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Scale

Is an arithmetically related set or series of musical tones, frequencies, elements and power scales. There are countless types or forms of scales.

Scale with Notes on Staff
(from Stone's Scientific Basis of Music)

Ramsay
SCALE - "groups of notes or chords in succession, which are bound and unified in some clear and definite way." [Scientific Basis and Build of Music, page 64.]


"Of these three chords, which constitute a scale or key, Nature next proceeds to generate, in a similar way, a family of scales or keys, and these in two lines, the Major and the Minor. The twice twelve-fold family of keys is brought forth in much the same way as were the chords which constitute them, and as were the notes which constitute the chords. There is a beautiful growth-like continuity in the production of all." [Scientific Basis and Build of Music, page 20]

"The system of musical sounds is derived from the laws of motion and a particular election of numbers which give the greatest variety of simple ratios. There are three primary and pregnant ratios which produce the chords and scales. The first is the ratio of 1:2, producing Octaves, and nothing else; the second is the ratio of 2:3, producing Fifths; the third is the ratio of 4:5, producing Thirds." [Scientific Basis and Build of Music, page 26]

"Gravity and levity, and centrifugal force; these musical forces do not here refer to the center of the earth, but the center of the musical system, e.g., E in the scale of C." [Scientific Basis and Build of Music, page 27]

"The third note of the octave scale, E, the center of the tonic chord in the key of C, is the center of the system. It is the note which has the least tendency either upward or downward, and it has immediately above it in the octave scale the note which has the greatest amount of specific gravity, F, the root of the major subdominant; and immediately beneath it the note which has the greatest amount of specific levity, D, the top of the major dominant. Thus the root of the subdominant chord and the top of the dominant are placed right above and below the center of the system, and the gravity of the one above, and the levity of the one below, causes each of them to move in the direction of the center. These tendencies are seen in the scale at whatever key it may be pitched, and by whatever names the notes may be called. And it is on account of this permanency of character of the notes that the third note of the scale, E, in the key of C, has a lower effect1 than the second, D; and that the fourth note, F, has a lower effect than either the first, second, or third; the fifth note, G, has a higher effect than the fourth, F; but the sixth, A, has a.." [Scientific Basis and Build of Music, page 28]

The extremes of the levities and gravities of a key-system are always at the extent of three fifths; and whatever notes are adopted for these three fifths, the center fifth is the tonic. As there never can be more than three fifths above each other on the same terms, so there can never be more than one such scale at the same time. A fourth fifth is a comma less than the harmonic fifth1; and this is Nature's danger-signal, to show that it is not admissible here. Nature does not sew with a knotless thread in music. The elements are so place that nothing can be added nor anything taken away without producing confusion or defect. What has been created is thus at the same time protected by Nature. [Scientific Basis and Build of Music, page 38]

The mathematical scales, if followed out regardless of other laws which rule in music, would read like a chapter in Astronomy. They would lead us on like the cycles of the moon, for example. In 19 years we have 235 moons; but the moon by that time is an hour and a-half fast. In 16 such cycles, or about 300 years, the moon is about a day fast; this, of course, is speaking roughly. This is the way seemingly through all the astronomical realm of creation. And had we only the mathematical ratios used in generating the notes of the scale as the sole law of music, we should be led off in the same way. And were we to follow up into the inaudible region of vibrations, we should possibly find ourselves where light, and heat, and chemical elective motions and electric currents are playing their unheard harmonies; or into the seemingly still region of solid substances, where an almost infinite tremor of vibrations is balancing the ultimate elements of the world. Music in this case would seem like some passing meteor coming in from among the silent oscillations of the planetary bodies of the solar system, and flashing past with its charming sound effects, and leaving us again to pass into the higher silence of those subtle vibrations to which we have referred, having no infolding upon itself, no systematic limit, no horizon. But music is not such a passing thing. Between the high silence of these intense vibrations, and the low silence of oscillating pendulums and revolving planets, God has constituted an audible sphere of vibrations, in which is placed a definite limit of systematic sounds; seven octaves are carried like a measuring line round twelve fifths; and motion and rest unite in placing a horizon for the musical world, and music comes [Scientific Basis and Build of Music, page 39]

