FORWARD---1.1
INTRODUCTION---1.3
GLIMPSES---2.1
MUSIC
OF WORLDS, HUMANITIES, INSTRUMENTS. (RE: ILLUSTRATION # P-1).---2.1
ORBIT OF PLUTO. (RE: ILLUSTRATION # P-2).---2.1
DOUBLING UNDERTONE, DIVIDING
OVERTONE, (RE: ILLUSTRATION # P-3).---2.3
THE MAYAN KATON WHEEL 8 (RE: ILLUSTRATION #
P-4).---2.3
VIBRATIONS OF A STRETCHED
STRING. (RE: ILLUSTRATION # P-5).---2.4
MACROCOSMOS MULTIPLY - MICROCOSMOS DIVIDE. (RE:
ILLUSTRATION # P-6).---2.5
SPIRAL
GALAXIES TO QUASI STELLAR SOURCES. 12 (RE: ILLUSTRATION # P-7).---2.5
COLOR SPECTRUM MUSICAL INTERVALS
PLANETS. (RE: ILLUSTRATION # P-8).---2.6
CHINESE COLOR MUSIC SCALE 15 VS.
PYTHAGORAS COLOR MUSIC SCALE. 16 (RE: ILLUSTRATION # P-9).---2.6
COLOR NOTE VIBRATION SCALE. (RE: ILLUSTRATION #
P-10).---2.6
COLOR NOTE VIBRATION
SCALE. (RE: ILLUSTRATION # P-11).---2.7
FIELD OF OCTAVES OVERTONES-UNDERTONE. (RE:
ILLUSTRATION # P-12).---2.7
FIELD
OF OCTAVES OVERTONES UNDERTONE. (RE: ILLUSTRATION # P-13).---2.8
SPACE FOLDS ON A FIELD OF 64 DOTS.
(RE: ILLUSTRATION # P-14).---2.8
EXPANDS. (RE: ILLUSTRATION # P-15).---2.9
PASCAL'S TRIANGLE. (RE: ILLUSTRATION # P-16).---2.9
SPACE FOLD CHART. (RE: ILLUSTRATION
# P-17).---2.9
INVOLUTION EVOLUTION
AXIS -ORBIT OF MUSICAL DIVISIONS. (RE: ILLUSTRATION # P-18).---2.10
BIRTH OF A MUSIC GALAXY. (RE:
ILLUSTRATION # P-19).---2.11
ORBITS OF MUSICAL DIVISIONS (PULLED
APART ON A FIELD OF NINE). (RE: ILLUSTRATION # P-20).---2.11
CORES OVERLAPPING. (RE:
ILLUSTRATION # P-21).---2.11 ---2.11
IMPLOSION BECOMES EXPLOSION. (RE:
ILLUSTRATION # P-22).---2.12
LOOP.
(RE: ILLUSTRATION # P-23).---2.12
CONTRACTING SPIRAL. (RE:
ILLUSTRATION # P-24).---2.12
CHANGING DIRECTIONS. (RE:
ILLUSTRATION # P-25).---2.13
PATTERNS OF MULTIPLES OF 2, 3, 5,
7. (RE: ILLUSTRATION # P-26).---2.13
BIBLIOGRAPHY---2.14
GLIMPSES OF BRIDGES OF ART---2.15
THOUGHTS WHILE WORKING---2.16
DIVISION OF STRING ON RIGHT ANGLES.
(RE. ILLUSTRATION P-33). ---2.16
EYE (CIRCLE) EXPANSION. EAR(SPIRAL)
CONTRACTION. (RE. ILLUSTRATION P-34). ---2.16
AREA OF HEARING - DISTANCECOVERED
BY A FALLING OBJECT. (RE. ILLUSTRATION P-35). ---2.17
MOBIUS STRIP. 4 (RE. ILLUSTRATION
P-36). ---2.18
SECTIONING OF CIRCLES. (RE.
ILLUSTRATIONS P-38 & P-39). ---2.19
I CHING PRIMAL ARRANGEMENT 10. (RE. ILLUSTRATION
P-40). ---2.20
PRIMAL AXIS - INNER WORLD AXIS 11.
