noun: a quantity of something that is a part or share of the whole
noun: the relationship between two or more quantities or parts of a whole
noun: harmonious arrangement or relation of parts or elements within a whole (as in a design)
noun: the quotient obtained when the magnitude of a part is divided by the magnitude of the whole

The ratio of two numbers or quantities to each other. Proportion is in three kinds: (1) multiplex. (2) Superparticularis. (3) Superpartiens. Proportio multiplex is when the larger number contains the smaller so many times without a remainder, as 2:1 (dupla), 3:1 (tripla), 4:1 (quadrupla). Proportio superparticularis is when the larger number exceeds the smaller by one only as 3:2 (sesquialtera), 4:3 (sesquitertia), 5:4 (sesquiquarta). Proportio superpartiens is when the larger number exceeds the smaller by more than one, as 5:3 (superbipartienstertias), 7:4 (supertripartiensquartas), 9:5 (superquadripartiensquintas). [See Ratio]

This would involve the propagation and build-up of fast-growing species of valuable timber by restoring cycloid-space-curve-motion through the re-establishment of naturalesque proportions in the intermixture of various crown and root systems. This will resuscitate the reactive temperature-differences (the reinstatement of microclimates through the graduated arrangement of over- and understoreys and juxtaposition of species) through which the heat-consuming upflows of refreshing and cooling substances ascend like cycloid whirlwinds, which trigger cold processes of oxidation enabling the propagation of species of fine timber on the forest floor (formation of the germinating zone). [The Energy Evolution - Harnessing Free Energy from Nature, New Forms of Motion and Energy]

This special form of motion, still unknown to conventional science, can magnetise a tripolar mass of air or water up to a maximum of 36% virtually without cost. To do this a particularly constructed, profiled and suitably alloyed form is required, which promotes the evolvement of a developmentally progressive energy, the power of which increases in proportion to the centripetating rotational velocity. In this process it is possible to overcome physical weight and mental torpor effortlessly at almost no expense. Accordingly, magnetism is therefore levitism, the creative (metaphysical) counterforce to electricism, the latter being the decomposive energy-form that actuates gravitism, or physical and mental relapse (the death state). [The Energy Evolution - Harnessing Free Energy from Nature, Magnetism - Electricism]

Precisely the opposite dissociation is inaugurated when the suctional component prevails or is dominant. This is because suction, which produces higher-grade coolness, increases in proportion to the centripetating rotational velocity. This invigorating (quality-enhancing) suctional effect can only be created when a tripolar mass of water or air is radially->axially rotated at high speed about its own axis. [The Energy Evolution - Harnessing Free Energy from Nature, Magnetism - Electricism]

In the unnatural, degenerative direction of acceleration, which operates along the transverse axis (centrifugally), i.e. in an axial->radial mode, the magnetism (= levitism) here acts as the resistance. Compared to the counter-flowing electricism, it appears to be in a certain state of rest, the magnitude of its resistance or support increasing commensurately with the acceleration of the downwardly flowing electricism (= gravitism). This is the origin of the tragic misconception that in all motion the resistance increases by the square of the starting velocity. However, in reality this only happens when any given mass (matter) is made to move technically, hydraulically or dynamically[2], i.e. axially->radially (centrifugally), therefore unnaturally. For if any given mass (matter) is made to move radially->axially (centripetally), then the upwardly flowing magnetism (levitism) increases at the expense of the disintegrative (destructive) electricism (gravitism) and thus the naturally ordained formative and levitative forces intensify in proportion to the starting (radial->axial) rotational velocity. With this type of motion, which is of course only possible with very special motion-inducing shapes (profiles), the effective performance amounts to about 96%. In this case only about 4% of the original formative energies are lost in producing the resistance to motion required by Nature. In technical, hydraulic and dynamic motion precisely the opposite is the case and this is how the enormous consumption of fuel came about, which is exclusively expended in a manner destructive of Nature. [The Energy Evolution - Harnessing Free Energy from Nature, Magnetism is the Function of Levitism and Electricism is the Function of Gravitism]

