10ed5: Difference between revisions

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 {{Infobox ET}}
-Half of [[20ed5|20ed5]]. But it has important characteristics of its own:
+In general, 10ed5 is simply a smashing tuning. The relatively large 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.
-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.
+It is especially important as a structural framework for the [[5.7.11.13 subgroup]].
-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|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 relates this tuning to [[43edo]], which divides the step in ten.
 == Harmonics ==
@@ Line 24: / Line 20: @@
 == 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
+|}
-: 1/1
+== Subsets and supersets ==
+Half of [[20ed5]].
-: 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
-: 1950.420 cents
-: 2229.051 cents "17/5"
-: 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
+Adding octaves relates this tuning to 13edo, which divides the step in three, although the octaves are 7 cents sharp. If octaves are instead made just, everything else (especially prime 7) becomes flatter. Alternatively, the step can be divided in 10 to get 43edo.
 == Music ==