User:Moremajorthanmajor/36wtn: Difference between revisions
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A '''36 tone well tempered nonet''' (36WTN) is related to well temperaments of [[30edo]] and [[31edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF|division of the just perfect fifth]] into 18 equal parts (18EDF) with sequences of eighteen equal steps of 33.3333 to 44.4444 cents each. This will create eighteen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth. | A '''36 tone well tempered nonet''' (36WTN) is related to well temperaments of [[30edo]] and [[31edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF|division of the just perfect fifth]] into 18 equal parts (18EDF) with sequences of eighteen equal steps of 33.3333 to 44.4444 cents each. This will create eighteen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth. | ||
== | == Patent Intervals == | ||
{| class="wikitable" | {| class="wikitable" | ||
|+ | |+ | ||
| Line 7: | Line 7: | ||
!Target a | !Target a | ||
!Target b | !Target b | ||
!Alternating [[edo]] and *ed(9/8) a | |||
!Alternating edo and *ed(9/8) b | |||
|- | |- | ||
!1 | !1 | ||
! colspan="2" |38.9975 | ! colspan="2" |38.9975 | ||
|40 | |||
|38.71 | |||
|- | |- | ||
!2 | !2 | ||
! colspan="2" |77.995 | ! colspan="2" |77.995 | ||
|80 | |||
|77.419 | |||
|- | |- | ||
!3 | !3 | ||
! colspan="2" |116.9925 | ! colspan="2" |116.9925 | ||
|120 | |||
|116.129 | |||
|- | |- | ||
!4 | !4 | ||
! colspan="2" |155.99 | ! colspan="2" |155.99 | ||
|160 | |||
|154.839 | |||
|- | |- | ||
!5 | !5 | ||
! colspan="2" |194.9875 | ! colspan="2" |194.9875 | ||
|200 | |||
|193.548 | |||
|- | |- | ||
!6 | !6 | ||
! colspan="2" |233.985 | ! colspan="2" |233.985 | ||
|240 | |||
|232.258 | |||
|- | |- | ||
!7 | !7 | ||
! colspan="2" |272.9825 | ! colspan="2" |272.9825 | ||
|280 | |||
|270.968 | |||
|- | |- | ||
!8 | !8 | ||
! colspan="2" |311.98 | ! colspan="2" |311.98 | ||
|320 | |||
|309.677 | |||
|- | |- | ||
!9 | !9 | ||
! colspan="2" |350.9775 | ! colspan="2" |350.9775 | ||
|360 | |||
|348.387 | |||
|- | |- | ||
!10 | !10 | ||
! colspan="2" |389.975 | ! colspan="2" |389.975 | ||
|400 | |||
|387.097 | |||
|- | |- | ||
!11 | !11 | ||
! colspan="2" |428.9725 | ! colspan="2" |428.9725 | ||
|440 | |||
|425.8065 | |||
|- | |- | ||
!12 | !12 | ||
! colspan="2" |467.97 | ! colspan="2" |467.97 | ||
|480 | |||
|464.516 | |||
|- | |- | ||
!13 | !13 | ||
! colspan="2" |506.9675 | ! colspan="2" |506.9675 | ||
|520 | |||
|503.226 | |||
|- | |- | ||
!14 | !14 | ||
! colspan="2" |545.965 | ! colspan="2" |545.965 | ||
|560 | |||
|541.9355 | |||
|- | |- | ||
!15 | !15 | ||
! colspan="2" |584.9625 | ! colspan="2" |584.9625 | ||
|600 | |||
|580.645 | |||
|- | |- | ||
!16 | !16 | ||
! colspan="2" |623.96 | ! colspan="2" |623.96 | ||
|640 | |||
|619.355 | |||
|- | |- | ||
!17 | !17 | ||
! colspan="2" |662.9575 | ! colspan="2" |662.9575 | ||
|680 | |||
|658.0645 | |||
|- | |- | ||
!18 | !18 | ||
! colspan="2" |701.955 | ! colspan="2" |701.955 | ||
|720 | |||
|696.764 | |||
|- | |- | ||
|19 | |19 | ||
|743.45875 | |743.45875 | ||
|740.26615 | |740.26615 | ||
|760 | |||
|735.484 | |||
|- | |- | ||
|20 | |20 | ||
|784.9625 | |784.9625 | ||
|778.5773 | |778.5773 | ||
|800 | |||
|774.1935 | |||
|- | |- | ||
|21 | |21 | ||
|826.46625 | |826.46625 | ||
|816.8885 | |816.8885 | ||
|840 | |||
|812.903 | |||
|- | |- | ||
|22 | |22 | ||
|867.97 | |867.97 | ||
|855.1996 | |855.1996 | ||
|880 | |||
|851.613 | |||
|- | |- | ||
|23 | |23 | ||
|909.47375 | |909.47375 | ||
|893.5108 | |893.5108 | ||
|920 | |||
|890.323 | |||
|- | |- | ||
|24 | |24 | ||
|950.9775 | |950.9775 | ||
|931.8119 | |931.8119 | ||
|960 | |||
|929.032 | |||
|- | |- | ||
|25 | |25 | ||
|993.48125 | |993.48125 | ||
|970.1331 | |970.1331 | ||
|1000 | |||
|967.742 | |||
|- | |- | ||
|26 | |26 | ||
|1033.985 | |1033.985 | ||
|1008.4492 | |1008.4492 | ||
|1040 | |||
|1006.452 | |||
|- | |- | ||
|27 | |27 | ||
|1075.48875 | |1075.48875 | ||
|1046.7554 | |1046.7554 | ||
|1080 | |||
|1045.161 | |||
|- | |- | ||
|28 | |28 | ||
|1116.9925 | |1116.9925 | ||
|1085.0665 | |1085.0665 | ||
|1120 | |||
|1083.871 | |||
|- | |- | ||
|29 | |29 | ||
|1158.49625 | |1158.49625 | ||
|1123.3777 | |1123.3777 | ||
|1160 | |||
|1122.581 | |||
|- | |- | ||
|30 | |30 | ||
|1200 | |1200 | ||
|1161.68885 | |1161.68885 | ||
|1200 | |||
|1161.29 | |||
|- | |- | ||
|31 | |31 | ||
|1241.50375 | |1241.50375 | ||
|1200 | |||
|1233.985 | |||
|1200 | |1200 | ||
|- | |- | ||
| Line 117: | Line 181: | ||
|1283.0075 | |1283.0075 | ||
|1238.31115 | |1238.31115 | ||
|1267.97 | |||
|1240.782 | |||
|- | |- | ||
|33 | |33 | ||
|1324.51125 | |1324.51125 | ||
|1276.6223 | |1276.6223 | ||
|1301.995 | |||
|1281.564 | |||
|- | |- | ||
|34 | |34 | ||
|1366.015 | |1366.015 | ||
|1314.9335 | |1314.9335 | ||
|1335.94 | |||
|1322.346 | |||
|- | |- | ||
|35 | |35 | ||
|1407.51875 | |1407.51875 | ||
|1353.2446 | |1353.2446 | ||
|1369.925 | |||
|1363.128 | |||
|- | |- | ||
|36 | |36 | ||
|1449.0225 | |1449.0225 | ||
|1391.5558 | |1391.5558 | ||
! colspan="2" |1403.91 | |||
|} | |} | ||