of the major being upward, and the genesis of the minor being downward. The ascending genesis, beginning with the root of the subdominant major F, produces in the ascent a scale of notes at varying distances, and of increasing levities; the middle note, D27, being carried a little above the center of the system. The descending genesis, beginning with the top of the dominant minor B, produces in the descent a scale of notes with identical variety of distances, but with increasing gravities; the middle note, D26 2/3, being pressed a little below the center of the system, thus giving rise to these two D's - one whose genetic number is 27, the major D, and one whose genetic number is 27 2/3, the minor D - the duality of D is thus residing in itself.1 [Scientific Basis and Build of Music, page 43]

It is according to the Law of Duality that the keys on the piano have the same order above and below D, and above and below G# and A♭, which is one note. In these two places the dual notes are given by the same key; but in every other case in which the notes are dual, the order above the one and below the other is the same. The black keys conform to the scale, and the fingering conforms to the black keys. On that account in the major scale with flats, for the right hand the thumb is always on F and C; and as the duals of F and C are B and E in the minor scale with sharps, for the left hand thumb is always on B and E. [Scientific Basis and Build of Music, page 44]

Here, then, we have an order of modes entirely symmetical in pairs placed thus; the only mode that can stand alone being the Dorian, built on D, whose duality has been discovered to reside in itself. All this build of symmetry, which was the watchword of Greek art, as it is also one of the watchwords of Nature, presupposes that the tones of the scale, with lesser and larger intervals lying between them, were resting in their ears exactly as they are in ours,1 and as they are in all humanity, save where it has sunk down into the savage condition, benighted in the evil that is in the world. It is not to be concluded that the Dorian mode is Nature's primitive scale, although it might have a certain pre-eminence [Scientific Basis and Build of Music, page 45]

It should not be supposed that this division of the notes into semitones, as we call them, is something invented by man; it is only something observed by him. The cutting of the notes into twelve semitones is Nature's own doing. She guides us to it in passing from one scale to another as she builds them up. When we pass, for example, from the key of C to the key of G, Nature divides one of the intervals into two nearly equal parts. This operation we mark by putting a # to F. We do not put the # to F to make it sharp, but to show [Scientific Basis and Build of Music, page 47]

that Nature has done so.1 And in every new key into which we modulate Nature performs the same operation, till in the course of the twelve scales she has cut every greater note into two, and made the notes of the scale into twelve instead of seven. These we, as a matter of convenience, call semitones; though they are really as much tones as are the small intervals which Nature gave us in the genesis of the first scale between B-C and E-F. She only repeats the operation for every new key which she had performed at the very first. It is a new key, indeed, but exactly like the first. The 5 and 9 commas interval between E and G becomes a 9 and 5 comma interval; and this Nature does by the rule which rests in the ear, and is uttered in the obedient voice, and not by any mathematical authority from without. She cuts the 9-comma step F to G into two, and leaving 5 commas as the last interval of the new key of G, precisely as she had made 5 commas between B and C as the last interval of the key of C, she adds the other 4 commas to the 5-comma step E to F, which makes this second-last step a 9-comma step, precisely as she had made it in the key of C.2 [Scientific Basis and Build of Music, page 48]

In the progression - that is, the going on from one to another - of these triplets in harmonizing the octave scale ascending, Nature goes on normally till we come to the passage from the sixth to the seventh note of the scale, whose two chords have no note in common, and a new step has to be taken to link them together. And here the true way is to follow the method of Nature in the birthplace of chords.1 The root of the subdominant chord, to which the sixth of the octave scale belongs, which then becomes a 4-note chord, and is called the dominant seventh; F, the root of the subdominant F, A, C, is added to G, B, D, the notes of the dominant, which then becomes G, B, D, F; the two chords have now a note in common, and can pass on to the end of the octave scale normally. In going down the octave scale with harmony, the passage from the seventh to the sixth, where this break exists, meets us at the very second step; but following Nature's method again, the top of the dominant goes over to the root of the subdominant, and F, A, C, which has no note in common with G, B, D, becomes D, F, A, C, and is called the subdominant sixth; and continuity being thus established, the harmony then passes on normally to the bottom of the scale, every successive chord being linked to the preceding note by a note in common. [Scientific Basis and Build of Music, page 49]

