Tritriadic scales
Take the triad
1, 5/4, 3/2
Make one copy starting on 3/2
3/2, 15/8, 9/4
and one copy starting on 4/3, the octave complement of 3/2, giving
4/3, 5/3, 2/1
Combining these three triads and octave-reducing each note gives the seven-note scale
1, 9/8, 5/4, 4/3, 3/2, 5/3, 15/8
which is the tritriadic scale built from 1, 5/4, 3/2.
In general, for a triad 1, M, D, the tritriadic scale consists of the notes
1, M, D, D*M, D*D, 1/D, M/D
octave reduced and sorted.
M->T variant: triads placed on M and its octave complement 1/M:
1, M, D, M*M, D*M, 1/M, D/M
D->M variant: triads placed on D/M and its octave complement M/D:
1, M, D, D/M, D*D/M, M/D, M*M/D
Further reading
- John Chalmers, Tritriadic Scales with Seven Tones, Xenharmonikon Online
Python code
from fractions import Fraction
from math import floor, log2
def reduce(x):
return x * Fraction(2) ** (-floor(log2(x)))
def tritriadic(M, D):
"""
>>> tritriadic(Fraction(5, 4), Fraction(3, 2))
[Fraction(1, 1), Fraction(9, 8), Fraction(5, 4), Fraction(4, 3), Fraction(3, 2), Fraction(5, 3), Fraction(15, 8)]
"""
triad1 = [1, M, D]
triad2 = [x * D for x in triad1]
triad3 = [x / D for x in triad1]
return sorted(set(reduce(x) for x in triad1 + triad2 + triad3))
def tritriadic_mt(M, D):
"""
>>> tritriadic_mt(Fraction(5, 4), Fraction(3, 2))
[Fraction(1, 1), Fraction(6, 5), Fraction(5, 4), Fraction(3, 2), Fraction(25, 16), Fraction(8, 5), Fraction(15, 8)]
"""
triad1 = [1, M, D]
triad2 = [x * M for x in triad1]
triad3 = [x / M for x in triad1]
return sorted(set(reduce(x) for x in triad1 + triad2 + triad3))
def tritriadic_dm(M, D):
"""
>>> tritriadic_dm(Fraction(5, 4), Fraction(3, 2))
[Fraction(1, 1), Fraction(25, 24), Fraction(6, 5), Fraction(5, 4), Fraction(3, 2), Fraction(5, 3), Fraction(9, 5)]
"""
triad1 = [1, M, D]
triad2 = [x * D / M for x in triad1]
triad3 = [x * M / D for x in triad1]
return sorted(set(reduce(x) for x in triad1 + triad2 + triad3))
Scales
| File | Call |
|---|---|
| xen09-chalmers-tritriadic-1-11-13 | tritriadic(Fraction(11, 8), Fraction(13, 8)) |
| xen09-chalmers-tritriadic-1-3-5 | tritriadic(Fraction(3, 2), Fraction(5, 4)) |
| xen09-chalmers-tritriadic-1-3-7 | tritriadic(Fraction(3, 2), Fraction(7, 4)) |
| xen09-chalmers-tritriadic-1-5-11 | tritriadic(Fraction(5, 4), Fraction(11, 8)) |
| xen09-chalmers-tritriadic-1-5-13 | tritriadic(Fraction(5, 4), Fraction(13, 8)) |
| xen09-chalmers-tritriadic-1-5-7 | tritriadic(Fraction(5, 4), Fraction(7, 4)) |
| xen09-chalmers-tritriadic-1-7-11 | tritriadic(Fraction(7, 4), Fraction(11, 8)) |
| xen09-chalmers-tritriadic-1-7-9 | tritriadic(Fraction(7, 4), Fraction(9, 8)) |
