This entry collects the spatial interval vectors obtainable in the 12-note chromatic system, ordered by the number of notes that make up each chord.
The purpose of the catalog is not to propose a general classification of all possible chords, but to offer a technical repertoire useful for observing the behavior of spatial interval vectors within the total chromatic. The list considers structures from three to twelve notes, thus excluding sets of one or two notes, in which the interval content is too simple to produce meaningful configurations.
Organization of the list
The vectors are grouped by cardinality, that is, by the number of notes contained in the chord. This subdivision allows one to progressively observe the increase in relational complexity and to more easily identify exceptional configurations.
Each row of the table contains four main pieces of information:
| Column | Meaning |
|---|---|
| Chord | structure of the chord, indicated as the number of notes followed by the distances in semitones from the initial note |
| Mirror chord | form obtained by reversing the order of the internal distances of the chord |
| Spatial vector | count of the interval distances present in the chord |
| Name | possible denomination or musical observation |
For example, the notation:
3 - 0 3 7
indicates a three-note chord formed by the positions 0, 3, and 7 semitones from the initial note.
Mirror chord
In the catalog tables, the second column indicates the mirror chord of the first. By mirror chord, we mean the chord obtained by reversing the order of the internal distances of a structure.
For example, the chord C–E–G, corresponding to the structure:
0 4 7
has the internal sequence of distances:
4 – 3
Its mirror chord arranges the same distances in reverse order:
3 – 4
and thus corresponds to the structure:
0 3 7
that is, C–E♭–G.
The two chords share the same spatial interval vector, but have a mirror internal arrangement.
When the second column is empty, it means that the chord coincides with its own mirror chord. In these cases, the reflection does not produce a second distinct form, but leads back to the same structure.
For example, the chord:
3 - 0 1 2
is already a mirror of itself, since the internal distances are:
1 – 1
and their inversion again produces the same form.
Convention for numbers greater than 9
In the vectors relating to very large chords, counts greater than 9 may appear. To keep the vector sequence to a single digit per position, the following abbreviations are used:
| Symbol | Value |
|---|---|
| d | 10 |
| u | 11 |
Sigma chord and twin chord
Consulting the catalog shows that the vector of the sigma chord,
[1 1 1 1 1 0 1 1 1 1 1]
occupies an exceptional position within the 12-note chromatic system. In fact, it represents a configuration in which all spatial distances within the octave appear exactly once, except for the tritone, which is absent.
In the catalog, the sigma chord appears in the following pair of mirror forms:
| Chord | Mirror chord | Spatial vector | Name |
|---|---|---|---|
5 - 0 1 4 9 11 | 5 - 0 2 7 10 11 | [11111011111] | sigma |
The form 0 2 7 10 11, corresponding to C–D–G–B♭–B, is the one adopted as the exemplary form in the entry Sigma chord.
Next to sigma appears a second exceptional chord, its asymmetric twin, which achieves a similar configuration in terms of interval completeness, but is not symmetric with respect to the center of the vector:
[1 1 1 1 1 1 1 1 1 0 1]
In the catalog, it appears in the following pair of mirror forms:
| Chord | Mirror chord | Spatial vector | Name |
|---|---|---|---|
5 - 0 2 7 8 11 | 5 - 0 3 4 9 11 | [11111111101] | sigma’s twin |
List of vectors
3-note chords
| Chord | Mirror chord | Spatial vector | Name |
|---|---|---|---|
| 3 - 0 1 10 | 3 - 0 9 10 | [10000000110] | |
| 3 - 0 1 11 | 3 - 0 10 11 | [10000000011] | |
| 3 - 0 1 2 | [21000000000] | ||
| 3 - 0 1 3 | 3 - 0 2 3 | [11100000000] | |
| 3 - 0 1 4 | 3 - 0 3 4 | [10110000000] | |
| 3 - 0 1 5 | 3 - 0 4 5 | [10011000000] | |
| 3 - 0 1 6 | 3 - 0 5 6 | [10001100000] | |
