18edt

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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.

step cents hekts approximated interval
0 1/1
1 105.664 72.222 16/15
2 211.328 144.444 9/8
3 316.993 216.667 6/5
4 422.657 288.889 9/7
5 528.321 361.111 27/20
6 633.985 433.333 13/9
7 739.649 505.556 17/13
8 845.313 577.778 5/3
9 950.978 650 19/11
10 1056.642 722.222 9/5
11 1162.306 794.444 49/25
12 1267.97 866.667 27/13
13 1373.634 938.889 20/9
14 1479.298 1011.111 7/3
15 1584.963 1083.333 5/2
16 1690.627 1155.556 8/3
17 1806.291 1227.778 45/16
18 1901.955 1300 3/1