# ellipse

Not round circle with two centers.

In mathematics, an ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve. As such, it is a generalization of a circle, which is a special type of an ellipse having both focal points at the same location. The shape of an ellipse (how "elongated" it is) is represented by its eccentricity, which for an ellipse can be any number from 0 (the limiting case of a circle) to arbitrarily close to but less than 1.

Ellipses are the closed type of conic section: a plane curve resulting from the intersection of a cone by a plane. Ellipses have many similarities with the other two forms of conic sections: parabolas and hyperbolas, both of which are open and unbounded. The cross section of a cylinder is an ellipse, unless the section is parallel to the axis of the cylinder. Wikipedia, Ellipse

Keely
"Given that force can be exerted by an act of will, do we understand the mechanism by which this is done? And if there is a gap in our knowledge between the conscious idea of a motion and the liberation of muscular energy needed to accomplish it, how do we know that a body may not be moved without ordinary material contact by an act of will? Keely contends that all metallic substances after having been subjected to a certain order of vibration may be so moved. "Scientists are verging rapidly toward the idea that immense volumes of energy exist in all conditions of corpuscular space. I accept Prof. Stoney's idea that an apsidal motion might be caused by an interaction between high and low tenuous matter, but such conditions, even of the highest accelerated motion are too far down below the etheric realm to influence it sympathetically, even in the most remote way. The conception of the molecule disturbing the ether, by electrical discharge from its parts is not correct... the highest conditions associated with electricity come under the fourth descending order of sympathetic conditions. The conjecture as regards the motion being a series of harmonic elliptic ones, accompanied by a slow apsidal one, I believe to be correct... The combination of these motions would necessarily produce two circular motions of different amplitudes whose differing periods might correspond to two lines of the spectrum as conjectured, and lead the experimenter, perhaps, into a position corresponding to an ocular illusion. Every line of the spectrum, I think, consists not of two close lines, but of compound triple lines; though not until an instrument has been constructed, which is as perfect in its parts as is the sympathetic field that environs matter, can any truthful conclusion be arrived at from demonstration." [Keely] [FORCE - Snell]

Russell
"At the left of the drawing two particles are turning upon their gravity shafts which could be electrons, planets or suns. Around these spinning masses are circles with arrows which show the direction of their turning. Naturally these circles show as an ellipse because they follow equators and are shown in perspective." [Atomic Suicide, page 295]

Ramsay
The Plate shows the Twelve Major and Minor Scales, with the three chords of their harmony - subdominant, tonic, and dominant; the tonic chord being always the center one. The straight lines of the three squares inside the stave embrace the chords of the major scales, which are read toward the right; e.g., F, C, G - these are the roots of the three chords F A C, C E G, G B D. The tonic chord of the scale of C becomes the subdominant chord of the scale of G, etc., all round. The curved lines of the ellipse embrace the three chords of the successive scales; e.g., D, A, E - these are the roots of the three chords D F A, A C E, E G B. The tonic chord of the scale of A becomes the subdominant of the scale of E, etc., all round. The sixth scale of the Majors may be written B with 5 sharps, and then is followed by F with 6 sharps, and this by C with 7 sharps, and so on all in sharps; and in this case the twelfth key would be E with 11 sharps; but, to simplify the signature, at B we can change the writing into C, this would be followed by G with 6 flats, and then the signature dropping one flat at every new key becomes a simpler expression; and at the twelfth key, instead of E with 11 sharps we have F with only one flat. Similarly, the Minors make a change from sharps to flats; and at the twelfth key, instead of C with 11 sharps we have D with one flat. The young student, for whose help these pictorial illustrations are chiefly prepared, must observe, however, that this is only a matter of musical orthography, and does not practically affect the music itself. When he comes to the study of the mathematical scales, he will be brought in sight of the exact very small difference between this B and C?, or this F# and G?; but meanwhile there is no difference for him. [Scientific Basis and Build of Music, page 108]

In the festoons of ellipses the signatures are given in the usual conventional way, the major F having one flat and minor E having one sharp. The major and minor keys start from these respective points, and each successive semitone is made a new keynote of a major and a minor respectively; and each ellipse in the festoons having the key shown in its two forms; for example, in the major F, one flat, or E#, eleven sharps; in the minor E, one sharp, or F?, eleven flats. Thus is seen all the various ways that notes may be named. The four minor thirds which divide the octave may be followed from an ellipse by the curved lines on which the ellipses are hung; and these four always constitute a chromatic chord. [Scientific Basis and Build of Music, page 115]

THE TWENTY-FOUR SCALES WITH THEIR SIGNATURES IN SHARPS AND FLATS.

The scales in this plate advance by semitones, not in their normal way by fifths; but their normal progress by fifths is shown by the spiral-ellipse line winding round under the stave and touching the ellipses containing the scales by semitonic advance; the scales being read to the right for the majors inside, and to the right for the minors outside. In each of the modes the scales are written in ?s and #s, as is usual in signatures; and since the scales [Scientific Basis and Build of Music, page 116]

advance by semitones, the keys with ?s and #s alternate in both modes. The open between G# and A? in the major, and between D# and E? in the minor, is closed in each mode, and the scale made one. The dotted lines across the plate lead from major to relative minor; and the solid spiral line starting from C, and winding left and right, touches the consecutive keys as they advance normally, because genetically, by fifths. The relative major and minor are in one ellipse at C and A; and in the ellipse right opposite this the relative to F# is D#, and that of G? and E?, all in the same ellipse, and by one set of notes, but read, of course, both ways. [Scientific Basis and Build of Music, page 117]

Schauberger
a maximal motion results, whose harmonic counterpart is the creation of the minimal form of motion, because the latter represents the totality in a single point. This is the turning or anomaly point out of which is born the creation-of-motion from which in turn the self-enclothing motion-of-creation arises.

This physical formation is the product of organic formative processes and it is obvious that in order to construct such physical forms, we must make use of certain basic shapes. This basic shape we find in the ellipse, which once set in motion, produces the mirror-image, opposite form. As the natural counterpart, the latter also creates the opposite temperament or reciprocal temperatures, which on their part give rise to the potentials and the form of motion associated with them.

Since we are here concerned with pure morphological patterns, there can be no state of equilibrium and therefore that state cannot exist, which we understand as 'rest'. In reality this apparent rest is the very highest state of motion and at the same time the point of material transformation, of the ur-generation [From Special Edition Mensch und Technik, Vol. 2, 1993, section 3.1]