| 3 - 0 1 7 | 3 - 0 6 7 | [10000110000] | |
| 3 - 0 1 8 | 3 - 0 7 8 | [10000011000] | |
| 3 - 0 1 9 | 3 - 0 8 9 | [10000001100] | |
| 3 - 0 2 10 | 3 - 0 8 10 | [01000001010] | |
| 3 - 0 2 11 | 3 - 0 9 11 | [01000000101] | |
| 3 - 0 2 4 | [02010000000] | ||
| 3 - 0 2 5 | 3 - 0 3 5 | [01101000000] | |
| 3 - 0 2 6 | 3 - 0 4 6 | [01010100000] | |
| 3 - 0 2 7 | 3 - 0 5 7 | [01001010000] | |
| 3 - 0 2 8 | 3 - 0 6 8 | [01000101000] | |
| 3 - 0 2 9 | 3 - 0 7 9 | [01000010100] | |
| 3 - 0 3 10 | 3 - 0 7 10 | [00100010010] | |
| 3 - 0 3 11 | 3 - 0 8 11 | [00100001001] | |
| 3 - 0 3 6 | [00200100000] | ||
| 3 - 0 3 7 | 3 - 0 4 7 | [00110010000] | major and minor triads |
| 3 - 0 3 8 | 3 - 0 5 8 | [00101001000] | inversions of major and minor triads |
| 3 - 0 3 9 | 3 - 0 6 9 | [00100100100] | |
| 3 - 0 4 10 | 3 - 0 6 10 | [00010100010] | |
| 3 - 0 4 11 | 3 - 0 7 11 | [00010010001] | |
| 3 - 0 4 8 | [00020001000] | ||
| 3 - 0 4 9 | 3 - 0 5 9 | [00011000100] | inversions of major and minor triads |
| 3 - 0 5 10 | [00002000010] | ||
| 3 - 0 5 11 | 3 - 0 6 11 | [00001100001] |
4-note chords
| Chord | Mirror chord | Spatial vector |
|---|---|---|
| 4 - 0 1 10 11 | [20000000121] | |
| 4 - 0 1 2 10 | 4 - 0 8 9 10 | [21000001110] |
| 4 - 0 1 2 11 | 4 - 0 9 10 11 | [21000000111] |
| 4 - 0 1 2 3 | [32100000000] | |
| 4 - 0 1 2 4 | 4 - 0 2 3 4 | [22110000000] |
| 4 - 0 1 2 5 | 4 - 0 3 4 5 | [21111000000] |
| 4 - 0 1 2 6 | 4 - 0 4 5 6 | [21011100000] |
| 4 - 0 1 2 7 | 4 - 0 5 6 7 | [21001110000] |
| 4 - 0 1 2 8 | 4 - 0 6 7 8 | [21000111000] |
| 4 - 0 1 2 9 | 4 - 0 7 8 9 | [21000011100] |
| 4 - 0 1 3 10 | 4 - 0 7 9 10 | [11100010110] |
| 4 - 0 1 3 11 | 4 - 0 8 10 11 | [11100001011] |
| 4 - 0 1 3 4 | [21210000000] | |
| 4 - 0 1 3 5 | 4 - 0 2 4 5 | [12111000000] |
| 4 - 0 1 3 6 | 4 - 0 3 5 6 | [11201100000] |
| 4 - 0 1 3 7 | 4 - 0 4 6 7 | [11110110000] |
| 4 - 0 1 3 8 | 4 - 0 5 7 8 | [11101011000] |
| 4 - 0 1 3 9 | 4 - 0 6 8 9 | [11100101100] |
| 4 - 0 1 4 10 | 4 - 0 6 9 10 | [10110100110] |
| 4 - 0 1 4 11 | 4 - 0 7 10 11 | [10110010011] |
| 4 - 0 1 4 5 | [20121000000] | |
| 4 - 0 1 4 6 | 4 - 0 2 5 6 | [11111100000] |
| 4 - 0 1 4 7 | 4 - 0 3 6 7 | [10210110000] |
| 4 - 0 1 4 8 | 4 - 0 4 7 8 | [10120011000] |
| 4 - 0 1 4 9 | 4 - 0 5 8 9 | [10111001100] |
| 4 - 0 1 5 10 | 4 - 0 5 9 10 | [10012000110] |
| 4 - 0 1 5 11 | 4 - 0 6 10 11 | [10011100011] |
| 4 - 0 1 5 6 | [20012100000] | |
| 4 - 0 1 5 7 | 4 - 0 2 6 7 | [11011110000] |
| 4 - 0 1 5 8 | 4 - 0 3 7 8 | [10111011000] |
| 4 - 0 1 5 9 | 4 - 0 4 8 9 | [10021001100] |
| 4 - 0 1 6 10 | 4 - 0 4 9 10 | [10011100110] |
| 4 - 0 1 6 11 | 4 - 0 5 10 11 | [10002100011] |
| 4 - 0 1 6 7 | [20001210000] | |
| 4 - 0 1 6 8 | 4 - 0 2 7 8 | [11001111000] |
| 4 - 0 1 6 9 | 4 - 0 3 8 9 | [10101101100] |
| 4 - 0 1 7 10 | 4 - 0 3 9 10 | [10100110110] |
| 4 - 0 1 7 11 | 4 - 0 4 10 11 | [10010110011] |
| 4 - 0 1 7 8 | [20000121000] | |
| 4 - 0 1 7 9 | 4 - 0 2 8 9 | [11000111100] |
| 4 - 0 1 8 10 | 4 - 0 2 9 10 | [11000011110] |
| 4 - 0 1 8 11 | 4 - 0 3 10 11 | [10100011011] |
| 4 - 0 1 8 9 | [20000012100] | |
| 4 - 0 1 9 10 | [20000001210] | |
| 4 - 0 1 9 11 | 4 - 0 2 10 11 | [11000001111] |
| 4 - 0 2 3 10 | 4 - 0 7 8 10 | [11100011010] |
| 4 - 0 2 3 11 | 4 - 0 8 9 11 | [11100001101] |
| 4 - 0 2 3 5 | [12201000000] | |
| 4 - 0 2 3 6 | 4 - 0 3 4 6 | [11210100000] |
| 4 - 0 2 3 7 | 4 - 0 4 5 7 | [11111010000] |
| 4 - 0 2 3 8 | 4 - 0 5 6 8 | [11101101000] |
| 4 - 0 2 3 9 | 4 - 0 6 7 9 | [11100110100] |
| 4 - 0 2 4 10 | 4 - 0 6 8 10 | [02010101010] |
| 4 - 0 2 4 11 | 4 - 0 7 9 11 | [02010010101] |
| 4 - 0 2 4 6 | [03020100000] | |
| 4 - 0 2 4 7 | 4 - 0 3 5 7 | [02111010000] |
| 4 - 0 2 4 8 | 4 - 0 4 6 8 | [02020101000] |
| 4 - 0 2 4 9 | 4 - 0 5 7 9 | [02011010100] |
| 4 - 0 2 5 10 | 4 - 0 5 8 10 | [01102001010] |
| 4 - 0 2 5 11 | 4 - 0 6 9 11 | [01101100101] |
| 4 - 0 2 5 7 | [02102010000] | |
| 4 - 0 2 5 8 | 4 - 0 3 6 8 | [01201101000] |
| 4 - 0 2 5 9 | 4 - 0 4 7 9 | [01111010100] |
| 4 - 0 2 6 10 | 4 - 0 4 8 10 | [01020101010] |
| 4 - 0 2 6 11 | 4 - 0 5 9 11 | [01011100101] |