It cannot be disputed that contemporary science, which is founded on far too low a level of basic knowledge, has made exclusive use of pressure-intensifying (development-crippling) motion and arbitrary dynamic shapes that in no way correspond to those required by Nature. The formative components of suctional force, which act in an enlivening (cooling) way, were completely neglected. Hence science created even more dangerous degenerative forces as purported successes were achieved to the detriment of the reactive formative forces. A more rapid economic decline was therefore inevitable, the more widespread and more intensive technology, hydraulics and dynamics became. The soil's energies must also become depleted in the same proportion, because the [The Energy Evolution - Harnessing Free Energy from Nature, Magnetism is the Function of Levitism and Electricism is the Function of Gravitism]

The interaction - or the inner motion, is only possible by way of the seemingly 'dormant' resistance to motion, whose resisting force also intensifies in proportion to the increase in the speed of the interaction. Were this otherwise, then the greatly amplified product of this interaction could not be concentrated in this atomic prison (lattice) - (viz. the increasingly consolidated resistance to motion associated with physical acceleration, without which the latter could not happen.) [The Energy Evolution - Harnessing Free Energy from Nature, Magnetism is the Function of Levitism and Electricism is the Function of Gravitism]

A small, temperature-increasing, material or physical axial->radial impulse suffices to transform such a concentration of highly critical threshold matter in a latent state into the relatively most powerful, destructive energy, whose decomposive force increases in proportion to the strength of the impulse. Thus, for example, a lightning-like recoil in the form of a descending ion is triggered, which with elemental ur-force disintegrates the resistance that brakes its lightning descent. [The Energy Evolution - Harnessing Free Energy from Nature, Magnetism is the Function of Levitism and Electricism is the Function of Gravitism]

The specific levity of notes increases in proportion to the number of times the ratios are multiplied in order to produce them, going upward by sharps; and their specific gravity increase in proportion to the number of times the ratios are divided in order to produce them, going downward by flats. The knowledge of this is attained when everything is in its perfect order. It is the discovery of the Law of Duality in music which shows the method of applying the ascending and the descending ratios so as to exhibit that perfect order of Nature. [Scientific Basis and Build of Music, page 43]

The great Genetic Scale, major and minor, the seed-bed and nursery of all, is that from which first of all the natural scale of the fifth arises into existence; and three fifths are generated in the major ascending side and three also in the descending minor side of the twofold genesis, giving us six fifths in all. At the top of the ascending genesis we find the major octave scale standing solid and in its perfect order and proportion; and at the bottom of the descending genesis we have the minor octave. [Scientific Basis and Build of Music, page 66]

In getting the length of a string, in inches or otherwise, to produce the scale of music, any number may be fixed on for the unit; or for the vibrations of the root note any number may be fixed on for the unit; but in the fractions which show the proportions of the notes of the scale, there is no coming and going here; this belongs to the invariables; there is just one way of it. Whatever is not sense here is nonsense. It is here we are to look for the truth. The numbers which express the quantities and the numbers which express the motions are always related as being of the same kind. The fractions bring their characters with them, and we know by this where they come from. 1/4 of a string gives a note 2 octaves above the whole string, no matter what may be its length; 2 has exactly the same character as 1; 2/4 gives the note which is 1 octave above the whole string; but in the case of 3/4 here is a new ingredient, 3; 3/4 of a string gives a note which is a fifth below the [Scientific Basis and Build of Music, page 75]

with her irrevocable proportions to measure his scales for him. The stars at the C of the first scale and at the B# of the last show the coincidence of 12 fifths and 7 octaves. The number of B# is 3113 467/512; C24 multiplied 7 times by 2 brings us to the number 3072; these two notes in the tempered system are made one, and the unbroken horizon of the musical world of twelve twofold keys is created. The very small difference between these two pitches is so distributed in the 12 tempered scales that no single key of the 12 has much to bear in the loss of perfect intonation. [Scientific Basis and Build of Music, page 118]