We have gone from vibrations to musical notes; from notes to chords; and now we proceed to scales - that is, groups of notes or chords in succession, which are bound and unified in some clear and definite way. [Scientific Basis and Build of Music, page 64]

The Chromatic Scale is naturally the last to come into view, for it is not generated by a mathematical process at all. Chromatic intervals are indeed found in the scale as mathematically generated. The semitones between B-C and E-F are two chromatic intervals, and the chord which occurs between the major and the minor in the chord-scale when it begins with the minor mode is a chromatic chord, though in an uncompleted condition. But the making of the octave into a chromatic scale of twelve small or semi-tones, is the work of modulation from one key to another through the whole twelve keys in either the major or minor sphere; and this process is fully set forth in the pre-note to the chromatic treatise. [Scientific Basis and Build of Music, page 69]

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]

There is nothing extraordinary in this. It is another fact which gives this one its importance, and that is that the musical system is composed of three fifths rising one out of another; so this note by 3/4 becomes the root not only of a chord, but the root of all the three chords, of which the middle one is the tonic; the chord of the balance of the system, the chord of the key; the one out of which it grows, and the one which grows out of it, being like the scales which sway on this central balance-beam. Thus F takes its place, C in the center, and G above. These are the 3 fifths of the system on its masculine or major side. The fractions for A, E, and B, the middle notes of the three chords, are 4/5, 3/5, and 8/15; this too tells a tale; 5 is a new ingredient; and as 3 gives fifths, 5 gives thirds. From these two primes, 3 and 5, along with the integer or unit, all the notes of the system are evolved, the octaves of all being always found by 2. When the whole system has been evolved, the numbers which are the lengths of the strings in the masculine or major mode are the numbers of the vibrations of the notes of the feminine or minor mode; and the string-length-numbers of the minor or feminine are the vibration-numbers of the notes of the major or masculine mode. These two numbers, the one for lengths and one for vibrations, when multiplied into each other, make in every case 720; the octave of 360, the number of the degrees of the circle. [Scientific Basis and Build of Music, page 76]

At the first, in the laws of quantities and motions adjusting musical vibrations, there is one chord of the three notes, F, A, C, the root, middle, and top of the five notes which compose the true natural scale; this one chord can be reproduced a fifth higher, C, E, G, in the same mathematical form, taking the top of the first for the root of the second chord. In like manner this second can be reproduced another fifth higher, G, B, D, still in the same mathematical form, and so fit to be a member of the chord-scale of a key. But the law does not admit of another reproduction without interfering with the first chord, so that a fourth fifth produces no new effect; but the whole key is simply a fifth higher, i.e., if the fifth has been properly produced by multiplying the top of the third fifth by 3 and by 5, the generating primes in music. That this carries us into a new scale is seen in that the F is no longer the F♮ but F#, and the A is no longer A♮ but A,. But if we suppose the fourth fifth to be simply the old notes with their own vibration numbers, then D, F, A would not be a fifth belonging either to the major or the minor mode, but a fifth a comma less. The letters of it would read like the minor subdominant, D, F, A; but the intervals, as found in the upward development of the major genesis, instead of being, when expressed in commas, 9, 5, 8, 9, which is the minor subdominant, would be 8, 5, 9, 8, which is not a fifth of the musical system; these having always, whether major or minor, two 9's, one [Scientific Basis and Build of Music, page 77]

