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User:Moremajorthanmajor/Greater sephiroid: Difference between revisions

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Line 35: Line 35:
==Scale tree==
==Scale tree==
{| class="wikitable center-all"
{| class="wikitable center-all"
! colspan="7" |Generator
!Generator
!Cents
!Cents
!Normalized Cents
!Normalized Cents
!''ed13\12''
!L
!L
!s
!s
Line 44: Line 43:
!Comments
!Comments
|-
|-
|3\10|| || || || ||
|3\10||360.000
| ||360.000
|360.000||1||1||1.000||
|360.000
|''390.000''||1||1||1.000||
|-
|-
|
|
|
|
|
|
|19\63
|19\63
|361.905
|361.905
|367.742
|407.143
|''392.0635''
|7
|7
|6
|6
Line 64: Line 54:
|
|
|-
|-
| || || || || ||16\53
| 16\53||362.264
| ||362.264
|408.511||6||5||1.200||Submajor
|369.231
|''392.453''||6||5||1.200||Submajor
|-
|-
|
|
|
|
|
|
|29\96
|29\96
|362.500
|362.500
|370.213
|409.412
|''392.708''
|11
|11
|9
|9
Line 84: Line 65:
|
|
|-
|-
| || || || ||13\43||
| 13\43||362.791
| ||362.791
|410.526||5||4||1.250||
|371.429
|''393.023''||5||4||1.250||
|-
|-
| || || || || ||23\76
| 23\76||363.158
| ||363.158
|411.940||9||7||1.286||
|372.973
|''393.421''||9||7||1.286||
|-
|-
|
|
|
|
|
|
|33\109
|33\109
|363.303
|363.303
|373.585
|412.500
|''393.578''
|13
|13
|10
|10
Line 109: Line 79:
|
|
|-
|-
| || || ||10\33|| ||
| 10\33||363.636
| ||363.636
|413.793||4||3||1.333||
|375.000
|''393.939''||4||3||1.333||
|-
|-
| || || || || ||27\89
|37\122
| ||364.045
|363.935
|376.744
|414.953
|''394.382''||11||8||1.375||
|15
|11
|1.455
|
|-
| 27\89||364.045
|415.385||11||8||1.375||
|-
|-
| || || || ||17\56||
| 17\56||364.286
| ||364.286
|416.327||7||5||1.400||
|377.778
|''394.643''||7||5||1.400||
|-
|-
| || || || || ||24\79
| 24\79||364.557
| ||364.557
|417.391||10||7||1.428||
|378.947
|''394.937''||10||7||1.428||
|-
|-
|
|
|
|
|
|
|31\102
|31\102
|364.706
|364.706
|379.592
|417.978
|''395.098''
|13
|13
|9
|9
Line 144: Line 107:
|
|
|-
|-
| || ||7\23|| || ||
| 7\23||365.217
| ||365.217
|420.000||3||2||1.500||L/s = 3/2
|381.818
|''395.652''||3||2||1.500||L/s = 3/2
|-
|-
|
|
|
|
|
|
|32\105
|32\105
|365.714
|365.714
|384.000
|421.978
|''396.1905''
|14
|14
|9
|9
Line 164: Line 118:
|
|
|-
|-
| || || || || ||25\82
| 25\82||365.854
| ||365.854
|422.535||11||7||1.571||
|384.615
|-
|''396.3415''||11||7||1.571||
| 18\59||366.102
|423.529||8||5||1.600||
|-
|-
| || || || ||18\59||
| 29\95||366.316
| ||366.102
|424.390||13||8||1.625||Unnamed golden tuning
|385.714
|''396.610''||8||5||1.600||
|-
|-
| || || || || ||29\95
| 11\36 ||366.667