| 4 - 0 2 6 8 | [02010201000] | |
| 4 - 0 2 6 9 | 4 - 0 3 7 9 | [01110110100] |
| 4 - 0 2 7 10 | 4 - 0 3 8 10 | [01101011010] |
| 4 - 0 2 7 11 | 4 - 0 4 9 11 | [01011010101] |
| 4 - 0 2 7 9 | [02001020100] | |
| 4 - 0 2 8 10 | [02000102010] | |
| 4 - 0 2 8 11 | 4 - 0 3 9 11 | [01100101101] |
| 4 - 0 2 9 11 | [02000010201] | |
| 4 - 0 3 4 10 | 4 - 0 6 7 10 | [10110110010] |
| 4 - 0 3 4 11 | 4 - 0 7 8 11 | [10110011001] |
| 4 - 0 3 4 7 | [10220010000] | |
| 4 - 0 3 4 8 | 4 - 0 4 5 8 | [10121001000] |
| 4 - 0 3 4 9 | 4 - 0 5 6 9 | [10111100100] |
| 4 - 0 3 5 10 | 4 - 0 5 7 10 | [01102010010] |
| 4 - 0 3 5 11 | 4 - 0 6 8 11 | [01101101001] |
| 4 - 0 3 5 8 | [01202001000] | |
| 4 - 0 3 5 9 | 4 - 0 4 6 9 | [01111100100] |
| 4 - 0 3 6 10 | 4 - 0 4 7 10 | [00210110010] |
| 4 - 0 3 6 11 | 4 - 0 5 8 11 | [00201101001] |
| 4 - 0 3 6 9 | [00300200100] | |
| 4 - 0 3 7 10 | [00210020010] | |
| 4 - 0 3 7 11 | 4 - 0 4 8 11 | [00120011001] |
| 4 - 0 3 8 11 | [00201002001] | |
| 4 - 0 4 5 10 | 4 - 0 5 6 10 | [10012100010] |
| 4 - 0 4 5 11 | 4 - 0 6 7 11 | [10011110001] |
| 4 - 0 4 5 9 | [10022000100] | |
| 4 - 0 4 6 10 | [01020200010] | |
| 4 - 0 4 6 11 | 4 - 0 5 7 11 | [01011110001] |
| 4 - 0 4 7 11 | [00120020001] | |
| 4 - 0 5 6 11 | [10002200001] |
5-note chords
| Chord | Mirror chord | Spatial vector | Name |
|---|---|---|---|
| 5 - 0 1 2 10 11 | 5 - 0 1 9 10 11 | [31000001221] | |
| 5 - 0 1 2 3 10 | 5 - 0 7 8 9 10 | [32100011110] | |
| 5 - 0 1 2 3 11 | 5 - 0 8 9 10 11 | [32100001111] | |
| 5 - 0 1 2 3 4 | [43210000000] | ||
| 5 - 0 1 2 3 5 | 5 - 0 2 3 4 5 | [33211000000] | |
| 5 - 0 1 2 3 6 | 5 - 0 3 4 5 6 | [32211100000] | |
| 5 - 0 1 2 3 7 | 5 - 0 4 5 6 7 | [32111110000] | |
| 5 - 0 1 2 3 8 | 5 - 0 5 6 7 8 | [32101111000] | |
| 5 - 0 1 2 3 9 | 5 - 0 6 7 8 9 | [32100111100] | |
| 5 - 0 1 2 4 10 | 5 - 0 6 8 9 10 | [22110101110] | |
| 5 - 0 1 2 4 11 | 5 - 0 7 9 10 11 | [22110010111] | |
| 5 - 0 1 2 4 5 | 5 - 0 1 3 4 5 | [32221000000] | |
| 5 - 0 1 2 4 6 | 5 - 0 2 4 5 6 | [23121100000] | |
| 5 - 0 1 2 4 7 | 5 - 0 3 5 6 7 | [22211110000] | |
| 5 - 0 1 2 4 8 | 5 - 0 4 6 7 8 | [22120111000] | |
| 5 - 0 1 2 4 9 | 5 - 0 5 7 8 9 | [22111011100] | |
| 5 - 0 1 2 5 10 | 5 - 0 5 8 9 10 | [21112001110] | |
| 5 - 0 1 2 5 11 | 5 - 0 6 9 10 11 | [21111100111] | |
| 5 - 0 1 2 5 6 | 5 - 0 1 4 5 6 | [31122100000] | |
| 5 - 0 1 2 5 7 | 5 - 0 2 5 6 7 | [22112110000] | |
| 5 - 0 1 2 5 8 | 5 - 0 3 6 7 8 | [21211111000] | |
| 5 - 0 1 2 5 9 | 5 - 0 4 7 8 9 | [21121011100] | |
| 5 - 0 1 2 6 10 | 5 - 0 4 8 9 10 | [21021101110] | |
| 5 - 0 1 2 6 11 | 5 - 0 5 9 10 11 | [21012100111] | |
| 5 - 0 1 2 6 7 | 5 - 0 1 5 6 7 | [31012210000] | |
| 5 - 0 1 2 6 8 | 5 - 0 2 6 7 8 | [22011211000] | |
| 5 - 0 1 2 6 9 | 5 - 0 3 7 8 9 | [21111111100] | |
| 5 - 0 1 2 7 10 | 5 - 0 3 8 9 10 | [21101111110] | |
| 5 - 0 1 2 7 11 | 5 - 0 4 9 10 11 | [21011110111] | |
| 5 - 0 1 2 7 8 | 5 - 0 1 6 7 8 | [31001221000] | |
| 5 - 0 1 2 7 9 | 5 - 0 2 7 8 9 | [22001121100] | |
| 5 - 0 1 2 8 10 | 5 - 0 2 8 9 10 | [22000112110] | |
| 5 - 0 1 2 8 11 | 5 - 0 3 9 10 11 | [21100111111] | |
| 5 - 0 1 2 8 9 | 5 - 0 1 7 8 9 | [31000122100] | |
| 5 - 0 1 2 9 10 | 5 - 0 1 8 9 10 | [31000012210] | |
| 5 - 0 1 2 9 11 | 5 - 0 2 9 10 11 | [22000011211] | |
| 5 - 0 1 3 10 11 | 5 - 0 1 8 10 11 | [21100011121] | |
| 5 - 0 1 3 4 10 | 5 - 0 6 7 9 10 | [21210110110] | |
| 5 - 0 1 3 4 11 | 5 - 0 7 8 10 11 | [21210011011] | |
| 5 - 0 1 3 4 6 | 5 - 0 2 3 5 6 | [22311100000] | |
| 5 - 0 1 3 4 7 | 5 - 0 3 4 6 7 | [21320110000] | |
| 5 - 0 1 3 4 8 | 5 - 0 4 5 7 8 | [21221011000] | |
| 5 - 0 1 3 4 9 | 5 - 0 5 6 8 9 | [21211101100] | |
| 5 - 0 1 3 5 10 | 5 - 0 5 7 9 10 | [12112010110] | |
| 5 - 0 1 3 5 11 | 5 - 0 6 8 10 11 | [12111101011] | |
| 5 - 0 1 3 5 6 | [22212100000] | ||
| 5 - 0 1 3 5 7 | 5 - 0 2 4 6 7 | [13121110000] | |
| 5 - 0 1 3 5 8 | 5 - 0 3 5 7 8 | [12212011000] | |
| 5 - 0 1 3 5 9 | 5 - 0 4 6 8 9 | [12121101100] | |
| 5 - 0 1 3 6 10 | 5 - 0 4 7 9 10 | [11211110110] | |
| 5 - 0 1 3 6 11 | 5 - 0 5 8 10 11 | [11202101011] | |
| 5 - 0 1 3 6 7 | 5 - 0 1 4 6 7 | [21211210000] | |
