User:Moremajorthanmajor/18wtn: Difference between revisions

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'''18WTN''' is the non-octave well temperament with patent tunings where [[EDF|equal division of the just perfect fifth]] into nine parts of 77.995 cents each (9ED3/2) alternates with sequences of nine equal steps of 66.667 to 88.889 cents each. This will create nine equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.
'''18WTN''' is optimally the non-octave well temperament with patent tunings where [[EDF|equal division of the just perfect fifth]] into nine parts of 77.995 cents each (9ED3/2) alternates with sequences of nine equal steps of 66.667 to 88.889 cents each. This will create nine equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth. It also has the peculiar property of being a patent wtn related to equal divisions of nonets of two different integer cent sizes.


== Optimal Intervals ==
== Patent Intervals ==
{| class="wikitable"
{| class="wikitable"
!
!
!Minimum a
!Target a
!Maximum a
!Target b
![3\5 83.0075¢]
!Alternating [[EDO|edo]] and *ed(9/8) a
!Minimum b
!Alternating edo and *ed(9/8) b
!Maximum b
|-
|-
| |1
| |1
! colspan="5" |77.995
! colspan="2" |77.995
|80
|75
|-
|-
| |2
| |2
! colspan="5" |155.99
! colspan="2" |155.99
|160
|150
|-
|-
| |3
| |3
! colspan="5" |233.985
! colspan="2" |233.985
|240
|225
|-
|-
| |4
| |4
! colspan="5" |311.98
! colspan="2" |311.98
|320
|300
|-
|-
| |5
| |5
! colspan="5" |389.975
! colspan="2" |389.975
|400
|375
|-
|-
| |6
| |6
! colspan="5" |467.97
! colspan="2" |467.97
|480
|450
|-
|-
| |7
| |7
! colspan="5" |545.965
! colspan="2" |545.965
|560
|525
|-
|-
| |8
| |8
! colspan="5" |623.96
! colspan="2" |623.96
|640
|600
|-
|-
| |9
| |9
! colspan="5" |701.955
! colspan="2" |701.955
|720
|675
|-
|-
| |10
| |10
|781.955
|787.669
|784.9625
|784.9625
|770.526
|773.104
|775.424
|800
|750
|-
|-
| |11
| |11
|861.955
|873.384
|867.97
|867.97
|839.098
|844.253
|848.893
|880
|825
|-
|-
| |12
| |12
|941.955
|959.098
|950.9775
|950.9775
|907.669
|915.403
|921.363
|960
|900
|-
|-
| |13
| |13
|1021.955
|1044.812
|1033.985
|1033.985
|976.241
|986.552
|995.833
|1040
|975
|-
|-
| |14
| |14
|1101.955
|1130.526
|1116.9925
|1116.9925
|1044.812
|1057.701
|1069.302
|1120
|1050
|-
|-
| |15
| |15
|1181.955
|1216.241
|1200
|1200
|1113.384
|1128.896
|1142.771
|1200
|1125
|-
|-
| |16
| |16
|1261.955
|1283.0075
|1301.955
|1200
|1273.985
|1267.97
|1181.955
|1200
|1216.241
|-
|-
| |17
| |17
|1341.955
|1366.015
|1387.669
|1262.2556
|1347.97
|1333.94
|1250.526
|1301.955
|1289.71
|-
|-
| |18
| |18
|1421.955
|1449.0225
|1473.384
|1324.511
|1421.955
! colspan="2" |1403.91
|1319.098
|1363.2245
|}
|}


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! colspan="4" |701.955
! colspan="4" |701.955
|}
|}
[[Category:Well tempered nonet]]

Latest revision as of 09:30, 1 September 2025

18WTN is optimally the non-octave well temperament with patent tunings where equal division of the just perfect fifth into nine parts of 77.995 cents each (9ED3/2) alternates with sequences of nine equal steps of 66.667 to 88.889 cents each. This will create nine equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth. It also has the peculiar property of being a patent wtn related to equal divisions of nonets of two different integer cent sizes.

Patent Intervals

Target a Target b Alternating edo and *ed(9/8) a Alternating edo and *ed(9/8) b
1 77.995 80 75
2 155.99 160 150
3 233.985 240 225
4 311.98 320 300
5 389.975 400 375
6 467.97 480 450
7 545.965 560 525
8 623.96 640 600
9 701.955 720 675
10 784.9625 773.104 800 750
11 867.97 844.253 880 825
12 950.9775 915.403 960 900
13 1033.985 986.552 1040 975
14 1116.9925 1057.701 1120 1050
15 1200 1128.896 1200 1125
16 1283.0075 1200 1267.97 1200
17 1366.015 1262.2556 1333.94 1301.955
18 1449.0225 1324.511 1403.91

Valentine Tunings

fifth 2 = 9\16 fifth 2 = 18\31 fifth 2 = Carlos Alpha fifth 2 = 3\5
1 77.995
2 155.99
3 233.985
4 311.98
5 389.975
6 467.97
7 545.965
8 623.96
9 701.955
10 776.955 779.374 779.92 781.955
11 851.955 856.794 857.885 861.955
12 925.955 934.213 935.85 941.955
13 1001.955 1011.632 1013.815 1021.955
14 1076.955 1089.051 1091.78 1101.955
15 1151.955 1166.471 1169.745 1181.955
16 1226.955 1243.8905 1247.71 1261.955
17 1301.955 1321.31 1325.675 1341.955
18 1376.955 1398.729 1403.64 1421.955
Fifths
1 698.96 701.379 701.925 703.96
2 695.965 700.803 701.895 705.965
3 692.97 700.228 701.865 707.97
4 689.975 699.652 701.835 709.975
5 686.98 699.077 701.805 711.98
6 683.985 698.501 701.775 713.985
7 680.99 697.9255 701.745 715.99
8 677.995 697.35 701.715 717.995
9 675 696.774 701.685 720
10 677.995 697.35 701.715 717.995
11 680.99 697.9255 701.745 715.99
12 683.985 698.501 701.775 713.985
13 686.98 699.077 701.805 711.98
14 689.975 699.652 701.835 709.975
15 692.97 700.228 701.865 707.97
16 695.965 700.803 701.895 705.965
17 698.96 701.379 701.925 703.96
18 701.955
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