18edt: Difference between revisions
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18edt | {{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. | |||
18edt 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" | {| class="wikitable" | ||
! | ! Step | ||
! | ! Cents | ||
! | ! Hekts | ||
! | ! Approximated interval | ||
! [[Electra]] notation (J = 1/1) | |||
|- | |- | ||
! colspan="3" | 0 | |||
| 1/1 | | 1/1 | ||
| J | |||
|- | |- | ||
| 1 | | 1 | ||
| Line 16: | Line 22: | ||
|72.222 | |72.222 | ||
| 16/15 | | 16/15 | ||
| J#, Kbb | |||
|- | |- | ||
| 2 | | 2 | ||
| Line 21: | Line 28: | ||
|144.444 | |144.444 | ||
| 9/8 | | 9/8 | ||
| Jx, Kb | |||
|- | |- | ||
| 3 | | 3 | ||
| Line 26: | Line 34: | ||
|216.667 | |216.667 | ||
| 6/5 | | 6/5 | ||
| K | |||
|- | |- | ||
| 4 | | 4 | ||
| Line 31: | Line 40: | ||
|288.889 | |288.889 | ||
| 9/7 | | 9/7 | ||
| K#, Lb | |||
|- | |- | ||
| 5 | | 5 | ||
| Line 36: | Line 46: | ||
|361.111 | |361.111 | ||
| 27/20 | | 27/20 | ||
| L | |||
|- | |- | ||
| 6 | | 6 | ||
| Line 41: | Line 52: | ||
|433.333 | |433.333 | ||
| 13/9 | | 13/9 | ||
| L#, Mbb | |||
|- | |- | ||
| 7 | | 7 | ||
| Line 46: | Line 58: | ||
|505.556 | |505.556 | ||
| 17/13 | | 17/13 | ||
| Lx, Mb | |||
|- | |- | ||
| 8 | | 8 | ||
| Line 51: | Line 64: | ||
|577.778 | |577.778 | ||
| 5/3 | | 5/3 | ||
| M | |||
|- | |- | ||
| 9 | | 9 | ||
| Line 56: | Line 70: | ||
|650 | |650 | ||
| 19/11 | | 19/11 | ||
| M#, Nbb | |||
|- | |- | ||
| 10 | | 10 | ||
| Line 61: | Line 76: | ||
|722.222 | |722.222 | ||
| 9/5 | | 9/5 | ||
| Mx, Nb | |||
|- | |- | ||
| 11 | | 11 | ||
| Line 66: | Line 82: | ||
|794.444 | |794.444 | ||
| 49/25 | | 49/25 | ||
| N | |||
|- | |- | ||
| 12 | | 12 | ||
| Line 71: | Line 88: | ||
|866.667 | |866.667 | ||
| 27/13 | | 27/13 | ||
| N#, Ob | |||
|- | |- | ||
| 13 | | 13 | ||
| Line 76: | Line 94: | ||
|938.889 | |938.889 | ||
| 20/9 | | 20/9 | ||
| O | |||
|- | |- | ||
| 14 | | 14 | ||
| Line 81: | Line 100: | ||
|1011.111 | |1011.111 | ||
| 7/3 | | 7/3 | ||
| O#, Pbb | |||
|- | |- | ||
| 15 | | 15 | ||
| Line 86: | Line 106: | ||
|1083.333 | |1083.333 | ||
| 5/2 | | 5/2 | ||
| Ox, Pb | |||
|- | |- | ||
| 16 | | 16 | ||
| Line 91: | Line 112: | ||
|1155.556 | |1155.556 | ||
| 8/3 | | 8/3 | ||
| P | |||
|- | |- | ||
| 17 | | 17 | ||
| Line 96: | Line 118: | ||
|1227.778 | |1227.778 | ||
| 45/16 | | 45/16 | ||
| P#, Jb | |||
|- | |- | ||
| 18 | | 18 | ||
| Line 101: | Line 124: | ||
|1300 | |1300 | ||
| 3/1 | | 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:macrotonal]] | ||
[[category:tritave]] | [[category:tritave]] | ||