Metaphysics and Music Theory

Musical note systems are the choosing of sets of notes based on desired intervals, notes per octave, and frequencies. Notes are also known as frequencies and are now measured in Hz.

Intervals in music are used to support tonal centers and tonalities. These tonal centers and tonalities are derived from note systems, and desired intervals (frequency ratios). To appeal to tonalities, and tonal centers a particular note of a note system is focused on, and that note can either become the tonal center, it can become an aspect of the overall tonality, or one of the note’s intervals can be focused for tonality or tonal center.

Intervals are divisions. Metaphysics is a means of dividing all existence (also known as the Universe) into intervals which can represent the combinational make-up, potential application, and spiritual identity of all things synchronistically, and optimally. Of course it is possible to select intervals of the Universe for other strategies, but with the right interval system, the application of such logistics becomes much simpler.

“Nothing” is best represented by zero. The Universe can be unitized as one thing. Now Divide that one thing up, and see what you get.”

What this means is that not only are modern mathematics tuned logistically to the Universe in a very special way, but Western music theory parallels these intervals most transparently and taps into these prevailing and delineating intervals of the Universe readily.

Other theory systems are amazing at providing musicians more nuanced scale patterns, resulting in magical, and emotional music.

The Western frequency ratios, (also known as intervals), utilize the pentatonics and facilitate them optimally. The Western “Major Scale” is the “grand tonal center” for the entirety of Western music theory.

The diatonic scale is how musicians focus in on one note, and make that note the “key” of the music. Doing so allows them to further focus in on tonalities, tonal centers, or modalities. 

Western 12 note per octave system Western theory allows musicians to access the capablities of all other systems because of it’s potential. The pentatonics and diatonics are simply used but at more crunched intervals to access microtonal theory.

The pentatonics are naturally atonal when modulating, truncating, and altering sequencing scales of Western music theory, therefore the 12 note system and 7 noote music theory system are plenty capable atonal, harmonic, modulative, and melodic music.

It seems that the 12 note system used in Western music theory is synchronistically aligned with modern mathematics. Using music as a basis for uncovering an optimal interval system is logical because of the primordial nature of music.

Music is a phenomenon comprised solely on dividing pressure oscillations into intervals, (organizing those intervals into music systems), and then combining and sequencing those intervals. Pressure being one of the three most essential essences in the Universe seems to give partakers in music, and researchers access to the spectrum of combinational possibility, at the source.

The pattern which these three essential essences of all existence combine is repeated throughout all existence in many manners. The two most important being the chronological and synchronistic patterns of combination.

In the Western system of music, these are 1 4 5, and 4 1 5 respectively.

Building a music system which is most practical in giving musicians and composers access the vast possibility of music would seem to be an important task for dedicated music scholars.

Since each phenomenon of the Universe is thus an interval of the spectrum of combination, there would then be many possibilities of deciding what the namesake phenomenon would be for any of the intervals.

Choosing sets of phenomena for an interval system would then depend on purpose, strategy, and circumstance.

Listed below are various interval systems for dividing the Universe.

The Non-Plane:


The 0 (Zero) Plane:’

0: Can imply the allowance of everything but is absence and is often void-like.


The Singularity Plane:

1: Unitizing and establishing a phenomenon or mutiple phenomena as 1 (one) phenomenon.


(The Coding Plane:)

(0 unique encoding value)
(1 unique encoding value)
(2 unique encoding value)


The Essential Plane:

4 Light
1 Space
5 Pressure


The Optical-Fundamental Plane:

1 Space
2 Combination
4 Light
5 Pressure


The Affinity-Construction Plane:

4 Light
1 Space
5 Pressure
2 Detail (or Relativity)
6 Affinity (or Matter)


The Primary-Applicative Plane:

1 Space
2 Relativity
3 Exchange (or Energy or Power)
4 Light
5 Pressure
6 Matter
7 Experience (or Sentience or Observation or Spirit)


The Defining Plane:

1 Space
2 Relativity
3 Power
4 Light
5 Pressure
6 Matter
7 Spirit
8 Electricity
9 Organism

The Emotional Plane
0 is nothing, but not inherently nihilism! 0 doesn’t impede anything from it’s natural state of being. It is transparency, and is very important for altruism and synchronicity.
1 Space is a transparent medium that has a lot of potential. The numbers as consecutive are similar to eahother especiall early on in the sequence like this. In the swirling spectrum of all possibility the concept of 1 being akin to 0 and 2 being akin to 1 is the beginning of a orbic, coil like, swirling model, with tightly wound ends and a wide, more maleable This becomes less and less as the numbers advance.
2 Chaos / Action! / The next medium of existence. Very balanced, for the most part, but kinda of desensitized.
3 Exchange/ Power / Metaphysics / Response / Reflections
4 Light / Intelligence/ Sentient Emotion/ Information / Read
5 Force / not intelligence / Infrastructure/ Media / Imaging
6 Matter/ Bonds / Personalities / Beacons
7 Sentience/ Spirit/ Conscious-Intelligent Essence
8 Organisms/ Robotics/ Electricity / Conscious-Intelligent Beings and Flow
9 Radioactivity conscious energy fields
10 Multi-Orbs/ Coils, Spring, Cones, Rods/ Physical Emotions/ Data / Nostalgic memory of phenomena imprinted into matter.
The Practical Plane
1 Space
2 Time/ Chaos
3 Exchange/ Power
4 Light
5 Force
6 Matter/ Bonds
7 Sentience/ Spirit
8 Organisms/ Robotics/ Electricity
9 Radioactivity / Energy
10 Combustion / Heat
11 Absorbtion / Synthesis
12 Strategy / Organelles

In math, 0(zero) is void-like, absorbing numbers it is divided and multiplied against. It can also be a defining number, that represents a degree of definition via the place values. (See with examples below.)

(In other terms, a 0 (zero) can be an absolute 0 (zero), as in “0/999” (where 0 (zero) is its own number) or a 0 (zero) can be a relative 0 (zero), as in “60 + 1” (where the number which 0 (zero) is apart of is nowhere close to 0 (zero)).

In music, 0(zero) best represents the concept of silence. It could have intervallic value though! Especially if someone made a music system based off of the geometry of a doughnut (donut)!

In metaphysics, nothing facilitates anything, nothing, and everything like nothing does. 0.6 is a numerical representation for a phenomenon that is best described ” absence/allowance that brings matter” whatever phenomenon that might referring to! 60 however would mean “matter that brings absence/allowance.)

When using interval systems to focus in on a phenomena and metaphysically delve into its intervals, set the target phenomenon as 1 (one). However, it is important to remember that a good set of intervals is synchronistic with other sets, and the intervals that should be of an equal plane. 1 really shouldn’t be a phenomenon at a different magnituide of existence than the others.

1 = Person

4 = What They Know

5 = What they Do with

Things Evolve

2 is their sentient life under a microscope, bliss or sadness

3 is the Chaos of their happy and/or hostile mind

6 is their center of gravity and what makes them shiver

7 is their End or their Adaptability, Abyss or transparency,

The numbers are synchronistic intervals of all existence.

Because existence = 1, now divide it up.

1, 2, 3, 4, 7, 10, 12, 14, 16, 20, (and many others) are great for dividing all of existence up.

