ResearchFrontier structures and internal systems
COMPLEMENTARY SCALES
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Scales that together form the complete chromatic total
When two or more complementary scales are combined, they contain all 12 chromatic pitches with no duplicates.
12 pairs/groups total
CHROMATIC COMPLEMENT
Complementary scales are sets that together contain all 12 chromatic pitches with no overlaps. For example, the two whole-tone scales (C-D-E-F#-G#-A# and Db-Eb-F-G-A-B) are perfect complements. These relationships reveal deep symmetries in the chromatic system.
Whole-Tone Complement
Two whole-tone scales form chromatic total
#1
Whole-Tone Scale 1
T-T-T-T-T
CDEF#G#A#
Whole-Tone Scale 2
T-T-T-T-T
DbEbFGAB
CHROMATIC TOTAL:
CDbDEbEFF#GG#AA#B
Diminished Complement
Three diminished 7th chords form chromatic total
#2
Diminished 1
m3-m3-m3-m3
CEbGbA
Diminished 2
m3-m3-m3-m3
DbEGBb
Diminished 3
m3-m3-m3-m3
DFAbB
CHROMATIC TOTAL:
CDbDEbEFGbGAbABbB
Augmented Complement
Four augmented triads form chromatic total
#3
Augmented 1
M3-M3-M3
CEAb
Augmented 2
M3-M3-M3
DbFA
Augmented 3
M3-M3-M3
DGbBb
Augmented 4
M3-M3-M3
EbGB
CHROMATIC TOTAL:
CDbDEbEFGbGAbABbB
Major-Minor Pentatonic Complement
Major and minor pentatonic + 2 notes
#4
C Major Pentatonic
T-T-m3-T
CDEGA
Eb Minor Pentatonic
T-T-m3-T
EbFGbBbDb
Chromatic Fill
Fill
F#B
CHROMATIC TOTAL:
CDbDEbEFF#GGbABbB
Hexatonic Complement
Two hexatonic scales form chromatic total
#5
Hexatonic 1
m2-m3-m2-m3-m2
CDbEFAbA
Hexatonic 2
m2-m3-m2-m3-m2
DEbF#GBbB
CHROMATIC TOTAL:
CDbDEbEFF#GAbABbB
Octatonic Complement
Octatonic scale + diminished 7th
#6
Octatonic 1
m2-T-m2-T-m2-T-m2
CDbEbEGbGABb
Octatonic Complement
m3-m3-m3
DFAbB
CHROMATIC TOTAL:
CDbDEbEFGbGAbABbB
Diatonic-Pentatonic Complement
Major scale + black key pentatonic
#7
C Major
T-T-ST-T-T-T
CDEFGAB
Pentatonic Complement
Black keys
DbEbGbAbBb
CHROMATIC TOTAL:
CDbDEbEFGbGAbABbB
Tritone Complement
Scales split at tritone
#8
C-F# Axis
Lower half
CDbDEbEFF#
F#-C Axis
Upper half
GAbABbB
CHROMATIC TOTAL:
CDbDEbEFF#GAbABbB
Chromatic Tetrachord Complement
Three chromatic tetrachords
#9
Chromatic Tetrachord 1
ST-ST-ST
CDbDEb
Chromatic Tetrachord 2
ST-ST-ST
EFF#G
Chromatic Tetrachord 3
ST-ST-ST
AbABbB
CHROMATIC TOTAL:
CDbDEbEFF#GAbABbB
Alternating Major-Minor
Alternating triadic qualities
#10
Major Triads
Two major triads
CEGDbFAb
Minor Triads
Two minor triads
DF#AEbGbBb
Fill
Chromatic fill
B
CHROMATIC TOTAL:
CDbDEbEFF#GAbABbB
Symmetric Partition
Even vs odd chromatic positions
#11
Even Semitones
0-2-4-6-8-10
CDEF#G#A#
Odd Semitones
1-3-5-7-9-11
DbEbFGAB
CHROMATIC TOTAL:
CDbDEbEFF#GG#AA#B
Quartal-Quintal Complement
Fourths and fifths complement
#12
Circle of Fourths
P4-P4-P4-P4-P4
CFBbEbAbDb
Circle of Fifths
P5-P5-P5-P5-P5
GDAEBF#
CHROMATIC TOTAL:
CDbDEbEFF#GAbABbB