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The generator range reflects two extremes: one where L = s (3\10), and another where s = 0 (2\7). Between these extremes, there is an infinite continuum of possible generator sizes. By taking freshman sums of the two edges (adding the numerators, then adding the denominators), we can fill in this continuum with compatible edos, increasing in number of tones as we continue filling in the in-betweens. Thus, the smallest in-between edIX would be (3+2)\(10+7) = 5\17 – five degrees of [[17edIX]]:
The generator range reflects two extremes: one where L = s (3\10), and another where s = 0 (2\7). Between these extremes, there is an infinite continuum of possible generator sizes. By taking freshman sums of the two edges (adding the numerators, then adding the denominators), we can fill in this continuum with compatible edos, increasing in number of tones as we continue filling in the in-betweens. Thus, the smallest in-between edIX would be (3+2)\(10+7) = 5\17 – five degrees of [[17edIX]]:


{| class="wikitable center-all"
{{Scale tree|7L 3s <15/7>}}
! colspan="9" rowspan="2" |Generator
! colspan="2" |Normalized Cents
! colspan="2" |Śata
! rowspan="2" |L
! rowspan="2" |s
! rowspan="2" |L/s
! rowspan="2" |Comments
|-
!Chroma-positive
!Chroma-negative
!Chroma-positive
!Chroma-negative
|-
|7\10||  ||  ||  ||  ||
|
|
|  ||933.333||400.000
|1190.000
|510.000||1||1||1.000||
|-
|  ||  ||  ||  ||  ||40\57
|
|
|  ||923.077||392.307
|1192.982
|507.018||6||5||1.200||Restles↑
|-
|
|
|
|
|
|
|73\104
|
|
|922.105
|391.579
|1193.269
|506.731
|11
|9
|1.222
|
|-
|  ||  ||  ||  ||33\47||
|
|
|  ||920.930||390.698
|1193.617
|506.383||5||4||1.250||
|-
|  ||  ||  ||  ||  ||59\84
|
|
|  ||919.481||389.610
|1194.048
|505.952||9||7||1.286||
|-
|
|
|
|
|
|
|85\121
|
|
|918.919
|389.189
|1194.215
|505.785
|13
|10
|1.000
|
|-
|  ||  ||  ||26\37||  ||
|
|
|  ||917.647||388.235
|1194.595
|505.405||4||3||1.333||
|-
|  ||  ||  ||  ||  ||71\101
|
|
|  ||916.129||387.097
|1195.050
|504.950||11||8||1.375||
|-
|  ||  ||  ||  ||45\64||
|
|
|  ||915.254||386.441
|1195.3125
|504.6875||7||5||1.400||Beatles
|-
|  ||  ||  ||  ||  ||64\91
|
|
|  ||914.286||385.714
|1195.604
|504.396||10||7||1.428||
|-
|  ||  ||19\27||  ||  ||
|
|
|  ||912.000||384.000
|1196.296
|503.704||3||2||1.500||L/s = 3/2, suhajira/ringo
|-
|
|
|
|
|
|
|
|
|126\179
|910.843
|383.133
|1196.648
|503.352
|20
|13
|1.538
|
|-
|
|
|
|
|
|
|
|107\152
|
|910.638
|382.988
|1196.711
|503.289
|17
|11
|1.545
|
|-
|
|
|
|
|
|
|88\125
|
|
|910.345
|382.759
|1196.800
|503.200
|14
|9
|1.556
|
|-
|  ||  ||  ||  ||  ||69\98
|
|
|  ||909.890||382.418
|1196.938
|503.062||11||7||1.571||
|-
|  ||  ||  ||  ||50\71||
|
|
|  ||909.091||381.818
|1197.183
|502.817||8||5||1.600||
|-
|  ||  ||  ||  ||  ||81\115
|
|
|  ||908.411||381.308
|1197.391
|502.609||13||8||1.625||Golden suhajira
|-
|  ||  ||  ||31\44||  ||
|
|
|  ||907.317||380.489
|1197.727
|502.273||5||3||1.667||
|-
|  ||  ||  ||  ||  ||74\105
|
|
|  ||906.122||379.592
|1198.095
|501.905||12||7||1.714||
|-
|  ||  ||  ||  ||43\61||
|
|
|  ||905.263||378.947
|1198.361
|501.639||7||4||1.750||
|-
|  ||  ||  ||  ||  ||55\78
|
|
|  ||904.110||378.082
|1198.561
|501.439||9||5||1.800||
|-
|
|
|
|
|
|
|67\95
|
|
|903.371
