The major scale staggers intervals across the 12-note system to establish a “tonic.” The sequence of intervals leads to the note, which is the tonic
No matter which note the musician makes the tonic, the major scale pattern is the same.
The major scale is not symmetrically modelled in the circle of notes:
This is because the major scale is part of the penta-tonic and “modal” scales, which are utilized to access “3-D” music. They are mathematical perfections relative to our existence in the universe, that come together logistically according to cyclic nature.
There are quite a few ways, other than pentatonic/”modal” scales, to stagger notes across the “Western” 12-note system. Some of these scales are symmetrical when modeled.
The dynamics of how a musician can manipulate all the possible variables of these symmetrical scales is called the Mountain Spring theory by Astrolabe.
Symmetry is important because music is divisible at many rational magnitudes and balances. These allignmnts are further justified by their harmonic relevance in many technical advances beyond Cyclic Balance Harmony, or the 4 5 1 (4.5) 2 3 6 7 .
Music relies on implied ambiguity, harmony, discord, rhythm, silence, for it relate to people in their own cognitive spectrum
Even though many planar symmetrical scales are intervals, set in stages of “dissonance,” they model “2-D” concepts of tonal balance which quantify harmonic, “3-D” music.
A hexagon imposed over the circle of notes yields the whole tone scale
it also displays the factors of 7-5-1-4-(1.5) when scruched into a variant form of a hexa-factor music model. This one quantifies immediate harmony with the harmonic 7 and even the disharmonic (1.5) leading tones.
Cyclic Balance Harmony accounts for the blues notes (most immediately they would be the 4.5 or the 6.5)
This is why the Hexagon is so important, it not only represents cyclic balance, but it has duality in purpose much like the 1 has much multiplicity in its.
When taking the penta tonic, or modal, view on music interpretation, a 7 note stagger across the sprctrum of notes, the major scale and more
a relative “hexagon” scale would consist of 3 and a half notes. This, Astrolabe believes, is quantification for, (and of!), cyclic nature, in accordance to Cyclic Balance Harmony (Tetrahedron of interception), the 1 4 5 and (4.5)
Tividing the spectrum into strands is another helpful modelling tool:
starting the second strand on other intervals simulates dividing the intepreted half of music in a spot other than the mathmatical opposite, 4.5.
since music is often moving in a direction, technicality almost always demands interpretation, and subsequently modulation. Simplified harmony doesnt populate subsequent harmonic centers becaus the harmonic home has been aggrandized in such cases. like the hexagon was rationed for 7 note major scale, the 4 factor cycl balance tetahedron with be fit unto the penta tonic scale. 2.857 notes from a pentatonic scale yields the smallest rational simplification of “pure note” scales.
Those fractions of notes may come in handy when going into micro-modal (sub-chromatic theories, since chromatic is harmonically quantified!),and mega-modal music (expansive yet finite, technical yet trite, x’s and o’s, inverts discord and pure notes.)
Ironically, or not, the sub chromatic theories are quantified by cyclic balance (harmonic) movements, and the mega-modal, including ambient tonalities, albeit harmonically functional, are more unitary and thus linear functions.
The pentagram is further quantified as a planar piece to the whole tone hexagon, removing the mathmatical opposite, 4.5.
Music is a simple activity that can’t truly be 3-D and is comparable to the depth possible when making pictures with the activity of additive color.
The planar scales are not just scales, but they act as note-systems, just like the “perfect” 12 note system they can be applied in, and deduced from. This creates a very broad spectrum of variability in their uses for transporting music/listeners/the musician from one tonic to another through the spectrum of dissolution and recreation (The Mountain Spring theory).
Planar scales, when applied harmonically, modulate music in the ways consonance naturally builds. The planar diagrams model phenomna winessable in shiftin tonic harmony logistics.
One of Albert Einstein’s lasting musical models was a two-strand note circle which modelled how a tonic moves away from center of naturally through the penta-tonics, when imposed across octaves. The octaves of C when lined up made a pentagram.
Music is always moving, the concept of additive color is a redundancy in music (as is in color, it’s all additive, but that is a fundamental error in long-held educatory practices.
