RainmanTime I will post some links, and information on a variety of these subjects here, so that we can share them with others whom may also find them of interest.
*Unitel Inc., (Our Partner)
Unitel Inc., is a technology development company that owns a generic patent with ten (10) claims both in the US (No. 4,817,102, March 28, 1989) and in Japan (No.1,864,717, August 8, 1994), with patents approved but not yet received in Austria, Belgium, France, Germany, Italy, Korea, Luxembourg, the Netherlands, Sweden and the United Kingdom (No. 89906639.3, September 11, 1990) on a system with multiple applications. This generic quantum electronics system design applications include computing and aerospace propulsion. Unitel is prepared to build a prototype quantum computer system entitled HOLO-1. HOLO-1 uses a specially designed crystal laser lens to store, retrieve, and process data using light instead of electricity. Former URL's - [
http://www.unitelnw.com ] - [
http://www.unitedmusiccorp.com/unitelnw]
http://www.unitel-aerospace.com
*Diatonics & Fibonocci Sequnces
**** DIATONICS! ****
Preface:
The diatonic scale in just intonation
The prominent notes of a given scale are tuned so that the ratios of their frequencies are comprised of relatively small integers. For example, in the key of G major, the ratio of the frequencies of the notes G
is 2:3, while that of G:C is 3:4. All ratios that involve the prime numbers of 2, 3 and 5 can be built out of the following 3 basic intervals:
http://en.wikipedia.org/wiki/Just_intonation
DIATONIC RATIOS
Notes in music are related to each other by specific ratios. These ratios determine the 'space' between each tone, and in turn define the notes. Although to the human ear the notes sound as if they are equally spaced, the following chart shows that in fact the ratios are more complex. For example, the ratio between C and D is 9/8:
What is the probability of this happening by chance?
With 26 letters in the alphabet there are 1/2 x26 x27 possible pairs of initials, AA, AB, AC etc. So the probability of any one random pair hitting any one of the 25 names on the list is 25/ (1/2 x26 x 27) = 0.071. There are 9 geometries with 9 hits. By Bernoulli's binomial theorem the probability is a siqnificant 1.7 billion-to-one in favour.
Interestingly enough, Littlebury Green <hawkinsb.html> gives by what we could call "mathematical art," one more name on the list Myers, a fouader of the Society and pioneer in telepathy.
The correlation is statistically compelling, with a confidence level much higher than 99.9%. Strict criteria have been used, with all available geometries included up to the date of publication of the code. Eight others are listed in the Andrews catalog but with no survey or photo data. Even assuming the worst case (i.e. that none of these would fit, making 9 hits in 17 tries) the odds remain a million-to-one in favor. What does this result mean? Skeptically one could say that a secret group of hoaxers knew of the list and decided to memorialize these famous pioneers of the paranormal in the fields of England.
Yet, as it stands, the list could be the target for confirming that a Paranormal code has indeed been received as suggested by R. Thouless, a later SPR president. (JSPR Vol.38, No.686, p.172, 1955.)
http://www.lovely.clara.net/crop_circles_diatonics.html
Diatonic Ratios and Crop Circles
In 1967 the scientist Hans Jenny used different substances to observe the patterns that sound vibrations made in the substances. By doing this he could use film to capture the exact shape that sound makes when traveling through the substances. Once he had a picture of sound, he could compare the picture that his sounds made to that of the shape of Crop Circles and found startling similarities.
The theorems that Dr. Hawkins had come up with also made diatonic ratios, so the first implications of the connection was formed. When the formation shown below was found it lead to the undeniable connection.
This formation, discovered in 1996, provided a combination of the two most important shapes in creating diatonic ratios, the 3,4,5 triangle and the Golden Mean.
http://my.inil.com/~wall5/diatonic%20ratios.html
Diatonic Ratios and Harmonic Geometries
One of the first researchers to point out links with musical scales was Gerald Hawkings, a retired professor of astronomy at Boston University. Having worked at the Harvard-Smithsonian Observatory in the 1960's, he had already done much research on the astronomical importance of Stonehenge. After earning a subsidiary degree in Pure Mathematics from London University he analysed aerial photographs and ground surveys of crop circles and was surprised to spot a clue to their possible origins - lying in the ratios of musical notes.
If we examine the exact frequency of the white notes on a piano we will find that, with perfect tuning, the note middle C has a pitch of 264Hz (vibrations per second). If we play the C note in the octave above (C') we will find that the frequency is 528Hz. This is exactly double, giving a ratio of 2:1.
If we now examine every note in the major scale we will find an elegant, yet exact, diatonic ratio - shown in the diagram below.
http://home.wanadoo.nl/mufooz/cropcircles/Crop-Sound.htm
Definitions of tuning terms
Diatonic
[Greek: "thru tones"]
1. diatonic scale: An adjective referring to a scale composed of five tones and two semitones <semi.htm>, such as the Pythagorean <pythag.htm> diatonic or the familiar 12-tone <12-eq.htm> version.