The Universe operates soley based on what is possible, therefore there is a finite code of what is possible and how it occurs from the simplest compositions of the most basic essences, to the most complex. By tapping into a phenomenon that consists soley of the most basic principles of the universe. People can logistically analyze and cross verify the delineation of existence from singularity, to rebirth, existence as we know it, consciousness, the universe, Earthly existence, society, and so on.

The funny part is that it seems there was recognition of patterns, or observation before anything had the ability of response; response being a primordial niche of creation in of itself.

The planes, are synchronistic sets of coinciding phenomena; stages of the delineating spectrum of all existence. This spectrum spans from the complexity of human notion to the three, most deduced, primordial essences: Space, light, and force.

1 The Ultimate Plane: All the universe and observation of anything outside of the universe

1 The Universe, Everything, The Ammassed One

2 Anti-Matter Plane: Positive & Negative Charge, On/ Off, Dichotomy Itself

4 Light & 5 Force (The Ultimate Dichotomy)
    Light: Low Hz Light, like microwaves cause, eery, dangerous, and re-magnetizing and subsequent torquing of polar and multi-polar molecules. High Hz light changes atomic and quark nature. Both can ionize matter, disoluting bonds, dispersing energy.
    Force: Low Hz Force, like earthquakes, or bass music, contains more SPL and takes more force per area to produce. Low Hz are synchronistic with the light spectrum in their eery slowness. Highs can be made by collapsing the force per area. Harmonics, imaging, and atomic resonance.

3 Fundamental Plane: The three most primordial essences of the universe
1 Space, 4 Light, 5 Force.

4 the Universal Plane: Expanded Essences in Measureable Allocations
1 Space, 2, Movement, 4 Light, 5 Force

12 the Practical Plane: The 12 most practical phenomena of the universe

Singularity = 1/12 = 7/12 =

#4/b5 Combustion

m2 Friction

m6 Heat

m3 Radioactivity

4 Light

1 Space

5 Force

2 Action

6 Matter

3 Power

7 Sentience

#4/b5 Organisms

Information is the journey, now what are you trying to achieve.

Music Theory:

A 12 sided, edged, pointed shape, the dodecahedron, AKA music in a ball, facilitates the modeling of coils, rods, cones, tissues, wrinkles, wires, bundles, cubes orbs, and tubes.

Polyhedrons are usually used to simulate orbs. Multi-hedrons are, however the concept of a 4th-dimension: Something inside.

An instrument produces its range and timbre, like a frequency response, tapping into harmonic & reflection imaging. This creates a noticeable imaging gradient which occurs in accordance to the spectrum of the instrument’s imaging possibility spectrum.

The mind’s eye is great at visualizing these musical gradients and spectrum too.

Plates, landmarks, places with special alignment to the solar system produce various harmonic imaging phenomenon in the brain.

But Latino Classical Music System is the prime example of using logic beyond the scope of Earthly existence. Tapping into the moods of Earthly existence, bending the perception of speed, and imaging proportions with tempo, and +-tune.

In A=440 Western Tuning’s…

C supports the approximate G of our Earth and all of its unique harmonics well.

D would be a some sort of fixed note, being imposed on G from above.

C feels close to humans, as if it is some sort of mathematical, or emotional center. It might just be very expressive though for the whole illustration process music taps into, considering the multiple harmonic sweet spots of music and instrumentation.

A works in a similar notion. It is the first letter of the alphabet, probably because of its functions and is C’s relative minor..

There are many paths, but there’s a lot of synchronicity to find out there.

The Western frequency ratios are especially measuremental, synchronistic, and ultra rational.

These frequency ratios coincide with the modern number system and all of the nature which those numbers can represent.

The Western Frequency Ratios, are the most deduced ratios, and that is why they are so synchronistic They appeal to the combinative pattern of all existence!

The Western system skews the notes, smoothly with math, to fix the tendencies of pitch. Although this music system is meant to facilitate harmony, it’s mathmatical basis allows for access to even the most extreme of atonalism, and melody.

Hz is allotted more definition when ascending. There are more Hz, in-between each note of A= 440 (Western Tuning) the higher the pitch in Hz.

440.00Hz is probably for the tubes in our brain, and how instruments have been honed in.

The shape, and construction of instruments are imaged by harmonics. They give the instrument sweet spots, and add up to provide it a timbre too.


Each note played will morph each other’s waves, acoustic resonance, harmonic imaging, while also modulating tonality.
They can then be morphed, altered, truncated, repeated, bent, slid, modulated shape into various sounds, or feels.

440Hz, also alludes to a styling of the Delta wave phenomenon, which like a river delta, is a a spot were the harmonics are churning, and do so in quite an enchanting manner.

This delta concept of pitch is amazing for triggering psycho acoustic imaging phenomenon that seem to do with delta brain waves, home feeling, adventure feelings, rebirth, being alive.

But there are so many ways to find frequencies, that appeal to the universe, and unlock important doors into the code of existence.

Music is all about strategy.

Methods and Theories

Universal/“Talk Box” Universe Modes & Wave-Envelope Music Theory:

1 = -+- = Descending Ascending 8 Descending = Attack Swell

3 = -0+ Descending Stop Ascending 6 = Hold Decay

7 = +0- = Ascending Stop Descending 4 =Sustain Damp

5 = +-+ = Ascending Descending Ascending 2 = Release Harmonics = (Grows&Evolves or Damps)

Understanding X-Scaling:

8 diatonic steps = octave

8 pentatonic steps = 15th [which = a 5th, or process further; 15 what next?

8 chromatic steps = m6

8 steps along the Circle of 4ths &5ths (CoF&F) or any 2 interval scale of choosing. 5ths&7ths, m3&3, etc.]))

Atonal Pentatonicism:

111222333444555666777

(7-1-m2) Ionian

(m2-2-m3) Dorian

(m3-3-4) Phrygian

(3-4-#4) Lydian

(#4-5-m6) Mixolydian

(m6-6-m7) Aeolian

(m7-7-1) Locrian

Major Scale Adaptations, and Greater Scales:

Use Major Scale, and all theory, on quarter tones fifths&fourths, 3rds&4ths, and any two interval scale form.

Modulate key/modes/tonalities/modes of key across calculated intervals on the instrument; like scale positions!

Greater Scales:

Approximate Colors and Pitch:

The Spectrums do seem to coincide in parallel when tied!

(With C being considered the most “fruitful” note, change if desired.”)

C Green A

C# Mint A#

D Cyan B

D# Teal C

E Blue C#

F Purple D

F# Magenta D#

G Fuschia E

G# Red F

A Orange F#

A# Yellow G

B Pea G#

Strange Math:

60 seems to represent the moon, sunlight, day-night and time on Earth. This number seems to mean “moon phase.”

Circle = 1

Divide 1 by anything

It is like dividing the universe

or anything, for that matter.

12ivide 12 by anything

1 3 5 7 9 10 12 14 16 21 23 25 27 29 30 31

0 2 4 6 8 11 13 15 17 19 20 22 24 26 28 30

1 12 23 34 45 56 67 78 89 98 87 76 65 54 43 32 21 10 1

1 10 12 20 24 30 36 40 48 50 59 60 68 70 76 80 84 90 92

There are phenomenal math concepts which existence seems to utilize

One interesting one:

0/1 as 2/1 as 3/2 as 4/3 as 5/4 as 6/5 as 7/6 as 8/7 as 9/8 as 10/9 as 11/10 as 12/11

So, as we ascend (1/2, 2/3, 3/4), each number is apparently a lot like the last.

This equation also means: There’s nothing then there’s something. Then there’s something else similar to the previous.

