18edt: Difference between revisions

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-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.
+{{Infobox ET}}
+'''18edt''' is 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.
+== Temperaments ==
+As the double of [[9edt]], it is the analog of 14edo insofar if treating 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.
+edt can also be used for the [[Electra]] temperament based on [[15/11]], although in this case its approximation to [[13/11]] is very sharp.
+== Intervals ==
 {| class="wikitable"
-! step
+! Step
-! cents
+! Cents
-! approximated interval
+! Hekts
+! Approximated interval
+! [[Electra]] notation (J = 1/1)
 |-
-| 0
+! colspan="3" | 0
-| 0.000
 | 1/1
+| J
 |-
 | 1
 | 105.664
+|72.222
 | 16/15
+| J#, Kbb
 |-
 | 2
 | 211.328
+|144.444
 | 9/8
+| Jx, Kb
 |-
 | 3
 | 316.993
+|216.667
 | 6/5
+| K
 |-
 | 4
 | 422.657
+|288.889
 | 9/7
+| K#, Lb
 |-
 | 5
 | 528.321
+|361.111
 | 27/20
+| L
 |-
 | 6
 | 633.985
+|433.333
 | 13/9
+| L#, Mbb
 |-
 | 7
 | 739.649
+|505.556
 | 17/13
+| Lx, Mb
 |-
 | 8
 | 845.313
+|577.778
 | 5/3
+| M
 |-
 | 9
 | 950.978
+|650
 | 19/11
+| M#, Nbb
 |-
 | 10
 | 1056.642
+|722.222
 | 9/5
+| Mx, Nb
 |-
 | 11
 | 1162.306
+|794.444
 | 49/25
+| N
 |-
 | 12
-| 1267.970
+| 1267.97
+|866.667
 | 27/13
+| N#, Ob
 |-
 | 13
 | 1373.634
+|938.889
 | 20/9
+| O
 |-
 | 14
 | 1479.298
+|1011.111
 | 7/3
+| O#, Pbb
 |-
 | 15
 | 1584.963
+|1083.333
 | 5/2
+| Ox, Pb
 |-
 | 16
 | 1690.627
+|1155.556
 | 8/3
+| P
 |-
 | 17
 | 1806.291
+|1227.778
 | 45/16
+| P#, Jb
 |-
 | 18
 | 1901.955
+|1300
 | 3/1
+| J
 |}
+== Harmonics ==
+{{Harmonics in equal
+| steps = 18
+| num = 3
+| denom = 1
+| intervals = integer
+}}
+{{Harmonics in equal
+| steps = 18
+| num = 3
+| denom = 1
+| start = 12
+| collapsed = 1
+| intervals = integer
+}}
 [[category:macrotonal]]
 [[category:tritave]]
-[[category:edt]]