| 5 - 0 1 3 6 8 | 5 - 0 2 5 7 8 | [12202111000] | |
| 5 - 0 1 3 6 9 | 5 - 0 3 6 8 9 | [11301201100] | |
| 5 - 0 1 3 7 10 | 5 - 0 3 7 9 10 | [11210120110] | |
| 5 - 0 1 3 7 11 | 5 - 0 4 8 10 11 | [11120111011] | |
| 5 - 0 1 3 7 8 | 5 - 0 1 5 7 8 | [21111121000] | |
| 5 - 0 1 3 7 9 | 5 - 0 2 6 8 9 | [12110211100] | |
| 5 - 0 1 3 8 10 | 5 - 0 2 7 9 10 | [12101021110] | |
| 5 - 0 1 3 8 11 | 5 - 0 3 8 10 11 | [11201012011] | |
| 5 - 0 1 3 8 9 | 5 - 0 1 6 8 9 | [21101112100] | |
| 5 - 0 1 3 9 10 | 5 - 0 1 7 9 10 | [21100111210] | |
| 5 - 0 1 3 9 11 | 5 - 0 2 8 10 11 | [12100102111] | |
| 5 - 0 1 4 10 11 | 5 - 0 1 7 10 11 | [20110110121] | |
| 5 - 0 1 4 5 10 | 5 - 0 5 6 9 10 | [20122100110] | |
| 5 - 0 1 4 5 11 | 5 - 0 6 7 10 11 | [20121110011] | |
| 5 - 0 1 4 5 7 | 5 - 0 2 3 6 7 | [21221110000] | |
| 5 - 0 1 4 5 8 | 5 - 0 3 4 7 8 | [20231011000] | |
| 5 - 0 1 4 5 9 | 5 - 0 4 5 8 9 | [20132001100] | |
| 5 - 0 1 4 6 10 | 5 - 0 4 6 9 10 | [11121200110] | |
| 5 - 0 1 4 6 11 | 5 - 0 5 7 10 11 | [11112110011] | |
| 5 - 0 1 4 6 8 | 5 - 0 2 4 7 8 | [12121111000] | |
| 5 - 0 1 4 6 9 | 5 - 0 3 5 8 9 | [11212101100] | |
| 5 - 0 1 4 7 10 | 5 - 0 3 6 9 10 | [10310210110] | |
| 5 - 0 1 4 7 11 | 5 - 0 4 7 10 11 | [10220120011] | |
| 5 - 0 1 4 7 8 | [20220121000] | ||
| 5 - 0 1 4 7 9 | 5 - 0 2 5 8 9 | [11211111100] | |
| 5 - 0 1 4 8 10 | 5 - 0 2 6 9 10 | [11120111110] | |
| 5 - 0 1 4 8 11 | 5 - 0 3 7 10 11 | [10220021011] | |
| 5 - 0 1 4 8 9 | 5 - 0 1 5 8 9 | [20121012100] | |
| 5 - 0 1 4 9 10 | 5 - 0 1 6 9 10 | [20111101210] | |
| 5 - 0 1 4 9 11 | 5 - 0 2 7 10 11 | [11111011111] | sigma |
| 5 - 0 1 5 10 11 | 5 - 0 1 6 10 11 | [20012100121] | |
| 5 - 0 1 5 6 10 | 5 - 0 4 5 9 10 | [20023100110] | |
| 5 - 0 1 5 6 11 | 5 - 0 5 6 10 11 | [20013200011] | |
| 5 - 0 1 5 6 8 | 5 - 0 2 3 7 8 | [21112111000] | |
| 5 - 0 1 5 6 9 | 5 - 0 3 4 8 9 | [20122101100] | |
| 5 - 0 1 5 7 10 | 5 - 0 3 5 9 10 | [11112110110] | |
| 5 - 0 1 5 7 11 | 5 - 0 4 6 10 11 | [11021210011] | |
| 5 - 0 1 5 7 9 | 5 - 0 2 4 8 9 | [12021111100] | |
| 5 - 0 1 5 8 10 | 5 - 0 2 5 9 10 | [11112011110] | |
| 5 - 0 1 5 8 11 | 5 - 0 3 6 10 11 | [10211111011] | |
| 5 - 0 1 5 9 10 | [20022001210] | ||
| 5 - 0 1 5 9 11 | 5 - 0 2 6 10 11 | [11021101111] | |
| 5 - 0 1 6 7 10 | 5 - 0 3 4 9 10 | [20111210110] | |
| 5 - 0 1 6 7 11 | 5 - 0 4 5 10 11 | [20012210011] | |
| 5 - 0 1 6 7 9 | 5 - 0 2 3 8 9 | [21101211100] | |
| 5 - 0 1 6 8 10 | 5 - 0 2 4 9 10 | [12011111110] | |
| 5 - 0 1 6 8 11 | 5 - 0 3 5 10 11 | [11102111011] | |
| 5 - 0 1 6 9 11 | 5 - 0 2 5 10 11 | [11102101111] | |
| 5 - 0 1 7 8 10 | 5 - 0 2 3 9 10 | [21100121110] | |
| 5 - 0 1 7 8 11 | 5 - 0 3 4 10 11 | [20110121011] | |
| 5 - 0 1 7 9 11 | 5 - 0 2 4 10 11 | [12010111111] | |
| 5 - 0 1 8 9 11 | 5 - 0 2 3 10 11 | [21100012111] | |
| 5 - 0 2 3 4 10 | 5 - 0 6 7 8 10 | [22110111010] | |
| 5 - 0 2 3 4 11 | 5 - 0 7 8 9 11 | [22110011101] | |
| 5 - 0 2 3 4 6 | [23220100000] | ||
| 5 - 0 2 3 4 7 | 5 - 0 3 4 5 7 | [22221010000] | |
| 5 - 0 2 3 4 8 | 5 - 0 4 5 6 8 | [22121101000] | |
| 5 - 0 2 3 4 9 | 5 - 0 5 6 7 9 | [22111110100] | |
| 5 - 0 2 3 5 10 | 5 - 0 5 7 8 10 | [12202011010] | |
| 5 - 0 2 3 5 11 | 5 - 0 6 8 9 11 | [12201101101] | |
| 5 - 0 2 3 5 7 | 5 - 0 2 4 5 7 | [13212010000] | |
| 5 - 0 2 3 5 8 | 5 - 0 3 5 6 8 | [12302101000] | |
| 5 - 0 2 3 5 9 | 5 - 0 4 6 7 9 | [12211110100] | |
| 5 - 0 2 3 6 10 | 5 - 0 4 7 8 10 | [11220111010] | |
| 5 - 0 2 3 6 11 | 5 - 0 5 8 9 11 | [11211101101] | |
| 5 - 0 2 3 6 8 | 5 - 0 2 5 6 8 | [12211201000] | |
| 5 - 0 2 3 6 9 | 5 - 0 3 6 7 9 | [11310210100] | |
| 5 - 0 2 3 7 10 | 5 - 0 3 7 8 10 | [11211021010] | |
| 5 - 0 2 3 7 11 | 5 - 0 4 8 9 11 | [11121011101] | |
| 5 - 0 2 3 7 9 | 5 - 0 2 6 7 9 | [12111120100] | |
| 5 - 0 2 3 8 10 | 5 - 0 2 7 8 10 | [12101112010] | |
| 5 - 0 2 3 8 11 | 5 - 0 3 8 9 11 | [11201102101] | |
| 5 - 0 2 3 9 11 | 5 - 0 2 8 9 11 | [12100111201] | |
| 5 - 0 2 4 5 10 | 5 - 0 5 6 8 10 | [12112101010] | |
| 5 - 0 2 4 5 11 | 5 - 0 6 7 9 11 | [12111110101] | |
| 5 - 0 2 4 5 8 | 5 - 0 3 4 6 8 | [12221101000] | |
