18edt: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
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.
'''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 it's approximation to [[13/11] is very sharp being closer to [[6/5]].
== Intervals ==
{| class="wikitable"
{| class="wikitable"
! step
! Step
! cents
! Cents
!hekts
! Hekts
! approximated interval
! Approximated interval
! [[Electra]] notation (J = 1/1)
|-
|-
! colspan="3" | 0
! colspan="3" | 0
| 1/1
| 1/1
| [[1/1]]
| J
|-
|-
| 1
| 1
Line 17: Line 23:
|72.222
|72.222
| 16/15
| 16/15
| J#, Kbb
|-
|-
| 2
| 2
Line 22: Line 29:
|144.444
|144.444
| 9/8
| 9/8
| Jx, Kb
|-
|-
| 3
| 3
Line 27: Line 35:
|216.667
|216.667
| 6/5
| 6/5
| K
|-
|-
| 4
| 4
Line 32: Line 41:
|288.889
|288.889
| 9/7
| 9/7
| K#, Lb
|-
|-
| 5
| 5
Line 37: Line 47:
|361.111
|361.111
| 27/20
| 27/20
| L
|-
|-
| 6
| 6
Line 42: Line 53:
|433.333
|433.333
| 13/9
| 13/9
| L#, Mbb
|-
|-
| 7
| 7
Line 47: Line 59:
|505.556
|505.556
| 17/13
| 17/13
| Lx, Mb
|-
|-
| 8
| 8
Line 52: Line 65:
|577.778
|577.778
| 5/3
| 5/3
| M
|-
|-
| 9
| 9
Line 57: Line 71:
|650
|650
| 19/11
| 19/11
| M#, Nbb
|-
|-
| 10
| 10
Line 62: Line 77:
|722.222
|722.222
| 9/5
| 9/5
| Mx, Nb
|-
|-
| 11
| 11
Line 67: Line 83:
|794.444
|794.444
| 49/25
| 49/25
| N
|-
|-
| 12
| 12
Line 72: Line 89:
|866.667
|866.667
| 27/13
| 27/13
| N#, Ob
|-
|-
| 13
| 13
Line 77: Line 95:
|938.889
|938.889
| 20/9
| 20/9
| O
|-
|-
| 14
| 14
Line 82: Line 101:
|1011.111
|1011.111
| 7/3
| 7/3
| O#, Pbb
|-
|-
| 15
| 15
Line 87: Line 107:
|1083.333
|1083.333
| 5/2
| 5/2
| Ox, Pb
|-
|-
| 16
| 16
Line 92: Line 113:
|1155.556
|1155.556
| 8/3
| 8/3
| P
|-
|-
| 17
| 17
Line 97: Line 119:
|1227.778
|1227.778
| 45/16
| 45/16
| P#, Jb
|-
|-
| 18
| 18
Line 102: Line 125:
|1300
|1300
| 3/1
| 3/1
| J
|}
|}


Revision as of 02:28, 5 March 2023

← 17edt 18edt 19edt →
Prime factorization 2 × 32
Step size 105.664 ¢ 
Octave 11\18edt (1162.31 ¢)
Consistency limit 3
Distinct consistency limit 3

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.

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 it's approximation to [[13/11] is very sharp being closer to 6/5.

Intervals

Step Cents Hekts Approximated interval Electra notation (J = 1/1)
0 1/1 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
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