An Harmonograph figure for a rotating Pentagon representing a Musical-Fifth tone.
Greetings,
Can someone (like me) with two degrees in Mathematics, along three Universities, one in Venezuela and two in Italy, know not this sacred Truth ?
**Geometry is "Number in Space" and Music is "Number in Time" **
Yes, is possible! ... I did not ever wonder that Truth, but The Universe send to me ... yesterday ... and I Giovanni say, "Thanks, Universe!".
That True comes from the book, written by Miranda Lundy - Sacred Geometry, pag 22.
Now, I want you to read that page and then I will back with comments,
From the book of Miranda Lundy, "Sacred Geometry" ...
# The Shapes of Sounds
# and three quarters
Geometry is 'number in space', music is 'number in time'. The basic set of musical intervals is the elementary set of simple ratios, 1:1 (unison), 2:1 (the octave), 3:2 (the fifth), 4:3 (the fourth) and so on. The difference between the fourth and the fifth, which works out at 9:8, is the value of one whole tone. Musical intervals, like geometrical proportions, always involve two elements in a certain ratio: two string-lengths, two periods (lengths of time) or two frequencies (beats per length of time).
We can see harmonic musical intervals as geometrical shapes by swinging a pen in a circle at one speed, and a table in an circle at another speed (a harmonograph). Shown opposite are two patterns from near-perfect intervals where the pen and table swing circles in opposite directions. The octave (upper) fascinatingly draws as a triangular shape, the fifth (lower) as a pentagonal form.
Two octaves, 4:1, or a quarter, can be exactly defined by two triangles, four squares, or by a pentagon in a pentagram (below).
(This is the image below) ...
(This is the image regarding upper and lower)
Now my comments.
Most of the concepts, not all ... regards the Harmonograph.
These functions are circular parametric functions ...
Of course there are ... several books to speak about this sacred concept ... not only in Mathematics but also in Physics, yes in Physics.
It is clear that also after two degree in Math at both sides of Atlantic Ocean or thirty years studying Mathematics and Science ... most bridge between disciplines must be built.
Let me say, that both of my degree has a Missing Link ... "Music" ... Yes, Mathematicians must learn and study Music up to the level to play an instrument, like a Piano, and not only a guitar or a violin. I know is not simple and immediate ... but must be made.
The second point is How Geometry made define matter ... and therefore also the chemical reactions between the components that lead us to Matter as well the speed of electrons that may lead to temperature.
I will include a special chapter in my book, "An Introduction to Mathematics" about this sacred Truth,
Have a nice day,
Thanks,
Giovanni A. Orlando.
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