(RE. ILLUSTRATION P-41). ---2.20
I CHING - PRIMAL AXIS, INNER WORLD
AXIS. (RE. ILLUSTRATION P-42). ---2.21
I CHING CHART. (RE. ILLUSTRATION P-43). ---2.22
FIELD OF NOTES - INVOLUTION EVOLUTION
AXIS. (RE. ILLUSTRATION P-44). ---2.22
I CHING SECOND ORDER. (RE.
ILLUSTRATION P-45). ---2.22
PROGRESSION BY SQUARES. (RE.
ILLUSTRATION P-46). ---2.23
CORES CONTRACTING EXPANDING. (RE.
ILLUSTRATION P-48). ---2.26
COMPLETION OF CYCLE. (RE.
ILLUSTRATION P-49). ---2.26
PROGRESSION BY SQUARES OVERLAPPING
IN AN (S) CURVE. (RE. ILLUSTRATION P-50). ---2.27
FIVE STEPS. (RE. ILLUSTRATION
P-51). ---2.27
DIAMETER OF EACH CIRCLE SECTIONED
BY ITS RADIUS. (RE. ILLUSTRATION P-52). ---2.27
EXPANDS - CONTRACTS. (RE.
ILLUSTRATION P-53). ---2.28
CONCAVE - CONVEX. (RE. ILLUSTRATION
P-54). ---2.28
TIME - SPACE. (RE. ILLUSTRATION
P-55). ---2.28
KEY. 15 (RE. ILLUSTRATION P-56).
---2.29
BIBLIOGRAPHY---2.30
SUGGESTED READING---2.30
GLIMPSES OF THE BRIDGES OF ART---3.1
MUSIC OF WORLDS HUMANITIES INSTRUMENTS---3.2
ILLUSTRATION: P-1---3.2
ILLUSTRATION: P-2---3.3
ORBIT OF PLUTO---3.3
DOUBLING - UNDERTONE / DIVIDING - OVERTONE---3.4
ILLUSTRATION: P-3---3.4
MAYAN KATON WHEEL---3.5
ILLUSTRATION: P-4---3.5
VIBRATIONS OF A STRETCHED STRING---3.6
ILLUSTRATION: P-5---3.6
ILLUSTRATION: P-6---3.7
MACROCOSMOS MULTIPLY MICROCOSMOS
DIVIDE---3.7
SPIRAL GALAXIES---3.8
ILLUSTRATION: P-7---3.8
ILLUSTRATION: P-8---3.9
COLOR SPECTRUM MUSICAL INTERVAL
PLANETS---3.9
CHINESE COLOR SCALE---3.10
ILLUSTRATION: P-9---3.10
ILLUSTRATION: P-10---3.11
COLOR NOTE VIBRATION SCALE---3.11
VIBRATING STRING---3.12
ILLUSTRATION: P-11---3.12
ILLUSTRATION: P-12---3.13
FIELD OF OCTAVES---3.13
FIELD OF OCTAVES---3.14
ILLUSTRATION: P-13---3.14
ILLUSTRATION: P-14---3.15
SPACE FOLDS ON A FIELD OF EIGHT---3.15
RE EXPANDS---3.16
ILLUSTRATION: P-15---3.16
ILLUSTRATION: P-16---3.17
PASCALS TRIANGLE---3.17
SPACE FOLD CHART---3.18
ILLUSTRATION: P-17---3.18
ILLUSTRATION: P-18---3.19
INVOLUTION AXIS EVOLUTION AXIS---3.19
BIRTH OF A MUSIC GALAXY---3.20
ILLUSTRATION: P-19---3.20
ILLUSTRATION: P-20---3.21
ORBITS OF MUSICAL DIVISIONS---3.21
CORES OVERLAPPING---3.22
ILLUSTRATION: P-21---3.22
ILLUSTRATION: P-22---3.23
IMPLOSION BECOMES EXPLOSION---3.23
LOOP---3.24
ILLUSTRATION: P-23---3.24
ILLUSTRATION: P-24---3.25
CONTRACTING
SPIRAL---3.25
CHANGING DIRECTIONS---3.26
ILLUSTRATION: P-25---3.26
PATTERNS OF MULTIPLES OF 2 3 5 7---3.27
ILLUSTRATION: P-26---3.27
CIRCLE OF FIFTHS---3.28
ILLUSTRATION: P-27---3.28
ILLUSTRATION: P-28---3.29
TIME CHART---3.29