The nature of consonance, implication, and processing music happens in fractal patterns resembling the planar scales, and all their rational modulations in tandem with harmonic one, Mountain Spring theory.
The essentials of harmony can be extended into a collective and the simulator of music works with the cogs of all the shapes resembling features of music, especiall even sided poly hedrons
Just like light, its practical and most definable modelling revolves around the harmonic tendencies towards the essential harmonic intervals: The 4 (Sub-dominant), 1 (Tonic), and 5 (Dominant). These are equilateral intervals that provide insight and allow logisticians to deduce how inversions, counters, and all possible styles of conversion/modulation are achievable.
Color combination works the same manner of consonance, this said the accepted “primary color” intervals are staggered across what Astrolabe calls dynamic modulation theory in music.
The accepted “primary colors” are the 1 5 6.5 intervals in music. This is a very pertinent harmonic modulation, on a greater scale of harmony. The accepted “primary colors” are the fire colors, that the sun portrays as well
This quantifies the magnitude shift of harmonic function in establishing these colors as “primary”. A grand, yet vague and impractical practical set of intervals that are less malleable than the ones established and accepted as the “primary additive colors”, which Astrolabe believes is a misnomer and a redundancy.
The side-effects of this educatory neglect becomes evident when applied to music. “Movement” in terms of manipulating the relativity of tones, can be implied onto combinative activities like light, music, and paint, in many ways that are best modeled, and executed with an understanding around cyclic harmony,
The 4.5 is the factor which balances music, but also allows musicians to crunch and crux their compositions. Each dissonant interval towards the tonic has a role down the road in perfect harmony, which can be manifested in a lot of different ways when incorporating all the tools a musician can acquire.
Even though the 4.5 is the opposite note from the tonic, it is not the least harmonic. The 1.5, less harmonic than the 7, is still more harmonic than others (seen mostly in dominant leading tonics) and this can be quantified simply by its parallel nature to the 7.
The simplest, most essential definitions, and models of these practices of activities is necessary for their crafts-people to understand the full breadth of possibility in inversions, conversions, flips, flops, and further attributes to depth, and quality of results.
A dodecahedron is a perfectly congruent polyhedron, or 3-D shape, that has 12 pentagon faces. This correlates with the 12-note system of music and it’s penta-tonic scales. The intervals are dispersed in a fashion where faces, points, and edges all have variable, and denotable representation for music simulation.
The Intervals are alligned in a much more linear fashion than most would expect but, because music is harmonically set to crawl forward in a fractal pattern this makes sense.
Depending on the composition, music will move from a tonic point to harmonic factors within that points realm, and possibly further modulating to one of those factors.
This can be diagrammed on a dodecahedron using rays and establishing an understanding of the relationships of each intervals face, edge, and point with all the other intervals.
In reality, the more a musician learns about how music models, the more they learn why playing is so intuitive. Opposed to circle modelling, which acts as a compass, the dodecahedron is more of a visual simulator which enacts all the moving parts of music in simple, ultimate, and most defined manner; 3-D.
Planar scales are the tonal building blocks for the chromatic utilities that operate harmonic function properly. Where their patterns intersect is parallel to the activity of atomic combination.
Trying to utilize it as a tool would only provide an omnipotent, and impractical visual of the musical realm. It is a 3-D model for a 2-D activity.
Philosophically this dodecahedron of simulative possible is Earth, and the hands at which dictate what happens in it would be the intelligent universe, whatever that entails.
When combustion, occurs, force and electromagnetism are in a state of unison, but they are not compatible intervals in the primary production of phenomena of the universe.
In music, the primary functions of the universe, substance, electro-magnetism, and kinetic force, combine parallel to the ways in which the 1, 4, and 5 do in cyclic harmony around the Circle of Fourths and fifths) (Not the Circle of Notes).
How a musician uses the Circle of Fourths and Fifths to extend beyond a set key is called modulation. Dynamic modulation theory separates all the directions a musician can move, flip, invert, crunch, expand, and much more.
