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INVERTIBLE DODECAPHONIC PROGRESSIONS

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Twelve-tone rows that are invertible with all different intervals
These patterns are all-interval series (AIS) - twelve-tone rows containing all 11 different intervals. They can be inverted around an axis while maintaining musical coherence.
18 progressions total
ALL-INTERVAL SERIES (AIS)
These twelve-tone rows contain all 11 different intervals (m2, M2, m3, M3, P4, TT, P5, m6, M6, m7, M7). They are "invertible" - meaning they can be inverted around an axis and maintain musical coherence. Slonimsky catalogued 18 fundamental types in 1947, predating much of the academic research on all-interval rows.
#NAMEORIGINAL ROWINVERSIONDESCRIPTION
1
Mother Chord
Pattern 1290
Original:
CDbFEEbDBBbG#AF#G
m2-M3-M7-m2-m2-m3-m2-M2-m2-m3-m2
Inverted:
CBAbBbCDEFGGbEbDb
The fundamental all-interval row, invertible and symmetrical
2
Grandmother Chord
Pattern 1317
Original:
CC#EFGAbBbBDEbF#A
m2-m3-m2-M2-m2-M2-m2-m3-m2-M2-m3
Inverted:
CBAbGFEEbDbBbAF#F
Variant of Mother Chord with different interval ordering
3
Chromatic Wedge Invertible
Pattern 1225
Original:
F#FGEAbDAC#BbCBEb
m2-M2-m3-M3-P5-P5-M3-m3-M2-m2-M3
Inverted:
F#GFAbEBEbCABbDbD
Expanding from center, invertible around F#
4
All-Interval Row Type 1
Pattern 1222
Original:
CDbEFGAbBbBDEbF#A
m2-m3-m2-M2-m2-M2-m2-m3-m2-M2-m3
Inverted:
CBAbGFEEbDbBbAF#F
Classic all-interval series with perfect inversion
5
All-Interval Row Type 2
Pattern 1223
Original:
CC#DFEbEG#AGF#BBb
m2-m2-m3-m3-m2-M3-m2-m2-m2-M3-m2
Inverted:
CBBbGAbAEEbFF#DbD
Alternate all-interval configuration
6
All-Interval Row Type 3
Pattern 1224
Original:
CDbFEEbDBBbG#AF#G
m2-M3-M7-m2-m2-m3-m2-M2-m2-m3-m2
Inverted:
CBAbBbCDEFGGbEbDb
Third variant of all-interval series
7
Symmetrical Inversion
Pattern 1229
Original:
CEAbDbFBbEbGBEbAbC
M3-M3-P4-m3-P4-P4-m3-M3-m3-M3-M3
Inverted:
CAbEbBGEbBbFDbAbEC
Rotationally symmetrical with perfect retrograde inversion
8
Berg-Style Invertible
Pattern 1221
Original:
GBbDF#ACEAbBC#EbF
m3-M3-M3-m3-m3-M3-M3-M3-m2-m2-m2
Inverted:
GECAbECAF#DBbGEb
Tonal implications with invertible structure
9
Webern-Style Invertible
Pattern 1220
Original:
BBbDC#CEEbGF#FAAb
m2-M3-m2-m2-m3-M7-M3-m2-m2-M3-m2
Inverted:
BCAbABbGAbEFF#DEb
Highly symmetrical with mirror properties
10
Tritone Axis Inversion
Original:
CDbF#GDEbABbEFBC
m2-P5-m2-P5-m2-P5-m2-P5-m2-P5-m2
Inverted:
CBF#FBbAEEbAbGDbC
Inverts around tritone axis, alternating semitone/fifth
11
Hexachordal Mirror
Original:
CC#EFAbADEbF#GBBb
m2-m3-m2-m3-m2-P5-m2-M2-m2-m3-m2
Inverted:
CBAbGEEbBbAFEDbD
Two hexachords that mirror each other
12
Combinatorial Inversion
Original:
CDbEFGAbC#DF#ABbB
m2-m3-m2-M2-m2-P5-m2-m3-m3-m2-m2
Inverted:
CBAbF#FEbBBbGEDDb
Hexachordal combinatoriality with inversion
13
Spiral Inversion
Original:
CGDAEBF#DbAbEbBbF
P5-P5-P5-P5-P5-P5-P5-P5-P5-P5-P5
Inverted:
CFBbEbAbDbF#BEADG
Circle of fifths forward, inverts to circle of fourths
14
Chromatic Cluster Invertible
Original:
CC#DEbEFF#GAbABbB
m2-m2-m2-m2-m2-m2-m2-m2-m2-m2-m2
Inverted:
CBBbAAbGF#FEEbDDb
Chromatic scale inverts to descending chromatic
15
Whole-Tone Invertible
Original:
CDEF#AbBbDbEbFGAB
T-T-T-T-T-T-T-T-T-T-T
Inverted:
CBbAbF#EDBAGFEbDb
Two whole-tone scales that invert
16
Mixed Interval Inversion
Original:
CEbEGAbBC#DFF#ABb
m3-m2-m3-m2-m3-m2-m2-m3-m2-m3-m2
Inverted:
CAAbF#FDC#BAbGEEb
Alternating minor thirds and semitones with inversion
17
Quartal Invertible
Original:
CFBbEbAbDbGbBEADG
P4-P4-P4-P4-P4-P4-P5-P4-P4-P4-P4
Inverted:
CGDAEBF#DbAbEbBbF
Circle of fourths inverts to circle of fifths
18
Asymmetric Invertible
Original:
CDbEbEF#GABbBDFAb
m2-M2-m2-M2-m2-M2-m2-m2-m3-m3-m3
Inverted:
CBBbAbGFEEbDbBAF#
Asymmetric row that becomes symmetric when inverted