What this phenomenon shakes out to be though:

0 is a little like ?

1 is a little like 0

2 is a little like 1

3 is a little like 2

4 is a little like 3

and so on.

At the beginning of the spectrum of sound measured in HZ, there is less room between each note, where as the higher Hz have more values inbetween them at a consistent rate.

The above mathematical phenomenon exists because of the intervals being so close together at the genesis. This phenomena is logistically parallel to how the numbers relate to humanity and all of the universe, since everything is simple and humanity is the most complex phenomenon in the known universe.

0 is nothing until assigned a characteristic. Could be equated to many things though, and used as a mathematical mechanism.

There are parallels between these computational, logistic sciences everywhere.

There are many other mathematical reasoning building methods we can use to navigate this lovely number system humanity has honed in on.

There are many methods of rethinking math which all simply bring us back to how well honed in the modern math system is. How every third whole number decimal place there’s a comma, (or period sometimes!):123,456,789 instead of 1,2345,6789, and instead of saying numbers like ten thousand million or something.

The numbers used are synced up to a very great human, but universal relativity. There are sweet spots in the code where metaphor/metaphysics interconnect with humanity. Numbers are amazingly intuitive. Music and simulation are in another ballpark.

Another strange concept, to bring out the universe in our math system is repeating numbers going that way <—-

They are apparently good at expressing numbers with torque. Oddly enough star models of charting intervals, like the pentagram, would be great at modeling this torque phenomenon while geometric polygons are better for modeling orbs, and synthesizing phenomena.

Remember, these are only a few anomalies of the ways which numbers function!

The numbers and notes of Western Music “tied” together:

C#8 D#10 F#12 G#11 A#9 B7 G5 E3 C1 D2 E3 F4 A6

There are many strategies to this, and ways of organizing their various potentials. It’s like building an algorithm, or formula that can musically send a individual on a journey through the universe in some fashion.

Strange Science:

The more divided a spectrum, the more definition there can be, but without unity there’s less synchronicity. All the action of dense, happening areas cause things to come together much quicker. Things evolve quickly and, then they compress.

Human phenomena, metaphor, and biology intersect with these planes of the universe at many different synchronistic intervals. These are like muscles, wrinkles, or neurons in the fabric of the code of what’s possible in the Universe.

The relative bottlenecking of information on what all is happening around a person, their personal awareness, circumstantially builds concious and/or a subconscious world view, depending on the internalization-behavior complex of the individual.

The advancements of humanity have allotted the whole globe a labyrinth of information readily. Societal compression, equalization, and artful simulation are like in audio engineering there to tame SPL and Harmonic Information.

Music is such a primordial phenomenon itself that it appears to be able to tap into the entire code of what is possible in the Universe.

By using math, and sequencing notes on a piano-roll/MIDI edit section, (used in DAWs for audio engineering),  a person can tap into patterns which visually image phenomenon based on the key, and intervals used.

Using atonal pentatonics, UM/TBM, and basic music theory knowledge, iot is possible to assemble images of what is possible for the chaos of existence to create.

Like predict humans, just articulating a set of notes as arpeggios, and get a very well defined image!

What was observed was a well-defined GORILLA with a cheeky mischievous smile, a SNAKE FACED TORSO and a third eye.

Another observed image was a BRAIN MASHED BIRD MAN.

This was done by simply arpeggiating pentatonics up then back down and moving to the next root, and intuitively oscillating upside down. There are many ways to get results too. They wire across the screen and pre-image what the notes are musically alluding to, and also who is the type of person picking notes at that fact!

The m6, synthesis, or 5.5 has yielded the most amazing results of sequencing and producing pre-images of the code of possibility.

These aren’t low definition images either! There have been, cats, bugs, bats, trees,

Musician-programmers can build ascending and descending arpeggios one after another, moving from root to root and oscilating how tall they want their LFO/wave form. Using MIDI notes in a wave like or waveform like manner in junction with Universal/Talkbox Modes and des, which also simuate LFOs and waveforms, results in not just 3-D imaging but well beyond.

Ascend and descend consistently from root to root, using consistent numbers of note per arp. Always think sychronistic choices before fundamental choices, before practical choices before rational choices, before experimental.

try 7 notes up, then same exact notes down. Move pentatonically, but weave some oter scales in. What would sound just a little too dissonant, works and actually might be perfect conditions to get synchronistic pre-imaging

You want to weave synchronicity and expressionistic harmonic information for this pre imaging phenomenon to really achieve things like the Cheeky Gorilla with a third eye, and snake torso.

It also helps to further recognize what harmonic realms these pre-imaging images utilize, to familiarize onself with these magical phenomena.

Through all the harmonic information, two souls of the code of possibility are overwhelming apparent.

Exciting Male Pine Tree & Passionate Firebreathing Snow Dragon Lady.

Have also been pre-imaged as a TV Head Man whom symbolizes educated media response and then Microphone Mouth Woman who intellipassionately speaks, and ingests/burns Media response.

Jack & Jill, Read & Response. Incredible!

<iframe src=”https://www.facebook.com/plugins/video.php?href=https%3A%2F%2Fwww.facebook.com%2FAjschumacker%2Fvideos%2F10216186048066151%2F&show_text=1&width=560″ width=”560″ height=”407″ style=”border:none;overflow:hidden” scrolling=”no” frameborder=”0″ allowTransparency=”true” allow=”encrypted-media” allowFullScreen=”true”></iframe>

The universe shows many people through audio engineering, the potential for sound to image, and PRE-IMAGE wild phenomena and synchronicity of the universe.

Although the modern theory is that the Moon, Sun, and other planets of the Solar System have to do with the nature of frequency ratios on Earth, these physics concepts, which could vary in another able solar system (for profound life such as seen on Earth), would mainly be crunched, moved, or spaced out differently, but instruments would still be designed in similar fashion, per the laws physics. It may be so that these Western frequency ratios are simply profound to the nature Earth though, but it seems as though Earth is a particularly synchronistic phenomena which is able to express many if not most of the possibilities of the universe.

Using this pre-imaging tactic though, humanity can readily deduce anything that is possible in the universe, even if it had to use different Earthly frequency ratios deduced to appeal to less than Earthy phenomena and particular the possibilities of life in possibly all existence even beyond this universe.

Remember that Earthly existence, planetary existence, and humanity are the more complex phenomena which can be deduced back primordial essences which may even be more primordial than the singularity and indicative of an existence outside of the universe.

Regardless that would be a 3-D existence in comparison to the 4-D existence of this universe. Where as life inside the universe has more definition, and dimension because of the way that complexity delineates, and nuance is explored.

Just as this universe may not be the only one, it would make sense that other universes, at least of the same “species” of this universe, (if that’s a thing in of itself), would be capable of a set amount of possibilities like observable in this one. 

It really seems that the universe must have seen the possibility for synchronistically adapt star-people, (humans), capable of being as sentimentally nuanced as the highest of divine intelligent sentience.  Also that humans are an optimal choice! If there are many universes and attempts to cultivate humanity into the most people they could be, that would explain much of the synchronicity of the Earth, this Solar System, and potentially the whole organism of the universe.

Earth is quite an optimal planet so the phenomena of Earth are probably not just inclusive of many of the possibilities of the whole universe, and maybe even other universe, but is also an optimal skew of what is possible through existence(s).