Cyclic harmony can lean either towards the 6.5 or the 2, depending on whether 1 is “moving” towards the 4 or the 5. It carries on in that manner through harmony.
This is the basis for subdominant, tonic, and dominant flow, contraction, expansion, and relevant cruxes, in this piece of dynamic modulation theory.
The 4.5 completes cyclic harmony, and creates cyclic balance. This is geometrically modelled by a 4-sided, 6 edged perfect geometrical shape, like the dodecahedron is perfect, and perfectly divides an equilateral sphere in their appropriate ways.
Music is perhaps the most malleable activity to display the sacred logistics of the universe.
The Circle of Fourths and Fifths provide four directions, ascending/descending to the 4th/5th. A player dictates their direction when they play the 1 as sub or dom. By Establishing sub/dom tendencies within any of the intervals we are allowed to keep track of many other parallel functions in music.
The 1-4 1-4.5 and 1-5 diatones are a balance of music that complexifies music enough, allowing the musician to imply quite, and its simplicities are adaptable into scales.
These scales are theories of theoretical distortion, but the principle can be applied to many facets of music.
Since music is adjustable on a geometric equilateral basis, as well as the harmonic one, musicians can work the magnitudes of their grasp on theory through enhancements on the laws of this logistic.
For example: play the penta-tonic scales, 1st as 1st, 1.5 as 2nd and onward.
This works because the music system is a spherical theoretical realm of possibility that parallels the universe. Even molecular science has musical quantification in cyclic nature.
Shifts in magnitude of complexity (dissolution/recreation) happen similarly like the changes Einstein modelled with a penta-tonic model shifting through octaves. These cyclic changes in magnitude also apply to concepts of tempo, melody, and notes. Music is always moving forward, in a way.
Playing to the fifth is as if a note is flying out an instrument and it crashed into its fifth on the way out, but the fourth, pulls the note up, and affects it a bit more. This is an example of how harmony accounts for the concept of time-event development and the activity of music, is so primal that is mostly a niche phenomena of law and force. The 4.5 and 5 respectively.
All the numbers have their own set of phenomenal representations, and their utility mechanical representation is correlative to their Greek tribe named “modes.”
Modulating music via these modes portrays their depth as such.
Take it from the 1st one way, and then the other way.
Melodies can be compressed into even smaller harmonic versions of themselves; notes, and their correlative beats played relatively faster according to mathematics very similar in algorithmic intervallic function on a linear spectrum.
This depends on the concepts of atones, pure tones, and implicative dissonance. Harmonic balance compression/distortion theory spins off of dynamic modulation theory.
This big dynamic modulation theory is as such because it gives the musician full accessibility, from any tone, into musical delineations not consistently, or properly, defined up to this point…
There are many instances where a musican has to choose to do one thing or another. Since music moves from perspectives, reevaluating options, and picking different variances enhance musicians’ work.
Sub-Dominant/Dominant theory: How a musician can move from the 1 (the tonic) towards the direction of the 4 (the sub-dominant) or the 5 (the dominant), and then further along the circle of fourths and fifths, in either direction. Each note/mode can be assigned a sub-dominant or dominant presence. This can be done in numerous ways, and can shift with modulation.
Expansion: 2, 3 , 4 are sub; 5 and 6 are dom, 7 is a sub
Condensation: 2, 3, 4 are dom; 5, and 6 are sub, 7 is a minor 3rd.
Distortion theory is as follows.
The intervals of music can be juxtaposed into exponentiall relevant scales that simulate the mathematical logistics working on a harmonic magnitude, to smaller sets.
Using this distortion theory, a musician transposes whatever scale they want into a 36 note system, by playing each note’s a diatonic “chords” 1-4, 1-4.5, 1-5.
Phrygian flip trick is something to tune of playing in the mode of Phrygian. It’s as if you chose to play the 3rd as the 4th, but it could be the one, and there’s a lot other contingencies with inversions, the 7th, and immediate note companionship that arise.
When modeling the Cyclic Balance Distortion theory, it’s apparent that Dom 2.5 is the compressed 7th. This is how Astrolabe justified a theory cited in Stephan Alexander’s The Jazz of Physics, which describes music as a series of interlocking springs.