| xen09-chalmers-tritriadic-10-11-12 | tritriadic(Fraction(11, 10), Fraction(6, 5)) |
| xen09-chalmers-tritriadic-10-11-15 | tritriadic(Fraction(11, 10), Fraction(3, 2)) |
| xen09-chalmers-tritriadic-10-12-15 | tritriadic(Fraction(6, 5), Fraction(3, 2)) |
| xen09-chalmers-tritriadic-10-13-15 | tritriadic(Fraction(13, 10), Fraction(3, 2)) |
| xen09-chalmers-tritriadic-10-13-18 | tritriadic(Fraction(13, 10), Fraction(9, 5)) |
| xen09-chalmers-tritriadic-10-14-15 | tritriadic(Fraction(7, 5), Fraction(3, 2)) |
| xen09-chalmers-tritriadic-10-15-11 | tritriadic(Fraction(3, 2), Fraction(11, 10)) |
| xen09-chalmers-tritriadic-11-13-15 | tritriadic(Fraction(13, 11), Fraction(15, 11)) |
| xen09-chalmers-tritriadic-11-14-20 | tritriadic(Fraction(14, 11), Fraction(20, 11)) |
| xen09-chalmers-tritriadic-11-15-20 | tritriadic(Fraction(15, 11), Fraction(20, 11)) |
| xen09-chalmers-tritriadic-11-16-20 | tritriadic(Fraction(16, 11), Fraction(20, 11)) |
| xen09-chalmers-tritriadic-11-18-15 | tritriadic(Fraction(18, 11), Fraction(15, 11)) |
| xen09-chalmers-tritriadic-11-20-18 | tritriadic(Fraction(20, 11), Fraction(18, 11)) |
| xen09-chalmers-tritriadic-11-8-6 | tritriadic(Fraction(16, 11), Fraction(12, 11)) |
| xen09-chalmers-tritriadic-12-13-18 | tritriadic(Fraction(13, 12), Fraction(3, 2)) |
| xen09-chalmers-tritriadic-12-17-18 | tritriadic(Fraction(17, 12), Fraction(3, 2)) |
| xen09-chalmers-tritriadic-13-14-16 | tritriadic(Fraction(14, 13), Fraction(16, 13)) |
| xen09-chalmers-tritriadic-14-15-17 | tritriadic(Fraction(15, 14), Fraction(17, 14)) |
| xen09-chalmers-tritriadic-14-16-17 | tritriadic(Fraction(8, 7), Fraction(17, 14)) |
| xen09-chalmers-tritriadic-14-16-21 | tritriadic(Fraction(8, 7), Fraction(3, 2)) |
| xen09-chalmers-tritriadic-14-17-21 | tritriadic(Fraction(17, 14), Fraction(3, 2)) |
| xen09-chalmers-tritriadic-14-18-21 | tritriadic(Fraction(9, 7), Fraction(3, 2)) |
| xen09-chalmers-tritriadic-15-18-22 | tritriadic(Fraction(6, 5), Fraction(22, 15)) |
| xen09-chalmers-tritriadic-16-19-24 | tritriadic(Fraction(19, 16), Fraction(3, 2)) |
| xen09-chalmers-tritriadic-16-21-24 | tritriadic(Fraction(21, 16), Fraction(3, 2)) |
| xen09-chalmers-tritriadic-17-15-14 | tritriadic(Fraction(30, 17), Fraction(28, 17)) |
| xen09-chalmers-tritriadic-17-16-14 | tritriadic(Fraction(32, 17), Fraction(28, 17)) |
| xen09-chalmers-tritriadic-17-19-21 | tritriadic(Fraction(19, 17), Fraction(21, 17)) |
| xen09-chalmers-tritriadic-18-22-27 | tritriadic(Fraction(11, 9), Fraction(3, 2)) |
| xen09-chalmers-tritriadic-21-19-17 | tritriadic(Fraction(38, 21), Fraction(34, 21)) |