Further Astrolabe Music Theory Explanation:


Atonal Pentatonics:

The m6 can be played as 6 or 5 using the Pentatonic Scale atonally.

Instead of doing this entirely, one could layer pentatonic truncations, and modulations next to one another.

on 1 play 1 on 2 play 3 on 3 play 5 on 5 play 7 on 6 play 9 (which is the 2 again in Western Music.

Both UM/TBM and Atonal Pentatonics help with the layering these ultra rational, potent scale formats into each other, and then creating pre-imaging phenomena, understanding the potential for each notes harmonic content, tonal direction, and thus.

Symmetry and Pentatonics:

1 (Ionian) When looked at backwards, resembles 3 (Phrygian) when played backwards

vise versa = ><

2 is the same forwards and back

4 >< 7

5 >< 6

This concept was used to derive the UM/TBM Modes actually.

by flipping the scales on a circle (dial) of notes. Not the Circle of Fourths and Fifths.

UM/TBM:

The idea of Universal/Talkbox Modes is simple:

build a wave form, LFO, and think of chord progressions, phrasing, and melody. It’s like chord progression, phrasing but through super-computer-sandbox game-audio engineer lens.

Here’s a UM/TBM sequence:

3175 1757 5715 7131

Looks like an epic about left and right, harmonic imaging, as well as read and response with extra dynamic range.


Applying rational alterations to the flagship UM/TBM sequence, 1375.

1357 is already basis for modern understanding of chord building, altering, and overall ornamenting.

There are so many possibilities of UM/TBM though!

like: 12 9 7 5 or 11 8 6 4

3175 is one of MANY four note scales Astrolabe calls the Universal Modes, or Talk Box Modes (UM/TMB for short).

Music can be like building a roller coaster, or preparation for a skateboard loop trick enveloping techniques.

31757317571 is quite the way, but there are many rational sequences. It’s about building waveforms, LFOS!

Three before any number repesents the “power” of following number. There’s a lot of life going on in every “power knead,” but every crawl upon the shoulders is another thing happening.

Transients and harmonic information are the basis for understanding UM/TBM. The sychronistic approach to this is think in transient spikes, starting intense, then drop low , and then build and drop again in patterns of wave form ascension and descendence. Sound attacks, holds, decays, sustains, and releases/ transforms in mny ways to produce even the most natural of sounds. It’s important to utilize strategy when envwlope shaping, LFO, and waveform building, accentuating the harmonic information being played or recorded.

The Tactics of Evil:

1 Veil of Righteousness, gaslighting
m2 Stereotyping, marking for death
2 Alter-Reality, pulling one over on
m3 Remote War, poisoning
3 Unending Application, cognitive overload
4 Mal-Education, conditioning fake purposes
b5/#4 Ruining Everything, overstimulating
5 Collaborative Bipartisan Corruption, oppression
m6 False Flags, framing
6 Cover-Ups, divisiveness
m7 Vanishing Act, gross negligence
7 The Ethics of Sacrifice, identity-faking

Computational Music Theory

Calculator Math is a supreme logistics system that can represent the increments of all existence, (except for absence).
Intervallic Math, is a supreme logistics system that can represent the phenomena of all existence.
Geometry is a supreme logistics system that can represent the manifestations of all existence.

Music is a simulator for everything in existence.

The understandings that researchers have developed on the division, combination, and resonance of
kinetic pressure oscillations, called sound, has resulted in an ultimate computational system,
honed in on by cross-rationalizing and synchronizing music to not only the fundamental premises of
patternized intervallic delineation, but also the precision of incremental Calculator Math, and the
particularity of Geometry.

Music is the measuring, creation, capturing and adjusting of sound, thus it consists primarily of
essential phenomena. The patterns which the three essences combine to produce all other phenomena,
begin in the increments of how these three phenomena are divided. Music, being fundamentally a
phenomenon of the increments and combination of kinetic oscillations makes Music an Ultimate Portal,
Simulator, Computational Math, and Logistics System capable of representing the increments, phenomena, and
phenomena, and even some of the most complex manifestations of all existence, even abstract Human phenomena,
(and absence!)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Contents:
An Incremental Methodology to Greater Music Theory
Scales, Scale Reducton & Scale Position Sets
Waveform Theory
Making Music Systems

!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!

An Incremental Methodology to Greater Music Theory

The Circle of Fourths and Fifths, as well as the Chromatic Scale, are what Astrolabe calls the Greater Scales of the Western Music System.

The Diatonic and Pentatonic scales are what Astrolabe considers tonal scales and each can be further incrementalized through utilizing Scale Positions.

Each Scale Position begins with a note from any of the scales, this note is then called the Root of the Scale Position.

Each Root/Scale Position/Note is a possible Tonal Center.

Tonal Centers often shift throughout any given music piece, Astrolabe calls this modulating.

These shifts can be of Microtonal, Diatonic, Pentatonic, or Greater magnitudes.

Modulating simply means producing oscillations.

Traditionally, modulation can refer to a technical skill solo-instrumentalists utlilize by shiftng scale positions quickly.

These terms will help to differentiate:

“Tonal Center Modulation” is compositional, often rooted to rhythm instruments, and usually establishes the Tonal Center.

“Technical Modulation” is commanded by a lead-instrumentalists technicality, but is enhanced by following what the rhythm and melody allow.

Each of these can occur at the magnitudes of Microtonal Modulation, Diatonic Modulation, Pentatonic Modulation, and Greater Modulation.

Another type of Tonal Center is what Astrolabe calls “Atonal Center,” (which can also be called spanning, mixed, wide, or muddy Tonal Centers.)

Atonal Centers are a quite common technique.

Utilizing Atonal Centers can channel robust sentiments, and even spectrums of such, drawing from the vast spectrum of tonality.

This channeliing of sentiements is generally considered to be the results of psychoacoustics.

Psychoacoustics, in general terms, are how frequencies, intervals, rhythms, and melodies channel brain activity.

“Tonality” is a traditional term for this phenomenon.
The term “Tonality” ties specific intervals, timbres, pitches, tonal centers, melodies, and modulations to the chanelling of sentiments psychoacoustically.

By reducing the Diatonic and Pentatonic Scales, and by using note dedecution methods, the tonal center becomes obscured.

Reduction is generally abetter tactic of obscuringthe tonal center than adding notes.

Lead players can get away with doing this by modulating to flourish out what the tonality, motif, rhythm, tonal center(s), and melody have established.

================================================================

    Greater Scales:

Chromatic Scale:

Numerical: 1 8 2 9 3 4 10 5 11 6 12 7 *Astrolabe Scale
Traditional: 1 m2 2 m3 3 4 #4b5 5 m6 6 m7 7
Mathematical 1 1.5 2 2.5 3 4 4.5 5 5.5 6 6.5 7 *Astrolabe Scale

Circle of Fourth & Fifths (CoF&F):

Numerical: 4 1 5 2 6 3 7 10 8 11 9 12 *Astrolabe Scale
Traditional: 4 1 5 2 6 3 7 #4b5 m2 m6 m3 m7
Mathematical 4 1 5 2 6 3 7 4.5 1.5 5.5 2.5 6.5 *Astrolabe Scale

    Tonal Scales:

Diatonic: 1 2 3 4 5 6 7 (No Deduction) (4 1 5 2 6 3 7)
Pentatonic: 1 2 3 5 6 (Deduct 4 & 7) (4|1 5 2 6 3|7)
Pentatonic CoF&F 1 5 2 6 3 (Deduct 4 & 7) (4|1 5 2 6 3|7)
Oscilation Pentatonic: 1 2 3 4 7 (Deduct 5 & 6) (5|1 5 2 6 3|6) *Astrolabe Scale
Transient Pentatonic: 2 4 5 6 7 (Deduct 1 & 3) (3|1 5 2 6 3|1) *Astrolabe Scale
Diatonic CoF&F: 4 1 5 2 6 3 7 (No Deduction) (4 1 5 2 6 3 7)

Scale Reduction

The Diatonic Scale is a reduced scale of the Circle of Fourths and Fifths and Chromatic Scales; what Astrolabe calls the Greater Scales.