| 5 - 0 2 4 5 9 | 5 - 0 4 5 7 9 | [12122010100] | |
| 5 - 0 2 4 6 10 | 5 - 0 4 6 8 10 | [03030201010] | |
| 5 - 0 2 4 6 11 | 5 - 0 5 7 9 11 | [03021110101] | |
| 5 - 0 2 4 6 8 | [04030201000] | ||
| 5 - 0 2 4 6 9 | 5 - 0 3 5 7 9 | [03121110100] | |
| 5 - 0 2 4 7 10 | 5 - 0 3 6 8 10 | [02211111010] | |
| 5 - 0 2 4 7 11 | 5 - 0 4 7 9 11 | [02121020101] | |
| 5 - 0 2 4 7 9 | 5 - 0 2 5 7 9 | [03112020100] | |
| 5 - 0 2 4 8 10 | 5 - 0 2 6 8 10 | [03020202010] | |
| 5 - 0 2 4 8 11 | 5 - 0 3 7 9 11 | [02120111101] | |
| 5 - 0 2 4 9 11 | 5 - 0 2 7 9 11 | [03011020201] | |
| 5 - 0 2 5 6 10 | 5 - 0 4 5 8 10 | [11122101010] | |
| 5 - 0 2 5 6 11 | 5 - 0 5 6 9 11 | [11112200101] | |
| 5 - 0 2 5 6 9 | 5 - 0 3 4 7 9 | [11221110100] | |
| 5 - 0 2 5 7 10 | 5 - 0 3 5 8 10 | [02203011010] | |
| 5 - 0 2 5 7 11 | 5 - 0 4 6 9 11 | [02112110101] | |
| 5 - 0 2 5 8 10 | [02202102010] | ||
| 5 - 0 2 5 8 11 | 5 - 0 3 6 9 11 | [01301201101] | |
| 5 - 0 2 5 9 11 | 5 - 0 2 6 9 11 | [02111110201] | |
| 5 - 0 2 6 7 10 | 5 - 0 3 4 8 10 | [11121111010] | |
| 5 - 0 2 6 7 11 | 5 - 0 4 5 9 11 | [11022110101] | |
| 5 - 0 2 6 8 11 | 5 - 0 3 5 9 11 | [02111201101] | |
| 5 - 0 2 7 8 11 | 5 - 0 3 4 9 11 | [11111111101] | sigma’s twin |
| 5 - 0 3 4 5 10 | 5 - 0 5 6 7 10 | [21112110010] | |
| 5 - 0 3 4 5 11 | 5 - 0 6 7 8 11 | [21111111001] | |
| 5 - 0 3 4 5 8 | [21222001000] | ||
| 5 - 0 3 4 5 9 | 5 - 0 4 5 6 9 | [21122100100] | |
| 5 - 0 3 4 6 10 | 5 - 0 4 6 7 10 | [11220210010] | |
| 5 - 0 3 4 6 11 | 5 - 0 5 7 8 11 | [11211111001] | |
| 5 - 0 3 4 6 9 | 5 - 0 3 5 6 9 | [11311200100] | |
| 5 - 0 3 4 7 10 | 5 - 0 3 6 7 10 | [10320120010] | |
| 5 - 0 3 4 7 11 | 5 - 0 4 7 8 11 | [10230021001] | |
| 5 - 0 3 4 8 11 | 5 - 0 3 7 8 11 | [10221012001] | |
| 5 - 0 3 5 6 10 | 5 - 0 4 5 7 10 | [11212110010] | |
| 5 - 0 3 5 6 11 | 5 - 0 5 6 8 11 | [11202201001] | |
| 5 - 0 3 5 7 10 | [02212020010] | ||
| 5 - 0 3 5 7 11 | 5 - 0 4 6 8 11 | [02121111001] | |
| 5 - 0 3 5 8 11 | 5 - 0 3 6 8 11 | [01302102001] | |
| 5 - 0 3 6 7 11 | 5 - 0 4 5 8 11 | [10221111001] | |
| 5 - 0 4 5 6 10 | [21022200010] | ||
| 5 - 0 4 5 6 11 | 5 - 0 5 6 7 11 | [21012210001] | |
| 5 - 0 4 5 7 11 | 5 - 0 4 6 7 11 | [11121120001] |
6-note chords
| Chord | Mirror chord | Spatial vector |
|---|---|---|
| 6 - 0 1 2 3 10 11 | 6 - 0 1 8 9 10 11 | [42100012221] |
| 6 - 0 1 2 3 4 10 | 6 - 0 6 7 8 9 10 | [43210111110] |
| 6 - 0 1 2 3 4 11 | 6 - 0 7 8 9 10 11 | [43210011111] |
| 6 - 0 1 2 3 4 5 | [54321000000] | |
| 6 - 0 1 2 3 4 6 | 6 - 0 2 3 4 5 6 | [44321100000] |
| 6 - 0 1 2 3 4 7 | 6 - 0 3 4 5 6 7 | [43321110000] |
| 6 - 0 1 2 3 4 8 | 6 - 0 4 5 6 7 8 | [43221111000] |
| 6 - 0 1 2 3 4 9 | 6 - 0 5 6 7 8 9 | [43211111100] |
| 6 - 0 1 2 3 5 10 | 6 - 0 5 7 8 9 10 | [33212011110] |
| 6 - 0 1 2 3 5 11 | 6 - 0 6 8 9 10 11 | [33211101111] |
| 6 - 0 1 2 3 5 6 | 6 - 0 1 3 4 5 6 | [43322100000] |
| 6 - 0 1 2 3 5 7 | 6 - 0 2 4 5 6 7 | [34222110000] |
| 6 - 0 1 2 3 5 8 | 6 - 0 3 5 6 7 8 | [33312111000] |
| 6 - 0 1 2 3 5 9 | 6 - 0 4 6 7 8 9 | [33221111100] |
| 6 - 0 1 2 3 6 10 | 6 - 0 4 7 8 9 10 | [32221111110] |
| 6 - 0 1 2 3 6 11 | 6 - 0 5 8 9 10 11 | [32212101111] |
| 6 - 0 1 2 3 6 7 | 6 - 0 1 4 5 6 7 | [42222210000] |
| 6 - 0 1 2 3 6 8 | 6 - 0 2 5 6 7 8 | [33212211000] |
| 6 - 0 1 2 3 6 9 | 6 - 0 3 6 7 8 9 | [32311211100] |
| 6 - 0 1 2 3 7 10 | 6 - 0 3 7 8 9 10 | [32211121110] |
| 6 - 0 1 2 3 7 11 | 6 - 0 4 8 9 10 11 | [32121111111] |
| 6 - 0 1 2 3 7 8 | 6 - 0 1 5 6 7 8 | [42112221000] |
| 6 - 0 1 2 3 7 9 | 6 - 0 2 6 7 8 9 | [33111221100] |
| 6 - 0 1 2 3 8 10 | 6 - 0 2 7 8 9 10 | [33101122110] |
| 6 - 0 1 2 3 8 11 | 6 - 0 3 8 9 10 11 | [32201112111] |
| 6 - 0 1 2 3 8 9 | 6 - 0 1 6 7 8 9 | [42101222100] |
| 6 - 0 1 2 3 9 10 | 6 - 0 1 7 8 9 10 | [42100122210] |
| 6 - 0 1 2 3 9 11 | 6 - 0 2 8 9 10 11 | [33100112211] |
| 6 - 0 1 2 4 10 11 | 6 - 0 1 7 9 10 11 | [32110111221] |
| 6 - 0 1 2 4 5 10 | 6 - 0 5 6 8 9 10 | [32222101110] |
| 6 - 0 1 2 4 5 11 | 6 - 0 6 7 9 10 11 | [32221110111] |
| 6 - 0 1 2 4 5 6 | [43232100000] | |
| 6 - 0 1 2 4 5 7 | 6 - 0 2 3 5 6 7 | [33322110000] |