| xen09-chalmers-tritriadic-22-24-27 | tritriadic(Fraction(12, 11), Fraction(27, 22)) |
| xen09-chalmers-tritriadic-22-24-33 | tritriadic(Fraction(12, 11), Fraction(3, 2)) |
| xen09-chalmers-tritriadic-22-25-27 | tritriadic(Fraction(25, 22), Fraction(27, 22)) |
| xen09-chalmers-tritriadic-22-26-33 | tritriadic(Fraction(13, 11), Fraction(3, 2)) |
| xen09-chalmers-tritriadic-22-27-33 | tritriadic(Fraction(27, 22), Fraction(3, 2)) |
| xen09-chalmers-tritriadic-22-28-33 | tritriadic(Fraction(14, 11), Fraction(3, 2)) |
| xen09-chalmers-tritriadic-22-33-24 | tritriadic(Fraction(3, 2), Fraction(12, 11)) |
| xen09-chalmers-tritriadic-24-33-44 | tritriadic(Fraction(11, 8), Fraction(11, 6)) |
| xen09-chalmers-tritriadic-24-35-26 | tritriadic(Fraction(35, 24), Fraction(13, 12)) |
| xen09-chalmers-tritriadic-26-30-39 | tritriadic(Fraction(15, 13), Fraction(3, 2)) |
| xen09-chalmers-tritriadic-26-32-39 | tritriadic(Fraction(16, 13), Fraction(3, 2)) |
| xen09-chalmers-tritriadic-26-33-39 | tritriadic(Fraction(33, 26), Fraction(3, 2)) |
| xen09-chalmers-tritriadic-26-34-39 | tritriadic(Fraction(17, 13), Fraction(3, 2)) |
| xen09-chalmers-tritriadic-26-35-48 | tritriadic(Fraction(35, 26), Fraction(24, 13)) |
| xen09-chalmers-tritriadic-27-24-22 | tritriadic(Fraction(16, 9), Fraction(44, 27)) |
| xen09-chalmers-tritriadic-27-25-22 | tritriadic(Fraction(50, 27), Fraction(44, 27)) |
| xen09-chalmers-tritriadic-28-33-42 | tritriadic(Fraction(33, 28), Fraction(3, 2)) |
| xen09-chalmers-tritriadic-3-4-5 | tritriadic(Fraction(4, 3), Fraction(5, 3)) |
| xen09-chalmers-tritriadic-3-5-7 | tritriadic(Fraction(5, 3), Fraction(7, 6)) |
| xen09-chalmers-tritriadic-3-7-9 | tritriadic(Fraction(7, 6), Fraction(3, 2)) |
| xen09-chalmers-tritriadic-32-39-48 | tritriadic(Fraction(39, 32), Fraction(3, 2)) |
| xen09-chalmers-tritriadic-34-36-51 | tritriadic(Fraction(18, 17), Fraction(3, 2)) |
| xen09-chalmers-tritriadic-34-39-51 | tritriadic(Fraction(39, 34), Fraction(3, 2)) |
| xen09-chalmers-tritriadic-34-42-51 | tritriadic(Fraction(21, 17), Fraction(3, 2)) |
| xen09-chalmers-tritriadic-38-48-47 | tritriadic(Fraction(24, 19), Fraction(47, 38)) |
| xen09-chalmers-tritriadic-4-5-6 | tritriadic(Fraction(5, 4), Fraction(3, 2)) |
| xen09-chalmers-tritriadic-5-6-7 | tritriadic(Fraction(6, 5), Fraction(7, 5)) |
| xen09-chalmers-tritriadic-5-7-9 | tritriadic(Fraction(7, 5), Fraction(9, 5)) |
| xen09-chalmers-tritriadic-5-9-8 | tritriadic(Fraction(9, 5), Fraction(8, 5)) |
| xen09-chalmers-tritriadic-54-64-81 | tritriadic(Fraction(32, 27), Fraction(3, 2)) |
| xen09-chalmers-tritriadic-6-10-11 | tritriadic(Fraction(5, 3), Fraction(11, 6)) |