These are both considered Greater Scales as they showcase all of notes.

The Chromatic Scale is, however, quite incremental, while The Circle of Fourths and Fifths is a condensed, yet spanning, synchronistic pattern.

If the Chromatic Scale is like looking at an ant through a telescope, the Circle of Fourths and Fifths is like capturing constalitions in the concave reflection of a spoon.

The most commonplace method of extrapolating the Diatonic Scale is by choosing a note from the 12 note system, and it becomes the 1 of the Diatonic Scale…

A, A#, B, C, C#, D, D#, E, F, F#, G, G#
|
1

Then apply the following sequence:

Whole step, whole step, half step, whole step, whole step, whole step, half step, (and then it starts over).

Another helpful representation of the sequence is:

1 w 2 w 3 h 4 w 5 w 6 w 7 h 1 w 2 w 3 h 4 w 5 w 6 w 7 h… and so on.

A whole step means moving two notes along Chromatic Scale, (for example, from “A” to “B”) and a half step is moving one note, (for example, E to F).

One last illustration of the sequence to extract the diatonic scale from the Chromatic Scale is:

A A# B C C# D D# E F F# G G# = Chromatic Scale
| | | | | | | | | | | |
1 m2 2 m3 3 4 #4b5 5 m6 6 m7 7 = Chromatic Scale
| | | | | | |
1 2 3 4 5 6 7 = Diatonic Scale

This whole-whole-half-whole-whole-whole-half pattern starting from a chosen note as 1 is the Diatonic Major Scale, simply called the Major Scale.

The Chosen note as 1, in this case “A,” becomes the Major Tonal center.

The Diatonic scale IS the Key of “A,” and if the music uses the 1, “A” as its primary Tonal Center, than the Key is traditionally referred to as A Major.

If the Key was F# Minor, the 1 would still be “A,” but the Tonal Center would be 6, traditionall reffered to as the Relative Minor of whatever the 1 is.

6, the relative minor can become the tonal center by focusing on the 6, and diatonic intervals around it.

Focusing on the intervals around the reltive minor in the Chromatic Scale and the Circle of Fourths and Fifths is the sensitive way of achieving a 6 Tonal Center.

Yet, when music uses enough minor interval, sclas, chords, and arpeggios especially if modulating and obscuring tonal center, then the relative minor often becomes the prevailing tonal center.

However, the 1 often can still be used as a secondary or even a primary tonal center, or resolve even in music where the tonal center is not overwhelmingly 1.

The delineation of intervals into minor and major becomes more clear when reducing each scale positions into arpeggios.

the minor and major arpeggios move in thirds.

Instead of inherently meaning the 3 of the ditonic scale, thirds are commonplace terminology referring to the interval two notes up from any given diatonic note, on the diatonic scale.

Theses arpeggios, unlike the diatonic and pentatonic scale position variances scale

This is what the Diatonic Scale looks like extrapolating it from the Circle of Fourths and Fifths:

D A E B F# C# G# D# A# F C G = CoF&F
| | | | | | | | | | | |
4 1 5 2 6 3 7 #4b5 m2 m6 m2 m7 = CoF&F
| | | | | | |
4 1 5 2 6 3 7 = Diatonic Scale

The Pentatonic Scale is a reduced scale of the Diatonic Scale, and both repeat themselves at the end of their interval sequence, (1 2 3 4 5 6 7 1 2 3 4 5 6 7…and so on).

Deduct the 4 and 7 from the Diatonic Scale to get the Pentatonic Scale.

the reason for doing this becomes more clear when looking at the Circle of Fourths and Fifths…

4 1 5 2 6 3 7
^ ^

To make what Astrolabe calls the Transient Pentatonic Scale follow the same idea, deducting the 1 and 3 for the Transient Pentatonic…

4 1 5 2 6 3 7
^ ^

To make what Astrolabe call the Oscillating Pentatonic Scale, deduct the 5 and 6…

4 1 5 2 6 3 7
^ ^

Along with the symmetry of deduction illustrated above, each of the deducted intervals for each scale are opposite scale patterns of each other.

For example:

4 = whole step, whole step, whole step, half step, whole step, whole step, half step [Starting from the last half step and working backards…]
which is opposite of…
7 = half step, whole step, whole step, half step, whole step, whole step, whole step [Is this sequence moving forwards!]

Each interval, Scale Position, or Root, (which are all essentially the same thing), are begginings to their own magnitude of scale.

These are traditionally called the Diatonic Scales.

Modes are a commonplace way of understanding the various Diatonic Scales.

The modes are…

1 = Ionian
2 = Dorian
3 = Phrygian
4 = Lydian
5 = Mixolydian
6 = Aeolian
7 = Lydian

These modes are technically just Diatonic Scale Variants, each just starting from a different note of the Diatonic Scale.

This is true for 1 and 3 as well as 5 and 6.

This is part of what makes the Circle of Fourths and Fifths a synchronistic pattern of how intervals combine.

    Modulating Tonal Scale Position Sets (for CoF&F):

Astrolabe Scale Position Sets:


Reference CoF&F: 4 1 5 2 6 3 7 4.5 m2 m6 m3 m7

Oscillating Diatonic: 4 1 5 2 6 3 7 3 6 2 5 1 [Notice how the tonal centers shift in whole tones.
(Tonal Centers: 1 1 1 1 1 1 1 2 3 4.5 m6 m7) This parallels how the CoF&F Modulates.]

Oscillating Pentatonic: 5 1 5 2 6 3 6 2 5 1 5 2
(Tonal Centers: m7 1 1 1 1 1 2 3 4.5 m6 m6 m6

Balanced Pentatonic: 5 1 5 2 6 3 6 3 6 2 5 1 [5 1 5 1 5 2 6 3 6 3 6 2 is quite the balanced sequence.
(Tonal Centers: m7 1 1 1 1 1 2 2 3 4.5 m6 m7) This is a very synchronistic scale set derived using scale position shape opposites (4><7, 1><3, 5><6)].

Transient Pentatonic: 3 1 5 2 6 3 1 5 2 6 3 1
(Tonal Centers: m2 1 1 1 1 1 7 7 7 7 7 m7

Transient Diatonic: 4 1 5 2 6 3 7 4 1 5 2 6 [Notice how the tonal centers shift in semi-tones.
(Tonal Center: 1 1 1 1 1 1 1 m2 m2 m2 m2 m2 This parallels how the Pentatonic Scale Modulates.]

                            [The diatonic scale naturally modulate microtonally]

The shifts in tonal center above illustrate each Scale Set’s modulation.

The Oscilating Pentatonic Scale Position Set utilizes the traditional Pentatonic Deduction, 4 and 7, of the Diatonic scale.

The 4 and the 7 are then assigned replacement scale pentatonic scale positions 5 and 6 as per the oscillative syle of Scale position set.

