46edo: Difference between revisions

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@@ Line 504: / Line 504: @@
 For a more complete list, see [[Ups and Downs Notation#Chords and Chord Progressions|Ups and Downs Notation - Chords and Chord Progressions]].
-=== Selected just intervals by error ===
+== Just approximation ==
+=== Selected just intervals ===
 {| class="wikitable center-all"
 ! colspan="2" |
@@ Line 551: / Line 553: @@
 | +6
 |}
-The following table shows how [[Just-24|some prominent just intervals]] are represented in 46edo. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italic''.
+The following table shows how [[15-odd-limit intervals]] are represented in 46edo. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italic''.
 {| class="wikitable center-all"
+|+Direct mapping (even if inconsistent)
 |-
 ! Interval, complement
@@ Line 630: / Line 633: @@
 | ''12.958''
 |}
+=== Temperament measures ===
+The following table shows [[TE temperament measures]] (RMS normalized by the rank) of 46et.
+{| class="wikitable center-all"
+! colspan="2" |
+! 3-limit
+! 5-limit
+! 7-limit
+! 11-limit
+! 13-limit
+! 17-limit
+! 23-limit no-19
+|-
+! colspan="2" |Octave stretch (¢)
+| -0.755
+| -1.219
+| -0.595
+| -0.274
+| +0.030
+| +0.047
+| +0.101
+|-
+! rowspan="2" |Error
+! absolute (¢)
+| 0.75
+| 0.90
+| 1.34
+| 1.36
+| 1.41
+| 1.31
+| 1.23
+|-
+! relative (%)
+| 2.89
+| 3.45
+| 5.12
+| 5.20
+| 5.42
+| 5.02
+| 4.72
+|}
+* 46et has a lower relative error than any previous ETs in the 17-, 19-, 23-limit, and others. The next ET that does better in the aforementioned subgroups is 72, 72, 94, respectively.
+* 46et is prominent in the no-19 23-limit. The next ET that does better in this subgroup is 140.
 == Linear temperaments ==