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.


== Optimal Intervals ==
== 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
|}
|}