Xenharmonic Wiki

User:Moremajorthanmajor/38wtn: Difference between revisions

Newer edit →
VisualWikitext
Created page with "A '''38 tone well tempered nonet''' (38WTN) is related to well temperaments of 32edo and 33edo, but with a nonet rather than the 2/1 being constant. Its patent tunings..."
 
No edit summary
Line 1: Line 1:
A '''38 tone well tempered nonet''' (38WTN) is related to well temperaments of [[32edo]] and [[33edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings alternate [[EDF|division of the just perfect fifth]] into 19 equal parts (19EDF) with sequences of nineteen equal steps of 31.579 to 42.105cents each. This will create nineteen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.
A '''38 tone well tempered nonet''' (38WTN) is related to well temperaments of [[32edo]] and [[33edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings alternate [[EDF|division of the just perfect fifth]] into 19 equal parts (19EDF) with sequences of nineteen equal steps of 31.579 to 42.105 cents each. This will create nineteen 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" |36.945
! colspan="2" |36.945
|37.5
|36.364
|-
|-
!2
|2
! colspan="2" |73.89
! colspan="2" |73.89
|75.0
|72.727
|-
|-
!3
|3
! colspan="2" |110.835
! colspan="2" |110.835
|112.5
|109.091
|-
|-
!4
|4
! colspan="2" |147.78
! colspan="2" |147.78
|150.0
|145.4545
|-
|-
!5
|5
! colspan="2" |184.725
! colspan="2" |184.725
|187.5
|181.818
|-
|-
!6
|6
! colspan="2" |221.67
! colspan="2" |221.67
|225.0
|218.182
|-
|-
!7
|7
! colspan="2" |258.615
! colspan="2" |258.615
|262.5
|254.5455
|-
|-
!8
|8
! colspan="2" |295.56
! colspan="2" |295.56
|300.0
|290.909
|-
|-
!9
|9
! colspan="2" |332.505
! colspan="2" |332.505
|337.5
|327.273
|-
|-
!10
|10
! colspan="2" |369.45
! colspan="2" |369.45
|375.0
|363.636
|-
|-
!11
|11
! colspan="2" |406.395
! colspan="2" |406.395
|412.5
|400.000
|-
|-
!12
|12
! colspan="2" |443.34
! colspan="2" |443.34
|450.0
|436.364
|-
|-
!13
|13
! colspan="2" |480.285
! colspan="2" |480.285
|487.5
|472.727
|-
|-
!14
|14
! colspan="2" |517.23
! colspan="2" |517.23
|525.0
|509.091
|-
|-
!15
|15
! colspan="2" |554.175
! colspan="2" |554.175
|562.5
|545.4545
|-
|-
!16
|16
! colspan="2" |591.12
! colspan="2" |591.12
|600.0
|581.818
|-
|-
!17
|17
! colspan="2" |628.065
! colspan="2" |628.065
|637.5
|618.182
|-
|-
!18
|18
! colspan="2" |665.01
! colspan="2" |665.01
|675.0
|654.5455
|-
|-
!19
|19
! colspan="2" |701.955
! colspan="2" |701.955
|712.5
|690.909
|-
|-
|20
|20
|740.266
|740.266
|733.53
|733.53
|750.0
|727.273
|-
|-
|21
|21
|778.577
|778.577
|773.104
|773.104
|787.5
|763.636
|-
|-
|22
|22
|816.8885
|816.8885
|808.679
|808.679
|825.0
|800.000
|-
|-
|23
|23
|855.2
|855.2
|844.2535
|844.2535
|862.5
|836.364
|-
|-
|24
|24
|893.511
|893.511
|879.828
|879.828
|900.0
|872.727
|-
|-
|25
|25
|931.812
|931.812
|915.403.
|915.403.
|937.5
|909.091
|-
|-
|26
|26
|970.133
|970.133
|950.9775
|950.9775
|975.0
|945.4545
|-
|-
|27
|27
|1008.449
|1008.449
|986.552
|986.552
|1012.5
|981.818
|-
|-
|28
|28
|1046.755
|1046.755
|1022.127
|1022.127
|1050.0
|1018.182
|-
|-
|29
|29
|1085.0665
|1085.0665
|1057.701
|1057.701
|1087.5
|1054.5455
|-
|-
|30
|30
|1123.378
|1123.378
|1093.276
|1093.276
|1125.0
|1090.909
|-
|-
|31
|31
|1161.689
|1161.689
|1128.851
|1128.851
|1162.5
|1127.273
|-
|-
|32
|32
|1200
|1200
|1164.425
|1164.425
|1200
|1163.636
|-
|-
|33
|33
|1238.311
|1238.311
|1200
|1233.985
|1200
|1200
|-
|-
Line 124: Line 192:
|1276.622
|1276.622
|1235.575
|1235.575
|1267.97
|1240.782
|-
|-
|35
|35
|1314.9335
|1314.9335
|1271.149
|1271.149
|1301.995
|1281.564
|-
|-
|36
|36
|1353.245
|1353.245
|1036.724
|1036.724
|1335.94
|1322.346
|-
|-
|37
|37
|1391.556
|1391.556
|1342.2985
|1342.2985
|1369.925
|1363.128
|-
|-
|38
|38
|1429.877
|1429.877
|1377.873
|1377.873
! colspan="2" |1403.91
|}
|}
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/38wtn"