See Diatonon <diatonon.htm>
[from John Chalmers <../chalmers/chalmers.htm>, Divisions of the Tetrachord] (The latter is also referred to as a '7oo12' or '7-out-of-12' scale.)
2. diatonic genus: In ancient Greek theory, one of the three basic types of <genus.htm>. It had a characteristic interval <ci.htm> of approximately a "<tone.htm>" at the top of the tetrachord <tetrachd.htm>, then two successive intervals of approximately a "tone" and then a semitone <semi.htm> at the bottom, making up a 4/3 "perfect 4th <p4.htm>". [see my Tutorial on ancient Greek tetrachord-theory <../monzo/aristoxenus/tutorial.htm>]
Below is a graph showing the comparative structures of tetrachords for the diatonic genus as explained by various ancient theorists:
http://sonic-arts.org/dict/diatonic.htm
A diatonic scale consists of three sets of major triads <MajorTriad.html>. Major triads <MajorTriad.html> are collections of three notes with frequencies in the ratio 4:5:6. Within an octave <Octave.html>, three major triads <MajorTriad.html> can be constructed as follows.
There are three intervals in this scale 9:8 (1.125), 10:9 (1.111), and 16:15 (1.067). The first two are called whole steps <WholeStep.html> and the third a half step <HalfStep.html> (or semitone <Semitone.html>
, even though two half steps <HalfStep.html> are larger than one whole step <WholeStep.html>.
The diatonic scale is of ancient origin, but the particular tuning incorporated into modern just intonation <JustIntonation.html> (see below) is due to Ptolemy <
http://www.treasure-troves.com/bios/Ptolemy.html>, and probably dates from the second century A.D. Ptolemy <
http://www.treasure-troves.com/bios/Ptolemy.html> gave it as one of a dozen or so possible tunings for the diatonic scale (calling it the "syntonic diatonic"). It was rediscovered by Gaffurio in the late 15th century, from whom Zarlino learned about it, and it has remained the basic scale used in western music ever since (Jeans 1938, p. 164). In particular, all of the church modes (dorian <DorianMode.html>, phrygian <PhrygianMode.html>, lydian <LydianMode.html>, myxolydian <MyxolydianMode.html>, and aeolian <AeolianMode.html>
are rotations of the so-called major scale <MajorScale.html> are diatonic.
http://www.ericweisstein.com/encyclopedias/music/DiatonicScale.html
A Pythagorean tuning of the diatonic scale [A tuning system based on the line of fifths]
It is said that the Greek philosopher and religious teacher Pythagoras (c. 550 BC) created a seven-tone scale from a series of consecutive 3:2 perfect fifths. The Pythagorean cult's preference for proportions involving whole numbers is evident in this scale's construction, as all of its tones may be derived from interval frequency ratios based on the first three counting numbers: 1, 2, and 3. This scale has historically been referred to as the Pythagorean scale, however, from the point of view of modern tuning theory, it is perhaps convenient to think of it as an alternative tuning system for our modern diatonic scale.
The white keys on a piano form a diatonic scale. One of the most important characteristics of this diatonic scale is that the octave is partitioned into adjacent intervals of the following type and quantities: five whole-steps and two half-steps arranged in the assymetrical pattern
http://www.music.sc.edu/fs/bain/atmi02/pst
Electrons and Musical Scales
The "Electron-matrix" Theory.
Found on 5/10/01.
(Note: This is a discussion of a 2D plane of musical notes wrapped into, not a 3D, but a 4D-torus with its implications of the electron not being in the 3rd dimension, in the form of the pentatonic 5 note and diatonic 7 note scales. Incorporating the ratio Phi, recursion and embedding, it begins to imply, to me, how the structure of the electron relates to music. Perhaps you can see it.)
From the Author: Andrew Duncan
<a href="mailto:
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[email protected]</a>
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[email protected]">
[email protected]">
[email protected]</a>
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[email protected]</a>
http://rgrace.org/100/100electronscales.html
Fibonacci Series and Music- 5, 7, 19, 31 notes
http://www.bikexprt.com/tunings/fibonaci.htm
Theorems in Wheat Fields - Ivars Peterson's MathTrek
It's no wonder that farmers with fields in the plains surrounding Stonehenge, in southern England, face late-summer mornings with dread. On any given day at the height of the growing season, as many as a dozen farmers are likely to find a field marred by a circle of flattened grain.
http://www.maa.org/mathland/mathtrek_06_30_03.html
The Bohlen-Pierce Site
Diatonic Modes and Scale Variants
http://members.aol.com/bpsite/modes.html
Explanation of John Chalmers's Lattice Diagrams
Powers of 3 are plotted on the horizontal axis, powers of 5 on the vertical, powers of 7 on an oblique axis 30 degrees to the horizontal, powers of 11 on a 120 degree axis, powers of 13 at 60 degrees, and powers of 17 at 150 degrees. Although there may be some coincidences when large scales are plotted, for small numbers of tones, this type of rectilinear display is useful as well as visually striking. The axes are color-coded with red assigned to 3, green to 5, blue to 7, yellow to 11, magenta to 13 and cyan to 17. The scale has 65 members and consists of 9 otonal (or major, harmonic) enneads 1 3 5 7 9 11 13 15 17 on the tones of the corresponding utonal (minor or subharmonic) chords.