Helmholtz falls into a mistake when he says- "The system of scales and modes, and all the network of harmony founded on them, do not seem to rest on any immutable laws of Nature, but are due to the aesthetical principle which is constantly subject to change, according to the progressive development of taste." It is true, indeed, that the ear is the last judge; but the ear is to judge something which it does not create, but simply judges. Nature is the maker of music in its scales and modes. The styles of composition may vary with successive generations, and in the different nations of men; but the scientific basis of music is another thing. It is a thing, belonging to the aesthetic element of our being and our environment; it is under the idea of the beautiful, rather than the idea of the useful or the just; but all these various aspects of our relation to creation have their laws which underlie whatever changes may be fashionable at any period in our practice. If the clang-farbe of a musical tone, that is, its quality or timbre, depends on the number and comparative strength of the partial tones or harmonics of which it is composed, and this is considered to be the great discovery of Helmholtz, it cannot be that the scales and modes are at the caprice of the fickle and varied taste of times and individuals, for these partials are under Nature's mathematical usages, and quite beyond any taste for man's to change. It is these very partials or harmonics brought fully into view as a system, and they lead us back and back till they have brought us to the great all-prevading law of gravitation; it is these very partials, which clothe as an audible halo every musical sound, which constitute the musical system of sounds. [Scientific Basis and Build of Music, page 78]

Mr. Pole, in his Philosophy of Music, begins his remarks about the scale by a reference to the savage condition of men, and their few and uncouth musical sounds. This is the fashionable way at present of viewing mankind's early days. It is not necessary, however, to conceive the first state of mankind [Scientific Basis and Build of Music, page 78]

as the savage state. The savage is the sunken state of man, consequent on falling away from God by distrust and disobedience, and the loss of paradisial converse with Him. We may presume that music in the beginning, when the first human pair sang out with unbroken voices the joy of their hearts, was in the scale to which mankind, risen and restored by God's mercy, have returned. Our last days are thus become like the first again; and the lost dominion of Nature has returned, in the Incarnate One, into the hands of mankind. [Scientific Basis and Build of Music, page 79]


Diverse Scales in SVPwiki
There are a number of scales or orderings of vibratory phenomena that are of interest. These tables and scales are useful in that they put related data sets into classifications, perspective and order revealing many relationships not otherwise seen.


12.01 - Scale of Locked Potentials
chord-scale
chromatic scale
compound scale
Diatonic scale
Enhanced Electromagnetic Spectrum Table
Etheric Elements
Genesis of the Scale
genetic scale
Major Scale
minor scale
natural scale
octave scale
Ramsay - CHAPTER VIII - SCALES
Ramsay - PLATE XXII - Mathematical Table of the Twelve Major Scales and their relative Minors
Ramsay - PLATE XXIII - The Mathematical and Tempered Scales
Ramsay - PLATE XXVII - The Mathematical Scale of Thirty two notes in Commas, Sharps and Flats
scale of A
scale of B sharp
scale of D
scale of G
Scale of Locked Potentials
scale of mathematical intonation
Scale of vitalized focalized intensity
Table 11.01 - Scale of Infinite Ninths its Structure and Base
three chords of the Diatonic Scale
twelve major scales
twelve minor scales
Keely's Scale of the Forces in Octaves
Pond's Etheric Vibratory Scale
See Tables
Click Here to Calculate Music Intervals in any Octave
[NOTE: the above list is not a complete list]

[A Dictionary of Music]
"The graduated sounds used in music. To give a history of the scale would be to give a history of music itself; it must suffice, therefore, to say a few words on the growth of the scale to its present shape. Nothing is known with certainty of the nature of the scales of any of the most ancient nations. If it be admitted that the Greeks obtained their notions from the Egyptians, it may be hazarded, merely as a supposition, that the Egyptian scale was tetrachordal, that is, consisting of groups of four notes.

