User:Moremajorthanmajor/38wtn: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
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
|}
|}

Revision as of 02:12, 4 June 2021

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 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.

Patent Intervals

Target a Target b Alternating edo and *ed(9/8) a Alternating edo and *ed(9/8) b
1 36.945 37.5 36.364
2 73.89 75.0 72.727
3 110.835 112.5 109.091
4 147.78 150.0 145.4545
5 184.725 187.5 181.818
6 221.67 225.0 218.182
7 258.615 262.5 254.5455
8 295.56 300.0 290.909
9 332.505 337.5 327.273
10 369.45 375.0 363.636
11 406.395 412.5 400.000
12 443.34 450.0 436.364
13 480.285 487.5 472.727
14 517.23 525.0 509.091
15 554.175 562.5 545.4545
16 591.12 600.0 581.818
17 628.065 637.5 618.182
18 665.01 675.0 654.5455
19 701.955 712.5 690.909
20 740.266 733.53 750.0 727.273
21 778.577 773.104 787.5 763.636
22 816.8885 808.679 825.0 800.000
23 855.2 844.2535 862.5 836.364
24 893.511 879.828 900.0 872.727
25 931.812 915.403. 937.5 909.091
26 970.133 950.9775 975.0 945.4545
27 1008.449 986.552 1012.5 981.818
28 1046.755 1022.127 1050.0 1018.182
29 1085.0665 1057.701 1087.5 1054.5455
30 1123.378 1093.276 1125.0 1090.909
31 1161.689 1128.851 1162.5 1127.273
32 1200 1164.425 1200 1163.636
33 1238.311 1200 1233.985 1200
34 1276.622 1235.575 1267.97 1240.782
35 1314.9335 1271.149 1301.995 1281.564
36 1353.245 1036.724 1335.94 1322.346
37 1391.556 1342.2985 1369.925 1363.128
38 1429.877 1377.873 1403.91
Retrieved from "https://en.xen.wiki/index.php?title=User:Moremajorthanmajor/38wtn&oldid=71811"