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User:Moremajorthanmajor/Greater dicoid: Difference between revisions

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Line 12: Line 12:
The generator (g) will fall between 343 cents (2\7 - two degrees of [[7edo]] and 400 cents (3\9 - three degrees of [[10edo|9edo]]), hence a neutral or major third.
The generator (g) will fall between 343 cents (2\7 - two degrees of [[7edo]] and 400 cents (3\9 - three degrees of [[10edo|9edo]]), hence a neutral or major third.


2g, then, will fall between 686 cents (4\7) and 800 cents (2\3), the range of [[5L 2s|diatonic]] fifths.
2g, then, will fall between 686 cents (4\7) and 800 cents (2\3), the range of [[5L 2s|diatonic]] fifths and subminor sixths.


The "large step" will fall between 171 cents (1\7) and 120 cents (1\10), ranging from a submajor second to a [[sinaic]].
The "large step" will fall between 171 cents (1\7) and 120 cents (1\10), ranging from a submajor second to a [[sinaic]].
Line 56: Line 56:
|3L+1s
|3L+1s
| -2
| -2
|6
|6v
|minor 6-step
|minor 6-step
|4L+2s
|4L+2s
Line 106: Line 106:
|-
|-
|8
|8
|6^
|6
|major 6-step
|major 6-step
|5L+1s
|5L+1s
Line 194: Line 194:


