18edt: Difference between revisions

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~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~

~~This~~ is ~~an imported revision from Wikispaces. The revision metadata is included below for reference: ~~

'''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.

~~: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-09-12 00:42:04 UTC</tt>. ~~

~~: The original revision id was <tt>591641538</tt>. ~~

~~: The revision comment was: <tt></tt> ~~

~~The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it. ~~

~~<h4>Original Wikitext content:</h4>~~

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">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.~~~~

~~~~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.

~~~~0: 1/1~~~~

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.

~~~~1: 105.664 ~~cents~~ 16/15~~~~

== Intervals ==

~~~~2: 211.328 ~~cents~~ 9/8~~~~

{| class="wikitable"

3: 316.993 ~~cents~~ 6/5

! Step

~~~~4: 422.657 ~~cents~~ 9/7~~~~

! Cents

5: 528.321 ~~cents~~ 27/20

! Hekts

~~~~6: 633.985 ~~cents~~ 13/9~~~~

! Approximated interval

7: 739.649 ~~cents~~ 17/13

! [[Electra]] notation (J = 1/1)

~~~~8: 845.313 ~~cents~~ 5/3~~~~

|-

9: 950.~~9775 cents~~ 19/11

! colspan="3" | 0

~~~~10: 1056.642 ~~cents~~ 9/5~~~~

| 1/1

11: 1162.306 ~~cents~~ 49/25

| J

~~~~12: 1267.~~970 cents~~ 27/13~~~~

|-

13: 1373.634 ~~cents~~ 20/9

| 1

~~~~14: 1479.298 ~~cents~~ 7/3~~~~

| 105.664

15: 1584.963 ~~cents~~ 5/2

|72.222

~~~~16: 1690.627 ~~cents~~ 8/3~~~~

| 16/15

17: 1806.~~2905 cents~~ 45/16

| J#, Kbb

~~~~18: 3/1~~</pre></div>~~

|-

~~<h4>Original HTML content:</h4>~~

| 2

~~<div style~~=~~"width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style~~=~~"margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class~~=~~"old-revision-html"><html><head><title>18edt</title></head><body>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. 

| 211.328

~~ ~~

|144.444

~~As the double of <a class="wiki_link" href~~="/9edt" target="_blank">9edt</a>, it is the analog of 14edo insofar as it has a doubled harmonic chain. However, it, like <a class="wiki_link" href="/8edt" target="_blank">8edt</a>, 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. ~~

| 9/8

~~ ~~

| Jx, Kb

~~0: 1/1 ~~

|-

~~~~1~~: 105.664 cents 16/15 ~~

| 3

~~2: 211.328 cents 9/8 ~~

| 316.993

~~3: 316.993 cents 6/5 ~~

|216.667

~~4: 422.657 cents 9/7 ~~

| 6/5

~~5: 528.321 cents 27/20 ~~

| K

~~6: 633.985 cents 13/9 ~~

|-

~~7: 739.649 cents 17/13 ~~

| 4

~~8: 845.313 cents 5/~~3~~ ~~

| 422.657

~~9: 950.9775 cents 19/11 ~~

|288.889

~~10: 1056.642 cents 9/5 ~~

| 9/7

~~11: 1162.306 cents 49/25 ~~

| K#, Lb

~~~~12~~: 1267.970 cents 27/13 ~~

|-

~~13: 1373.634 cents 20/9 ~~

| 5

~~14: 1479.298 cents 7/3 ~~

| 528.321

~~15: 1584.963 cents 5/2 ~~

|361.111

~~16: 1690.627 cents 8/3 ~~

| 27/20

17: ~~1806.2905 cents 45/16 ~~

| L

~~18: 3/1</body></html></pre></div>~~

|-

| 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

|}

== 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]]

