# Modal System: 0 1 2 4 7 8

## "mM#11b9 modal system"

(mode 0) 0: 0 1 2 4  7  8 | all-trichord hexachord
(mode 1) 1: 0 1 3 6  7 11 | mM#11b9 = all-trichord hexachord
(mode 2) 2: 0 2 5 6 10 11 |
(mode 3) 4: 0 3 4 8  9 10 | M#13#5#9 no 11th = all-trichord hexachord
(mode 4) 7: 0 1 5 6  7  9 |
(mode 5) 8: 0 4 5 6  8 11 |

## Clock Diagrams of All 12 Transpositions in Cycle of 5ths

• T
Geometric x7
Spectral x7
Geometric x1
Spectral x1
Chord Types Sorted By Rootedness
0   1.342(mode 0)0:0 1 2 4  7  8 |all-trichord hexachord
1.317(mode 1)1:0 1 3 6  7 11 |mM#11b9 = all-trichord hexachord
.975(mode 3)4:0 3 4 8  9 10 |M#13#5#9 no 11th = all-trichord hexachord
.633(mode 4)7:0 1 5 6  7  9 |
.300(mode 2)2:0 2 5 6 10 11 |
.233(mode 5)8:0 4 5 6  8 11 |
7   1.342(mode 2)7:0 1 2 4  7  8 |all-trichord hexachord
1.317(mode 3)8:0 1 3 6  7 11 |mM#11b9 = all-trichord hexachord
.975(mode 5)11:0 3 4 8  9 10 |M#13#5#9 no 11th = all-trichord hexachord
.633(mode 0)2:0 1 5 6  7  9 |
.300(mode 4)9:0 2 5 6 10 11 |
.233(mode 1)3:0 4 5 6  8 11 |
2   1.342(mode 0)2:0 1 2 4  7  8 |all-trichord hexachord
1.317(mode 1)3:0 1 3 6  7 11 |mM#11b9 = all-trichord hexachord
.975(mode 3)6:0 3 4 8  9 10 |M#13#5#9 no 11th = all-trichord hexachord
.633(mode 4)9:0 1 5 6  7  9 |
.300(mode 2)4:0 2 5 6 10 11 |
.233(mode 5)10:0 4 5 6  8 11 |
9   1.342(mode 3)9:0 1 2 4  7  8 |all-trichord hexachord
1.317(mode 4)10:0 1 3 6  7 11 |mM#11b9 = all-trichord hexachord
.975(mode 0)1:0 3 4 8  9 10 |M#13#5#9 no 11th = all-trichord hexachord
.633(mode 1)4:0 1 5 6  7  9 |
.300(mode 5)11:0 2 5 6 10 11 |
.233(mode 2)5:0 4 5 6  8 11 |
4   1.342(mode 1)4:0 1 2 4  7  8 |all-trichord hexachord
1.317(mode 2)5:0 1 3 6  7 11 |mM#11b9 = all-trichord hexachord
.975(mode 4)8:0 3 4 8  9 10 |M#13#5#9 no 11th = all-trichord hexachord
.633(mode 5)11:0 1 5 6  7  9 |
.300(mode 3)6:0 2 5 6 10 11 |
.233(mode 0)0:0 4 5 6  8 11 |
11   1.342(mode 5)11:0 1 2 4  7  8 |all-trichord hexachord
1.317(mode 0)0:0 1 3 6  7 11 |mM#11b9 = all-trichord hexachord
.975(mode 2)3:0 3 4 8  9 10 |M#13#5#9 no 11th = all-trichord hexachord
.633(mode 3)6:0 1 5 6  7  9 |
.300(mode 1)1:0 2 5 6 10 11 |
.233(mode 4)7:0 4 5 6  8 11 |
6   1.342(mode 2)6:0 1 2 4  7  8 |all-trichord hexachord
1.317(mode 3)7:0 1 3 6  7 11 |mM#11b9 = all-trichord hexachord
.975(mode 5)10:0 3 4 8  9 10 |M#13#5#9 no 11th = all-trichord hexachord
.633(mode 0)1:0 1 5 6  7  9 |
.300(mode 4)8:0 2 5 6 10 11 |
.233(mode 1)2:0 4 5 6  8 11 |
1   1.342(mode 0)1:0 1 2 4  7  8 |all-trichord hexachord
1.317(mode 1)2:0 1 3 6  7 11 |mM#11b9 = all-trichord hexachord
.975(mode 3)5:0 3 4 8  9 10 |M#13#5#9 no 11th = all-trichord hexachord
.633(mode 4)8:0 1 5 6  7  9 |
.300(mode 2)3:0 2 5 6 10 11 |
.233(mode 5)9:0 4 5 6  8 11 |
8   1.342(mode 3)8:0 1 2 4  7  8 |all-trichord hexachord
1.317(mode 4)9:0 1 3 6  7 11 |mM#11b9 = all-trichord hexachord
.975(mode 0)0:0 3 4 8  9 10 |M#13#5#9 no 11th = all-trichord hexachord
.633(mode 1)3:0 1 5 6  7  9 |
.300(mode 5)10:0 2 5 6 10 11 |
.233(mode 2)4:0 4 5 6  8 11 |
3   1.342(mode 0)3:0 1 2 4  7  8 |all-trichord hexachord
1.317(mode 1)4:0 1 3 6  7 11 |mM#11b9 = all-trichord hexachord
.975(mode 3)7:0 3 4 8  9 10 |M#13#5#9 no 11th = all-trichord hexachord
.633(mode 4)10:0 1 5 6  7  9 |
.300(mode 2)5:0 2 5 6 10 11 |
.233(mode 5)11:0 4 5 6  8 11 |
10   1.342(mode 4)10:0 1 2 4  7  8 |all-trichord hexachord
1.317(mode 5)11:0 1 3 6  7 11 |mM#11b9 = all-trichord hexachord
.975(mode 1)2:0 3 4 8  9 10 |M#13#5#9 no 11th = all-trichord hexachord
.633(mode 2)5:0 1 5 6  7  9 |
.300(mode 0)0:0 2 5 6 10 11 |
.233(mode 3)6:0 4 5 6  8 11 |
5   1.342(mode 2)5:0 1 2 4  7  8 |all-trichord hexachord
1.317(mode 3)6:0 1 3 6  7 11 |mM#11b9 = all-trichord hexachord
.975(mode 5)9:0 3 4 8  9 10 |M#13#5#9 no 11th = all-trichord hexachord
.633(mode 0)0:0 1 5 6  7  9 |
.300(mode 4)7:0 2 5 6 10 11 |
.233(mode 1)1:0 4 5 6  8 11 |