| xen09-chalmers-tritriadic-6-7-8 | tritriadic(Fraction(7, 6), Fraction(4, 3)) |
| xen09-chalmers-tritriadic-6-7-9 | tritriadic(Fraction(7, 6), Fraction(3, 2)) |
| xen09-chalmers-tritriadic-6-8-11 | tritriadic(Fraction(4, 3), Fraction(11, 6)) |
| xen09-chalmers-tritriadic-64-81-96 | tritriadic(Fraction(81, 64), Fraction(3, 2)) |
| xen09-chalmers-tritriadic-7-10-13 | tritriadic(Fraction(10, 7), Fraction(13, 7)) |
| xen09-chalmers-tritriadic-7-11-13 | tritriadic(Fraction(11, 7), Fraction(13, 7)) |
| xen09-chalmers-tritriadic-7-8-11 | tritriadic(Fraction(8, 7), Fraction(11, 7)) |
| xen09-chalmers-tritriadic-7-9-11 | tritriadic(Fraction(9, 7), Fraction(11, 7)) |
| xen09-chalmers-tritriadic-7-9-13 | tritriadic(Fraction(9, 7), Fraction(13, 7)) |
| xen09-chalmers-tritriadic-8-11-12 | tritriadic(Fraction(11, 8), Fraction(3, 2)) |
| xen09-chalmers-tritriadic-8-14-13 | tritriadic(Fraction(7, 4), Fraction(13, 8)) |
| xen09-chalmers-tritriadic-8-9-10 | tritriadic(Fraction(9, 8), Fraction(5, 4)) |
| xen09-chalmers-tritriadic-9-10-11 | tritriadic(Fraction(10, 9), Fraction(11, 9)) |
| xen09-chalmers-tritriadic-9-11-13 | tritriadic(Fraction(11, 9), Fraction(13, 9)) |
| xen09-chalmers-tritriadic-9-13-10 | tritriadic(Fraction(13, 9), Fraction(10, 9)) |
| xen09-chalmers-tritriadic-9-7-10 | tritriadic(Fraction(14, 9), Fraction(10, 9)) |
| xen10-chalmers-tritriadic-13-23-21 | tritriadic(Fraction(23, 13), Fraction(21, 13)) |
| xen10-chalmers-tritriadic-15-27-25 | tritriadic(Fraction(9, 5), Fraction(5, 3)) |
| xen10-chalmers-tritriadic-17-13-19 | tritriadic(Fraction(26, 17), Fraction(19, 17)) |
| xen10-chalmers-tritriadic-17-21-25 | tritriadic(Fraction(21, 17), Fraction(25, 17)) |
| xen10-chalmers-tritriadic-17-25-19 | tritriadic(Fraction(25, 17), Fraction(19, 17)) |
| xen10-chalmers-tritriadic-17-5-25 | tritriadic(Fraction(20, 17), Fraction(25, 17)) |
| xen10-chalmers-tritriadic-17-7-23 | tritriadic(Fraction(28, 17), Fraction(23, 17)) |
| xen10-chalmers-tritriadic-19-21-23 | tritriadic(Fraction(21, 19), Fraction(23, 19)) |
| xen10-chalmers-tritriadic-19-27-21 | tritriadic(Fraction(27, 19), Fraction(21, 19)) |
| xen10-chalmers-tritriadic-19-7-21 | tritriadic(Fraction(28, 19), Fraction(21, 19)) |
| xen10-chalmers-tritriadic-21-1-23 | tritriadic(Fraction(32, 21), Fraction(23, 21)) |
| xen10-chalmers-tritriadic-21-15-23 | tritriadic(Fraction(10, 7), Fraction(23, 21)) |
| xen10-chalmers-tritriadic-23-17-25 | tritriadic(Fraction(34, 23), Fraction(25, 23)) |
| xen10-chalmers-tritriadic-3-11-15 | tritriadic(Fraction(11, 6), Fraction(5, 4)) |
| xen10-chalmers-tritriadic-5-1-27 | tritriadic(Fraction(8, 5), Fraction(27, 20)) |
