noun: a scale with eight notes in an octave; all but two are separated by whole tones. See natural scale
Keely
In all molecular dissociation or disintegration of both simple and compound elements, whether gaseous or solid, a stream of vibratory antagonistic thirds, sixths, or ninths, on their chord mass will compel progressive subdivisions. In the disintegration of water the instrument is set on thirds, sixths, and ninths, to get the best effects. These triple conditions are focalized on the neutral center of said instrument so as to induce perfect harmony or concordance to the chord note of the mass chord of the instruments full combination, after which the diatonic and the enharmonic scale located at the top of the instrument, or ring, is thoroughly harmonized with the scale of ninths which is placed at the base of the vibratory transmitter with the telephone head. The next step is to disturb the harmony on the concentrative thirds, between the transmitter and the disintegrator. This is done by rotating the siren so as to induce a sympathetic communication along the nodal transmitter, or wire, that associates the two instruments. When the note of the siren becomes concordant to the neutral center of the disintegrator, the highest order of sympathetic communication is established. It is now necessary to operate the transferable vibratory negatizer or negative accelerator, which is seated in the center of the diatonic and enharmonic ring, at the top of the disintegrator, and complete disintegration will follow (from the antagonisms induced on the concordants by said adjunct) in triple progression, thus: First thirds: Molecular dissociation resolving the water into a gaseous compound of hydrogen and oxygen. Second: sixths, resolving the hydrogen and oxygen into a new element by second order of dissociation, producing what I call low atomic ether. Third: ninths, the low atomic ether resolved into a new element, which I denominate high or second atomic harmonic. All these transmissions being simultaneous on the disturbance of sympathetic equilibrium by said negative accelerator. [Snell Manuscript - The Book, page 4]
Ramsay
"When Nature, who weighs the mountains in scales and the hills in a balance, and number and names the stars, takes hold of this vibration-material, she subjects it to the most rigorous measurement in marshalling that series of notes which constitute The Musical System. She is in no hurry in giving us all her gifts in this matter. She first of all gives us the interval of an Octave at one stroke, and in generating the seven notes which compose the three chords of the Diatonic Scale she carries the process up through six octaves..." [Scientific Basis and Build of Music, page 19]
"Since Savart and Chladni and Helmholtz and Tyndal, and others, have studied the notes of our diatonic scale by the aid of such instruments as mechanical art has put into the hands of science in these last days, we have come to have a much more perfect understanding of music in its acoustical domain, and have been given to behold the beautiful mathematical measurements which Nature has applied in the marshalling of this host of the lower heavens; and which may suggest similar, though grander, and probably more complicated rhythms and harmonies in the astral heavens far off." [Scientific Basis and Build of Music, page 21]
she is found to have produced the Chromatic scale of twelve semitones, derived from her own vital operations; so that there are no anomalies. It is a degradation of the mathematical primes to apply them to the getting of the semitones of the chromatic scale, as even Euler himself mistakenly does. The mathematical ratios lead the way in getting the notes of the diatonic scale, and that is all that is required of them. The true praise to the ratios is that they have constituted an organic structure with form and life-powers adapted for self-development. It would be little credit to the mother if the child required to be all its life-long pinned to her apron-strings. As the bird when developed so far leaves the shell, and is afterwards fully developed in new conditions; so the System of music when developed so far leaves the law of ratios, its mathematical shell, and is afterwards fully developed by other laws. Music has an inspirational as well as a mathematical basis, and when mathematicians do not recognize this they reckon without their host. [Scientific Basis and Build of Music, page 35]
Mathematicians have not recognized the life-power of the notes, and so they have misapplied their calculations, though these were perfect in themselves. Assuming the place of dictators, they say with an air of authority that, "strictly speaking, nothing could be more scientifically and musically untrue than the chromatic scale of twelve equal semitones as played on a tempered instrument; for in it, as in the diatonic scale, the same natural law prevails that no two tones of equal mathematical relations can melodically succeed each other." Saying that the same natural law prevails implies that they are reasoning from analogy; but in this assumption they are dictating to Nature. In a similar way they might assume that the interval of the octave, like the other intervals, should have a grave harmonic.2 But the fact that the octave interval has not a [Scientific Basis and Build of Music, page 36]