| ||366.316
|425.806||5||3||1.667||
|386.667
|''396.842''||13||8||1.625||Unnamed golden tuning
|-
|-
|37\121
|366.942
|426.923
|17
|10
|1.700
|
|
|-
| 26\85 ||367.059
|427.397||12||7||1.714||
|-
| 15\49 ||367.347
|428.571||7||4||1.750||
|-
| 19\62 ||367.742
|430.189||9||5||1.800||
|-
|23\75
|368.000
|431.250
|11
|6
|1.833
|
|
|-
|27\88
|368.182
|432.000
|13
|7
|1.857
|
|
|-
|31\101
|368.317
|432.558
|15
|8
|1.875
|
|
|-
|35\114
|368.421
|432.990
|17
|9
|1.889
|
|
|-
|39\127
|368.504
|433.333
|19
|10
|1.900
|
|
|40\131
|-
|366.412
|43\140
|387.097
|368.571
|''396.947''
|433.614
|18
|21
|11
|11
|1.636
|1.909
|
|
|-
|-
| || || ||11\36|| ||
|47\153
| ||366.667
|368.627
|388.235
|433.846
|''397.222''||5||3||1.667||
|23
|12
|1.917
|
|-
|-
|51\166
|368.675
|434.042
|25
|13
|1.923
|
|
|-
|55\179
|368.715
|434.210
|27
|14
|1.929
|
|
|-
|59\192
|368.750
|434.356
|29
|15
|1.933
|
|
|-
|63\205
|368.780
|434.483
|31
|16
|1.9375
|
|
|-
|67\218
|368.807
|434.595
|33
|17
|1.941
|
|
|-
|71\231
|368.831
|434.694
|35
|18
|1.944
|
|
|37\121
|-
|366.942
|75\244
|389.474
|368.852
|''397.521''
|434.782
|17
|37
|10
|19
|1.700
|1.947
|
|-
|79\257
|368.872
|434.862
|39
|20
|1.950
|
|
|-
|-
| || || || || ||26\85
|83\270
| ||367.059
|368.889
|390.000
|434.834
|''397.647''||12||7||1.714||
|41
|21
|1.953
|
|-
|-
| || || || ||15\49||
|87\283
| ||367.347
|368.905
|391.304
|435.000
|''397.959''||7||4||1.750||
|43
|22
|1.955
|
|-
|-
| || || || || ||19\62
| 4\13 ||369.231
| ||367.742
|436.364||2||1||2.000||Basic sephiroid<br>(Generators smaller than this are proper)
|393.103
|''398.387''||9||5||1.800||
|-
|-
|77\250
|369.600
|437.915
|39
|19
|2.053
|
|
|-
|73\237
|369.620
|438.000
|37
|18
|2.056
|
|
|-
|69\224
|369.643
|438.085
|35
|17
|2.059
|
|
|-
|65\211
|369.668
|438.202
|33
|16
|2.0625
|
|
|-
|61\198
|369.697
|438.323
|31
|15
|2.067
|
|
|-
|57\185
|369.730
|438.462
|29
|14
|2.071
|
|
|23\75
|-
|368.000
|53\172
|394.286
|369.767
|''398.667''
|438.621
|11
|27
|6
|13
|1.833
|2.077
|
|
|-
|-
| ||4\13|| || || ||
|49\159
| ||369.231
|369.811
|400.000
|438.806
|''400.000''||2||1||2.000||Basic sephiroid<br>(Generators smaller than this are proper)
|25
|12
|2.083
|
|-
|-
|45\146
|369.863
|439.024
|23
|11
|2.091
|
|
|-
|41\133
|369.925
|439.286
|21
|10
|2.100
|
|
|-
|37\120
|370.000
|439.604
|19
|9
|2.111
|
|
|-
|33\107
|370.093
|440.000
|17
|8
|2.125
|
|
|-
|29\94
|370.213
|440.506
|15
|7
|2.143
|
|
|-
|25\81
|370.370
|441.176
|13
|6
|2.167
|
|
|-
|21\68
|21\68
|370.588
|370.588
|406.452
|442.105
|''401.471''
