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

**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 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]

See Also

**Apsidal**
**Apogee**
**eccentric orbit**
**Figure 9.7 - Two Centers Showing Complex Attraction Dynamics**
**off-center flywheel**
**Orbital Plane**
**Perigee**
**Prolate**
**Quantum Arithmetic Elements**
**Quantum Arithmetic**
**Sphere**
**two centers**
**two controlling points of stillness**
**two dividing poles**
**two lights of the spectrum**
**two opposed electric forces**
**two points of stillness**
**two poles**
**two-way compression-expansion sequence**
**two-way divided effects of motion**
**two-way effect**
**two-way extension of a point in space**
**two-way motion**
**two-way opening and closing universe**
**two-way universe**
**12.38 - Orbital revolution**
**9.23 - Circular Harmonic Orbit**
**9.24 - Elliptical Enharmonic Orbit**