It runs in all the polarities of Nature. Music, as belonging to Nature - as one of the things which the Great Numberer hath created - is under this Law of Duality as well as that of mathematical ratios and other laws. The Law of Duality in music gives the major and minor systems. As the major is derived from certain primes in ratios ascending, and the minor from the same primes in the same ratios descending, they are inversely related; and these diatonic scales have in the responding parts exactly the same quantities. But as multiplying by 3 three times gives the framework of the major system in the ascending genesis, and dividing by 3 three times gives the framework of the minor system in the descending genesis. They are in this view also directly related. The Law of Duality in music emerges into view from the genesis [Scientific Basis and Build of Music, page 42]
Pole's researches led him to conclude that the Diatonic Scale has remained essentially unchanged; as the series of notes was when Euclid described it, so it is now; and as it formed the basis of the melodies of the Greeks 2,000 years ago, so it forms the basis of the tunes of the present day." - Philosophy of Music. [Scientific Basis and Build of Music, page 45]
Nature has not finished when she has given us the Diatonic Scale of notes as first generated. In the diatonic scale, in ascending from C, the root of the tonic, the first step is an interval of 9 commas, supposing that we adopt the common division of the octave into 53 commas, which is the nearest practical measuring rule; the second step has 8 commas; the third has 5; the fourth has 9; the fifth has 8; the sixth has 9; and the seventh and last has 5 commas. So we have three steps of 9 commas, two steps of 8, and two of 5. The order of the steps in the major is 9, 8, 5, 9, 8, 9, 5. In the minor the magnitudes are the same, but the order is 9, 5, 8, 9, 5, 9, 8. So there are three magnitudes.1 But Nature has an equalizing process in the course of her musical marshallings, in which these greater ones get cut down, and have to change places with the lesser, when her purpose requires them so to do. [Scientific Basis and Build of Music, page 47]
"Some of the elements of the Chromatic System were known 200 years ago. The Diatonic scale, being called the "Natural scale," implied that the chromatic chords were consider to be artificial; but the notes of the chromatic chords, from their PROXIMITY to the notes of the tonic chord, fit to them like hand and glove. Nothing in music is more sweetly natural and pleasingly effective than such resolutions; and hence their extensive use in the hands of the Masters. The chromatic chords have close relations to the whole system of music, making the progressions of its harmonies easy and delectable, and producing effects often enchanting and elevating, as well as often subtle and profound; and while they are ever at hand at the call of the Composer, they are ever in loyal obedience to the laws of their own structure and system. When a diatonic chord precedes another diatonic chord belonging to the same scale, it has one note moving in semitonic progression;1 but when a chromatic chord precedes a diatonic chord, it may have three semitonic progressions.2 The primary chromatic chord resolves into 8 of the 24 diatonic tonic chords, with 3 semitonic progressions. These identical notes of the chromatic chord, with only some changes of names, resolve into another 8 of the 24 tonic chords, with 2 semitonic progressions and one note in common; and when they resolve into the third and last 8 of the 24 tonic chords, they move with one semitonic progression and 2 notes in common. So to the chromatic chord there are no foreign keys.3 And as it is with the first chromatic chord, so with the other two." [Scientific Basis and Build of Music, page 51]
In the laws of quantities and motions the three primary ratios, 1:2, 1:3, 1:5, with the three different units, F1, C3, and G9, the roots of the chords of the subdominant, tonic, and dominant, produce the three chords of the musical system major, the one not interfering with the other; and by an inverse process are produced, from B720, E240, and A80, its generating notes, the three chords of the musical system minor; the one chord not interfering with the other. In a similar way the chromatic chords can be produced from three different units, without the one interfering with the other; and, like the subdominant, tonic, and dominant chords of the diatonic scale, they are fifths apart. So we may call them the subdominant, tonic, and dominant chromatic chords. Each of the three chromatic chords has also kinship with the major and minor modes, from the way in which the diatonic minor triad is constituted a chromatic chord by its supplement coming in the one side from the minor, and on the other side from the major system. [Scientific Basis and Build of Music, page 53]