|377.528
|1198.947
|501.053
|11
|6
|1.833
|
|-
|
|
|
|
|
|
|
|79\112
|
|902.857
|377.143
|1199.107
|500.803
|13
|7
|1.857
|
|-
|
|
|
|
|
|
|
|
|91\129
|902.479
|376.860
|1199.224
|500.776
|15
|8
|1.875
|
|-
|  ||12\17||  ||  ||  ||
|
|
|  ||900.000||375.000
|1200.000
|500.000||2||1||2.000||Basic Greater dicoid<br>(Generators smaller than this are proper)
|-
|
|
|
|
|
|
|
|
|89\126
|897.479
|373.109
|1200.793
|499.207
|15
|7
|2.143
|
|-
|
|
|
|
|
|
|
|77\109
|
|897.087
|372.816
|1200.917
|499.083
|13
|6
|2.167
|
|-
|
|
|
|
|
|
|65\92
|
|
|896.552
|372.414
|1201.087
|498.913
|11
|5
|2.200
|
|-
|  ||  ||  ||  ||  ||53\75
|
|
|  ||895.775||371.831
|1201.333
|498.667||9||4||2.250||
|-
|  ||  ||  ||  ||41\58||
|
|
|  ||894.545||370.909
|1201.724
|498.276||7||3||2.333||
|-
|  ||  ||  ||  ||  ||70\99
|
|
|  ||893.617||370.213
|1202.020
|497.979||12||5||2.400||Hemif/hemififths
|-
|  ||  ||  ||29\41||  ||
|
|
|  ||892.307||369.231
|1202.439
|497.561||5||2||2.500||Mohaha/neutrominant
|-
|  ||  ||  ||  ||  ||75\106
|
|
|  ||891.089||368.317
|1202.830
|497.170||13||5||2.600||Hemif/salsa/karadeniz
|-
|  ||  ||  ||  ||46\65||
|
|
|  ||890.322||367.742
|1203.077
|496.923||8||3||2.667||Mohaha/mohamaq
|-
|  ||  ||  ||  ||  ||63\89
|
|
|  ||889.412||367.059
|1203.371
|496.629||11||4||2.750||
|-
|
|
|
|
|
|
|80\113
|
|
|888.889
|366.667
|1203.540
|496.460
|14
|5
|2.800
|
|-
|  ||  ||17\24||  ||  ||
|
|
|  ||886.957||365.213
|1204.167
|495.833||3||1||3.000||L/s = 3/1
|-
|
|
|
|
|
|
|
|90\127
|
|885.246
|363.934
|1204.724
|495.276
|16
|5
|3.200
|
|-
|
|
|
|
|
|
|73\103
|
|
|884.848
|363.636
|1204.854
|495.146
|13
|4
|3.250
|
|-
|  ||  ||  ||  ||  ||56\79
|
|
|  ||884.210||363.158
|1205.063
|494.937||10||3||3.333||
|-
|  ||  ||  ||  ||39\55||
|
|
|  ||883.018||362.264
|1205.455
|494.545||7||2||3.500||
|-
|  ||  ||  ||  ||  ||61\86
|
|
|  ||881.928||361.446
|1205.814
|494.186||11||3||3.667||
|-
|  ||  ||  ||22\31||  ||
|
|
|  ||880.000||360.000
|1206.452
|493.548||4||1||4.000||Mohaha/migration/mohajira
|-
|
|
|
|
|
|
|
|93\131
|
|878.740
|359.055
|1206.870
|493.130
|17
|4
|4.250
|
|-
|
|
|
|
|
|
|71\100
|
|
|878.351
|358.762
|1207.000
|493.000
|13
|3
|4.333
|
|-
|  ||  ||  ||  ||  ||49\69
|
|
|  ||877.612||358.209
|1207.246
|492.754||9||2||4.500||
|-
|
|
|
|
|
|
|76\107
|
|
|876.923
|357.692
|1207.477
|492.523
|14
|3
|4.667
|
|-
|  ||  ||  ||  ||27\38||
|
|
|  ||875.676||356.757
|1207.895
|492.105||5||1||5.000||
|-
|
|
|
|
|
|
|59\83
|
|
|874.074
|355.556
|1208.434
|491.566
|11
|2
|5.500
|
|-
|  ||  ||  ||  ||  ||32\45
|
|
|  ||872.727||354.545
|1208.889
|491.111||6||1||6.000||Mohaha/ptolemy
|-
|5\7||  ||  ||  ||  ||
|
|
|  ||857.143||342.857
|1214.286
|485.714||1||0||→ inf||
|}


The scale produced by stacks of 5\17 is the [[17edIX neutral scale]]. Between 11/38 and 16/55, with 9/31 in between, is the mohajira/mohaha/mohoho range, where mohaha and mohoho use the MOS as the chromatic scale of a [[Chromatic pairs|chromatic pair]].
The scale produced by stacks of 5\17 is the [[17edIX neutral scale]]. Between 11/38 and 16/55, with 9/31 in between, is the mohajira/mohaha/mohoho range, where mohaha and mohoho use the MOS as the chromatic scale of a [[Chromatic pairs|chromatic pair]].
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