18edt

18edt means the division of the tritave into 18 equal parts of size 105.664 cents each. It has a decent 7 and an excellent 13, but a 5 which is 39 cents flat; if octaves were added and it was a sixth, it would count as a neutral sixth. The corresponding 5/3 is 845 cents, which is a neutral sixth between 8/5 and 5/3, which is really more of a 13/8, though this is allegedly a no-twos tuning. With octaves added, it also has a minor third and a major tenth which are both excellent as well as a minor thirteenth and major seventeenth which are still decent even though it skips actual octaves (in fact it is the non-octave semitone scale of 34edo). On the 3.7.13 subgroup it tempers out 351/343 and 2197/2187.

As the double of 9edt, it is the analog of 14edo insofar as it has a doubled harmonic chain. However, it, like 8edt, is not schismatic because 3:5:7 is a redundant chord. As a multiple of 9edt, it is the widest variety of 'White-Extraterrestrial-Tree' temperament.

0: 1/1

1: 105.664 cents 16/15

2: 211.328 cents 9/8

3: 316.993 cents 6/5

4: 422.657 cents 9/7

5: 528.321 cents 27/20

6: 633.985 cents 13/9

7: 739.649 cents 17/13

8: 845.313 cents 5/3

9: 950.9775 cents 19/11

10: 1056.642 cents 9/5

11: 1162.306 cents 49/25

12: 1267.970 cents 27/13

13: 1373.634 cents 20/9

14: 1479.298 cents 7/3

15: 1584.963 cents 5/2

16: 1690.627 cents 8/3

17: 1806.2905 cents 45/16

18: 3/1