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The Ketradektriatoh Scale


This is a type of scale which denotes the use of a scale placed between 11 and 14 ED2's, employing a ratio generator between 41/32 ~ 9/7 (being 25-ED2 the middle size of the Ketradektriatoh spectrum, in the 2;1 relation), resulting in a variant of tetradecatonic scale comforms by this scheme: LLLsLLLLsLLLLs.

ED2s that contains this scale:

2 2 2 1 2 2 2 2 1 2 2 2 2 1: 25 (Middle range)
3 3 3 1 3 3 3 3 1 3 3 3 3 1: 36 (Lufsur range)
3 3 3 2 3 3 3 3 2 3 3 3 3 2: 39 (Fuslur range)

4 4 4 1 4 4 4 4 1 4 4 4 4 1: 47
4 4 4 2 4 4 4 4 2 4 4 4 4 2: 50
4 4 4 3 4 4 4 4 3 4 4 4 4 3: 53

5 5 5 1 5 5 5 5 1 5 5 5 5 1: 58
5 5 5 2 5 5 5 5 2 5 5 5 5 2: 61 Split-φ
5 5 5 3 5 5 5 5 3 5 5 5 5 3: 64 φ
5 5 5 4 5 5 5 5 4 5 5 5 5 4: 67

6 6 6 1 6 6 6 6 1 6 6 6 6 1: 69
6 6 6 5 6 6 6 6 5 6 6 6 6 5: 81

7 7 7 1 7 7 7 7 1 7 7 7 7 1: 80
7 7 7 2 7 7 7 7 2 7 7 7 7 2: 83
7 7 7 3 7 7 7 7 3 7 7 7 7 3: 86
7 7 7 4 7 7 7 7 4 7 7 7 7 4: 89
7 7 7 5 7 7 7 7 5 7 7 7 7 5: 92
7 7 7 6 7 7 7 7 6 7 7 7 7 6: 95

8 8 8 1 8 8 8 8 1 8 8 8 8 1: 91
8 8 8 3 8 8 8 8 3 8 8 8 8 3: 97 Split-φ
8 8 8 5 8 8 8 8 5 8 8 8 8 5: 103 φ
8 8 8 7 8 8 8 8 7 8 8 8 8 7: 109

9 9 9 1 9 9 9 9 1 9 9 9 9 1: 102
9 9 9 2 9 9 9 9 2 9 9 9 9 2: 105
9 9 9 4 9 9 9 9 4 9 9 9 9 4: 111
9 9 9 5 9 9 9 9 5 9 9 9 9 5: 114
9 9 9 7 9 9 9 9 7 9 9 9 9 7: 120
9 9 9 8 9 9 9 9 8 9 9 9 9 8: 123

10 10 10 1 10 10 10 10 1 10 10 10 10 1:113
10 10 10 3 10 10 10 10 3 10 10 10 10 3: 119
10 10 10 7 10 10 10 10 7 10 10 10 10 7: 131
10 10 10 9 10 10 10 10 9 10 10 10 10 9: 137

11 11 11 1 11 11 11 11 1 11 11 11 11 1: 124
11 11 11 2 11 11 11 11 2 11 11 11 11 2: 127
11 11 11 3 11 11 11 11 3 11 11 11 11 3: 130
11 11 11 4 11 11 11 11 4 11 11 11 11 4: 133
11 11 11 5 11 11 11 11 5 11 11 11 11 5: 136
11 11 11 6 11 11 11 11 6 11 11 11 11 6: 139
11 11 11 7 11 11 11 11 7 11 11 11 11 7: 142
11 11 11 8 11 11 11 11 8 11 11 11 11 8: 145
11 11 11 9 11 11 11 11 9 11 11 11 11 9 :148
11 11 11 10 11 11 11 11 10 11 11 11 11 10: 151

12 12 12 1 12 12 12 12 1 12 12 12 12 1: 135
12 12 12 5 12 12 12 12 5 12 12 12 12 5: 147
12 12 12 7 12 12 12 12 7 12 12 12 12 7: 153
12 12 12 11 12 12 12 12 11 12 12 12 12 11: 165

13 13 13 1 13 13 13 13 1 13 13 13 13 1: 146
13 13 13 2 13 13 13 13 2 13 13 13 13 2: 149
13 13 13 3 13 13 13 13 3 13 13 13 13 3: 152
13 13 13 4 13 13 13 13 4 13 13 13 13 4: 155
13 13 13 5 13 13 13 13 5 13 13 13 13 5: 158 Split-φ
13 13 13 6 13 13 13 13 6 13 13 13 13 6: 161
13 13 13 7 13 13 13 13 7 13 13 13 13 7: 164
13 13 13 8 13 13 13 13 8 13 13 13 13 8: 167 φ
13 13 13 9 13 13 13 13 9 13 13 13 13 9: 170
13 13 13 10 13 13 13 13 10 13 13 13 13 10: 173
13 13 13 11 13 13 13 13 11 13 13 13 13 11: 176
13 13 13 12 13 13 13 13 12 13 13 13 13 12: 179

