all-trichord hexachords
all-interval twelve tone rows
link chords
micro-metric modulation
musical group theory
computer-assisted composition software
lilypond parsers
abcmusic parsers
miscellaneous readings
all the possible trichords belonging to SG1 (transposition is the binary operator)
| prime form |
lilypond string |
interval-class vector |
| 0 1 2 |
"c cs d" |
210000 |
| 0 1 3 |
"c cs ds" |
111000 |
| 0 2 3 |
"c d ds" |
111000 |
| 0 1 4 |
"c cs e" |
101100 |
| 0 3 4 |
"c ds e" |
101100 |
| 0 1 5 |
"c cs f" |
100110 |
| 0 4 5 |
"c e f" |
100110 |
| 0 1 6 |
"c cs fs" |
100011 |
| 0 5 6 |
"c f fs" |
100011 |
| 0 2 4 |
"c d e" |
020100 |
| 0 2 5 |
"c d f" |
011010 |
| 0 3 5 |
"c ds f" |
011010 |
| 0 2 6 |
"c d fs" |
010101 |
| 0 4 6 |
"c e fs" |
010101 |
| 0 2 7 |
"c d g" |
010020 |
| 0 3 6 |
"c ds fs" |
003000 |
| 0 3 7 |
"c ds g" |
001110 |
| 0 4 7 |
"c e g" |
001110 |
| 0 4 8 |
"c e gs" |
000300 |
all the possible trichords belonging to SG2 (transposition and inversion are the binary operators)
| prime form |
lilypond string |
interval-class vector |
| 0 1 2 |
"c cs d" |
210000 |
| 0 1 3 |
"c cs ds" |
111000 |
| 0 1 4 |
"c cs e" |
101100 |
| 0 1 5 |
"c cs f" |
100110 |
| 0 1 6 |
"c cs fs" |
100011 |
| 0 2 4 |
"c d e" |
020100 |
| 0 2 5 |
"c d f" |
011010 |
| 0 2 6 |
"c d fs" |
010101 |
| 0 2 7 |
"c d g" |
010020 |
| 0 3 6 |
"c ds fs" |
003000 |
| 0 3 7 |
"c ds g" |
001110 |
| 0 4 8 |
"c e gs" |
000300 |