The octave system became practically a part of the ancient tetrachordal system, which it was destined afterwards to supersede entirely. Although our modern scale was unquestionably a development of the Diatonic scale of the Greeks, yet for several centuries, a hexachordal system was in use. The Church modes were probably the connecting link between the ancient Greek music and the modern Diatonic scale. The division of the octave into twelve parts, called semitones, each of which can be used as a keynote, became only feasible when keyed instruments were tuned on the system known as equal temperament. This gives to the chromatic notes of our scale a far greater value than the chromatic or enharmonic notes of the ancients, as it is probable they were never used but as passing or auxiliary notes. The whole system of music hangs upon the relationship of the sounds used to a tonic, which, in modern music, is always the first note of whatever octave system (key) is chosen, but in Greek music and early Church-song was a note at or near the middle of the scale.

The old Church mode corresponding to the modern scale was the Ionic or Iastian, but when this was finally adopted as the normal scale, a still older form was retained for use with it, founded on the Dorian and HypoDorian modes, to which, now slightly modified, we give the name minor mode, and by starting from any one note in the semitonal scale, we can have twelve minor modes. As a minor mode largely consists of the notes of the major scale beginning on its third degree, it is said to be relative to that scale. The form of the minor mode has varied from time to time and even now cannot be said to be definitely settled.

The musical scales of extra-European countries are so varied in character that it is impossible to draw any reliable conclusions from their form. The Arabs, Indians, and many uncultured tribes in all quarters of the globe have more than twelve divisions in the octave, that is, use enharmonic scales. The Chinese have the old five-note scale, called by Engel, Pentatonic. This five-note scale is also associated with Scotch and other Celtic melodies.

In some nations the natural harmonic, known as the sharp eleventh, which we discard, is in use, probably because it is produced upon their simple tube instruments.

The degrees of the ascending scale are distinguished in harmony by the following names:

FirstTonic
SecondSupertonic
ThirdMediant
FourthSubdominant
FifthDominant
SixthSuperdominant
SeventhSubtonic or Leading Note

[A Dictionary of Music]


A = 432 or 440? 432 vs 440 - Harmony is determined by having low numbers. High numbers therefore equal discord. A frequency is a composite or resultant of its aliquot parts. 432 = 2^4 * 3^3 all low numbers 440 = 2^3 * 55 * 11 dangling higher numbers Therefore 432 is has greater harmonicity than 440. Of course, there is a lot more to this but the above ought to get you thinking. see Law of Harmony


Note
12 Step
Type
7 Step
JUST
EqualTemp
Pyth/Step
Pythagorean
C
12/12
7/7
523.25
523.25
2/1
Tone/Octave
512
B
11/12
6/7
490.55
493.88
243/128
486
Bf
10/12
470.93
466.16
A
9/12
5/7
436.05
440.00
27/16
Tone
432
G#
8/12
418.60
415.30
G
7/12
4/7
392.44
392.00
3/2
Tone
384
F#
6/12
367.92
369.99
F
5/12
3/7
348.83
349.23
4/3
Tone
341.33
E
4/12
2/7
327.03
329.63
81/64
324
D#
3/12
313.96
311.13
D
2/12
1/7
294.33
293.66
9/8
Tone
288
C#
1/12
272.63
277.18
C
1/1
1/1
261.63
261.63
1/1
Tone
256

See Also


chord-scale
Diatonic Scale Ring
Diatonic scale
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
Overtones Developed Musically
Figure 18.06 - Hubbard Tone Scale of Degrees or Levels of Consciousness
Figure 9.12 - Scale of Locked Potentials over Time
Harmonic
harmony scale
mathematical scales
Major Scale
minor fifth
Minor Second
Minor Seventh
Minor Sixth
Minor Third
minor
musical scale
octave tonal scale
Overtone series
Overtone
Part 11 - SVP Music Model
Part 12 - Russells Locked Potentials
Scale
scale divisions
Scale of Locked Potentials
Scale of the Forces in Octaves
Scale of vitalized focalized intensity
Table 11.01 - Scale of Infinite Ninths its Structure and Base
Table 11.05 - Comparison of Scale Structural Components and Relations
twelve major scales
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

Created by Dale Pond. Last Modification: Monday November 23, 2020 04:54:33 MST by Dale Pond.