A Modern Analysis of Music theory
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Basic Tonal Scales:
Diatonic Scale = 1 2 3 4 5 6 7 In the Key of A this = A B C# D E F# G#
Pentatonic Scale = 1 2 3 5 6 In the Key of A this = A B C# E F#
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Basic Chords:
Western 12-Note Scale Intervals: Usages:
Augmented 7 = 1, 3, m6, 7 Non-diatonic.
Major 7 = 1, 3, 5, 7 Use on the 1st & 4th Diatonic Scale positions.
Dominant (7) = 1, 3, 5, m7 Use on the 5th Diatonic Scale position.
Minor 7 = 1, m3, 5, m7 Use on the 2nd, 3rd, & 6th Diatonic Scale positions.
Diminished 7 = 1, m3, tritone, m7 Use on the 7th Diatonic Scale position.
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The Chord Spelling, Building, & Altering Methodology:
This common method addss, alters, and subtracts Diatonic Scale values from the basic chords listed in the previous section.
Notice how the basic chords conist of consecutive diatonic third steps starting from each of the Diatonic Scale positions.
Rootless(Drop1)
Drop3
Drop5
(Drop7)
Sus2
Sus4
b5
#5
Add6
Add8
Add9
Add10
Add11
Add#11
Add12
Add13
Add14
Add15
Add16
Add17...
The number values of above terms refers a number of Diatonic Scale steps away from any root:
For Example: Utilizing the Drop3 b5 m7 chord with the root on the 7th Diatonic Scale position, G# in the Key of A
The Diatonic third step above the 7th, (the 2nd) gets dropped not the the 3 of the key, (which in the key of A = C#.)
The chord would consist of the 7th, 4th, & 6th. In the key of A this = G#, D, & F#. (This chord consists of the tritone and the the m7 intervals.)
Utilize "The Chord Spelling, Building, & Altering Methodology" to build chords and name them.
Names get truncated because many of the chords attributes become imperative when applied to the various Diatonic Scale values which only facilitate certain chord tones when playing in key.
For Example: the Drop3 b5 m7 only maintains the key of the music when utilizing the 7th Diatonic Scale position as the root of the chord.
truncating this name to a "Drop3 7" chord allows for applying the same chord structure to various Diatonic Scale positions.
the Nashville Number System:
The Nashville Number System allows musicians and composers to make chord charts for them and other musicians to read while playing instead of sheet music.
Roman Numerals (I,II,III,IV, etc.) Represent what Diatonic Scale position the root of the chord goes to.
Major Diatonic Scale values have capitalized Roman Numerals while minor Diatonic Scale values do not.
Instead of writing the chord name next to each Roman Numeral, often the same chord structure continues when shifting roots. In cases like that the chord's truncated name gets written first and then the Roman Numerals of the chord progression follow.
For example:
Drop3 7: I, vii, I, vii
Drop3&5 Add9: I, vii, vi, V, IV
However, these charts don't typically provide information about which octaves roots of the chords belong to.
Lead players, even if they utilize no chords whatsoever in their playing can still utilize chord charts to know what to play, and they do so often.
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The 1st, 2nd, & 3rd Chord Inversion Method:
1st inversion of 1 3 5 7 is 3 1 5 7
2nd inversion of 1 3 5 7 is 5 1 3 7
3rd inversion of 1 3 5 7 is 7 1 3 5
1st = 1 6 3 5
1st->2nd = 1 6 4 3
1st->3rd = 1 4 2 6
1st->2nd->3rd = 1 6 4 2
1st->3rd->2nd = 1 7 3 5 *
1st->3rd->3rd = 1 3 6 4
1st->2nd->3rd->3rd = 1 7 5 3
1st->3rd->2nd->3rd = 1 4 3 6
1st->3rd->3rd->3rd = 1 5 7 3
1st->2nd->3rd->3rd->3rd = 1 6 5 3
1st->3rd->2nd->3rd->3rd = 1 3 6 5
1st->3rd->2nd->3rd->3rd->3rd = 1 4 6 2
2nd = 1 4 6 3
2nd->1st = 1 5 3 7 **
2nd->3rd = 1 6 2 4
2nd->1st->3rd = 1 2 6 4
2nd->3rd->3rd = 1 5 3 6
2nd->1st->3rd->3rd = 1 5 6 3
2nd->3rd->3rd->3rd = 1 3 7 5 ***
2nd->1st->3rd->3rd->3rd = 1 6 3 4
3rd = 1 2 4 6
3rd->3rd = 1 3 4 6
3rd->3rd->3rd = 1 3 5 6
3rd->3rd->3rd->3rd = 1 3 5 7
[* ** *** = Inversions only listed once, but occured more than once.]