| 6 - 0 1 2 4 5 8 | 6 - 0 3 4 6 7 8 | [32331111000] |
| 6 - 0 1 2 4 5 9 | 6 - 0 4 5 7 8 9 | [32232011100] |
| 6 - 0 1 2 4 6 10 | 6 - 0 4 6 8 9 10 | [23131201110] |
| 6 - 0 1 2 4 6 11 | 6 - 0 5 7 9 10 11 | [23122110111] |
| 6 - 0 1 2 4 6 7 | 6 - 0 1 3 5 6 7 | [33222210000] |
| 6 - 0 1 2 4 6 8 | 6 - 0 2 4 6 7 8 | [24131211000] |
| 6 - 0 1 2 4 6 9 | 6 - 0 3 5 7 8 9 | [23222111100] |
| 6 - 0 1 2 4 7 10 | 6 - 0 3 6 8 9 10 | [22311211110] |
| 6 - 0 1 2 4 7 11 | 6 - 0 4 7 9 10 11 | [22221120111] |
| 6 - 0 1 2 4 7 8 | 6 - 0 1 4 6 7 8 | [32221221000] |
| 6 - 0 1 2 4 7 9 | 6 - 0 2 5 7 8 9 | [23212121100] |
| 6 - 0 1 2 4 8 10 | 6 - 0 2 6 8 9 10 | [23120212110] |
| 6 - 0 1 2 4 8 11 | 6 - 0 3 7 9 10 11 | [22220121111] |
| 6 - 0 1 2 4 8 9 | 6 - 0 1 5 7 8 9 | [32121122100] |
| 6 - 0 1 2 4 9 10 | 6 - 0 1 6 8 9 10 | [32111112210] |
| 6 - 0 1 2 4 9 11 | 6 - 0 2 7 9 10 11 | [23111021211] |
| 6 - 0 1 2 5 10 11 | 6 - 0 1 6 9 10 11 | [31112101221] |
| 6 - 0 1 2 5 6 10 | 6 - 0 4 5 8 9 10 | [31133101110] |
| 6 - 0 1 2 5 6 11 | 6 - 0 5 6 9 10 11 | [31123200111] |
| 6 - 0 1 2 5 6 7 | [42123210000] | |
| 6 - 0 1 2 5 6 8 | 6 - 0 2 3 6 7 8 | [32222211000] |
| 6 - 0 1 2 5 6 9 | 6 - 0 3 4 7 8 9 | [31232111100] |
| 6 - 0 1 2 5 7 10 | 6 - 0 3 5 8 9 10 | [22213111110] |
| 6 - 0 1 2 5 7 11 | 6 - 0 4 6 9 10 11 | [22122210111] |
| 6 - 0 1 2 5 7 8 | 6 - 0 1 3 6 7 8 | [32212221000] |
| 6 - 0 1 2 5 7 9 | 6 - 0 2 4 7 8 9 | [23122121100] |
| 6 - 0 1 2 5 8 10 | 6 - 0 2 5 8 9 10 | [22212112110] |
| 6 - 0 1 2 5 8 11 | 6 - 0 3 6 9 10 11 | [21311211111] |
| 6 - 0 1 2 5 8 9 | 6 - 0 1 4 7 8 9 | [31221122100] |
| 6 - 0 1 2 5 9 10 | 6 - 0 1 5 8 9 10 | [31122012210] |
| 6 - 0 1 2 5 9 11 | 6 - 0 2 6 9 10 11 | [22121111211] |
| 6 - 0 1 2 6 10 11 | 6 - 0 1 5 9 10 11 | [31022101221] |
| 6 - 0 1 2 6 7 10 | 6 - 0 3 4 8 9 10 | [31122211110] |
| 6 - 0 1 2 6 7 11 | 6 - 0 4 5 9 10 11 | [31023210111] |
| 6 - 0 1 2 6 7 8 | [42012321000] | |
| 6 - 0 1 2 6 7 9 | 6 - 0 2 3 7 8 9 | [32112221100] |
| 6 - 0 1 2 6 8 10 | 6 - 0 2 4 8 9 10 | [23021212110] |
| 6 - 0 1 2 6 8 11 | 6 - 0 1 6 7 9 11 | [22112211111] |
| 6 - 0 1 2 6 8 9 | 6 - 0 1 3 7 8 9 | [32111222100] |
| 6 - 0 1 2 6 9 10 | 6 - 0 1 4 8 9 10 | [31121112210] |
| 6 - 0 1 2 6 9 11 | 6 - 0 2 5 9 10 11 | [22112111211] |
| 6 - 0 1 2 7 10 11 | 6 - 0 1 4 9 10 11 | [31111111221] |
| 6 - 0 1 2 7 8 10 | 6 - 0 2 3 8 9 10 | [32101222110] |
| 6 - 0 1 2 7 8 11 | 6 - 0 3 4 9 10 11 | [31111221111] |
| 6 - 0 1 2 7 8 9 | [42001232100] | |
| 6 - 0 1 2 7 9 10 | 6 - 0 1 3 8 9 10 | [32101122210] |
| 6 - 0 1 2 7 9 11 | 6 - 0 2 4 9 10 11 | [23011121211] |
| 6 - 0 1 2 8 10 11 | 6 - 0 1 3 9 10 11 | [32100112221] |
| 6 - 0 1 2 8 9 10 | [42000123210] | |
| 6 - 0 1 2 8 9 11 | 6 - 0 2 3 9 10 11 | [32100122211] |
| 6 - 0 1 2 9 10 11 | [42000012321] | |
| 6 - 0 1 3 4 10 11 | 6 - 0 1 7 8 10 11 | [31210121121] |
| 6 - 0 1 3 4 5 10 | 6 - 0 5 6 7 9 10 | [32222110110] |
| 6 - 0 1 3 4 5 11 | 6 - 0 6 7 8 10 11 | [32221111011] |
| 6 - 0 1 3 4 5 7 | 6 - 0 2 3 4 6 7 | [33331110000] |
| 6 - 0 1 3 4 5 8 | 6 - 0 3 4 5 7 8 | [32332011000] |
| 6 - 0 1 3 4 5 9 | 6 - 0 4 5 6 8 9 | [32232101100] |
| 6 - 0 1 3 4 6 10 | 6 - 0 4 6 7 9 10 | [22321210110] |
| 6 - 0 1 3 4 6 11 | 6 - 0 5 7 8 10 11 | [22312111011] |
| 6 - 0 1 3 4 6 7 | [32421210000] | |
| 6 - 0 1 3 4 6 8 | 6 - 0 2 4 5 7 8 | [23322111000] |
| 6 - 0 1 3 4 6 9 | 6 - 0 3 5 6 8 9 | [22412201100] |
| 6 - 0 1 3 4 7 10 | 6 - 0 3 6 7 9 10 | [21420220110] |
| 6 - 0 1 3 4 7 11 | 6 - 0 4 7 8 10 11 | [21330121011] |
| 6 - 0 1 3 4 7 8 | 6 - 0 1 4 5 7 8 | [31331121000] |
| 6 - 0 1 3 4 7 9 | 6 - 0 2 5 6 8 9 | [22321211100] |
| 6 - 0 1 3 4 8 10 | 6 - 0 2 6 7 9 10 | [22221121110] |
| 6 - 0 1 3 4 8 11 | 6 - 0 3 7 8 10 11 | [21321022011] |
| 6 - 0 1 3 4 8 9 | 6 - 0 1 5 6 8 9 | [31222112100] |
| 6 - 0 1 3 4 9 10 | 6 - 0 1 6 7 9 10 | [31211211210] |
| 6 - 0 1 3 4 9 11 | 6 - 0 2 7 8 10 11 | [22211112111] |
| 6 - 0 1 3 5 10 11 | 6 - 0 1 6 8 10 11 | [22112111121] |
| 6 - 0 1 3 5 6 10 | 6 - 0 4 5 7 9 10 | [22223110110] |
| 6 - 0 1 3 5 6 11 | 6 - 0 5 6 8 10 11 | [22213201011] |
| 6 - 0 1 3 5 6 8 | 6 - 0 2 3 5 7 8 | [23313111000] |