{| class="wikitable center-all"
{| class="wikitable center-all"
! colspan="9" rowspan="2" |Generator
! rowspan="2" |Generator
! colspan="2" |Normalized Cents
! colspan="2" |Normalized Cents
! colspan="2" |Śata
! rowspan="2" |L
! rowspan="2" |L
! rowspan="2" |s
! rowspan="2" |s
Line 202: Line 201:
! rowspan="2" |Comments
! rowspan="2" |Comments
|-
|-
!Chroma-positive
!Bright
!Chroma-negative
!Dark
!Chroma-positive
!Chroma-negative
|-
|-
|7\10|| || || || ||
|7\10||933.333||400.000||1||1||1.000||
|
|
| ||933.333||400.000
|1190.000
|510.000||1||1||1.000||
|-
|-
| || || || || ||40\57
| 40\57||923.077||392.307||6||5||1.200||Restles↑
|
|
| ||923.077||392.307
|1192.982
|507.018||6||5||1.200||Restles↑
|-
|-
|
|
|
|
|
|
|73\104
|73\104
|
|
|922.105
|922.105
|391.579
|391.579
|1193.269
|506.731
|11
|11
|9
|9
Line 239: Line 216:
|
|
|-
|-
| || || || ||33\47||
|106\151
|921.739
|391.304
|16
|13
|1.231
|
|
|-
| 33\47 ||920.930||390.698||5||4||1.250||
|-
|92\131
|920.000
|390.000
|13
|11
|1.273
|
|
| ||920.930||390.698
|1193.617
|506.383||5||4||1.250||
|-
|-
| || || || || ||59\84
| 59\84 ||919.481||389.610||9||7||1.286||
|
|
| ||919.481||389.610
|1194.048
|505.952||9||7||1.286||
|-
|-
|
|
|
|
|
|
|85\121
|85\121
|
|
|918.919
|918.919
|389.189
|389.189
|1194.215
|505.785
|13
|13
|10
|10
Line 271: Line 244:
|
|
|-
|-
| || || ||26\37|| ||
|111\158
|918.621
|388.966
|17
|13
|1.308
|
|
|-
| 26\37 ||917.647||388.235||4||3||1.333||
|-
|97\138
|916.535
|387.401
|15
|11
|1.364
|
|
| ||917.647||388.235
|1194.595
|505.405||4||3||1.333||
|-
|-
| || || || || ||71\101
| 71\101 ||916.129||387.097||11||8||1.375||
|
|-
| 45\64 ||915.254||386.441||7||5||1.400||Beatles
|-
| 64\91 ||914.286||385.714||10||7||1.428||
|-
|83\118
|913.716
|385.321
|13
|9
|1.444
|
|
| ||916.129||387.097
|1195.050
|504.950||11||8||1.375||
|-
|-
| || || || ||45\64||
| 19\27 ||912.000||384.000||3||2||1.500||L/s = 3/2, suhajira/ringo
|
|
| ||915.254||386.441
|1195.3125
|504.6875||7||5||1.400||Beatles
|-
|-
| || || || || ||64\91
|164\233
|911.111
|383.333
|26
|17
|1.529
|
|
|
| ||914.286||385.714
|1195.604
|504.396||10||7||1.428||
|-
|-
| || ||19\27|| || ||
|145\206
|
|910.995
|383.246
|23
|15
|1.533
|
|
| ||912.000||384.000
|1196.296
|503.704||3||2||1.500||L/s = 3/2, suhajira/ringo
|-
|-
|
|
|
|
|
|
|
|
|126\179
|126\179
|910.843
|910.843
|383.133
|383.133
|1196.648
|503.352
|20
|20
|13
|13
Line 324: Line 302:
|
|
|-
|-
|
|
|
|
|
|
|
|107\152
|107\152
|
|910.638
|910.638
|382.988
|382.988
|1196.711
|503.289
|17
|17
|11
|11
Line 342: Line 310:
|
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|-
|-
|
|
|
|
|
|
|88\125
|88\125
|
|
|910.345
|910.345
|382.759
|382.759
|1196.800
|503.200
|14
|14
|9
|9
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|
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|-
|-
| || || || || ||69\98
| 69\98 ||909.890||382.418||11||7||1.571||
|
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| ||909.890||382.418
|1196.938
|503.062||11||7||1.571||
|-
|-
| || || || ||50\71||
| 50\71 ||909.091||381.818||8||5||1.600||
|
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| ||909.091||381.818
|1197.183
|502.817||8||5||1.600||
|-
|-
| || || || || ||81\115
| 81\115 ||908.411||381.308||13||8||1.625||Golden suhajira
|
|
| ||908.411||381.308
|1197.391
|502.609||13||8||1.625||Golden suhajira
