Also, can you elucidate the origin of the numbers in the line headed
Key Pair (tone)? If these are meant to represent the natural notes,
then they should be in eights (C-D-E-F-G-A-B-C). If they represent
the whole tone scale (C-D-E-F#-G#-A#-C) then what is the relevance
or significance of grouping these scales like this? VERY little music
is based on the whole tone scale, after all.
I think you have presented nothing more than a mathematical coincidence
here, of very little relevance; and that this just goes to show that
you can find this sort of pattern in just about anything, if you try
hard enough.
/Gary
> The Music Lesson
>
> 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 music's 'chromatic scale'.
>
> 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
> 'natural scale' 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 'black
> notes' it is little wonder that such 'modal' 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 'equal temperament',
> 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
> reader's 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 '1';
> let us assume that the musical note associated with it has the
> frequency 'f'.
> 2) Proceeding stepwise up the keyboard, mark the keys '2', '3',
> and so on; we shall then find the octave above our starting point
> numbered '13' (there being 12 semitones to the octave) with an
> associated note frequency, '2f'.
> 3) Continuing this process (and extending the keyboard in our
> mind's 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 'Jesus Christ' (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
> 'and the earth'; the product 8x37 = 296 - value of the 7th word
> of Gen.1:1, translated 'earth', 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 man's
> 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
> God's 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
>
>