6th octave the group {64, 73, 37} appears. 6
is triangular and first perfect number, and the number of
creation days; the product 37x73 = 2701 - triangular number and
value of Genesis 1:1 (reading its 7 Hebrew words as numbers); the
product 37x64 = 2368 - value of ĪJesus Christā (from the NT
Greek).
Again, observe the situation at the 3rd octave. 3 is a
frequently used biblical number; the product 19x37 = 703 -
triangular number and value of the two Gen.1:1 words translated
Īand the earthā; the product 8x37 = 296 - value of the 7th word
of Gen.1:1, translated Īearthā, also factor of both name and
title of the Lord.
In an age in which consensus speculation masquerades as
scientific truth it needs to be firmly stated that no account of
origins that fails to find a satisfactory explanation for manās
interest in music can, or should, be regarded seriously. The
universality, variety, and intensity of this interest are proof
enough that music is much more than mere pastime: indeed, life
would be unthinkable without it, and its mysterious influence
seems to have its roots in the very bedrock of existence. Is man
Godās Special Creation, as the Bible maintains, or is he rather a
cosmological and biological accident? The answer now seems clear
enough!
Vernon Jenkins
http://www.compulink.co.uk/~indexer/miracla1.htm