Tuesday, December 28, 2010

Measure and Half Measures

Pythagoras, the man in the center with the book, teaching music, in The School of Athens by Raphael
Most of  you will recognize the partial image of the much larger I have used as the heading of this blog.

The Greek Pythagoras, for instance, was able to use abstract but simple mathematics to describe a natural phenomenon very precisely. He discovered the fractions that govern the harmonious musical notes. For example, a stretched string on a violin that produces a C note when you strike it, will give a C an octave higher when you divide its length by two. (Similarly, when we cut of a quarter of the length of the original string, the new string will sound like an E note) This is a famous early example of the use of mathematics to describe a physical phenomenon accurately. Pythagoras used the mathematics of fractions to describe the frequency of musical notes. In the ages that followed, of Galilei, Kepler, Newton and Einstein, mathematics became the prime language to depict nature. The mathematics of numbers, sets, functions, surfaces et cetera turned out to be the most useful tool for those people that felt the urge to understand the laws governing nature. See: Beyond String Theory-Introduction-Natural Language

However esoteric the following may seem to you, I was always enchanted with the idea of sound  as a manifestation of the world we live in, or, as color,  as a meaningful expression of the nature of the world we live in. Not really the artist of sound and color, but much more the artist in conceptual makings of the relation of the world with such ideas, hence, the idea of "Color of gravity."

Hence my interest in gravity, and what we as human beings can gather around our selves, in the ever quest for understanding the consequences of our causal relations to the events that follow us in the making of the reality we live.

The future consequences of probabilistic outcomes according to those positions adopted....can we say indeed that we are predictors of our futures and that at some level this predictability is a far reaching effect of understanding our choices and positions in life? We know this deep down within ourselves, "so as we think" we may become some "ball bouncing on the ocean of life?" Emotive consequences, without recourse to our choosing to excel from the primitive natures of our being in the moment?

Major scale

In music theory, the major scale or Ionian scale is one of the diatonic scales. It is made up of seven distinct notes, plus an eighth which duplicates the first an octavesolfege these notes correspond to the syllables "Do, Re, Mi, Fa, Sol, La, Ti/Si, (Do)", the "Do" in the parenthesis at the end being the octave of the root. The simplest major scale to write or play on the piano is C major, the only major scale not to require sharps or flats, using only the white keys on the piano keyboard:

Could we every conceive of the human being as being one full Octave? I thought so as I read, and such comparisons however esoterically contrived by association I found examples to such "predictable outcomes" as ever wanting to be "divined by principle by such choices we can make."  However unassociated these connections may seem.

I mean,  if one was a student of esoteric traditions and philosophies, it might have been "as traveling through a span and phase of one's life time"  leads us to the issues where we sit,  where we are at,  in the presences of the sciences today. We demanded accountability of ourselves in  that presence within the world as to being responsible and true to ourselves on this quest for understanding.

So if I had ever given the comment as to some iconic symbol as the Seal of Solomon, not just on the context of any secular religion as ownership, it is with the idea that representation could have enshrine the relationship between what exists as a "trinity of the above"  with that of "the below,"  when we are centered as to choice being the position with that of the heart.

See also:New Synesthete Character on Heroes

It was with this understanding that the full Octave could be entranced as too, resonances in the human being, that we could be raised and raise ourselves from such a position, so as to be freed from our emotive and ancient predicaments arising from evolutionary states of beings of the past.


Monochord is a one-stringed instrument with movable bridges, used for measuring intervals. The first monochord is attributed to Pythagoras. 

The story is told that Pythagoras wished to invent an instrument to help the ear measure sounds the same way as a ruler or compass helps the eye to measure space or a scale to measure weights. As he was thinking these thoughts, he passed by a blacksmith's shop. By a happy chance, he heard the iron hammers striking the anvil. The sounds he heard were all consonant to each other, in all combinations but one. He heard three concords, the diaspason (octave), the diapente (fifth), and the diatessaron (fourth). But between the diatessaron (fourth) and the diapente (fifth), he found a discord (second). This interval he found useful to make up the diapason (octave). Believing this happy discovery came to him from God, he hastened into the shop and, by experimenting a bit, found that the difference in sounds were determined by the weight of the hammers and not the force of the blows. He then took the weight of the hammers and went straight home. When he arrived home, he tied strings from the beams of his room. After that, he proceeded to hang weights from the strings equal to the weights he found in the smithy's shop. Setting the strings into vibration, he discovered the intervals of the octave, fifth and fourth. He then transferred that idea into an instrument with pegs, a string and bridges. The monochord was the very instrument he had dreamed of inventing.
See: String Instruments including Oud, Folk Fiddle, and Monochord, dan bau, from Carousel Publications Ltd

So what is the theory, then?
Pythagoras could be called the first known string theorist. Pythagoras, an excellent lyre player, figured out the first known string physics -- the harmonic relationship. Pythagoras realized that vibrating Lyre strings of equal tensions but different lengths would produce harmonious notesratio of the lengths of the two strings were a whole number. (i.e. middle C and high C) if the

   Pythagoras discovered this by looking and listening. Today that information is more precisely encoded into mathematics, namely the wave equation for a string with a tension T and a mass per unit length m. If the string is described in coordinates as in the drawing below, where x is the distance along the string and y is the height of the string, as the string oscillates in time t, 

See: Official String Theory Web Site

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Tyler Dresden said...
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