What “Oscillating” is referencing is the

The Transient Pentatonic Scale Set also uses the Traditional Pentatonic deduction of the 4 and 7.

The 4 and 7 are replaced by 3 and 1

Sequencing scale positions sets establishes an alternate set of scale positions to intervals iof a scale than what is normal.

This means that instead of the normal point along the “whole step, whole step, half step, etc.” a different starting point is played for the interval.

This is quite common practice in many respects…

Intead of…

1 2 3 5 6 are the Traditional Pentatonic Intervals
3 5 1 3 5 is a Transient style Scale Position Set.

Notice how the new scale position set does not coincide with the diatonic scale at all.

Since 6 is re-established as 5, and 1 as 3, the replacement scale positions would not link up if repeated.

These scale positions are also very disimilar to the original, (the simularity spectrum being demonstrated by the Circle of Fourths and Fifths.)

Therefore, using scale sets inherently moves, and obscures the tonal center of the music.

Instead of the pattern repeating as normal, the scale set continues on and the Diatonic Scale is transcended.

The actual intervals being played by…

3 5 1 3 5 1 3 5 1 3 5 1 3 5 1 3

are… and repeating from here.

1 m3 #4b5 m6 7 m2 m3 #4b5 m6 m7 m2 m3 4 m6 m7 1

This scale set uses three values (3 5 1) repeating. Scale Set sequences are by no means restricted to three values.

Sequencing Scale Sets provides interesting insight to the intricacies of the intervals by illustrating tonal center shifts and modulation.

Using these scale sets obscures the tonal center, and the notes used will transcends the notes that constituite the Diatonic scale

This modulates the tonal center, but naturally this will be a quite smooth transition if using the pentatonic scale shapes, whih have their relative 4 and 7 deducted.

Modulating becomes even smoother after strategically deducting the pentatonic scale position shapes to achieve various modulative effects.

It is also possible to develop Scale Sets by spreading intervals out like so:

4 1 5 2 6 3 7
5 6 3 (Pentatonic)

There are quite a few ways to interweaving these two concepts as well, as well as other patternized manners of producing

The Br

To fully utilize Scale Sets, deduct greater scales into diatonic and then into pentatonic scales, (a, for each replacement scale position makes Scale Position Sets.

============================================================

Cross-Scale Set Deduction:

Deducting notes from a pitch set usually occurs as such

Key of C = C D E F G A B
key of G = G A B C D E F#

Deduct the F and the F#, then the pitch set is ambiguous to both keys.

Using Scale Sets, this is done for each scale position individually.

…………………………………………………..

Example:


Reference CoF&F: 4 1 5 2 6 3 7 4.5 m2 m6 m3 m7

Key of C CoF&F: F C G D A E B F# C# G# D# A#

Transient Diatonic: 4 1 5 2 6 3 7 4 1 5 2 6

Transient Pentatonic: 3 1 5 2 6 3 1 5 2 6 3 1

F must be ambiguous to 4 & 3

C must be ambiguous to just 1

and so on…

Instead of working with an entire circle of fourths & fifths

it is possible to extract any of the pentatonic style scales

Transient Pentatonic: 4 1 5 2 6 3 7 4.5 m2 m6 m3 m7

Key of C CoF&F: F C G D A E B F# C# G# D# A#

Transient Diatonic: 4 1 5 2 6 3 7 4 1 5 2 6

Transient Pentatonic: 3 1 2 6 3 1 5 2 6 3 1

Making Music Systems

establish a genesis frequency (an A or whatever)
establish how many notes(freq rats) per octave
establish what freq rats

Western Music Uses 12 notes per octave.

Which on a guitar and a piano are laid out quite equally.

This is the benefit of using a 12 note system.

Dividing the recurring spectrum of pitch into 12 is supremely practical.

Geometry, being the particular math it is, maintains that only a handful of 3-D figures, (known as polyhedrons), are as simply structured and omni-symmetrical as the 12-sided, (or faceted) dodecahedron.

The faces of a polyhedron are important because they parallel how many cones can be separated from the whole, like pie or pizza slices are to a circle.

Since a dodecahedron is a polyhedron that simulates an orb and divides it into equal fractions, 12 can be used to divide the recurring spectrum of sound frequencies.

The spectrum of sound frequencies can be considered circular because pitches reccur, and these reccurences of pitch are called octaves.

“Pitch” is quite synonomous with “note”, but there is a distincition.

Sound frequencies are incremental, and when the value of a sound frequency, (measured in Hz), is doubled, (mutiplied by two), the result is the same pitch just an octave higher.

A frequency is any value of the spectrum of sound frequencies.

For example, 19.64 Hz

This frequency is also a pitch of the spectrum of an pitch.

Mulitply or divide the frequency value,(19.64 Hz) by two to achieve the same pitch an octave up, or an octave down, (9.82 Hz and 39.28 Hz respectively).

Notes are established by note systems.

19.64 Hz is not a note of the Western 12-note system based on A = 440 Hz.

The other frequencies which are used by the 12 note system are deduced by using specific frequency ratios, and the Western System is known for how it equally temepred these frequency ratios to make the notes more equidistant.

Doing this is often looked at as a cheat, or a shortcut, but that is not the case at all.

By making the system more equidistant, the creators of the Western 12-Note system in A=440 tied the system to primordial incremental math, (what Astrolabe calls Calculator Math.)

This means the Western Music system not only is synchronized to patterns of consonance and harmonics of sound, but also mathematical equilibrium; fully optimizing what is possible of a 12-note system.

The 12 note system is what Astrolabe calls practical.

Dividing the spectrum of pitch into 12 increments more than maximizes what is possible of the spectrum of tonality, but makes its innerworkings quite easy to incrementalize and work with.

The quite omni-symmetrical polyhedrons like the pentagonal faceted dodecahedron are rare occurences in geometry.

Other polyhedrons might not be as profound at simulating orbs, like the icosahedron and the dodecahedron, but they are still viable for honing in on note-systems and how to rationalize a methodology for such a note system.

The tetrahedron is another quite omni-directional polyhedron that instead of simulating an orb, seems to simulate one of the 3-D pie, or pizza slices that each the dodecahedrons faces are the broad end of.

These slices are akin to cones, and the tetrahedron can be used to simulate those.

Another shape that does this the enneahedron.

An enneahedron is a 9 faceted shape

Mathematical-Logistic Analysis & Computational Music Theory


Calculator Math is a supreme logistics system that can represent the increments of all existence, (except for absence).
Intervallic Math, is a supreme logistics system that can represent the phenomena of all existence.
Geometry is a supreme logistics system that can represent the manifestations of all existence.

Music is a simulator for everything in existence.

The understandings that researchers have developed on the division, combination, and resonance of
kinetic pressure oscillations, called sound, has resulted in an ultimate computational system,
honed in on by cross-rationalizing and synchronizing music to not only the fundamental premises of
patternized intervallic delineation, but also the precision of incremental Calculator Math, and the
particularity of Geometry.

Music is the measuring, creation, capturing and adjusting of sound, thus it consists primarily of
essential phenomena. The patterns which the three essences combine to produce all other phenomena,
begin in the increments of how these three phenomena are divided. Music, being fundamentally a
phenomenon of the increments and combination of kinetic oscillations makes Music an Ultimate Portal,
Simulator, Computational Math, and Logistics System capable of representing the increments, phenomena, and
phenomena, and even some of the most complex manifestations of all existence, even abstract Human phenomena,
(and absence!)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Contents:
An Incremental Methodology to Greater Music Theory
Scales, Scale Reducton & Scale Position Sets
Waveform Theory
Making Music Systems

!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!