This how Astrolabe believes this idea works logistically:
Each note would have a spring for all of their diatonic functions, which are the spectrum represented by Dynamic Modulation theory.
The spring itself is a note chain, intervals along the spring are unique identities in relation to the point of interest.
Simply it would look like this:
2- (1.5)- 1
When playing the major scale backwards at the 1st, it becomes the 3rd of its 5.5.
Astrolabe theories drawn from “Coil-Spring” theory are: That the 5th is an impactful harmony. That the 3rd is the linear opposite, the 4.5 is the physical opposite, the five is the harmonic opposite, to the 1st. That music is most simply something can happen in between modern understanding of 1-3. Hence compression/ Cyclic Balance, and Balanced Chromatic Distortion theory.
Distortion theory can be applied to other diatonic renditions speficially of 1 in unison with 3-4-4.5-5-5.5-6. This is Melodic distortion theory, it could include the 2.5 in immdiate fashion.
where as the 2, and 7 (6.5 and 1.5 symmetrically) are more maneuvarable intervals, utilitarian with bends(!) slides and most importantly(!) modulating in niches of music undenfinable except by math, and then intuition.
Every number has variabilities from its set intervals that match with modal usages. The ways in which numbers occur as intervals of 1 coincide with music, and furthermore, physics. ach note represents ocilation trajectories. But on a greater scale represent actual physics of music. Each interval is responsible for harmonic/melodic logistics in a different realm of cognated music.
let this model the impactive harmony of 5 and ascending harmony of 4, among many other direction cues of notes. These show how fundamental their identities are in symmetry not hamony. One side would hav its arrows inverted this case.
Here are more definitions for the intervals:
(Start at one, go towards the 4th or the 5, then go back the other way.)
Planar Note System Scales:
Since the spectrum of sound is best modeled as a circle with set intervals, musicians can experiment with music, by making an instrument and note-system.
If a musician wanted to use their standard 12-note instrument, they can still elaborate on planar scales because the 12-note system represents the circle of music perfectly, due to the 12-faced dodecahedron being a uncommonly congruent shape.
These scales are planar because they are symmetrical 2-D shapes drawn into the “12-point” circle of fourths and fifths.
They depict linear yet modulating sequences of notes, and are essential shapes that provide insight in how the notes naturally fractal.
The Harmonic Hexagon is the whole-tone scale:
When using a compressed hexagon, the model expresses planar movement and to Astrolabe, is a further justification for how music fractals, making chromatic music obviously harmonically relevant.
It further represents how Cyclic Balance and Cyclic Harmony (Circle of 4ths and 5ths) are the point of creation in music logistics, and everything else, that reverberates from those tight corners, are the story.
The octagon can be juxtaposed over the Circle of Notes, in three different intervals. This scale is the descent from 12-note harmonic music, to reaching into different means of harmony in the chaos of planar note-system scales (Mountain Spring theory).
The octagon allows for modal, and penta-tonic access, while also giving way for sub-modal, or micro-tonal music.
This also allows the musician to use implicative dissonance. They can use diatones to separate music into destinations and travel along the cruxes that distortion allows you to manipulate in time.
This scale in Dynamic Modulation theory is a means for travel deep in Cyclic Harmony, or during the inversion oriented “Behavioral Modes.”
They are modes of greater harmony dynamics, applied to perspective dia-tonic/penta-tonic modes/scales-
in-between phase for the tonic and note to arrange and composite their future.
-Astrolabe on “Behavioral Modes:”
-and further on hexa-tonic scales:
How numbers are relative to each other has much to do with many of the concepts used to deduce harmony, and structure in music. Numbers are based off of a linear, standardized spectrum.
Since the Earth is a sphere, and the solar system is arranged in more-or-less balanced orbits of consonance, there’s a perfection that can used to reform current phenomenal occurrences, even in human societal workings.
The power of numbers comes from their ability to divide the intervals of existence into utilities to be measured by variabilities descendenting from essential harmony.