2.3.7 subgroup: Difference between revisions

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 ==== Trienstonian ====
-{{Todo|expand|inline=1}}
+'''Trienstonian''' temperament tempers out 28/27 in the 2.3.7 subgroup, mapping 7/4 to +3 fifths, and equating 9/8 with 7/6 and 9/7 with 4/3. This temperament equates the outer intervals in each cluster of three intervals without setting the middle to them. Due to its inaccuracy, it can reasonably be considered an exotemperament, which in a pentatonic system can be considered an analog to [[mavila]].
+The [[DKW theory|DKW]] (2.3.7) optimum tuning states ~3/2 is tuned to 723.494c, and therefore ~8/7 to 229.517c; a chart of mistunings of simple intervals is below.
+{| class="wikitable center-1 center-2 center-3 center-4"
+|+ style="font-size: 105%;" | Trienstonian (1029/1024)
+|-
+! rowspan="2" | Interval !! rowspan="2" | Just tuning !! colspan="2" | Tunings*
+|-
+! Optimal tuning !! Deviation
+|-
+| 9/8 || 203.910 || 246.989 || +43.079
+|-
+| 8/7 || 231.174 || 229.517 || -1.868
+|-
+| 7/6 || 266.871 || 246.989 || -19.882
+|-
+| 9/7 || 435.084 || 476.506 || +41.422
+|-
+| 21/16 || 470.781 || 493.977 || +23.196
+|-
+| 4/3 || 498.045 || 476.506 || -21.539
+|-
+| '''3/2''' || 701.955 || '''723.494''' || +21.539
+|-
+| 32/21 || 729.219 || 706.023 || -23.196
+|-
+| 14/9 || 764.916 || 723.494 || -41.422
+|-
+| 12/7 || 933.129 || 953.011 || +19.882
+|-
+| 7/4 || 968.826 || 970.483 || +1.868
+|-
+| 16/9 || 996.090 || 953.011 || -43.079
+|}
+<nowiki>*</nowiki> In 2.3.7-targeted DKW tuning
 == Music ==