Subject: New lattice
> Joe: I was reading a book on the 4th dimension in art and saw a partial
> diagram of a 7-D hypercube and realize that my latticing program could
> reproduce it. Here's a 7-D hypercube interpreted as a 19-limit scale
> with 1/1 in the middle (and the point 1*3*5*7*11*13*17*19 on top of it).
> In other words, it's the 1.3.5.7.11.13.17.19 Euler genus <../dict/euler.htm>
http://sonic-arts.org/chalmers/diagrams.htm
"How the numerical ratios of the notes were discovered"
from The Enchiridon by Nicomachus (ca. 2nd century C.E.)
http://users.rcn.com/dante.interport/nico.html
Relationships.......................................
http://www.noteaccess.com/relationships
Musical Mathematics
a practice in the mathematics of tuning instruments and analyzing scales
© 2004 Cristiano M.L. Forster
All rights reserved.
www.Chrysalis-Foundation.org</a>
FLEXIBLE STRINGS
Part V: Musical, Mathematical, and Linguistic Origins of Length Ratios
<a href="http://www.chrysalis-foundation.org/origins_of_length_ratios.htm]http://www.chrysalis-foundation.org/origins_of_length_ratios.htm[/url]
MP3 music created from crop circle geometry.
http://orionsplace.com/anomalist/cropcirc.htm
Mathematics of Tuning and Temperament With audio examples
http://home.broadpark.no/~rbrekne/referhtml/musicmaths.html
The Scientific Sonification project is based on the concept that sounds are dynamic events which evolve in a multidimensional space. Each sound is a superposition of component waves (partials), whose evolution is determined by a set of static and dynamic control parameters. By defining a mapping from the data space to the sound space, we create a formalism for the faithful rendition of data in sounds.
<
http://www-unix.mcs.anl.gov/~kaper/Sonification/index.html>
Diatonic Music in Greece:
A Reassessment of its Antiquity
http://www.kingmixers.com/Diatonic.html%20
These are the same ratios found in popular music.
was led to the concept of crop circle music by way of two long time interests, music and paranormal studies. Although I have had no formal musical training and my experience playing live was limited to local garage bands in the 60s and 70s, I am an avid lover of music and sometime composer. The possibilities for music composition increased substantially each time we upgraded our computer, leading me to an interest in computer generated music.
My interest in paranormal events has been an intense lifelong pursuit. In the 1980s I first became aware of the phenomenon known as crop circles and read everything I could get my hands on about them. Again, with the advent of computers and the World Wide Web, my interest level and the information available to me increased radically. This is how I heard of Prof. Gerald Hawkins who I believe was the first person to uncover the presence of diatonic ratios in some crop circle formations. These are the same ratios found in popular music. This led me to search for crop circle formations with enough diatonic ratios to form a scale. To date, I have found three scales; the same three scales used in creating my CD "Crop Song."
I am 47 years old and live in the "purple house" in Shelburne, Vermont, with my wife Carol. I am a decorative house painter by trade and a cyber musician by night.
http://kalvos.org/smithst.html
Drone Music AB - Catalogue
http://www.drone.se/english/catalogue.html
The Baroque
The Baroque period lasted from 1600-1750. The composers were influenced by the ancient Greeks. The affections, rationalized emotional states or passions in which the Greeks believed, were used as the basis for their works. Compositions depicted emotions like anger and fear. A composition depicted one affection which was the unifying aspect of the piece. Certain musical figures came to stand for ideas or emotions.
http://www.mnsu.edu/emuseum/cultural/music/baroque.shtml
Related Information:
Fibonacci Spirals and how they reflect the natural forces within nature & the kosmos (from the micro-to the macro)
Did you know that Fibonacci numbers and Phi are related to spiral growth? - If you sum the squares of any series of Fibonacci numbers, they will equal the last Fibonacci number used in the series times the next Fibonacci number. This property results in the Fibonacci spiral seen in everything from sea shells to galaxies: 12 + 12 + 22 + 32 + 52 = 5 x 8 {SO} 12 + 12 + . . . + F(n)2 = F(n) x F(n+1) Note: The Fibonacci series spiral on the left is slightly different from the perfect spiral generated by Phi (1.61804...) because of the approximations early in the series leading to Phi. (1, 1, 2, 3, 5, 8 and 13 produce ratios of 1, 2, 1.5, 1.67, 1.6 and 1.625)
http://goldennumber.net/spirals.htm
I wonder of a connection here to that of the Trumpets used to take down the walls of Jericho according to biblical history?
Could it be?
Could it be the same technology used in the construction of the Coral Castle?
or the Druid Stone Henge, the Egyptian Pyramids?
I understand the quantum randomness of probability, but I do not believe that such re-occuring synchronicities are just chance random coincidence!