MAN SPACE CHART---3.30
ILLUSTRATION: P-29---3.30
ILLUSTRATION: P-30---3.31
PERFECTION TRANSFORMATION CHART---3.31
SPACE IMMORTALITY CHART---3.32
ILLUSTRATION: P-31---3.32
ILLUSTRATION: P-32---3.33
TIME MOON CHART---3.33
DIVISION OF STRING ON RIGHT ANGLE---3.34
ILLUSTRATION: P-33---3.34
ILLUSTRATION: P-34---3.35
EYE CIRCLE EXPANSION---3.35
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AREA OF HEARING---3.36
ILLUSTRATION: P-35---3.36
MOBIUS STRIP---3.37
ILLUSTRATION: P-36---3.37
I CHING HEXAGRAMS---3.38
MUSICAL RATIO AXIS---3.38
ILLUSTRATION: P-37---3.38
ILLUSTRATIONS: P-38 & P-39---3.39
SECTIONING OF CIRCLES---3.39
I CHING PRIMAL ARRANGEMENT---3.40
ILLUSTRATION: P-40---3.40
ILLUSTRATION: P-41---3.41
PRIMAL AXIS INNER WORLD AXIS---3.41
I CHING PRIMAL AXIS---3.42
INNER WORLD AXIS---3.42
ILLUSTRATION: P-42---3.42
ILLUSTRATION: P-43---3.43
I CHING CHART---3.43
FIELD OF NOTES---3.44
INVOLUTION-EVOLUTION AXIS---3.44
ILLUSTRATION: P-44---3.44
ILLUSTRATION: P-45---3.45
I CHING SECOND ORDER---3.45
PROGRESSION BY SQUARES---3.46
ILLUSTRATION: P-46---3.46
THE END BECOMES THE BEGINNING---3.47
ILLUSTRATION: P-47---3.47
CORES---3.48 CONTRACTING EXPANDING---3.48
ILLUSTRATION: P-48---3.48
ILLUSTRATION: P-49---3.49
COMPLETION OF CYCLE---3.49
PROGRESSION BY SQUARES OVERLAPPING IN AN (S) CURVE---3.50
ILLUSTRATION: P-50---3.50
ILLUSTRATION: P-51---3.51
FIVE STEPS---3.51
DIAMETER OF EACH CIRCLE SECTIONED BY ITS
RADIUS---3.52
ILLUSTRATION: P-52---3.52
EXPANDS-CONTRACTS---3.53
ILLUSTRATION: P-53---3.53
CONCAVE-CONVEX---3.54
ILLUSTRATION: P-54---3.54
ILLUSTRATION: P-55---3.55
TIME-SPACE---3.55
KEY---3.56
ILLUSTRATION: P-56---3.56
STOP AND THINK---4.1
THE PAST CONTRACTS THE FUTURE EXPANDS 3" X 9"---4.2
ILLUSTRATION: S-1---4.2
PROJECTION OF A POLYGON 4" X 7"---4.3
ILLUSTRATION: S-2---4.3
PI EQUALS SIX 6" X 7"---4.4
ILLUSTRATION: S-3---4.4
ILLUSTRATION: S-4---4.5
RE ORBIT TI ORBIT LA ORBIT---4.5
THESE ARE SHAPES FOUND IN NATURE---4.6
ILLUSTRATION: S-5---4.6
ILLUSTRATION: S-6---4.7
WAVE LENGTHS OF SOUND WITH RINGS IN ORDER
OF PROGRESSION 9" X 9"---4.7
INSIDE OUTSIDE---4.8
ILLUSTRATION: S-7---4.8
BLUES GREENS SEPARATE OUTWARDS REDS
YELLOWS SEPARATE INWARDS---4.9
ILLUSTRATION:
S-8---4.9
BLACKS AND WHITES ARE BOUNDARY
COLORS---4.10
ILLUSTRATION: S-9---4.10
ILLUSTRATION: S-10---4.11
COLORS BREATHE IN COLORS BREATHE OUT
VIBRATIONS OF EACH NOTE---4.11
TRAPEZOID (MULTIPLES OF TWOs AND
THREEs)---4.12
ILLUSTRATION: S-11---4.12
TWO UNIVERSES BACK TO BACK---4.13