An Incremental Methodology to Greater Music Theory

The Circle of Fourths and Fifths, as well as the Chromatic Scale, are what Astrolabe calls the Greater Scales of the Western Music System.

The Diatonic and Pentatonic scales are what Astrolabe considers tonal scales and each can be further incrementalized through utilizing Scale Positions.

Each Scale Position begins with a note from any of the scales, this note is then called the Root of the Scale Position.

Each Root/Scale Position/Note is a possible Tonal Center.

Tonal Centers often shift throughout any given music piece, Astrolabe calls this modulating.

These shifts can be of Microtonal, Diatonic, Pentatonic, or Greater magnitudes.

Modulating simply means producing oscillations.

Traditionally, modulation can refer to a technical skill solo-instrumentalists utlilize by shiftng scale positions quickly.

These terms will help to differentiate:

“Tonal Center Modulation” is compositional, often rooted to rhythm instruments, and usually establishes the Tonal Center.

“Technical Modulation” is commanded by a lead-instrumentalists technicality, but is enhanced by following what the rhythm and melody allow.

Each of these can occur at the magnitudes of Microtonal Modulation, Diatonic Modulation, Pentatonic Modulation, and Greater Modulation.

Another type of Tonal Center is what Astrolabe calls “Atonal Center,” (which can also be called spanning, mixed, wide, or muddy Tonal Centers.)

Atonal Centers are a quite common technique.

Utilizing Atonal Centers can channel robust sentiments, and even spectrums of such, drawing from the vast spectrum of tonality.

This channeliing of sentiements is generally considered to be the results of psychoacoustics.

Psychoacoustics, in general terms, are how frequencies, intervals, rhythms, and melodies channel brain activity.

“Tonality” is a traditional term for this phenomenon.
The term “Tonality” ties specific intervals, timbres, pitches, tonal centers, melodies, and modulations to the chanelling of sentiments psychoacoustically.

By reducing the Diatonic and Pentatonic Scales, and by using note dedecution methods, the tonal center becomes obscured.

Reduction is generally abetter tactic of obscuringthe tonal center than adding notes.

Lead players can get away with doing this by modulating to flourish out what the tonality, motif, rhythm, tonal center(s), and melody have established.

================================================================

    Greater Scales:

Chromatic Scale:

Numerical: 1 8 2 9 3 4 10 5 11 6 12 7 *Astrolabe Scale
Traditional: 1 m2 2 m3 3 4 #4b5 5 m6 6 m7 7
Mathematical 1 1.5 2 2.5 3 4 4.5 5 5.5 6 6.5 7 *Astrolabe Scale

Circle of Fourth & Fifths (CoF&F):

Numerical: 4 1 5 2 6 3 7 10 8 11 9 12 *Astrolabe Scale
Traditional: 4 1 5 2 6 3 7 #4b5 m2 m6 m3 m7
Mathematical 4 1 5 2 6 3 7 4.5 1.5 5.5 2.5 6.5 *Astrolabe Scale

    Tonal Scales:

Diatonic: 1 2 3 4 5 6 7 (No Deduction) (4 1 5 2 6 3 7)
Pentatonic: 1 2 3 5 6 (Deduct 4 & 7) (4|1 5 2 6 3|7)
Pentatonic CoF&F 1 5 2 6 3 (Deduct 4 & 7) (4|1 5 2 6 3|7)
Oscilation Pentatonic: 1 2 3 4 7 (Deduct 5 & 6) (5|1 5 2 6 3|6) *Astrolabe Scale
Transient Pentatonic: 2 4 5 6 7 (Deduct 1 & 3) (3|1 5 2 6 3|1) *Astrolabe Scale
Diatonic CoF&F: 4 1 5 2 6 3 7 (No Deduction) (4 1 5 2 6 3 7)

Scale Reduction

The Diatonic Scale is a reduced scale of the Circle of Fourths and Fifths and Chromamatic Scales; what Astrolabe calls the Greater Scales.

They are both considered Greater Scales because of them showcasing all of the possible intervals, despite the Chromatic Scale being quite incremental.

A commonplace method of reducing the Chromatic Scale into a Diatonic Scale is starting at any of the notes of the 12 note system…

A, A#, B, C, C#, D, D#, E, F, F#, G, G#

and utilizing the the following sequence the “Whole step, whole step, half step, whole step, whole step, whole step, half step,” sequence.

A whole step means moving two notes along Chromatic Scale, (for example, from “A” to “B”) and a half step is moving one note, (for example, E to F).

This happens because the spectrum of sound frequencies is circular, pitches reccur

Different music systems, or methods of dividing the spectrum of

The equ

On a g

Starting from any note and using this pattern will reduce the Greater Scales into a Diatonic Scale.

Example:

A A# B C C# D D# E F F# G G# = Chromatic Scale
| | | | | | | | | | | |
1 m2 2 m3 3 4 #4b5 5 m6 6 m7 7 = Chromatic Scale
| | | | | | |
1 2 3 4 5 6 7 = Diatonic Scale

The Pentatonic Scale is a reduced scale of the Diatonic Scale.

To produce the Traditional Pentatonic Scale remove the 4 and 7 from the Diatonic Scale above

the reason for doing this becomes more clear when looking at the Circle of Fourths and Fifths…

4 1 5 2 6 3 7
^ ^

To make what Astrolabe calls the Transient and Oscillating Pentatonic Scales

Follow the same idea, deducting the 1 and 3 for the Transient Pentatonic…

4 1 5 2 6 3 7
^ ^

and deduct the 5 and 6 for the Oscillating Pentatonic…

4 1 5 2 6 3 7

  ^     ^

Along with the symmetry illustrated above, which simply describes what’s happening on a Greater Scale.

Each of the deducted intervals are opposite scale patterns of each other.

Since each scale position starts at a different chronological location of the scale, each scale position starts at a different spot of…

1 Whole-step 2 whole-step 3 half-step 4 whole step 5 whole step 6 whole step 7 half-step (1 again)

Each interval number is it’s starting point of the recrring scale, thus they are their own scales in an incremental way.

4 = whole step, whole step, whole step, half step, whole step, whole step, half step
which is opposite of…
7 = half step, whole step, whole step, half step, whole step, whole step, whole step

This is true for 1 and 3 as well as 5 and 6.

This is part of what makes the Circle of Fourths and Fifths a synchronistic pattern of how intervals combine.

    Modulating Tonal Scale Position Sets (for CoF&F):

Astrolabe Scale Position Sets:


Reference CoF&F: 4 1 5 2 6 3 7 4.5 m2 m6 m3 m7

Oscillating Diatonic: 4 1 5 2 6 3 7 3 6 2 5 1 [Notice how the tonal centers shift in whole tones.
(Tonal Centers: 1 1 1 1 1 1 1 2 3 4.5 m6 m7) This parallels how the CoF&F Modulates.]

Oscillating Pentatonic: 5 1 5 2 6 3 6 2 5 1 5 2
(Tonal Centers: m7 1 1 1 1 1 2 3 4.5 m6 m6 m6

Balanced Pentatonic: 5 1 5 2 6 3 6 3 6 2 5 1 [5 1 5 1 5 2 6 3 6 3 6 2 is quite the balanced sequence.
(Tonal Centers: m7 1 1 1 1 1 2 2 3 4.5 m6 m7) This is a very synchronistic scale set derived using scale position shape opposites (4><7, 1><3, 5><6)].

