User:Moremajorthanmajor/16wtn

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16WTN is the equal division of the fifth into 8 steps of 87.7444 cents each, alternated with a sequence of eight equal steps of another interval between 75 and 100 cents making its best tunings very nearly 88cET. Its best tunings are related to the octacot temperament.

Intervals

The best tunings of 16WTN can be interpreted as tunings for the Natural and Harmonic Minor modes of Annapolis[6L 4s]. For the notation of these modes, Greek numerals 1-10 can be used (Α,Β,Γ,Δ,Ε,Ϛ/Ϝ,Ζ,Η,Θ,Ι [J]).

“fifth” 2 = 600¢ “nonet” = 1351.429¢ “nonet” = 1460¢ “fifth” 2 = 800¢
1 87.7444
2 175.48875
3 263.2331
4 350.9775
5 438.7219
6 526.46625
7 614.2106
8 701.955
9 776.955 783.1392 796.7106 801.955
10 851.955 864.3234 891.46625 901.955
11 925.955 945.5076 986.2219 1001.955
12 1001.955 1026.692 1080.9775 1101.955
13 1076.955 1107.876 1175.7331 1201.955
14 1151.955 1189.0602 1270.48875 1301.955
15 1225.955 1270.2444 1365.2444 1401.955
16 1301.955 1351.4286 1460 1501.955

Common Tunings

Fifth 2 = 4\7 step 2 = 88¢ Fifth 2 = 8\13 Annapolis[6L 4s]
1 87.7444 Α#
2 175.48875 Β
3 263.2331 Γ
4 350.9775 Γ#
5 438.7219 Δ
6 526.46625 Δ#
7 614.2106 Ε
8 701.955 Ϛ/Ϝ
9 787.6692 789.955 794.263 Ϛ#/Ϝ#
10 873.3835 877.955 886.57 Ζ
11 959.0979 965.955 978.878 Η
12 1044.8121 1053.955 1071.186 Η#
13 1130.5264 1141.955 1163.4935 Θ
14 1216.2407 1229.955 1255.801 Θ#
15 1301.955 1317.955 1348.109 I (J)
16 1387.6693 1405.955 1440.4165 A
Fifths
1 699.9249 702.2016 706.5183 Α#-Ϛ#/Ϝ#
2 697.8948 702.46625 711.0816 Β-Z
3 695.8647 702.7219 715.645 Γ-H
4 693.8346 702.9775 720.2083 Γ#-H#
5 691.80455 703.2331 724.7716 Δ-Θ
6 689.7745 703.48875 729.3349 Δ#-Θ#
7 687.7444 703.7448 733.8982 Ε-I (J)
8 685.7143 704 738.4615 Ϛ/Ϝ-A
9 687.7444 703.7448 733.8982 Ϛ#/Ϝ#-A#
10 689.7745 703.48875 729.3349 Ζ-B
11 691.80455 703.2331 724.7716 Η-Γ
12 693.8346 702.9775 720.2083 Η#-Γ#
13 695.8647 702.7219 715.645 Θ-Δ
14 697.8948 702.46625 711.0816 Θ#-Δ#
15 699.9249 702.2016 706.5183 I (J)-Ε
16 701.955 A-Ϛ/Ϝ