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+{{Infobox ET}}
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
+'''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.
-: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-09-12 00:42:04 UTC</tt>.<br>
-: The original revision id was <tt>591641538</tt>.<br>
-: The revision comment was: <tt></tt><br>
-The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
-<h4>Original Wikitext content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">18edt means the division of the tritave into 18 equal parts &lt;span style="background-color: rgba(255,255,255,0);"&gt;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.&lt;/span&gt;
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;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.&lt;/span&gt;
+== 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.
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;0: 1/1&lt;/span&gt;
+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.
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;1: 105.664 cents 16/15&lt;/span&gt;
+== Intervals ==
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;2: 211.328 cents 9/8&lt;/span&gt;
+{| class="wikitable"
-: 316.993 cents 6/5
+! Step
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;4: 422.657 cents 9/7&lt;/span&gt;
+! Cents
-: 528.321 cents 27/20
+! Hekts
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;6: 633.985 cents 13/9&lt;/span&gt;
+! Approximated interval
-: 739.649 cents 17/13
+! [[Electra]] notation (J = 1/1)
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;8: 845.313 cents 5/3&lt;/span&gt;
+|-
-: 950.9775 cents 19/11
+! colspan="3" | 0
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;10: 1056.642 cents 9/5&lt;/span&gt;
+| 1/1
-: 1162.306 cents 49/25
+| J
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;12: 1267.970 cents 27/13&lt;/span&gt;
+|-
-: 1373.634 cents 20/9
+| 1
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;14: 1479.298 cents 7/3&lt;/span&gt;
+| 105.664
-: 1584.963 cents 5/2
+|72.222
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;16: 1690.627 cents 8/3&lt;/span&gt;
+| 16/15
-: 1806.2905 cents 45/16
+| J#, Kbb
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;18: 3/1&lt;/span&gt;</pre></div>
+|-
-<h4>Original HTML content:</h4>
+| 2
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;18edt&lt;/title&gt;&lt;/head&gt;&lt;body&gt;18edt means the division of the tritave into 18 equal parts &lt;span style="background-color: rgba(255,255,255,0);"&gt;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.&lt;/span&gt;&lt;br /&gt;
+| 211.328
-&lt;br /&gt;
+|144.444
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;As the double of &lt;a class="wiki_link" href="/9edt" target="_blank"&gt;9edt&lt;/a&gt;, it is the analog of 14edo insofar as it has a doubled harmonic chain. However, it, like &lt;a class="wiki_link" href="/8edt" target="_blank"&gt;8edt&lt;/a&gt;, 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.&lt;/span&gt;&lt;br /&gt;
+| 9/8
-&lt;br /&gt;
+| Jx, Kb
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;0: 1/1&lt;/span&gt;&lt;br /&gt;
+|-
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;1: 105.664 cents 16/15&lt;/span&gt;&lt;br /&gt;
+| 3
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;2: 211.328 cents 9/8&lt;/span&gt;&lt;br /&gt;
+| 316.993
-: 316.993 cents 6/5&lt;br /&gt;
+|216.667
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;4: 422.657 cents 9/7&lt;/span&gt;&lt;br /&gt;
+| 6/5
-: 528.321 cents 27/20&lt;br /&gt;
+| K
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;6: 633.985 cents 13/9&lt;/span&gt;&lt;br /&gt;
+|-
-: 739.649 cents 17/13&lt;br /&gt;
+| 4
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;8: 845.313 cents 5/3&lt;/span&gt;&lt;br /&gt;
+| 422.657
-: 950.9775 cents 19/11&lt;br /&gt;
+|288.889
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;10: 1056.642 cents 9/5&lt;/span&gt;&lt;br /&gt;
+| 9/7
-: 1162.306 cents 49/25&lt;br /&gt;
+| K#, Lb
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;12: 1267.970 cents 27/13&lt;/span&gt;&lt;br /&gt;
+|-
-: 1373.634 cents 20/9&lt;br /&gt;
+| 5
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;14: 1479.298 cents 7/3&lt;/span&gt;&lt;br /&gt;
+| 528.321
-: 1584.963 cents 5/2&lt;br /&gt;
+|361.111
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;16: 1690.627 cents 8/3&lt;/span&gt;&lt;br /&gt;
+| 27/20
-: 1806.2905 cents 45/16&lt;br /&gt;
+| L
-&lt;span style="background-color: rgba(255,255,255,0);"&gt;18: 3/1&lt;/span&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
+|-
+| 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
+|}
+== 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]]