The number sequences above also refer to Diatonic Scale steps.
The inversion consisting of the Diatonic Scale steps of 1, 5, 3, 7, (A, E, C#, & G# in the Key of A), utilized on the 5th Diatonic Scale position results in a chord consisting of the 5, 2, 7, and 4 Diatonic Scale values, (E, B, G#, & D in the key of A).
(Notice that the A, E, C#, G# chord results in a slightly different set of intervals, (consisting of the 5, 3, & 7 Western 12-Note Scale intervals also known as the Chromatic Scale), compared to the E, B, G#, D chord (consisting of the 5, 3, & m7 Western 12-Note intervals).
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Which Diatonic Scale Positions Fascilitate Which Western 12-Note Scale Intervals:
Intervals = Diatonic Scale Positions
1 = any
m2 = 3, 7
2 = 1, 2, 4, 5, 6
m3 = 2, 3, 6, 7
3 = 1, 4, 5
4 = any except for 4
tritone = 4, 7
5 = any except for 7
m6 = 3, 6, 7
6 = 1, 2, 4, 5
m7 = 2, 3, 5, 6, 7
7 = 1, 4
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Consecutive Steps Along the Chromatic Scale
1 m2 2 m3 3 4 t 5 m6 6 m7 7 = Chromatic Scale
^---^---^---^---^---^---^---^---^---^---^---^----Seventh <-&-> Minor Seconds
^-------^-------^-------^-------^-------^--------Minor Sevenths <-&-> Seconds
^-----------^-----------^-----------^------------Sixths <-&-> Minor Thirds
^---------------^---------------^----------------Minor Sixths <-&-> Thirds
^-------------------^-------------------^--------Fifths <-&-> Fourths
------------^-------------------^----------------
----^-------------------^-------------------^----
----------------^-------------------^------------
--------^-------------------^--------------------
^-----------------------^------------------------Tritones <-&-> Tritones
^---------------------------^--------------------Fourths <-&-> Fifth
--------^---------------------------^------------
----------------^---------------------------^----
------------------------^------------------------
----^---------------------------^----------------
------------^---------------------------^--------
--------------------^----------------------------
^-------------------------------^----------------Thirds <-&-> Minor Sixths
----------------^--------------------------------
^-----------------------------------^------------Minor Thirds <-&-> Sixths
------------^------------------------------------
^---------------------------------------^--------Seconds <-&-> Minor Sevenths
--------------------------------^----------------
------------------------^------------------------
----------------^--------------------------------
--------^----------------------------------------Minor Seconds <-&-> Sevenths
^-------------------------------------------^----
----------------------------------------^--------
------------------------------------^------------
--------------------------------^----------------
----------------------------^--------------------
------------------------^------------------------
--------------------^----------------------------
----------------^--------------------------------
------------^------------------------------------
--------^----------------------------------------
----^--------------------------------------------
Consecutive Steps Along the Chromatic Scale Arranged in the Pattern of the Circle of Fourths & Fifths
4 1 5 2 6 3 7 t m2 m6 m3 m7 = Circle of Fourths <-&-> Fifths
^---^---^---^---^---^---^---^---^---^---^---^----Fourths <-&-> Fifths (4 1 5 2 6 3 7 t m2 m6 m3 m7 repeat)
^-------^-------^-------^-------^-------^--------Minor Sevenths <-&-> Seconds (4 5 6 7 m2 m3 repeat)
^-----------^-----------^-----------^------------Minor Thirds <-&-> Sixths (4 2 7 m6 repeat)
^---------------^---------------^----------------Minor Sixths <-&-> Thirds (4 6 m2 repeat)
^-------------------^-------------------^--------Minor Seconds <-&-> Sevenths (4 3 m3 2 m2 1 7 m7 6 m6 5 t repeat)
------------^-------------------^----------------
----^-------------------^-------------------^----
----------------^-------------------^------------
--------^-------------------^--------------------
^-----------------------^------------------------Tritones (4 7 repeat)
^---------------------------^--------------------Sevenths <-&-> Minor Seconds (4 t 5 m6 6 m7 7 1 m2 2 m3 3 repeat)
--------^---------------------------^------------
----------------^---------------------------^----
------------------------^------------------------
----^---------------------------^----------------
------------^---------------------------^--------
--------------------^----------------------------
^-------------------------------^----------------Thirds <-&-> Minor Sixths (4 m2 6 repeat)
----------------^--------------------------------
^-----------------------------------^------------Sixths <-&-> Minor Thirds (4 m6 2 repeat)
------------^------------------------------------
^---------------------------------------^--------Seconds <-&-> Minor Sevenths
--------------------------------^----------------
------------------------^------------------------
----------------^--------------------------------
--------^----------------------------------------
^-------------------------------------------^----Fifths <-&-> Fourths
----------------------------------------^--------
------------------------------------^------------
--------------------------------^----------------
----------------------------^--------------------
------------------------^------------------------
--------------------^----------------------------
----------------^--------------------------------
------------^------------------------------------
--------^----------------------------------------
----^--------------------------------------------
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Alternate Pentatonic-Style & Hexatonic-Style Scales
[Warning! Highly Experimental!]