(THE DIRECTION OF A CURRENT IS COUNTERCLOCK-WISE FROM
NEGATIVE TO POSITIVE)---4.13
ILLUSTRATION:
S-12---4.13
TWO UNIVERSES BACK TO BACK
THE FUTURE EXPANDS THE PAST CONTRACTS---4.14
(MORE PARTICLES AT THE SOUTH POLE)---4.14
KLEIN: "THE FIFTH DIMENSION CURVES BACK
UPON ITSELF).---4.14
ILLUSTRATION: S-13---4.14
VIBRATIONS ON FOUR DECREASING SOLIDS---4.15
(THE FIFTH CONTRACTS TO A LIGHT FORCE)---4.15
ILLUSTRATION: S-14---4.15
UNIVERSAL LADDER OF SOUNDS---4.16
ILLUSTRATION: S-15---4.16
NORTH OR NEGATIVE POLE SOUTH OR POSITIVE
POLE---4.17
ILLUSTRATION: S-16---4.17
PATTERN OF NOTES ON A GRID---4.18
ILLUSTRATION: S-17(1-5)---4.18
A NEW RULER FOR MEASUREMENT---4.19
ILLUSTRATION: S-18---4.19
PROJECTION OF ZIG ZAG ACCORDING TO PROGRESSION BY
SQUARES.---4.20
ILLUSTRATION: S-19---4.20
PERIODIC TABLE OF ELEMENTS---4.21
(APPLIED TO RATIOS OF INTERVALS IN MUSIC)---4.21
ILLUSTRATION: S-20---4.21
PERIODIC TABLE OF ELEMENTS SEVEN OCTAVES---4.22
ILLUSTRATION: S-21 (1-2)---4.22
ILLUSTRATION: S-22---4.23
FOLDING BACK INTO A SEED---4.23
ANGLES OF EACH NOTE PUT ON AN ANGLED AXIS---4.24
ILLUSTRATION: S-23---4.24
CLUSTER OF NOTES IN FIRST OCTAVE.---4.25
(16:15 ON A FIELD OF C (DO) 54)---4.25
ILLUSTRATION: S-24---4.25
DOES THE SOUND WAVE TWIST?---4.26
ILLUSTRATION: S-25---4.26
ILLUSTRATION: S-26---4.27
OVERTONE SERIES ONE VERSION---4.27
THINGS BEAR THEIR OWN MEASURE IN THEMSELVES
(OUSPENSKY)---4.28
ILLUSTRATION:
S-27---4.28
ILLUSTRATION: S-28---4.29
LENGTH OF STRING---4.29
MACROCOSMOS MICROCOSMOS---4.30
(THE ORBITS RESEMBLE ELECTRON ORBITS.)---4.30
ILLUSTRATION: S-29---4.30
ILLUSTRATION: S-30---4.31
(A) EXPANSION CONTRACTION ---4.31
(B) SPACE FOLD---4.32
ILLUSTRATION: S-31---4.32
ILLUSTRATION: S-32---4.33
(C) ANGLES---4.33
(D)
MUSICAL INTERVALS---4.34
ILLUSTRATION: S-33---4.34
ILLUSTRATION: S-34---4.35
(E) ECHO---4.35
I CHING---4.36
ILLUSTRATION: S-35---4.36
ILLUSTRATION: S-36---4.37
STOP AND THINK---4.37
STOP AND THINK ---4.38
ILLUSTRATION: S-37---4.38
ILLUSTRATION: S-38---4.39
STOP AND THINK ---4.39
OTHER SIDE OF ART---5.1
EXPANSION-CONTRACTION---5.2
ILLUSTRATION: A-3---5.2
ILLUSTRATION: B-1---5.3
SHOWING HOW "256/243" EQUALS THE LIMIT OF A
CYCLE---5.3
ANOTHER TYPE OF NUMBERED
GRID---5.4
ILLUSTRATION: B-2---5.4
UNIVERSAL LADDER OF SOUNDS ON A WAVE FORM---5.5
ILLUSTRATION: B-3---5.5
TONES ADAPTED TO A DOUBLE HELIX---5.6
ILLUSTRATION: B-04---5.6
THE MULTIPLICATION TABLE AS A FRAMEWORK FOR THE RATIOS OF
RELATIVE PITCH---5.7
ILLUSTRATION: B-5,
B-6, B-7 & B-8---5.7
CLUSTER OF RINGS AT CENTER EQUALS