|11
|11
|5
|5
Line 264: Line 406:
|
|
|-
|-
| || || || || ||17\55
| 17\55 ||370.909
| ||370.909
|443.478||9||4||2.250||
|408.000
|''401.818''||9||4||2.250||
|-
|-
|
|
|
|
|
|
|30\97
|30\97
|371.134
|371.134
|409.091
|444.444
|''402.062''
|16
|16
|7
|7
Line 284: Line 417:
|
|
|-
|-
| || || || ||13\42||
| 13\42 ||371.429
| ||371.429
|445.714||7||3||2.333||
|410.526
|''402.381''||7||3||2.333||
|-
|-
|
|
|
|
|
|
|35\113
|35\113
|371.681
|371.681
|411.765
|446.809
|''402.655''
|19
|19
|8
|8
Line 304: Line 428:
|
|
|-
|-
| || || || || ||22\71
| 22\71 ||371.831
| ||371.831
|447.458||12||5||2.400||
|412.500
|''402.817''||12||5||2.400||
|-
|-
|
|
|
|
|
|
|31\100
|31\100
|372.000
|372.000
|413.333
|448.193
|''403.000''
|17
|17
|7
|7
Line 324: Line 439:
|
|
|-
|-
| || || ||9\29|| ||
|40\129
| ||372.414
|372.093
|415.385
|448.598
|''403.448''||5||2||2.500||Sephiroth
|22
|9
|2.444
|
|-
|-
|49\158
|372.152
|448.855
|27
|11
|2.455
|
|
|-
|58\187
|372.193
|449.032
|32
|13
|2.462
|
|
|
|-
|
| 9\29 ||372.414
|
|450.000||5||2||2.500||Sephiroth
|
|-
|32\103
|32\103
|372.8155
|372.816
|417.391
|451.765
|''403.8835''
|18
|18
|7
|7
Line 344: Line 474:
|
|
|-
|-
| || || || || ||23\74
| 23\74 ||372.973
| ||372.973
|452.459||13||5||2.600||
|418.182
|''404.054''||13||5||2.600||
|-
|-
|
|
|
|
|
|
|37\119
|37\119
|373.109
|373.109
|418.868
|453.061
|''404.202''
|21
|21
|8
|8
Line 364: Line 485:
|Golden sephiroth
|Golden sephiroth
|-
|-
| || || || ||14\45||
| 14\45 ||373.333
| ||373.333
|454.054||8||3||2.667||
|420.000
|''404.444''||8||3||2.667||
|-
|-
|33\106
|373.585
|455.172
|19
|7
|2.714
|
|
|-
| 19\61 ||373.770
|456.000||11||4||2.750||
|-
|24\77
|374.000
|457.143
|14
|5
|2.800
|
|
|-
|29\93
|374.194
|457.895
|17
|6
|2.833
|
|
|-
|34\109
|374.312
|458.427
|20
|7
|2.857
|
|
|-
|39\125
|374.400
|458.824
|23
|8
|2.875
|
|
|-
|44\141
|374.468
|459.130
|26
|9
|2.889
|
|
|33\106
|-
|373.585
|49\157
|421.277
|374.522
|''404.717''
|459.375
|19
|29
|7
|10
|2.714
|2.900
|
|
|-
|-
| || || || || ||19\61
|54\173
| ||373.770
|374.566
|422.222
|459.574
|''404.981''||11||4||2.750||
|32
|11
|2.909
|
|-
|-
|59\189
|374.603
|459.740
|35
|12
|2.917
|
|
|-
|64\205
|374.634
|459.880
|38
|13
|2.923
|
|
|-
|69\221
|374.660
|460.000
|41
|14
|2.929
|
|
|-
| 5\16 ||375.000
|461.538||3||1||3.000||L/s = 3/1
|-
|76\243
|375.309
|462.944
|46
|15
|3.067
|
|
|-
|71\227
|375.330
|463.043
|43
|14
|3.071
|
|
|-
|66\211
|375.355
|463.158
|40
|13
|3.077
|
|
|24\77
|-
|374.000
|61\195
|423.529
|375.385
|''405.195''
|463.291
|14
|37
|5
|12
