User:Moremajorthanmajor/12wtn: Difference between revisions

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'''12WTN''' is the [[EDF|equal division of the just perfect fifth]] into six parts of 116.9925 [[cent|cents]] each alternated with a sequence of six equal steps of another interval between 100 and 133.333 cents. Its best tunings are related to the [[Gamelismic clan|miracle temperament]], which tempers out 225/224 and 1029/1024 in the 7-limit.
'''12WTN''' is the [[EDF|equal division of the just perfect fifth]] into six parts of 116.9925 [[cent|cents]] each alternated with a sequence of six equal steps of another interval between 100 and 133.333 cents. Its best tunings are related to the [[Gamelismic clan|miracle temperament]], which tempers out 225/224 and 1029/1024 in the 7-limit.


== Intervals ==
== Optimal Intervals ==
{| class="wikitable"
{| class="wikitable"
|
|
!''“fifth” 2 = 600¢''
!Minimum a
!“nonet” = 1351.429¢
!Maximum a
!“nonet” = 1460¢
!Minimum b
!''“fifth” 2 = 800¢''
!Maximum b
|-
|-
!1
!1
Line 28: Line 28:
|-
|-
|7
|7
|''801.955''
|810.201
|828.296
|''835.328''
|-
|8
|''901.955''
|918.446
|954.637
|''968.662''
|-
|9
|''1001.955''
|1026.692
|1080.9775
|''1101.955''
|-
|10
|''1101.955''
|1134.937
|1207.318
|''1235.328''
|-
|11
|''1201.955''
|1243.183
|1333.695
|''1368.662''
|-
|12
|''1301.955''
|1351.429
|1460
|''1501.955''
|}
== Common Tunings ==
{| class="wikitable"
|+
!
!fifth 2 = 6\11
!fifth 2 = 3\5
|-
!1
! colspan="2" |116.9925
|-
!2
! colspan="2" |233.985
|-
!3
! colspan="2" |350.9775
|-
!4
! colspan="2" |467.97
|-
!5
! colspan="2" |584.9625
|-
!6
! colspan="2" |701.955
|-
|7
|811.046
|821.955
|821.955
|830.526
|797.955
|804.812
|-
|-
|8
|8
|920.137
|941.955
|941.955
|959.098
|893.955
|907.669
|-
|-
|9
|9
|1029.228
|1061.955
|1061.955
|1087.67
|989.955
|1010.526
|-
|-
|10
|10
|1138.319
|1181.955
|1181.955
|1216.241
|1085.955
|1113.384
|-
|-
|11
|11
|1247.4095
|1301.955
|1301.955
|1344.812
|1181.955
|1216.241
|-
|-
|12
|12
|1356.5005
|1421.955
|1421.955
|-
|1473.384
!
|1277.955
! colspan="2" |Fifths
|1319.098
|-
|1
|694.053
|704.9625
|-
|2
|686.152
|707.97
|-
|3
|678.25
|710.9775
|-
|4
|670.349
|713.985
|-
|5
|662.4705
|716.9925
|-
|6
|654.5455
|720
|-
|7
|662.4705
|716.9925
|-
|8
|670.349
|713.985
|-
|9
|678.25
|710.9775
|-
|10
|686.152
|707.97
|-
|11
|694.053
|704.9625
|-
!12
! colspan="2" |701.955
|}
|}

Revision as of 05:21, 30 May 2021

12WTN is the equal division of the just perfect fifth into six parts of 116.9925 cents each alternated with a sequence of six equal steps of another interval between 100 and 133.333 cents. Its best tunings are related to the miracle temperament, which tempers out 225/224 and 1029/1024 in the 7-limit.

Optimal Intervals

Minimum a Maximum a Minimum b Maximum b
1 116.9925
2 233.985
3 350.9775
4 467.97
5 584.9625
6 701.955
7 821.955 830.526 797.955 804.812
8 941.955 959.098 893.955 907.669
9 1061.955 1087.67 989.955 1010.526
10 1181.955 1216.241 1085.955 1113.384
11 1301.955 1344.812 1181.955 1216.241
12 1421.955 1473.384 1277.955 1319.098