Transient Pentatonic: 3 1 5 2 6 3 1 5 2 6 3 1
(Tonal Centers: m2 1 1 1 1 1 7 7 7 7 7 m7

Transient Diatonic: 4 1 5 2 6 3 7 4 1 5 2 6 [Notice how the tonal centers shift in semi-tones.
(Tonal Center: 1 1 1 1 1 1 1 m2 m2 m2 m2 m2 This parallels how the Pentatonic Scale Modulates.]

                            [The diatonic scale naturally modulate microtonally]

The shifts in tonal center above illustrate each Scale Set’s modulation.

The Oscilating Pentatonic Scale Position Set utilizes the traditional Pentatonic Deduction, 4 and 7, of the Diatonic scale.

The 4 and the 7 are then assigned replacement scale pentatonic scale positions 5 and 6 as per the oscillative syle of Scale position set.

What “Oscillating” is referencing is the

The Transient Pentatonic Scale Set also uses the Traditional Pentatonic deduction of the 4 and 7.

The 4 and 7 are replaced by 3 and 1

Sequencing scale positions sets establishes an alternate set of scale positions to intervals iof a scale than what is normal.

This means that instead of the normal point along the “whole step, whole step, half step, etc.” a different starting point is played for the interval.

This is quite common practice in many respects…

Intead of…

1 2 3 5 6 are the Traditional Pentatonic Intervals
3 5 1 3 5 is a Transient style Scale Position Set.

Notice how the new scale position set does not coincide with the diatonic scale at all.

Since 6 is re-established as 5, and 1 as 3, the replacement scale positions would not link up if repeated.

These scale positions are also very disimilar to the original, (the simularity spectrum being demonstrated by the Circle of Fourths and Fifths.)

Therefore, using scale sets inherently moves, and obscures the tonal center of the music.

Instead of the pattern repeating as normal, the scale set continues on and the Diatonic Scale is transcended.

The actual intervals being played by…

3 5 1 3 5 1 3 5 1 3 5 1 3 5 1 3

are… and repeating from here.

1 m3 #4b5 m6 7 m2 m3 #4b5 m6 m7 m2 m3 4 m6 m7 1

This scale set uses three values (3 5 1) repeating. Scale Set sequences are by no means restricted to three values.

Sequencing Scale Sets provides interesting insight to the intricacies of the intervals by illustrating tonal center shifts and modulation.

Using these scale sets obscures the tonal center, and the notes used will transcends the notes that constituite the Diatonic scale

This modulates the tonal center, but naturally this will be a quite smooth transition if using the pentatonic scale shapes, whih have their relative 4 and 7 deducted.

Modulating becomes even smoother after strategically deducting the pentatonic scale position shapes to achieve various modulative effects.

It is also possible to develop Scale Sets by spreading intervals out like so:

4 1 5 2 6 3 7
5 6 3 (Pentatonic)

There are quite a few ways to interweaving these two concepts as well, as well as other patternized manners of producing

The Br

To fully utilize Scale Sets, deduct greater scales into diatonic and then into pentatonic scales, (a, for each replacement scale position makes Scale Position Sets.

============================================================

Cross-Scale Set Deduction:

Deducting notes from a pitch set usually occurs as such

Key of C = C D E F G A B
key of G = G A B C D E F#

Deduct the F and the F#, then the pitch set is ambiguous to both keys.

Using Scale Sets, this is done for each scale position individually.

…………………………………………………..

Example:


Reference CoF&F: 4 1 5 2 6 3 7 4.5 m2 m6 m3 m7

Key of C CoF&F: F C G D A E B F# C# G# D# A#

Transient Diatonic: 4 1 5 2 6 3 7 4 1 5 2 6

Transient Pentatonic: 3 1 5 2 6 3 1 5 2 6 3 1

F must be ambiguous to 4 & 3

C must be ambiguous to just 1

and so on…

Instead of working with an entire circle of fourths & fifths

it is possible to extract any of the pentatonic style scales

Transient Pentatonic: 4 1 5 2 6 3 7 4.5 m2 m6 m3 m7

Key of C CoF&F: F C G D A E B F# C# G# D# A#

Transient Diatonic: 4 1 5 2 6 3 7 4 1 5 2 6

Transient Pentatonic: 3 1 2 6 3 1 5 2 6 3 1

Making Music Systems

establish a genesis frequency (an A or whatever)
establish how many notes(freq rats) per octave
establish what freq rats

Western Music Uses 12 notes per octave.

Which on a guitar and a piano are laid out quite equally.

This is the benefit of using a 12 note system.

Dividing the recurring spectrum of pitch into 12 is supremely practical.

Geometry, being the particular math it is, maintains that only a handful of 3-D figures, (known as polyhedrons), are as simply structured and omni-symmetrical as the 12-sided, (or faceted) dodecahedron.

The faces of a polyhedron are important because they parallel how many cones can be separated from the whole, like pie or pizza slices are to a circle.

Since a dodecahedron is a polyhedron that simulates an orb and divides it into equal fractions, 12 can be used to divide the recurring spectrum of sound frequencies.

The spectrum of sound frequencies can be considered circular because pitches reccur, and these reccurences of pitch are called octaves.

“Pitch” is quite synonomous with “note”, but there is a distincition.

Sound frequencies are incremental, and when the value of a sound frequency, (measured in Hz), is doubled, (mutiplied by two), the result is the same pitch just an octave higher.

A frequency is any value of the spectrum of sound frequencies.

For example, 19.64 Hz

This frequency is also a pitch of the spectrum of an pitch.

Mulitply or divide the frequency value,(19.64 Hz) by two to achieve the same pitch an octave up, or an octave down, (9.82 Hz and 39.28 Hz respectively).

Notes are established by note systems.

19.64 Hz is not a note of the Western 12-note system based on A = 440 Hz.

The other frequencies which are used by the 12 note system are deduced by using specific frequency ratios, and the Western System is known for how it equally temepred these frequency ratios to make the notes more equidistant.

Doing this is often looked at as a cheat, or a shortcut, but that is not the case at all.

By making the system more equidistant, the creators of the Western 12-Note system in A=440 tied the system to primordial incremental math, (what Astrolabe calls Calculator Math.)

This means the Western Music system not only is synchronized to patterns of consonance and harmonics of sound, but also mathematical equilibrium; fully optimizing what is possible of a 12-note system.

The 12 note system is what Astrolabe calls practical.

Dividing the spectrum of pitch into 12 increments more than maximizes what is possible of the spectrum of tonality, but makes its innerworkings quite easy to incrementalize and work with.

The quite omni-symmetrical polyhedrons like the pentagonal faceted dodecahedron are rare occurences in geometry.

Other polyhedrons might not be as profound at simulating orbs, like the icosahedron and the dodecahedron, but they are still viable for honing in on note-systems and how to rationalize a methodology for such a note system.

The tetrahedron is another quite omni-directional polyhedron that instead of simulating an orb, seems to simulate one of the 3-D pie, or pizza slices that each the dodecahedrons faces are the broad end of.

These slices are akin to cones, and the tetrahedron can be used to simulate those.

Another shape that does this the enneahedron.

An enneahedron is a 9 faceted shape