18edt: Difference between revisions

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-edt means the division of the tritave into 18 equal parts <span style="background-color: rgba(255,255,255,0);">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.</span>[[category:macrotonal]]
+edt 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.
-<span style="background-color: rgba(255,255,255,0);">As the double of [[9edt|9edt]], it is the analog of 14edo insofar as it has a doubled harmonic chain. However, it, like [[8edt|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.</span>
+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.
-<span style="background-color: rgba(255,255,255,0);">0: 1/1</span>
+{| class="wikitable"
+! step
+! cents
+! approximated interval
+|-
+| 0
+| 0.000
+| 1/1
+|-
+| 1
+| 105.664
+| 16/15
+|-
+| 2
+| 211.328
+| 9/8
+|-
+| 3
+| 316.993
+| 6/5
+|-
+| 4
+| 422.657
+| 9/7
+|-
+| 5
+| 528.321
+| 27/20
+|-
+| 6
+| 633.985
+| 13/9
+|-
+| 7
+| 739.649
+| 17/13
+|-
+| 8
+| 845.313
+| 5/3
+|-
+| 9
+| 950.978
+| 19/11
+|-
+| 10
+| 1056.642
+| 9/5
+|-
+| 11
+| 1162.306
+| 49/25
+|-
+| 12
+| 1267.970
+| 27/13
+|-
+| 13
+| 1373.634
+| 20/9
+|-
+| 14
+| 1479.298
+| 7/3
+|-
+| 15
+| 1584.963
+| 5/2
+|-
+| 16
+| 1690.627
+| 8/3
+|-
+| 17
+| 1806.291
+| 45/16
+|-
+| 18
+| 1901.955
+| 3/1
+|}
-<span style="background-color: rgba(255,255,255,0);">1: 105.664 cents 16/15</span>
+[[category:macrotonal]]
+[[category:tritave]]
-<span style="background-color: rgba(255,255,255,0);">2: 211.328 cents 9/8</span>
+[[category:edt]]
-: 316.993 cents 6/5
-<span style="background-color: rgba(255,255,255,0);">4: 422.657 cents 9/7</span>
-: 528.321 cents 27/20
-<span style="background-color: rgba(255,255,255,0);">6: 633.985 cents 13/9</span>
-: 739.649 cents 17/13
-<span style="background-color: rgba(255,255,255,0);">8: 845.313 cents 5/3</span>
-: 950.9775 cents 19/11
-<span style="background-color: rgba(255,255,255,0);">10: 1056.642 cents 9/5</span>
-: 1162.306 cents 49/25
-<span style="background-color: rgba(255,255,255,0);">12: 1267.970 cents 27/13</span>
-: 1373.634 cents 20/9
-<span style="background-color: rgba(255,255,255,0);">14: 1479.298 cents 7/3</span>
-: 1584.963 cents 5/2
-<span style="background-color: rgba(255,255,255,0);">16: 1690.627 cents 8/3</span>
-: 1806.2905 cents 45/16
-<span style="background-color: rgba(255,255,255,0);">18: 3/1</span>