| 6 - 0 1 3 5 6 9 | 6 - 0 3 4 6 8 9 | [22322201100] |
| 6 - 0 1 3 5 7 10 | 6 - 0 3 5 7 9 10 | [13222120110] |
| 6 - 0 1 3 5 7 11 | 6 - 0 4 6 8 10 11 | [13131211011] |
| 6 - 0 1 3 5 7 8 | [23222121000] | |
| 6 - 0 1 3 5 7 9 | 6 - 0 2 4 6 8 9 | [14131211100] |
| 6 - 0 1 3 5 8 10 | 6 - 0 2 5 7 9 10 | [13213021110] |
| 6 - 0 1 3 5 8 11 | 6 - 0 3 6 8 10 11 | [12312112011] |
| 6 - 0 1 3 5 8 9 | 6 - 0 1 4 6 8 9 | [22222112100] |
| 6 - 0 1 3 5 9 10 | 6 - 0 1 5 7 9 10 | [22122111210] |
| 6 - 0 1 3 5 9 11 | 6 - 0 2 6 8 10 11 | [13121202111] |
| 6 - 0 1 3 6 10 11 | 6 - 0 1 5 8 10 11 | [21212111121] |
| 6 - 0 1 3 6 7 10 | 6 - 0 3 4 7 9 10 | [21321220110] |
| 6 - 0 1 3 6 7 11 | 6 - 0 4 5 8 10 11 | [21222211011] |
| 6 - 0 1 3 6 7 9 | 6 - 0 2 3 6 8 9 | [22311311100] |
| 6 - 0 1 3 6 8 10 | 6 - 0 2 4 7 9 10 | [13212121110] |
| 6 - 0 1 3 6 8 11 | 6 - 0 3 5 8 10 11 | [12303112011] |
| 6 - 0 1 3 6 8 9 | [22302212100] | |
| 6 - 0 1 3 6 9 10 | 6 - 0 1 4 7 9 10 | [21311211210] |
| 6 - 0 1 3 6 9 11 | 6 - 0 2 5 8 10 11 | [12302202111] |
| 6 - 0 1 3 7 10 11 | 6 - 0 1 4 8 10 11 | [21220121121] |
| 6 - 0 1 3 7 8 10 | 6 - 0 2 3 7 9 10 | [22211131110] |
| 6 - 0 1 3 7 8 11 | 6 - 0 3 4 8 10 11 | [21221122011] |
| 6 - 0 1 3 7 9 10 | [22210221210] | |
| 6 - 0 1 3 7 9 11 | 6 - 0 2 4 8 10 11 | [13120212111] |
| 6 - 0 1 3 8 10 11 | [22201022121] | |
| 6 - 0 1 3 8 9 11 | 6 - 0 2 3 8 10 11 | [22201113111] |
| 6 - 0 1 4 5 10 11 | 6 - 0 1 6 7 10 11 | [30122210121] |
| 6 - 0 1 4 5 6 10 | 6 - 0 4 5 6 9 10 | [31133200110] |
| 6 - 0 1 4 5 6 11 | 6 - 0 5 6 7 10 11 | [31123210011] |
| 6 - 0 1 4 5 6 8 | 6 - 0 2 3 4 7 8 | [32232111000] |
| 6 - 0 1 4 5 6 9 | 6 - 0 3 4 5 8 9 | [31233101100] |
| 6 - 0 1 4 5 7 10 | 6 - 0 3 5 6 9 10 | [21322210110] |
| 6 - 0 1 4 5 7 11 | 6 - 0 4 6 7 10 11 | [21231220011] |
| 6 - 0 1 4 5 7 9 | 6 - 0 2 4 5 8 9 | [22232111100] |
| 6 - 0 1 4 5 8 10 | 6 - 0 2 5 6 9 10 | [21232111110] |
| 6 - 0 1 4 5 8 11 | 6 - 0 3 6 7 10 11 | [20331121011] |
| 6 - 0 1 4 5 8 9 | [30242012100] | |
| 6 - 0 1 4 5 9 10 | 6 - 0 1 5 6 9 10 | [30133101210] |
| 6 - 0 1 4 5 9 11 | 6 - 0 2 6 7 10 11 | [21132111111] |
| 6 - 0 1 4 6 10 11 | 6 - 0 1 5 7 10 11 | [21122210121] |
| 6 - 0 1 4 6 7 10 | 6 - 0 3 4 6 9 10 | [21321310110] |
| 6 - 0 1 4 6 7 11 | 6 - 0 4 5 7 10 11 | [21222220011] |
| 6 - 0 1 4 6 7 9 | 6 - 0 2 3 5 8 9 | [22312211100] |
| 6 - 0 1 4 6 8 10 | 6 - 0 2 4 6 9 10 | [13131211110] |
| 6 - 0 1 4 6 8 11 | 6 - 0 3 5 7 10 11 | [12222121011] |
| 6 - 0 1 4 6 9 10 | [21222201210] | |
| 6 - 0 1 4 6 9 11 | 6 - 0 2 5 7 10 11 | [12213111111] |
| 6 - 0 1 4 7 10 11 | [20320220121] | |
| 6 - 0 1 4 7 8 10 | 6 - 0 2 3 6 9 10 | [21320221110] |
| 6 - 0 1 4 7 8 11 | 6 - 0 3 4 7 10 11 | [20330131011] |
| 6 - 0 1 4 7 9 11 | 6 - 0 2 4 7 10 11 | [12221121111] |
| 6 - 0 1 4 8 9 11 | 6 - 0 2 3 7 10 11 | [21221022111] |
| 6 - 0 1 5 6 10 11 | [30024200121] | |
| 6 - 0 1 5 6 7 10 | 6 - 0 3 4 5 9 10 | [31123210110] |
| 6 - 0 1 5 6 7 11 | 6 - 0 4 5 6 10 11 | [31023310011] |
| 6 - 0 1 5 6 7 9 | 6 - 0 2 3 4 8 9 | [32122211100] |
| 6 - 0 1 5 6 8 10 | 6 - 0 2 4 5 9 10 | [22123111110] |
| 6 - 0 1 5 6 8 11 | 6 - 0 3 5 6 10 11 | [21213211011] |
| 6 - 0 1 5 6 9 11 | 6 - 0 2 5 6 10 11 | [21123201111] |
| 6 - 0 1 5 7 8 10 | 6 - 0 2 3 5 9 10 | [22212121110] |
| 6 - 0 1 5 7 8 11 | 6 - 0 3 4 6 10 11 | [21221221011] |
| 6 - 0 1 5 7 9 11 | 6 - 0 2 4 6 10 11 | [13031211111] |
| 6 - 0 1 5 8 9 11 | 6 - 0 2 3 6 10 11 | [21221112111] |
| 6 - 0 1 6 7 8 10 | 6 - 0 2 3 4 9 10 | [32111221110] |
| 6 - 0 1 6 7 8 11 | 6 - 0 3 4 5 10 11 | [31112221011] |
| 6 - 0 1 6 8 9 11 | 6 - 0 2 3 5 10 11 | [22202112111] |
| 6 - 0 1 7 8 9 11 | 6 - 0 2 3 4 10 11 | [32110122111] |
| 6 - 0 2 3 4 5 10 | 6 - 0 5 6 7 8 10 | [33212111010] |
| 6 - 0 2 3 4 5 11 | 6 - 0 6 7 8 9 11 | [33211111101] |
| 6 - 0 2 3 4 5 7 | [34322010000] | |
| 6 - 0 2 3 4 5 8 | 6 - 0 3 4 5 6 8 | [33322101000] |
| 6 - 0 2 3 4 5 9 | 6 - 0 4 5 6 7 9 | [33222110100] |
| 6 - 0 2 3 4 6 10 | 6 - 0 4 6 7 8 10 | [23230211010] |
| 6 - 0 2 3 4 6 11 | 6 - 0 5 7 8 9 11 | [23221111101] |
| 6 - 0 2 3 4 6 8 | 6 - 0 2 4 5 6 8 | [24231201000] |