## General Statistics

Cardinality:                     6
Forte Number:                    6-z17
Forte Prime Form:                [0,1,2,4,7,8]

Interval Stacking:               1 1 2 3 1 4
Interval Vector:                 3 2 2 3 3 2

Inversional Symmetry:            no
Transpositional Symmetry:        no
Modal-system-invariant under multiplication by: 1 7

All Transpositions
• +0= 0 1 2 4  7  8 |all-trichord hexachord
+1= 1 2 3 5  8  9 |
+2= 2 3 4 6  9 10 |
+3= 3 4 5 7 10 11 |
+4= 0 4 5 6  8 11 |
+5= 0 1 5 6  7  9 |
+6= 1 2 6 7  8 10 |
+7= 2 3 7 8  9 11 |
+8= 0 3 4 8  9 10 |M#13#5#9 no 11th = all-trichord hexachord
+9= 1 4 5 9 10 11 |
+10= 0 2 5 6 10 11 |
+11= 0 1 3 6  7 11 |mM#11b9 = all-trichord hexachord
Modes:
• (mode 0) 0: 0 1 2 4  7  8 | all-trichord hexachord
(mode 1) 1: 0 1 3 6  7 11 | mM#11b9 = all-trichord hexachord
(mode 2) 2: 0 2 5 6 10 11 |
(mode 3) 4: 0 3 4 8  9 10 | M#13#5#9 no 11th = all-trichord hexachord
(mode 4) 7: 0 1 5 6  7  9 |
(mode 5) 8: 0 4 5 6  8 11 |
Modes Sorted by Rootedness:
•   1.342(mode 0)0:0 1 2 4  7  8 |all-trichord hexachord
1.317(mode 1)1:0 1 3 6  7 11 |mM#11b9 = all-trichord hexachord
.975(mode 3)4:0 3 4 8  9 10 |M#13#5#9 no 11th = all-trichord hexachord
.633(mode 4)7:0 1 5 6  7  9 |
.300(mode 2)2:0 2 5 6 10 11 |
.233(mode 5)8:0 4 5 6  8 11 |