If we view the Diatonic scale from the standpoint of their harmonizing, it is the first five notes of the octave which are the natural scale. The eight notes of the octave form a compound scale. So, in this view, in the octave of notes we have before us two scales; and this is true in both major and minor modes after their own dual fashion. In each of these two diatonic modes, the major and the minor, there are two semitones; but there are only two semitones altogether in the twofold system. When the major is generated by itself it has them both; and when the minor is generated by itself it also has both; but when the major and the minor are generated simultaneously, or as one great dual outgrowth, while the major in the ascending genesis is producing the semitone E-F, the third and fourth of its octave scale, the minor responsively in the descending genesis is producing the semitone B-C, the second and third of its octave scale. In this view of them, therefore, the semitone E-F belongs genetically to the major, and B-C to the minor; and this claim is asserted in the major tonic chord C E G, in which its own semitone is [Scientific Basis and Build of Music, page 64]
The number of Chromatic Chords. Three chromatic chords exhaust the semitonic 12-foldness of the octave. The chromatic scale is a much more even thing than the diatonic; contrast is not its feature, and we may expect [Scientific Basis and Build of Music, page 72]
Fig. 1 - The pendulums in this illustration are suspended from points determined by the division of the Octave into Commas; the comma-measured chords of the Major key being S, 9, 8, 9, 5; T, 9, 8, 5, 9; D, 8, 9, 5, 9. The pendulums suspended from these points are tuned, as to length, to swing the mathematical ratios of the Diatonic scale. The longest pendulum is F, the chords being properly arranged with the subdominant, tonic, and dominant, the lowest, center, and upper chords respectively. Although in "Nature's Grand Fugue" there are 25 pendulums engaged, as will be seen by reference to it, yet for the area of a single key 13 pendulums, as here set forth, are all that are required. It will not fail to be observed that thus arranged, according to the law of the genesis of the scale, they form a beautiful curve, probably the curve of a falling projectile. It is an exceedingly interesting sight to watch the unfailing coincidences of the pendulums perfectly tuned, when started in pairs such as F4, A5, and C6; or started all together and seen in their manifold manner of working. The eye is then treated to a sight, in this solemn silent harp, of the order in which the vibrations of sounding instruments play their sweet coincidences on the drum of the delighted ear; and these two "art senses," the eye and the ear, keep good company. Fig. 2 is an illustration of the correct definition of a Pendulum Oscillation, as defined in this work. In watching the swinging pendulums, it will be observed that the coincidences [Scientific Basis and Build of Music, page 104]
Hughes
suspected. Let us take as our standard of colours the series given by the disintegration of white light, the so-called spectrum: as our standard of musical notes, let us take the natural or diatonic scale. We may justly compare the two, for the former embraces all possible gradations of simple colours, and the latter a similar gradation of notes of varying pitch. Further, the succession of colours in the spectrum is perfectly harmonious to the eye. Their invariable order is— red, orange, yellow, green, blue, indigo, and violet; any other arrangement of the colours is less enjoyable. Likewise, the succession of notes in the scale is the most agreeable that can be found. The order is—C, D, E, F, G, A, B; any attempt to ascend or descend the entire scale by another order is disagreeable. The order of colours given in the spectrum is exactly the order of luminous wave-lengths, decreasing from red to violet. The order of notes in the scale is also exactly the order of sonorous wave-lengths, decreasing from C to B." [Harmonies of Tones and Colours, On Colours as Developed by the same Laws as Musical Harmonies2, page 19]
See Also
Chromatic Scale
Diatonic
Diatonic Scale Ring
Dominant
Dominant Chord
Etheric Vibratory Scale
Figure 1.8 - Electromagnetic Scale in Octaves
Figure 12.01 - Russells 4 Power Centered Scale
Figure 12.02 - 0 Inertia Centered Scale
Figure 12.03 - Scale Showing Relations of Light Color and Tones
Figure 18.06 - Hubbard Tone Scale of Degrees or Levels of Consciousness
Figure 9.12 - Scale of Locked Potentials over Time
Major Scale
musical scale
Natural Scale
octave tonal scale
Scale
scale divisions
Scale of Locked Potentials
Scale of the Forces in Octaves
Subdominant
Subdominant Chord
Table 11.01 - Scale of Infinite Ninths its Structure and Base
Table 11.05 - Comparison of Scale Structural Components and Relations
three chords of the Diatonic Scale
Tonic
Tonic Chord
05 - The Melodic Relations of the sounds of the Common Scale
11.02 - Attributes of the Scale of Infinite Ninths
11.03 - Development of the Scale of Infinite Ninths
11.04 - Nature Dances to a Natural Music Scale
11.11 - Explanations of the Scale of Infinite Ninths
12.01 - Scale of Locked Potentials
12.03 - Russell scale divisions correspond to Keelys three-way division of currents
18.03 - Hubbard Scale of Consciousness