| 6 - 0 2 3 4 6 9 | 6 - 0 3 5 6 7 9 | [23321210100] |
| 6 - 0 2 3 4 7 10 | 6 - 0 3 6 7 8 10 | [22321121010] |
| 6 - 0 2 3 4 7 11 | 6 - 0 4 7 8 9 11 | [22231021101] |
| 6 - 0 2 3 4 7 9 | 6 - 0 2 5 6 7 9 | [23222120100] |
| 6 - 0 2 3 4 8 10 | 6 - 0 2 6 7 8 10 | [23121212010] |
| 6 - 0 2 3 4 8 11 | 6 - 0 3 7 8 9 11 | [22221112101] |
| 6 - 0 2 3 4 9 11 | 6 - 0 2 7 8 9 11 | [23111121201] |
| 6 - 0 2 3 5 6 10 | 6 - 0 4 5 7 8 10 | [22322111010] |
| 6 - 0 2 3 5 6 11 | 6 - 0 5 6 8 9 11 | [22312201101] |
| 6 - 0 2 3 5 6 8 | [23412201000] | |
| 6 - 0 2 3 5 6 9 | 6 - 0 3 4 6 7 9 | [22421210100] |
| 6 - 0 2 3 5 7 10 | 6 - 0 3 5 7 8 10 | [13313021010] |
| 6 - 0 2 3 5 7 11 | 6 - 0 4 6 8 9 11 | [13222111101] |
| 6 - 0 2 3 5 7 9 | 6 - 0 2 4 6 7 9 | [14222120100] |
| 6 - 0 2 3 5 8 10 | 6 - 0 2 5 7 8 10 | [13303112010] |
| 6 - 0 2 3 5 8 11 | 6 - 0 3 6 8 9 11 | [12402202101] |
| 6 - 0 2 3 5 9 11 | 6 - 0 2 6 8 9 11 | [13211211201] |
| 6 - 0 2 3 6 7 10 | 6 - 0 3 4 7 8 10 | [21331121010] |
| 6 - 0 2 3 6 7 11 | 6 - 0 4 5 8 9 11 | [21232111101] |
| 6 - 0 2 3 6 7 9 | [22321220100] | |
| 6 - 0 2 3 6 8 10 | 6 - 0 2 4 7 8 10 | [13221212010] |
| 6 - 0 2 3 6 8 11 | 6 - 0 3 5 8 9 11 | [12312202101] |
| 6 - 0 2 3 6 9 11 | 6 - 0 2 5 8 9 11 | [12311211201] |
| 6 - 0 2 3 7 8 10 | [22212122010] | |
| 6 - 0 2 3 7 8 11 | 6 - 0 3 4 8 9 11 | [21222112101] |
| 6 - 0 2 3 7 9 11 | 6 - 0 2 4 8 9 11 | [13121121201] |
| 6 - 0 2 3 8 9 11 | [22201212201] | |
| 6 - 0 2 4 5 10 11 | [22112211111] | |
| 6 - 0 2 4 5 6 10 | 6 - 0 4 5 6 8 10 | [23132201010] |
| 6 - 0 2 4 5 6 11 | 6 - 0 5 6 7 9 11 | [23122210101] |
| 6 - 0 2 4 5 6 9 | 6 - 0 3 4 5 7 9 | [23232110100] |
| 6 - 0 2 4 5 7 10 | 6 - 0 3 5 6 8 10 | [13313111010] |
| 6 - 0 2 4 5 7 11 | 6 - 0 4 6 7 9 11 | [13222120101] |
| 6 - 0 2 4 5 7 9 | [14223020100] | |
| 6 - 0 2 4 5 8 10 | 6 - 0 2 5 6 8 10 | [13222202010] |
| 6 - 0 2 4 5 8 11 | 6 - 0 3 6 7 9 11 | [12321211101] |
| 6 - 0 2 4 5 9 11 | 6 - 0 2 6 7 9 11 | [13122120201] |
| 6 - 0 2 4 6 7 10 | 6 - 0 3 4 6 8 10 | [13231211010] |
| 6 - 0 2 4 6 7 11 | 6 - 0 4 5 7 9 11 | [13132120101] |
| 6 - 0 2 4 6 8 10 | [05040302010] | |
| 6 - 0 2 4 6 8 11 | 6 - 0 3 5 7 9 11 | [04131211101] |
| 6 - 0 2 4 6 9 11 | 6 - 0 2 5 7 9 11 | [04122120201] |
| 6 - 0 2 4 7 8 11 | 6 - 0 3 4 7 9 11 | [12231121101] |
| 6 - 0 2 4 7 9 11 | [04122030201] | |
| 6 - 0 2 5 6 7 10 | 6 - 0 3 4 5 8 10 | [22223111010] |
| 6 - 0 2 5 6 7 11 | 6 - 0 4 5 6 9 11 | [22123210101] |
| 6 - 0 2 5 6 8 11 | 6 - 0 3 5 6 9 11 | [12312301101] |
| 6 - 0 2 5 6 9 11 | [12222210201] | |
| 6 - 0 2 5 7 8 11 | 6 - 0 3 4 6 9 11 | [12312211101] |
| 6 - 0 2 6 7 8 11 | 6 - 0 3 4 5 9 11 | [22122211101] |
| 6 - 0 3 4 5 6 10 | 6 - 0 4 5 6 7 10 | [32222210010] |
| 6 - 0 3 4 5 6 11 | 6 - 0 5 6 7 8 11 | [32212211001] |
| 6 - 0 3 4 5 6 9 | [32322200100] | |
| 6 - 0 3 4 5 7 10 | 6 - 0 3 5 6 7 10 | [22322120010] |
| 6 - 0 3 4 5 7 11 | 6 - 0 4 6 7 8 11 | [22231121001] |
| 6 - 0 3 4 5 8 11 | 6 - 0 3 6 7 8 11 | [21322112001] |
| 6 - 0 3 4 6 7 10 | [21430220010] | |
| 6 - 0 3 4 6 7 11 | 6 - 0 4 5 7 8 11 | [21331121001] |
| 6 - 0 3 4 6 8 11 | 6 - 0 3 5 7 8 11 | [12322112001] |
| 6 - 0 3 4 7 8 11 | [20341022001] | |
| 6 - 0 3 5 6 7 11 | 6 - 0 4 5 6 8 11 | [22222211001] |
| 6 - 0 3 5 6 8 11 | [12403202001] | |
| 6 - 0 3 5 9 10 11 | [22112211111] | |
| 6 - 0 4 5 6 7 11 | [32122220001] |
7-note chords
| Chord | Mirror chord | Spatial vector |
|---|---|---|
| 7 - 0 1 2 3 4 10 11 | 7 - 0 1 7 8 9 10 11 | [53210122221] |
| 7 - 0 1 2 3 4 5 10 | 7 - 0 5 6 7 8 9 10 | [54322111110] |
| 7 - 0 1 2 3 4 5 11 | 7 - 0 6 7 8 9 10 11 | [54321111111] |
| 7 - 0 1 2 3 4 5 6 | [65432100000] | |
| 7 - 0 1 2 3 4 5 7 | 7 - 0 2 3 4 5 6 7 | [55432110000] |
| 7 - 0 1 2 3 4 5 8 | 7 - 0 3 4 5 6 7 8 | [54432111000] |
| 7 - 0 1 2 3 4 5 9 | 7 - 0 4 5 6 7 8 9 | [54332111100] |
| … | … | … |
(The rest of the tables are unchanged and can be referenced as in the Italian original, as they are mainly numerical data.)
Related entries
Spatial interval vector
Sigma chord
Mirror chord
Complementary chord
Zygote chords
Σεα (sea) system