| xen10-chalmers-tritriadic-5-17-27 | tritriadic(Fraction(17, 10), Fraction(27, 20)) |
| xen10-chalmers-tritriadic-5-27-9 | tritriadic(Fraction(27, 20), Fraction(9, 5)) |
| xen10-chalmers-tritriadic-7-19-25 | tritriadic(Fraction(19, 14), Fraction(25, 14)) |
| xen10-chalmers-tritriadic-7-23-19 | tritriadic(Fraction(23, 14), Fraction(19, 14)) |
| xen10-chalmers-tritriadic-7-25-23 | tritriadic(Fraction(25, 14), Fraction(23, 14)) |
| xen10-chalmers-tritriadic-7-3-19 | tritriadic(Fraction(12, 7), Fraction(19, 14)) |
| xen10-chalmers-tritriadic-7-9-25 | tritriadic(Fraction(9, 7), Fraction(25, 14)) |
| xen12-chalmers-tritriadic-dm-1-21-23 | tritriadic_dm(Fraction(21, 16), Fraction(23, 16)) |
| xen12-chalmers-tritriadic-dm-1-3-11 | tritriadic_dm(Fraction(3, 2), Fraction(11, 8)) |
| xen12-chalmers-tritriadic-dm-1-5-27 | tritriadic_dm(Fraction(5, 4), Fraction(27, 16)) |
| xen12-chalmers-tritriadic-dm-1-7-17 | tritriadic_dm(Fraction(7, 4), Fraction(17, 16)) |
| xen12-chalmers-tritriadic-dm-11-27-9 | tritriadic_dm(Fraction(27, 22), Fraction(18, 11)) |
| xen12-chalmers-tritriadic-dm-11-5-3 | tritriadic_dm(Fraction(20, 11), Fraction(12, 11)) |
| xen12-chalmers-tritriadic-dm-13-17-19 | tritriadic_dm(Fraction(17, 13), Fraction(19, 13)) |
| xen12-chalmers-tritriadic-dm-13-23-7 | tritriadic_dm(Fraction(23, 13), Fraction(14, 13)) |
| xen12-chalmers-tritriadic-dm-13-9-5 | tritriadic_dm(Fraction(18, 13), Fraction(20, 13)) |
| xen12-chalmers-tritriadic-dm-15-11-5 | tritriadic_dm(Fraction(22, 15), Fraction(4, 3)) |
| xen12-chalmers-tritriadic-dm-15-21-23 | tritriadic_dm(Fraction(7, 5), Fraction(23, 15)) |
| xen12-chalmers-tritriadic-dm-17-21-7 | tritriadic_dm(Fraction(21, 17), Fraction(28, 17)) |
| xen12-chalmers-tritriadic-dm-17-23-25 | tritriadic_dm(Fraction(23, 17), Fraction(25, 17)) |
| xen12-chalmers-tritriadic-dm-17-27-5 | tritriadic_dm(Fraction(27, 17), Fraction(20, 17)) |
| xen12-chalmers-tritriadic-dm-19-21-17 | tritriadic_dm(Fraction(21, 19), Fraction(34, 19)) |
| xen12-chalmers-tritriadic-dm-19-25-7 | tritriadic_dm(Fraction(25, 19), Fraction(28, 19)) |
| xen12-chalmers-tritriadic-dm-21-23-19 | tritriadic_dm(Fraction(23, 21), Fraction(38, 21)) |
| xen12-chalmers-tritriadic-dm-21-25-17 | tritriadic_dm(Fraction(25, 21), Fraction(34, 21)) |
| xen12-chalmers-tritriadic-dm-23-19-7 | tritriadic_dm(Fraction(38, 23), Fraction(28, 23)) |
| xen12-chalmers-tritriadic-dm-23-21-13 | tritriadic_dm(Fraction(42, 23), Fraction(26, 23)) |
| xen12-chalmers-tritriadic-dm-25-19-17 | tritriadic_dm(Fraction(38, 25), Fraction(34, 25)) |
| xen12-chalmers-tritriadic-dm-25-23-7 | tritriadic_dm(Fraction(46, 25), Fraction(28, 25)) |
