26ed5: Difference between revisions

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+== Scales ==
+=== 13ed5plus ===
+[[Category:14-tone scales]] Inspired by the [[elevenplus]] scale of [[22edo]], the '''13ed5plus scale''' is [[13ed5]] plus a step of 26ed5 in between two of its steps.
+In other words, 13ed5plus is all of the odd-numbered steps of 26ed5, plus step 26.
+This makes it a 14-tone scale.
+The scale is useful because it includes all of 26ed5’s [[consonance]]s while leaving out many of the less-used intervals. Making it practical to use on an instrument.
+{| class="wikitable mw-collapsible"
+|+
+The 13ed5plus scale
+! rowspan="2" |Step
+! rowspan="2" |Cents
+! colspan="7" |Just intonation approximation
+|-
+!60th-prime
+!68th-prime
+!88th-prime
+!90th-prime
+!112th-prime
+!Integer (5.6.12.22.32... as above)
+!Integer (simplified)
+|-
+!1
+!107.2
+|16/15
+|18/17
+|47/44
+|16/15
+|17/16
+|36/34, 34/32
+|18/17, 17/16
+|-
+!3
+!321.5
+|6/5
+|41/34
+|53/44
+|6/5
+|
+|6/5, 41/34
+|6/5, 41/34
+|-
+!5
+!535.8
+|41/30
+|
+|15/11
+|41/30
+|19/14
+|
+|
+|-
+!7
+!750.2
+|23/15
+|
+|17/11
+|23/15
+|
+|34/22
+|17/11
+|-
+!9
+!964.5
+|7/4
+|7/4
+|7/4
+|
+|7/4
+|56/32
+|7/4
+|-
+!11
+!1178.8
+|
+|67/34
+|
+|
+|
+|49/25
+|49/25
+|-
+!13
+!1393.2
+|9/4
+|9/4
+|9/4
+|
+|9/4
+|
+|
+|-
+!15
+!1607.5
+|38/15
+|43/17
+|28/11
+|38/15
+|
+|56/22
+|28/11
+|-
+!17
+!1821.8
+|43/15
+|
+|63/22
+|43/15
+|20/7
+|63/22
+|63/22
+|-
+!19
+!2036.2
+|13/4
+|13/4
+|13/4
+|
+|13/4
+|
+|
+|-
+!21
+!2250.5
+|11/3
+|
+|
+|11/3
+|
+|22/6
+|11/3
+|-
+!23
+!2464.8
+|25/6
+|
+|
+|25/6
+|29/7
+|25/6
+|25/6
+|-
+!25
+!2679.1
+|47/10
+|80/17
+|
+|47/10
+|33/7
+|
+|
+|-
+!26
+!2786.3
+|5/1
+|5/1
+|5/1
+|5/1
+|5/1
+|5/1
+|5/1
+|}