EXPANSION---5.8
ILLUSTRATION: B-9---5.8
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IS ... AN EXPANSION CONCAVE... OR CONVEX?---5.9
ILLUSTRATION: B-10---5.9
THE MISSING HARMONIC OF NATURE THE
PENTAGON---5.10
ILLUSTRATION: B-11---5.10
A NEW KEYBOARD INSTRUMENT---5.11
ILLUSTRATION: B-12---5.11
ILLUSTRATION: B-13---5.12
MULTIPLES ON CURVED AXIS---5.12
ILLUSTRATION: B-14---5.13
MULTIPLES OF TWO, THREE, FIVE, SIXTEEN, EIGHTEEN FORM
SOLID CUBES.---5.13
UNITS OF MEASUREMENT FOR EACH RELATIVE PITCH
BASED ON THE HYPOTENUSE AND THE SIDES OF DIMINISHING TRIANGLES.---5.14
ILLUSTRATION: B-015---5.14
A SYNTHESIS OF SERIES IN THE FIRST OCTAVE COMBINING THE
GRID AND WAVE DIVISIONS---5.15
ILLUSTRATION: B-16---5.15
THE FIRST CYCLE MIGHT END IN A DISINTEGRATION.---5.16
ILLUSTRATION: B-17---5.16
ILLUSTRATION: B-18---5.17
MULTIPLES OF TWO AND FIVE AND THREE AND FIVE---5.17
B CONTRACTS---5.18
ILLUSTRATION: B-19---5.18
ILLUSTRATION: B-20---5.19
THE INVISIBLE VIBRATION WORLD---5.19
DEPICTING A RANGE OF FREQUENCIES FROM 256 TO
4000---5.20
ILLUSTRATION: B-21---5.20
ILLUSTRATION: B-22---5.21
EXPANDING CONTRACTING---5.21
UNIVERSAL LADDER OF SOUND---5.22
ILLUSTRATION: B-23---5.22
ILLUSTRATION: B-24---5.23
I CHING PRIMAL ARRANGEMENT---5.23
EXPANDING DIMINISHED ASCENDING SCALE---5.24
CONTRACTING INCREASING DESCENDING SCALE---5.24
ILLUSTRATION: B-25---5.24
THE FINITE WITHIN THE INFINITE WITHOUT---5.25
ILLUSTRATION: B-26---5.25
INVISIBLE WORLD MATERIAL WORLD---5.26
ILLUSTRATION: B-27---5.26
ILLUSTRATION: B-28---5.27
TRIANGLES IN ORBIT---5.27
THE REASON FOR THE REVERSE AXIS---5.28
ILLUSTRATION: B-29---5.28
ILLUSTRATION: B-30---5.29
THE FINITE NUMBERED GRID---5.29
MULTIPLES OF 2, 3, 5 AND 16 ---5.30
ILLUSTRATION: B-31---5.30
ASCENDING DESCENDING---5.31
ILLUSTRATION: B-32---5.31
THE CHINESE MAGIC SQUARE---5.32
ILLUSTRATION: B-33---5.32
MAYAN KATON WHEEL AS APPLIED TO EARTH'S MAGNETIC FIELD
AND MUSIC TONES.---5.33
ILLUSTRATION: B-34---5.33
THE MEASUREMENT OF MANKIND---5.34
ILLUSTRATION: B-35---5.34
ILLUSTRATION: B-36---5.35
LIMITS OF THE CYCLES HIGHER MULTIPLES.---5.35
LIMITS OF THE CYCLES---5.36
ILLUSTRATION: B-37---5.36
ILLUSTRATION: B-38---5.37
GROWTH VIBRATIONS OF A BUTTERFLY---5.37
THE PUZZLE OF 125---5.38
ILLUSTRATION: B-39---5.38
REPRINT OF LEONARDO ARTICLE --- 6.1
THEORIES AND QUERIES---6.6
SPHERES OF SOUND---6.7
ILLUSTRATION: C-1---6.7
LIMITS OF THE CYCLES---6.8
LIMITS OF EXPANSION---6.8
ILLUSTRATION: C-2---6.8
ILLUSTRATION: C-3---6.9
THE BEGINNING OF THE PENTAGON---6.9