The Pentatonic Scale Results from deducting the 4th and 7th Diatonic Scale Positions.
These rational alternate deductions do not function as practically as deducting the 4th and/or 7th to produce the Pentatonic and Hexatonic Scales.
Pentatonic-Style Scales
Pentatonic Scale: 1 2 3 5 6
Factoral Variants:
1 2 4 5 7
1 3 4 6 7
2 3 5 6 7
1 2 4 5 6
1 3 4 5 7
2 3 4 6 7
Complicated Pentatonic: 2 4 5 6 7
Factoral Variants:
1 3 4 5 6
2 3 4 5 7
1 2 3 4 6
1 2 3 5 7
1 2 4 6 7
1 3 5 6 7
Simple Pentatonic: 1 2 3 4 7
Factoral Variants:
1 2 3 6 7
1 2 5 6 7
1 4 5 6 7
3 4 5 6 7
2 3 4 5 6
1 2 3 4 5
Hexatonic-Style Scales
2 3 4 5 6 7
1 3 4 5 6 7
1 2 4 5 6 7
1 2 3 4 5 6
1 2 3 4 6 7
1 2 3 4 5 7
1 2 3 5 6 7
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Rationalizing Alternate Pentatonic-Style Deductions
[Warning! Highly Experimental!]
4 1 5 2 6 3 7 = Pentatonic
^-----------^---Deduct These
4 1 5 2 6 3 7 = Complicated Pentatonic
^-------^-----Deduct These
4 1 5 2 6 3 7 = Simple
^---^-------Deduct These
4 1 5 2 6 3 7 = Chaotic Hexatonic
^---------Deduct This
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Synchronizing a Base-12 Number System to the Chromatic Scale
[Warning! Highly Experimental!]
4 1 5 2 6 3 7 t m2 m6 m3 m7
| | | | | | | | | | | |
4 1 5 2 6 3 7 10 8 11 9 12
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Assigning Diatonic & Pentatonic Scale Values to Non-Diatonic & Non-Pentatonic Chromatic Scale Positions:
[Warning! Highly Experimental!]
4 1 5 2 6 3 7 10 8 11 9 12 = The Chromatic Scale Arranged in the Pattern of the Circle of Fourths & Fifths
4 1 5 2 6 3 7 4 1 5 2 6 = Transient Diatonic (TD)
3 1 5 2 6 3 1 5 2 6 3 1 = Transient Pentatonic (TP)
5 1 5 2 6 3 6 3 6 2 5 1 = Balanced (B)
4 1 5 2 6 3 7 3 6 2 5 1 = Oscillating Diatonic (OD)
5 1 5 2 6 3 6 2 5 1 5 1 = Oscillating Pentatonic (OP)
For example: According to the Balanced Scale utilizing the 4th means treating it like the 5th.
"Transient" in this context refers to number sequences that repeat from the start: 1, 2, 3, 1, 2, 3, 1, 2, 3... These simulate like stairs
"Oscillating" in tis conext refers to number sequences that descend and repeat : 1, 2, 3, 2, 1, 2, 3, 2... These simulate like hills
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Waveform Theory:
[Warning! Highly Experimental!]
1, 3, 5, & 7 = attack, hold, sustain, & release.
The factors of chords might correlate to various waveshapes and audio engineering phenomena.
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Assigning Diatonic & Pentatonic Scale Values to Adjacent Non-Diatonic & Non-Pentatonic Chromatic Scale Positions
[Warning! Highly Experimental!]