| xen12-chalmers-tritriadic-dm-25-27-11 | tritriadic_dm(Fraction(27, 25), Fraction(44, 25)) |
| xen12-chalmers-tritriadic-dm-27-21-19 | tritriadic_dm(Fraction(14, 9), Fraction(38, 27)) |
| xen12-chalmers-tritriadic-dm-27-23-17 | tritriadic_dm(Fraction(46, 27), Fraction(34, 27)) |
| xen12-chalmers-tritriadic-dm-27-25-15 | tritriadic_dm(Fraction(50, 27), Fraction(10, 9)) |
| xen12-chalmers-tritriadic-dm-27-9-5 | tritriadic_dm(Fraction(4, 3), Fraction(40, 27)) |
| xen12-chalmers-tritriadic-dm-3-11-27 | tritriadic_dm(Fraction(11, 6), Fraction(9, 8)) |
| xen12-chalmers-tritriadic-dm-3-5-15 | tritriadic_dm(Fraction(5, 3), Fraction(5, 4)) |
| xen12-chalmers-tritriadic-dm-3-7-19 | tritriadic_dm(Fraction(7, 6), Fraction(19, 12)) |
| xen12-chalmers-tritriadic-dm-5-15-27 | tritriadic_dm(Fraction(3, 2), Fraction(27, 20)) |
| xen12-chalmers-tritriadic-dm-5-17-25 | tritriadic_dm(Fraction(17, 10), Fraction(5, 4)) |
| xen12-chalmers-tritriadic-dm-5-17-7 | tritriadic_dm(Fraction(17, 10), Fraction(7, 5)) |
| xen12-chalmers-tritriadic-dm-5-3-1 | tritriadic_dm(Fraction(6, 5), Fraction(8, 5)) |
| xen12-chalmers-tritriadic-dm-5-9-11 | tritriadic_dm(Fraction(9, 5), Fraction(11, 10)) |
| xen12-chalmers-tritriadic-dm-7-13-1 | tritriadic_dm(Fraction(13, 7), Fraction(8, 7)) |
| xen12-chalmers-tritriadic-dm-7-17-23 | tritriadic_dm(Fraction(17, 14), Fraction(23, 14)) |
| xen12-chalmers-tritriadic-dm-7-19-21 | tritriadic_dm(Fraction(19, 14), Fraction(3, 2)) |
| xen12-chalmers-tritriadic-dm-7-9-5 | tritriadic_dm(Fraction(9, 7), Fraction(10, 7)) |
| xen12-chalmers-tritriadic-dm-9-11-15 | tritriadic_dm(Fraction(11, 9), Fraction(5, 3)) |
| xen12-chalmers-tritriadic-dm-9-25-7 | tritriadic_dm(Fraction(25, 18), Fraction(14, 9)) |
| xen12-chalmers-tritriadic-dm-9-5-1 | tritriadic_dm(Fraction(10, 9), Fraction(16, 9)) |
| xen12-chalmers-tritriadic-mt-1-21-23 | tritriadic_mt(Fraction(21, 16), Fraction(23, 16)) |
| xen12-chalmers-tritriadic-mt-11-27-9 | tritriadic_mt(Fraction(27, 22), Fraction(18, 11)) |
| xen12-chalmers-tritriadic-mt-11-5-3 | tritriadic_mt(Fraction(20, 11), Fraction(12, 11)) |
| xen12-chalmers-tritriadic-mt-13-17-19 | tritriadic_mt(Fraction(17, 13), Fraction(19, 13)) |
| xen12-chalmers-tritriadic-mt-13-23-7 | tritriadic_mt(Fraction(23, 13), Fraction(14, 13)) |
| xen12-chalmers-tritriadic-mt-13-9-5 | tritriadic_mt(Fraction(18, 13), Fraction(20, 13)) |
| xen12-chalmers-tritriadic-mt-15-11-5 | tritriadic_mt(Fraction(22, 15), Fraction(4, 3)) |
| xen12-chalmers-tritriadic-mt-15-21-23 | tritriadic_mt(Fraction(7, 5), Fraction(23, 15)) |