A SQUARING OF THE CIRCLE---6.9
A VISUAL COMPARISON OF RELATIVE PITCH AND
PLANETS IN THE SOLAR SYSTEM BOTH MEASURED ON A SCALE OF 360.---6.10
ILLUSTRATION: C-4---6.10
RELATIVE PITCH ARRANGED ON A HELICAL
STRUCTURE.---6.11
ILLUSTRATION: C-5---6.11
PLANETARY ORBITS OF THE SOLAR SYSTEM.---6.12
ILLUSTRATION: C-6---6.12
ILLUSTRATION: C-7---6.13
MATTER---6.13
ZONE OF MATTER ZONE OF NON-MATTER---6.14
ILLUSTRATION: C-8---6.14
THE HANDS WITH RINGS---6.15
ILLUSTRATION: C-9---6.15
THE SHELL AND RELATIVE PITCH---6.16
ILLUSTRATION: C-10---6.16
ILLUSTRATION: C-11---6.17
THE SENSES AND RELATIVE
PITCH---6.17
HOW TO DETERMINE PROPORTIONS WITHIN A
SPECIFIC RANGE ON MULTIPLES OF 5 X 2 AND 2 X 2---6.18
ILLUSTRATION: C-12---6.18
A HOROSCOPE BASED ON THE CIRCLE OF FIFTHS
IN MUSIC.---6.19
ILLUSTRATION: C-13---6.19
DESCENDING CONTRACTING SCALE---6.20
ILLUSTRATION: C-14---6.20
ILLUSTRATION: C-15---6.21
A REVERES PROGRESSION BY SQUARES.---6.21
MODULES ILLUSTRATING RATIOS.---6.22
ILLUSTRATION: C-16---6.22
ILLUSTRATION: C-17---6.23
BARS REPRESENTING EACH TONE PERIODICITY ON A LAMBDOMA
GRID.---6.23
SPACE FOLDS---6.24
ILLUSTRATION: C-18---6.24
ILLUSTRATION: C-19---6.25
COLOR MODULATION ON THE LAMBDOMA DIAGRAM.---6.25
SQUARING THE CIRCLE---6.26
ILLUSTRATION: C-20---6.26
ILLUSTRATION: C-21---6.27
UNIFIED FIELD THEORY OF INTERVALS OF RELATIVE PITCH LAID
ON AN ARRAY OF FRACTIONS (PYTHAGOREAN TABLE, OR LAMBDOMA DIAGRAM).---6.27
SIXTY FOUR SQUARES OF THE LAMBDOMA DIAGRAM COLORED
ACCORDING TO COLOR TONE THEORIES.---6.28
ILLUSTRATION:
C-22---6.28
ILLUSTRATION: C-23---6.29
PATTERNS OF THE SPHERES TAKE PLACE ON THE OTHER
DIMENSION SPACE.---6.29
SHOWING HOW RATIOS CAN BE LINKED TO DEGREES OF A CIRCLE
---6.30
HOW THE SMALLER THE ANGLE THE
MORE FREQUENT THE PULSE BEAT---6.30
ILLUSTRATION: C-24---6.30
ILLUSTRATION: C-25---6.31
COORDINATE AXES IN SIX DIMENSIONS.---6.31
RULES FOR LAMBDOMA DIAGRAM. ---6.32
ILLUSTRATION: C-26, C-27 & C-28---6.32
ILLUSTRATION: C-29 & C-30---6.33
UNDERTONE-------- OVERTONE---6.34
ILLUSTRATION: C-31---6.34
UNDERTONE----- OVERTONE---6.35
5 ILLUSTRATION: C-32---6.35
LAMBDOMA ON EITHER SIDE OF TUNING TUBE.---6.36
ILLUSTRATION: C-33---6.36
ILLUSTRATION: C-34---6.37
A LAMBDOMA GRID FORMED BY TWO INTERSECTING
ELLIPTICALS.---6.37
PLAN FOR A SERIES OF
TRIANGLES DROPPED AT ANGLES WITHIN A CIRCLE.---6.38
ILLUSTRATION: C-35---6.38
EXTENSION OF THE FOURTH DIMENSION OF SPACE.---6.39
ILLUSTRATION: C-36---6.39
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