1 m2 2 m3 3 4 #4b5 5 m6 6 m7 7
1 1or2 2 2or3 3 3or4or5 4or5 5 5or6 6 6or7 6or7or1
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Enantiomer Theory:
[Warning! Highly Experimental!]
1 2 3 4 5 6 7
m2 m3 m6 m7
*--*
1 2 3 4 5 6 7
m2 m3 m6 m7
[Sets become more and more experimental, but still rational.]
1 2 3 4 5 6 7
m2 m3 m6 m7
1 2 3 4 5 6 7
m2 m3 m6 m7
*-----* *--*
1 2 3 4 5 6 7
m2 m3 m6 m7
1 2 3 4 5 6 7
m2 m3 m6 m7
*-----*
1 2 3 4 5 6 7
m2 m3 m6 m7
*-----*
1 2 3 4 5 6 7
m2 m3 m6 m7
1 2 3 4 5 6 7
m7 m6 m3 m2
1 2 3 4 5 6 7
m7 m6 m3 m2
*-----*
1 2 3 4 5 6 7
m7 m6 m3 m2
1 2 3 4 5 6 7
m7 m6 m3 m2
*-----*
1 2 3 4 5 6 7
m7 m6 m3 m2
1 2 3 4 5 6 7
m7 m6 m3 m2
*-----* *--*
1 2 3 4 5 6 7
m7 m6 m3 m2
*--*
1 2 3 4 5 6 7
m7 m6 m3 m2
[*---* = Switch for another rational Enantiomer set.]
Each Set above assigns non-Diatonic Scale values to Diatonic Scale values.
To utilize this theory substituite a Diatonic Scale value with a non-Diatonic Scale values.
The non-Diatonic Scale behaves as the assigned Diatonic Scale value would.
For example: Switching a 1 out for a m2 means that the m2 behaves like a 1.
Using this method requires finesse, just like with the "Assigning Diatonic & Pentatonic Scale Values to Non-Diatonic & Non-Pentatonic Chromatic Scale Positions" theory.
This theory arose from the premise of the Chromatic Scale values relative to any of the keys.
The intervals in-between the Diatonic Scale values have the consist of the names m2, m3, m6, and m7.
Enantiomer Theory not only correlates these non-Diatonic Scale values to the 2, 3, 6, and 7 respectively, but also hypothesizes various rational patterns for assigning Diatonic Scale values to non-Diatonic Scale values.
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Interval Matching:
A few number sequences seem to have great potential when utilized for metaphysics, math, and music purposes.
1 2 3 4 5 6 7 8 9 10 11 12 ...
4 1 5 2 6 3 7 10 8 11 9 12
1 8 2 9 3 4 10 5 11 6 12 7
The natural number chronology first and foremost takes precedent.
Stacking sequence like the above provides insight to how the different intervals relate to one another sequentially.
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Correlations Between Base Number Systems & The Spectrum of Pitch:
The spectrum of pitch repeats.
What music theory regarding the Western 12-Note Scale calls octaves correlates to this repitions of the spectrum of pitch.
The notes repeat throughout octaves.
Music scales divide each octave into a quantity of notes and intervals.
This directly corelates to dividing the spectrum of natural numbers into quantities of symbols as with base-number system.
The Base-10 number system has 10 unique symbols that represent 0 through 9. At 10 the symbols repeat with place value added to the left of the number that contains another number count that increases depending on the number of place values.
Audio Engineers use numbers to set parameters that effect ratios, time based effects, and volume measured in decibels.
Often times, adjusting the current that subeqently activates the speaker to move air and produce sound results in.
The numbers not only effect intensity but can also add various characteristics.
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Number Sequencing:
444.444 = repeating number sequence = smoothness = I use these on highpass, lowpass, shelves EQ parameters as well as mix, volume, gain, time based parameters. They make good values for everything from frequency to values of miliseconds.
494.949 = alternating number sequence = clarity = i use these for notches, bells, and for the q intensity. Sometimes it's a case by case basis when you want a smoothness number or a clarity number for a parameter.
Hybrid Number Sequences:
4.449 = clip-style sequence
4.999 = lip-style sequences
Complimentary Number Sets:
Since dividing the octave into intervals directly correlates to dividing the spectrum of natural numbers in intervals, comparing numbers of the same base number system together can translate to any scale.
For example: Intervals of the base 10 number sytem produces naturally relevant results when translates to any music scale such as the Pentatonic, Diatonic, or Chromatic.
