Xenharmonic Wiki

18edt: Difference between revisions

← Older edit
VisualWikitext
Wikispaces>FREEZE
No edit summary
Fredg999 category edits (talk | contribs)
autopatrolled, Bots
4,330 edits
m Removing from Category:Edt using Cat-a-lot
 
(12 intermediate revisions by 6 users not shown)
Line 1: Line 1:
18edt 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>
{{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.


<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>
== 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.


<span style="background-color: rgba(255,255,255,0);">0: 1/1</span>
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"
! Step
! Cents
! Hekts
! Approximated interval
! [[Electra]] notation (J = 1/1)
|-
! colspan="3" | 0
| 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
| 1267.97
|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
|}


<span style="background-color: rgba(255,255,255,0);">1: 105.664 cents 16/15</span>
== 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
}}


<span style="background-color: rgba(255,255,255,0);">2: 211.328 cents 9/8</span>
[[category:macrotonal]]
 
[[category:tritave]]
3: 316.993 cents 6/5
 
<span style="background-color: rgba(255,255,255,0);">4: 422.657 cents 9/7</span>
 
5: 528.321 cents 27/20
 
<span style="background-color: rgba(255,255,255,0);">6: 633.985 cents 13/9</span>
 
7: 739.649 cents 17/13
 
<span style="background-color: rgba(255,255,255,0);">8: 845.313 cents 5/3</span>
 
9: 950.9775 cents 19/11
 
<span style="background-color: rgba(255,255,255,0);">10: 1056.642 cents 9/5</span>
 
11: 1162.306 cents 49/25
 
<span style="background-color: rgba(255,255,255,0);">12: 1267.970 cents 27/13</span>
 
13: 1373.634 cents 20/9
 
<span style="background-color: rgba(255,255,255,0);">14: 1479.298 cents 7/3</span>
 
15: 1584.963 cents 5/2
 
<span style="background-color: rgba(255,255,255,0);">16: 1690.627 cents 8/3</span>
 
17: 1806.2905 cents 45/16
 
<span style="background-color: rgba(255,255,255,0);">18: 3/1</span>
Retrieved from "https://en.xen.wiki/w/18edt"