| xen12-chalmers-tritriadic-mt-17-21-7 | tritriadic_mt(Fraction(21, 17), Fraction(28, 17)) |
| xen12-chalmers-tritriadic-mt-17-23-25 | tritriadic_mt(Fraction(23, 17), Fraction(25, 17)) |
| xen12-chalmers-tritriadic-mt-17-27-5 | tritriadic_mt(Fraction(27, 17), Fraction(20, 17)) |
| xen12-chalmers-tritriadic-mt-19-21-17 | tritriadic_mt(Fraction(21, 19), Fraction(34, 19)) |
| xen12-chalmers-tritriadic-mt-19-25-7 | tritriadic_mt(Fraction(25, 19), Fraction(28, 19)) |
| xen12-chalmers-tritriadic-mt-21-23-19 | tritriadic_mt(Fraction(23, 21), Fraction(38, 21)) |
| xen12-chalmers-tritriadic-mt-21-25-17 | tritriadic_mt(Fraction(25, 21), Fraction(34, 21)) |
| xen12-chalmers-tritriadic-mt-23-19-7 | tritriadic_mt(Fraction(38, 23), Fraction(28, 23)) |
| xen12-chalmers-tritriadic-mt-23-21-13 | tritriadic_mt(Fraction(42, 23), Fraction(26, 23)) |
| xen12-chalmers-tritriadic-mt-25-19-17 | tritriadic_mt(Fraction(38, 25), Fraction(34, 25)) |
| xen12-chalmers-tritriadic-mt-25-23-7 | tritriadic_mt(Fraction(46, 25), Fraction(28, 25)) |
| xen12-chalmers-tritriadic-mt-25-27-11 | tritriadic_mt(Fraction(27, 25), Fraction(44, 25)) |
| xen12-chalmers-tritriadic-mt-27-21-19 | tritriadic_mt(Fraction(14, 9), Fraction(38, 27)) |
| xen12-chalmers-tritriadic-mt-27-23-17 | tritriadic_mt(Fraction(46, 27), Fraction(34, 27)) |
| xen12-chalmers-tritriadic-mt-27-25-15 | tritriadic_mt(Fraction(50, 27), Fraction(10, 9)) |
| xen12-chalmers-tritriadic-mt-27-5-1 | tritriadic_mt(Fraction(40, 27), Fraction(32, 27)) |
| xen12-chalmers-tritriadic-mt-27-9-5 | tritriadic_mt(Fraction(4, 3), Fraction(40, 27)) |
| xen12-chalmers-tritriadic-mt-3-11-27 | tritriadic_mt(Fraction(11, 6), Fraction(9, 8)) |
| xen12-chalmers-tritriadic-mt-3-5-15 | tritriadic_mt(Fraction(5, 3), Fraction(5, 4)) |
| xen12-chalmers-tritriadic-mt-3-7-19 | tritriadic_mt(Fraction(7, 6), Fraction(19, 12)) |
| xen12-chalmers-tritriadic-mt-5-15-27 | tritriadic_mt(Fraction(3, 2), Fraction(27, 20)) |
| xen12-chalmers-tritriadic-mt-5-17-25 | tritriadic_mt(Fraction(17, 10), Fraction(5, 4)) |
| xen12-chalmers-tritriadic-mt-5-17-7 | tritriadic_mt(Fraction(17, 10), Fraction(7, 5)) |
| xen12-chalmers-tritriadic-mt-5-9-11 | tritriadic_mt(Fraction(9, 5), Fraction(11, 10)) |
| xen12-chalmers-tritriadic-mt-7-17-23 | tritriadic_mt(Fraction(17, 14), Fraction(23, 14)) |
| xen12-chalmers-tritriadic-mt-7-19-21 | tritriadic_mt(Fraction(19, 14), Fraction(3, 2)) |
| xen12-chalmers-tritriadic-mt-7-9-5 | tritriadic_mt(Fraction(9, 7), Fraction(10, 7)) |
| xen12-chalmers-tritriadic-mt-9-11-15 | tritriadic_mt(Fraction(11, 9), Fraction(5, 3)) |
| xen12-chalmers-tritriadic-mt-9-25-7 | tritriadic_mt(Fraction(25, 18), Fraction(14, 9)) |