Base-5 Base-7 Base-12
1 : 3 1 : 4 1 : 7
2 : 4 2 : 5 2 : 8
3 : 5 3 : 6 3 : 9
4 : 1 4 : 7 4 : 10
5 : 2 5 : 1 5 : 11
6 : 2 6 : 12
or 7 : 3 7 : 1
8 : 2
Base-5 (PI) x2 9 : 3
1 : 3 10 : 4
2 : 5 Base-14 11 : 5
3 : 6 1 : 8 12 : 6
5 : 1 2 : 9
6 : 2 3 : 10 x2
4 : 11
x2 5 : 12 Base-24
6 : 13 1 : 13
Base-10 7 : 14 2 : 14
1 : 6 8 : 1 3 : 15
2 : 7 9 : 2 4 : 16
3 : 8 10 : 3 5 : 17
4 : 9 11 : 4 6 : 18
5 : 10 12 : 5 7 : 19
6 : 1 13 : 6 8 : 20
7 : 2 14 : 7 9 : 21
8 : 3 10 : 22
9 : 4 11 : 23
10 : 5 12 : 24
13 : 1
or 14 : 2
15 : 3
Base-10 (PI) 16 : 4
1 : 6 17 : 5
2 : 8 18 : 6
3 : 9 19 : 7
5 : 10 20 : 8
6 : 12 21 : 9
8 : 13 22 : 10
9 : 1 23 : 11
10 : 2 24 : 12
12 : 3
13 : 5 *PI - Pentatonic Intervals*
The above lists of ratios function as complimentary number sets for number sequencing.
For example: 166.6Hz, 1666.6 Hz, 611.1 Hz, etc channel the characteristics of those numbers.
Using Complimentary Number setsappeals to characteristics of numbers, their relationships, and the sets themselves
These number sequences work well for ratios out of 100 as well.
For example: Setting the mix of a reverb to 61%.
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Complimentary Numbers in Music Theory:
Use complimentary number sets to establish chord tones and roots.
For example:
Use the Complimentary Numbers 17:5 of the Base-24 Complimentary Number set
In the key of A
Since 24 is the chromatic scale multiplied by two, 17 refers to 17 semitones above the root, or the major third transposed two octaves up.
To stay in key use this chord tone only on the 1st and 4th scale positions.
Use the chord tone 5 chromatic steps above any of the diatonic scale positions to result in that note's 4th.
To avoid going out of key do not use this chord tone on the 4th scale position.
If desired use both chord tones where applicable, or only use one of the chord tones and add an octave in there.
Using more than two complimentary number ratios greatly washes out the characteristics of the numbers used.
However, take any number and multply it or divide it by any othe to produce more detailed numbers.
Traverse those numbers by combining the numbers of adjacent place values for chords or arpeggios
For example:
17*1 = 17
17*2 = 34
17*3 = 51
17*4 = 68
17*5 = 85
17*6 = 102
17*7 = 119
in the key of A play in the diatonic scale
1, 7, 3, 4, 5, 1, 6, 8, 8, 5, 1, 2, 1, 1, & 9
That's A, G#, C#, D, E, A, F#, A, A, E, A, B, A, A, B
you can reasonably use many of these values for higher intervals like 17, 16, 21, 11, & 19.
instead of always travelling an octave up to reach higher numbered intervals going to the octave below of any root also works well.
This strategy organizes the Western 12-Note Scale into intervals comprised two values compared to eachother like frequency ratios.
It also correlates the spectrum of natural numbers to the spectrum of sound measured in Hz, as well as other complimetnary number sets
Use derived notes not only as roots but as the central scale position that a phrase moves around or towards.
You can also derive toanl points by travelling to an agreeable interval from that point.
If the last phrase ended on an agreeable interval from the tonal point, when transferring to another tonal point you can start the new phrase or part on a parallel agreeable interval from the new tonal point
BPM:
Multiply any frequency by 60 to change the value into a BPM based on the standard time keeping method.
For example:
440Hz n
_____ = _____
1 60
cross multiply 60 with 440 to produce 26,400 = 1n.
1n simplifies to n
So, 440Hz = 26,400BPM
Dividing and multiplying BPM by 2 results in half time and double time respectively,
Similar to dividing and multiplying the Hz of a note by 2 results in the same note across octaves.