14 14 14 1 14 14 14 14 1 14 14 14 14 1: 157
14 14 14 3 14 14 14 14 3 14 14 14 14 3: 163
14 14 14 5 14 14 14 14 5 14 14 14 14 5: 169
14 14 14 9 14 14 14 14 9 14 14 14 14 9: 181
14 14 14 11 14 14 14 14 11 14 14 14 14 11: 187
14 14 14 13 14 14 14 14 13 14 14 14 14 13: 193

15 15 15 1 15 15 15 15 1 15 15 15 15 1: 168
15 15 15 2 15 15 15 15 2 15 15 15 15 2: 171
15 15 15 4 15 15 15 15 4 15 15 15 15 4: 177
15 15 15 7 15 15 15 15 7 15 15 15 15 7: 186
15 15 15 8 15 15 15 15 8 15 15 15 15 8: 189
15 15 15 11 15 15 15 15 11 15 15 15 15 11: 198
15 15 15 13 15 15 15 15 13 15 15 15 15 13: 204
15 15 15 14 15 15 15 15 14 15 15 15 15 14: 207

16 16 16 1 16 16 16 16 1 16 16 16 16 1: 179
16 16 16 3 16 16 16 16 3 16 16 16 16 3: 185
16 16 16 5 16 16 16 16 5 16 16 16 16 5: 191
16 16 16 7 16 16 16 16 7 16 16 16 16 7: 197
16 16 16 9 16 16 16 16 9 16 16 16 16 9: 203
16 16 16 11 16 16 16 16 11 16 16 16 16 11: 209
16 16 16 13 16 16 16 16 13 16 16 16 16 13: 215
16 16 16 15 16 16 16 16 15 16 16 16 16 15: 221

17 17 17 1 17 17 17 17 1 17 17 17 17 1: 190
17 17 17 2 17 17 17 17 2 17 17 17 17 2: 193
17 17 17 3 17 17 17 17 3 17 17 17 17 3: 196
17 17 17 4 17 17 17 17 4 17 17 17 17 4: 199
17 17 17 5 17 17 17 17 5 17 17 17 17 5: 202 (Top limit for Lufsur range)
17 17 17 6 17 17 17 17 6 17 17 17 17 6: 205
17 17 17 7 17 17 17 17 7 17 17 17 17 7: 208
17 17 17 8 17 17 17 17 8 17 17 17 17 8: 211
17 17 17 9 17 17 17 17 9 17 17 17 17 9: 214
17 17 17 10 17 17 17 17 10 17 17 17 17 10: 217
17 17 17 11 17 17 17 17 11 17 17 17 17 11: 220
17 17 17 12 17 17 17 17 12 17 17 17 17 12: 223 (Top limit for Fuslur range)
17 17 17 13 17 17 17 17 13 17 17 17 17 13: 226
17 17 17 14 17 17 17 17 14 17 17 17 17 14: 229
17 17 17 15 17 17 17 17 15 17 17 17 17 15: 232
17 17 17 16 17 17 17 17 16 17 17 17 17 16: 235

The next table below shows an extension of ED2s which supports the Ketradektriatoh scale, with respect to the principal generator and their results for each L/s sizes:
4\11






436.364
109.091
0







29\80
435
105
15






25\69

434.783
104.348
17.391





21\58


434.483
103.448
20.69




17\47



434.043
102.128
25.532





30\83


433.735
101.208
28.916







73\202
433.663
100.990
29.703
Since here are the optimal range Lufsur mode (?)





43\119

433.613
100.840
30.252








433.459
100.377
31.95



13\36




433.333
100
33.333








433.048
99.144
36.473





35\97


432.99
98.969
37.113








432.933
98.799
37.738




22\61



432.787
98.361
39.344


9\25





432
96
48
Boundary of propriety;
generators smaller than this are proper







431.417
94.25
54.4155




23\64



431.25
93.75
56.25








431.1185
93.355
57.697





37\103


431.068
93.204
58.25








430.984
92.952
58.175



14\39




430.769
92.308
61.538






47\131

430.534
91.603
64.122







80\223
430.493
91.480
64.575
Until here are the optimal range Fuslur mode (?)




33\92


430.435
91.304
65.217




19\53



430.189
90.566
67.925





24\67


429.851
89.552
71.642






29\81

429.63
88.889
74.074







34\95
429.474
88.421
75.7895

5\14






428.571
85.714
85.714