The curved lines enclose the three chords of the major mode of the scale, with the ratio-numbers for the vibration in their simplest expression, counted, in the usual way in this work, from F1, the root of the major subdominant. The chords stand in their genetic position of F F C A, that is F1 by 2, 3, and 5; and so with the other two. The proportions for a set of ten pendulums are then placed in file with the ten notes from 1 to 1/2025 part of 1. Of course the one may be any length to begin with, but the proportions rule the scale after that. [Scientific Basis and Build of Music, page 121]

The tones between the seven white notes of keyed instruments, and the tints and shades between the seven colours, cause the multequivalency of colours and of tones; consequently every colour, as every musical harmony, has the capability of ascending or descending, to and fro in circles, or advancing and retiring in musical clef. It is a curious coincidence that Wünsch, nearly one hundred years ago, believed in his discovery of the primary colours to be red, green, and violet; and in this scheme, red, answering to the note C, must necessarily be the first visible colour, followed by green and violet, but these not as primary colours, all colours in turn becoming primaries and secondaries in the development of the various harmonies. To gain facts by experiment, the colours must be exactly according to natural proportions—certain proportions producing white, and others black. In this scheme, green and red are shown to be a complementary pair, and therefore (as Clerk Maxwell has proved) red and green in right proportions would produce yellow. The same fact has been proved in Lord Rayleigh's experiments with the spectroscope. Yellow and ultra-violet, [Harmonies of Tones and Colours, On Colours as Developed by the same Laws as Musical Harmonies3, page 20]

R. A. Schwaller de Lubicz
"Proportion belongs to geometry and harmony, measurement to the object and to arithmetic; and one necessitates the other. Proportion is the comparison of sizes; harmony is the relationship to measures; geometry is the function of numbers." [R. A. Schwaller de Lubicz, The Temple in Man, page 61]

John Stainer
Thus, it will be understood, that instead of giving simply the ratio between two numbers, early writers on arithmetic and geometry, as well as music, coined a single word to express that ratio; for example, 17:5 was said to be Triplasuperbipartiensquintas, i.e., that the larger number contained the smaller number three times (tripla) with two remainder (bipariens). Again, Triplasupertripartiensquartas proportio, signified that the larger contained the smaller three times and three over, as 15:4, 27:8, etc., the last part of the compound word always pointing out the smaller of the numbers compared, or an exact multiple of it. Lastly, the addition of sub showed that the smaller number was compared to the larger, e.g., 4:15 would be called Subtriplasupertripartiensquartas proportio. This system of proportion was used not only with reference to intervals but also to the comparative length of notes (time). [Stainer, John; Barrett, W.A.; A Dictionary of Musical Terms; Novello, Ewer and Co., London, pre-1900]

See Also

12.00 - Reciprocating Proportionality
13.15 - Principle of Proportion
13.18 - Naturaly Occuring Reciprocity and Proportionality
3.13 - Reciprocals and Proportions of Motions and Substance
6.8 - Proportionate and Relative Geometries
9.12 - Velocity of Sound and its Propagation Rate are Proportional
constant of proportionality
Figure 14.10 - Proportionate Tonal Relations dictate Contraction or Expansion
Figure 6.17 - Areas and Volumes - Relations and Proportions
Figure 6.19 - Sphere to Cube - Relations and Proportions
inversely proportionally
Law of Definite Proportions
law of multiple proportions
Ramsay - The Great Chord of Chords, the Three-in-One17
Reciprocating Proportionality
system of proportion
Table 2 - Controlling Modes and Proportions

Created by Dale Pond. Last Modification: Sunday September 11, 2022 04:51:56 MDT by Dale Pond.