Last Example:
According to Diatonic Scale steps
7 = Major Seventh
12th = Fifth an Octave above the root
Using number theory the 12th can also get broken down, or read as, as numbers like DNA sequences of nucleotides
12 consists of a 1 and a 2
12 also effectively separates into a 10 and a 2
10 in Diatonic scale steps results in a diatonic third step, depending on which scale position, a minor or major tird.
10 in Chromatic scale steps results in a major sixth,
play 1, 10, 2 with 10 as diatonic steps
in the key of A that's A, C#, and B
this 10 to 2, an effective move to incoroprate into lead playing intuitively.
play 1, 10, 2 with 10 and 2 as chromatic scale steps, the minor 2 and the major 6th intervals
should only utiliz chromatic values on a diatonic scale postion that can facillitate without you travelling out of key
No diatonic scale positions facillitate such a chord
however, the knowledge remains that travelling to Diatonic 6th followed by a diatonic 2nd on any scale position functions as an effective move.
Play your instrument and derive a number ratio based on what you play.
Say you play a chord consisting of root, major 7, and fifth in the key of a on the 1st scale position of the diatonic scale
the comparisons here = 1:2 diatonic, 1:12 chromatic, 1:5 diatonic, 1:8 chromatic, 7:12 Diatonic, 12:8 chromatic
multiply values to get large numbers and read them for parts, strategically do alot.
That the chromatic scale here claims the fifth represented by 8 might confuse people familiar with using arpeggiators or modular synthesizers.
on those devices the root = 0 because no modulation occurs to stay on the root, in this method the root = 1 as with intervals in music.
feel free to make a complimentary number set starting at 0:0 to familiarixze the chromatic scale in such step like terms.
remember that this strategy seeks to draw comparison between the spectrum of nature, the spectrum of natural numbers, an the spectrum of music.
THat all of these spectrums correlate to each other and intervals of traversing these spectrums occur multirationally.
Advanced number reading:
11:19
11 = 2, two octave up pentatonically, 4 one octave up diatonically, and a minor 7 chromatically
(1 stays the same.
10 = the root two octaves up, the 3rd one octave up, and the major 6th)
19 = the 6th four octaves up, the fifth two octaves up, and the tritone
(alternating between the root octave and the octave above it also works as to not climb many octaves)
9 = 6th an octave up, a 2nd an octave up, and minor 6th
notice how 19 and 9 result in the same scale position factor in different octaves.
multiply the complimentary number ratio together and each number with itself to result in:
11*19= 209
11*11= 121
19*19= 361
read these values in the same manner and rember to combine the chords as well as sequence them as arpeggios.
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Extrapolating Numbers by Defining the spectrum of relationships between numbers complimented to one another relationships
product = positive = the extension of two numbers
sum = positive = compounding of two numbers
average = neutral = blending of two numbers
difference = negative = comparison literally means this
quotient = negative = ratios depsite being self-proclaimed comparisons of numbers mean this
55:5
product = 275 = second
sum = 60 = fourth
average = 30 = second
difference = |5| = fifth
quotient I = 11 = fourth
quotient II = 0.0909090909090909
Find the idnetity of numbers less than 1
since they are fractions of a whole we enlargen them by imposing them against 100.
It's basically like zooming in on the number to find it's intervallic identity
Quotient Identity:
0.0909090909090909 x 100 = 9.0909090909090909 = 9th
QI Product = 100 x 9.0909090909090909 = 909.09090909090909090909
QI Sum = 100 + 9.0909090909090909 = 109.09090909090909
QI Difference = 100 - 9.0909090909090909 = 90.909090909090
QI QI
(sometimes averages result in decimals use the method above for decimals
or round to the nearest interval downward.
Rounding to chromatic notes represented is risky business,
it' better to stay in keyi
for example: 20.5 -7 = 13.5 - 7 = 6.5 = m7 interval
the only scale positiond of the diatonic scale that use a m7 interval are the 2, 3, 5, 6, and 7
the m7 interval of the 1 is non diatonic.
Product, sum, and difference, when working with natural number complimentary number sets
never yield decimals.
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Correlating the Western 12-Note Scale to the 12 practical intervals of color
Green = A, C, F
Mint = A#, C#, F#
Cyan = B, D, G
Teal = C, D#, G#
Blue = C#, E, A
Purple = D, F, A#
Magenta = D#, F#, B
Fuschia = E, G, C
Red = F, G#, C#
Orange = F#, A, D
Yellow = G, A#, D#
Pea = G#, A#, E
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