|-
|-
| || || ||31\44|| ||
| 31\44 ||907.317||380.489||5||3||1.667||
|
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| ||907.317||380.489
|1197.727
|502.273||5||3||1.667||
|-
|-
| || || || || ||74\105
| 74\105 ||906.122||379.592||12||7||1.714||
|
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| ||906.122||379.592
|1198.095
|501.905||12||7||1.714||
|-
|-
| || || || ||43\61||
| 43\61 ||905.263||378.947||7||4||1.750||
|
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| ||905.263||378.947
|1198.361
|501.639||7||4||1.750||
|-
|-
| || || || || ||55\78
| 55\78 ||904.110||378.082||9||5||1.800||
|
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| ||904.110||378.082
|1198.561
|501.439||9||5||1.800||
|-
|-
|
|
|
|
|
|
|67\95
|67\95
|
|
|903.371
|903.371
|377.528
|377.528
|1198.947
|501.053
|11
|11
|6
|6
Line 427: Line 340:
|
|
|-
|-
|
|
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|
|
|
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|79\112
|79\112
|
|902.857
|902.857
|377.143
|377.143
|1199.107
|500.803
|13
|13
|7
|7
Line 445: Line 348:
|
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|-
|-
|
|
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|
|
|
|
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|91\129
|91\129
|902.479
|902.479
|376.860
|376.860
|1199.224
|500.776
|15
|15
|8
|8
Line 463: Line 356:
|
|
|-
|-
| ||12\17|| || || ||
|103\146
|902.190
|376.642
|17
|9
|1.889
|
|
|-
|115\163
|901.961
|376.471
|19
|10
|1.900
|
|
| ||900.000||375.000
|1200.000
|500.000||2||1||2.000||Basic Greater dicoid<br>(Generators smaller than this are proper)
|-
|-
| 12\17 ||900.000||375.000||2||1||2.000||Basic Greater dicoid<br>(Generators smaller than this are proper)
|-
|173\245
|898.701
|374.026
|29
|14
|2.071
|
|
|-
|161\228
|898.605
|373.953
|27
|13
|2.077
|
|
|-
|149\211
|898.492
|373.869
|25
|12
|2.083
|
|
|-
|137\194
|898.361
|373.770
|23
|11
|2.091
|
|
|-
|125\177
|898.204
|373.653
|21
|10
|2.100
|
|
|-
|113\160
|898.013
|373.510
|19
|9
|2.111
|
|
|-
|101\143
|897.778
|373.333
|17
|8
|2.125
|
|
|
|-
|89\126
|89\126
|897.479
|897.479
|373.109
|373.109
|1200.793
|499.207
|15
|15
|7
|7
Line 488: Line 438:
|
|
|-
|-
|
|
|
|
|
|
|
|77\109
|77\109
|
|897.087
|897.087
|372.816
|372.816
|1200.917
|499.083
|13
|13
|6
|6
Line 506: Line 446:
|
|
|-
|-
|
|
|
|
|
|
|65\92
|65\92
|
|
|896.552
|896.552
|372.414
|372.414
|1201.087
|498.913
|11
|11
|5
|5
Line 524: Line 454:
|
|
|-
|-
| || || || || ||53\75
| 53\75 ||895.775||371.831||9||4||2.250||
|
|
| ||895.775||371.831
|1201.333
|498.667||9||4||2.250||
|-
|-
| || || || ||41\58||
| 41\58 ||894.545||370.909||7||3||2.333||
|
|
| ||894.545||370.909
|1201.724
|498.276||7||3||2.333||
|-
|-
| || || || || ||70\99
| 70\99 ||893.617||370.213||12||5||2.400||Hemif/hemififths
|
|
| ||893.617||370.213
|1202.020
|497.979||12||5||2.400||Hemif/hemififths
|-
|-
| || || ||29\41|| ||
| 29\41 ||892.307||369.231||5||2||2.500||Mohaha/neutrominant
|
|
| ||892.307||369.231
|1202.439
|497.561||5||2||2.500||Mohaha/neutrominant
|-
|-
| || || || || ||75\106
| 75\106 ||891.089||368.317||13||5||2.600||Hemif/salsa/karadeniz
|
|
| ||891.089||368.317
|1202.830
|497.170||13||5||2.600||Hemif/salsa/karadeniz
|-
|-
| || || || ||46\65||
| 46\65 ||890.322||367.742||8||3||2.667||Mohaha/mohamaq
|
|
