10ed5: Difference between revisions

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 {{Infobox ET}}
-Half of [[20ed5|20ed5]] (obviously). But it has important characteristics of its own:
 In general, 10ed5 is simply a smashing tuning. The relatively large small steps, about the size of a minor third or an orwell generator, actually work for melodies, and it's harmonies while strange have no lack of impact. It can be used such that the fifth harmonic is equivalent, but of course, doesn't have to.
-As 5ed5 is the simplest [[Hyperpyth|hyperpyth]] tuning, analogous to [[5edo|5edo]] and [[4edt|4edt]] in their own spheres, this, its double, can be compared, structurally, to, [[10edo|10edo]]. While its approximations of 9/5, 17/5 and 21/5 are quite far off, these are still categorically important intervals.
+It is especially important as a structural framework for the [[5.7.11.13 subgroup]].
-Adding octaves, strangely enough, relates this tuning to [[43edo]].
-: 1/1
-: 278.631 cents 13/11
-: 557.263 cents 7/5
-: 835.894 cents
-: 1114.525 cents "9/5"
-: 1393.157 cents 11/5
-: 1671.788 cents 13/5
+== Harmonics ==
+{{Harmonics in equal
+| steps = 10
+| num = 5
+| denom = 1
+}}
+{{Harmonics in equal
+| steps = 10
+| num = 5
+| denom = 1
+| start = 12
+| collapsed = 1
+}}
-: 1950.420 cents
+== Intervals ==
+{| class="wikitable"
+|+
+!Degree
+!Cents
+!5.7.11.13 intervals
+|-
+|0
+|0.000
+|1/1
+|-
+|1
+|278.631
+|13/11, 55/49
+|-
+|2
+|557.263
+|7/5
+|-
+|3
+|835.894
+|11/7
+|-
+|4
+|1114.525
+|13/7, 25/13
+|-
+|5
+|1393.157
+|11/5, 25/11
+|-
+|6
+|1671.788
+|13/5, 35/13
+|-
+|7
+|1950.420
+|35/11
+|-
+|8
+|2229.051
+|49/13
+|-
+|9
+|2507.682
+|49/11
+|-
+|10
+|2786.314
+|5/1
+|}
-: 2229.051 cents "17/5"
+== Subsets and supersets ==
+Half of [[20ed5]].
-: 2507.682 cents 21/5
+As 5ed5 is the simplest [[hyperpyth]] tuning (analogous to [[5edo]] and [[4edt]] in their own spheres) this, its double, can be compared structurally to [[10edo]]. While its approximations of 9/5, 17/5 and 21/5 are quite far off, these are still categorically important intervals.
-: 5/1
+Octaves can be added by dividing the step in three to get [[13edo]] with octaves 7 cents sharp. If octaves are instead made just, prime 7 becomes very flat, as well as prime 5 to a lesser extent. Alternatively, the step can be divided in ten to get [[43edo]].
-Music:
+== Music ==
 [http://www.youtube.com/watch?v=tjD7Es05zuI Weird Blues] -- Kosmorsky
 [[Category:5th_harmonic]]
-[[Category:ed5]]
-[[Category:edonoi]]