Scale Expansion Sequences
by Benjamin Tubb
16 December 1975

Original Scale Degree Sequences of Tonal Expansions for Chord
Structures

Note: A=10, B=11, C=12

     E0
S1   1
S2   12
S3   123
S4   1234
S5   12345
S6   123456
S7   1234567
S8   12345678
S9   123456789
S10  123456789A
S11  123456789AB
S12  123456789ABC

     E1
S3   132
S4   1324
S5   13524
S6   135246
S7   1357246
S8   13572468
S9   135792468
S10  135792468A
S11  13579B2468A
S12  13579B2468AC

     E2
S4   1432
S5   14253
S6   142536
S7   1473625
S8   14725836
S9   147258369
S10  147A369258
S11  147A258B369
S12  147A258B369C

     E3
S5   15432
S6   153264
S7   1526374
S8   15263748
S9   159483726
S10  15826A4837
S11  15926A37B48
S12  15926A37B48C

     E4
S6   165432
S7   1642753
S8   16385274
S9   162738495
S10  162738495A
S11  16B5A493827
S12  16B4927C5A38

     E5
S7   1765432
S8   17538642
S9   174285396
S10  17395284A6
S11  1728394A5B6
S12  1728394A5B6C

     E6
S8   18765432
S9   186429753
S10  1852963A74
S11  184B73A6295
S12  183A5C7294B6

     E7
S9   198765432
S10  197532A864
S11  1952A743B86
S12  1952A63B74C8

     E8
S10  1A98765432
S11  1A8642B9753
S12  1A742B853C96

     E9
S11  1BA98765432
S12  1B97532CA864

     E10
S12  1CBA98765432

Chord structures built on scale degrees determined by
reading the original sequence in a clockwise direction for
a given expansion, e.g. S4E2, 1432 starting on 4 is 4321.
Total number of sequences are 67.

Reference: "The Schillinger System of Musical Composition",
Vol. I, Bk. II, Chap. 5, by Joseph Schillinger