| ||890.322||367.742
|1203.077
|496.923||8||3||2.667||Mohaha/mohamaq
|-
|-
| || || || || ||63\89
| 63\89 ||889.412||367.059||11||4||2.750||
|
|
| ||889.412||367.059
|1203.371
|496.629||11||4||2.750||
|-
|-
|
|
|
|
|
|
|80\113
|80\113
|
|
|888.889
|888.889
|366.667
|366.667
|1203.540
|496.460
|14
|14
|5
|5
Line 591: Line 476:
|
|
|-
|-
| || ||17\24|| || ||
|97\137
|888.550
|366.412
|17
|6
|2.833
|
|
|-
|114\161
|888.312
|366.234
|20
|7
|2.857
|
|
| ||886.957||365.213
|1204.167
|495.833||3||1||3.000||L/s = 3/1
|-
|-
|131\185
|888.136
|366.102
|23
|8
|2.875
|
|
|-
|148\209
|888.000
|366.000
|26
|9
|2.889
|
|
|-
|165\233
|887.892
|365.919
|29
|10
|2.900
|
|
|
|-
|
| 17\24 ||886.957||365.213||3||1||3.000||L/s = 3/1
|
|-
|
|90\127
|90\127
|
|885.246
|885.246
|363.934
|363.934
|1204.724
|495.276
|16
|16
|5
|5
Line 616: Line 526:
|
|
|-
|-
|
|
|
|
|
|
|73\103
|73\103
|
|
|884.848
|884.848
|363.636
|363.636
|1204.854
|495.146
|13
|13
|4
|4
Line 634: Line 534:
|
|
|-
|-
| || || || || ||56\79
| 56\79 ||884.210||363.158||10||3||3.333||
|
|-
|
| 39\55 ||883.018||362.264||7||2||3.500||
| ||884.210||363.158
|-
|1205.063
| 61\86 ||881.928||361.446||11||3||3.667||
|494.937||10||3||3.333||
|-
|-
| || || || ||39\55||
| 22\31 ||880.000||360.000||4||1||4.000||Mohaha/migration/mohajira
|
|
| ||883.018||362.264
|1205.455
|494.545||7||2||3.500||
|-
|-
| || || || || ||61\86
|137\193
|879.144
|359.358
|25
|6
|4.167
|
|
|
| ||881.928||361.446
|1205.814
|494.186||11||3||3.667||
|-
|-
| || || ||22\31|| ||
|115\162
|
|878.980
|359.236
|21
|5
|4.200
|
|
| ||880.000||360.000
|1206.452
|493.548||4||1||4.000||Mohaha/migration/mohajira
|-
|-
|
|
|
|
|
|
|
|93\131
|93\131
|
|878.740
|878.740
|359.055
|359.055
|1206.870
|493.130
|17
|17
|4
|4
Line 680: Line 566:
|
|
|-
|-
|
|
|
|
|
|
|71\100
|71\100
|
|
|878.351
|878.351
|358.762
|358.762
|1207.000
|493.000
|13
|13
|3
|3
Line 698: Line 574:
|
|
|-
|-
| || || || || ||49\69
| 49\69 ||877.612||358.209||9||2||4.500||
|
|
| ||877.612||358.209
|1207.246
|492.754||9||2||4.500||
|-
|-
|
|
|
|
|
|
|76\107
|76\107
|
|
|876.923
|876.923
|357.692
|357.692
|1207.477
|492.523
|14
|14
|3
|3
Line 723: Line 584:
|
|
|-
|-
| || || || ||27\38||
| 27\38 ||875.676||356.757||5||1||5.000||
|
|
| ||875.676||356.757
|1207.895
|492.105||5||1||5.000||
|-
|-
|
|
|
|
|
|
|59\83
|59\83
|
|
|874.074
|874.074
|355.556
|355.556
|1208.434
|491.566
|11
|11
|2
|2
Line 748: Line 594:
|
|
|-
|-
| || || || || ||32\45
|91\128
|873.600
|355.200
|17
|3
|5.667
|
|
|
| ||872.727||354.545
|1208.889
|491.111||6||1||6.000||Mohaha/ptolemy
|-
|-
|5\7|| || || || ||
| 32\45 ||872.727||354.545||6||1||6.000||Mohaha/ptolemy
|
|-
|
|5\7||857.143||342.857||1||0||→ inf||
| ||857.143||342.857
|1214.286
|485.714||1||0||→ inf||
|}
|}


Line 812: Line 656:
== See also ==
== See also ==
[[7L 3s (33/16-equivalent)]] - harmonic subminor ninth tuning
[[7L 3s (33/16-equivalent)]] - harmonic subminor ninth tuning
[[7L 3s (44/21-equivalent)]] - Neogothic minor ninth tuning


[[7L 3s (21/10-equivalent)]] - septimal chromatic minor ninth tuning
[[7L 3s (21/10-equivalent)]] - septimal chromatic minor ninth tuning


[[7L 3s (15/7-equivalent)]] - septimal diatonic minor ninth tuning
[[7L 3s (15/7-equivalent)]] - septimal diatonic minor ninth tuning
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/Greater_dicoid"