|2.800
|3.083
|
|
|-
|-
| || ||5\16|| || ||
|56\179
| ||375.000
|375.419
|428.571
|463.448
|''406.250''||3||1||3.000||L/s = 3/1
|34
|11
|3.091
|
|-
|-
|51\163
|375.460
|463.636
|31
|10
|3.100
|
|
|-
|46\147
|375.510
|463.866
|28
|9
|3.111
|
|
|-
|41\131
|375.573
|464.151
|25
|8
|3.125
|
|
|-
|36\115
|375.652
|464.516
|22
|7
|3.143
|
|
|-
|31\99
|375.756
|465.000
|19
|6
|3.167
|
|
|-
|26\83
|375.904
|465.672
|16
|5
|3.200
|
|
|-
|21\67
|21\67
|376.119
|376.119
|434.483
|466.667
|''407.463''
|13
|13
|4
|4
Line 424: Line 678:
|
|
|-
|-
| || || || || ||16\51
|37\118
| ||376.471
|376.271
|436.364
|457.368
|''407.843''||10||3||3.333||
|23
|7
|3.286
|
|-
| 16\51 ||376.471
|468.293||10||3||3.333||
|-
|-
|
|
|
|
|
|
|27\86
|27\86
|376.744
|376.744
|437.838
|469.565
|''408.1395''
|17
|17
|5
|5
Line 444: Line 697:
|
|
|-
|-
| || || || ||11\35||
|38\121
| ||377.143
|376.860
|440.000
|470.103
|''408.571''||7||2||3.500||
|24
|7
|3.429
|
|-
| 11\35 ||377.143
|471.429||7||2||3.500||
|-
|-
|39\124
|377.419
|472.727
|25
|7
|3,571
|
|
|
|-
|
|
|
|
|28\89
|28\89
|377.528
|377.528
|442.105
|473.239
|''408.989''
|18
|18
|5
|5
Line 464: Line 724:
|
|
|-
|-
| || || || || ||17\54
| 17\54 ||377.778
| ||377.778
|474.419||11||3||3.667||Muggles
|443.478
|''409.259''||11||3||3.667||Muggles
|-
|-
|23\73
|378.082
|475.862
|15
|4
|3.750
|
|
|-
|29\92
|378.261
|476.712
|19
|5
|3.800
|
|
|-
|35\111
|378.378
|477.273
|23
|6
|3.833
|
|
|-
|41\130
|378.462
|477.670
|27
|7
|3.857
|
|
|-
|47\149
|378.523
|477.966
|31
|8
|3.875
|
|
|-
|53\168
|378,571
|478.195
|35
|9
|3.889
|
|-
|59\187
|378.607
|478.378
|39
|10
|3.900
|
|
|23\73
|-
|378.082
|65\206
|445.161
|378.641
|''409.589''
|478.528
|15
|43
|4
|11
|3.750
|3.909
|
|-
|71\225
|378.667
|478.652
|47
|12
|3.917
|
|
|-
|-
| || || ||6\19|| ||
|77\244
| ||378.947
|378.689
|450.000
|478.756
|''410.526''||4||1||4.000||Magic/horcrux
|51
|13
|3.923
|
|-
|-
|83\263
|378.707
|478.846
|55
|14
|3.929
|
|
|-
|89\282
|378.723
|478.924
|59
|15
|3.933
|
|
|-
|95\301
|378.738
|478.992
|63
|16
|3.9375
|
|
|-
|101\320
|378.750
|479.051
|67
|17
|3.941
|
|
|-
| 6\19 ||378.947
|480.000||4||1||4.000||Magic/horcrux
|-
|25\79
|379.747
|483.871
|17
|4
|4.250
|
|
|-
|44\139
|379.856
|484.404
|30
|7
|4.286
|
|
|-
|19\60
|19\60
|380.000
|380.000
|456.000
|485.105
|''411.667''
|13
|13
|3
|3
Line 504: Line 866:
|
|
|-
|-
| || || || || ||13\41
|32\101
| ||380.488
|380.198
|458.8235
|486.076
|''412.195''||9||2||4.500||Magic/witchcraft
|22
|5
|4.400
|
|-
| 13\41 ||380.488
|487.500||9||2||4.500||Magic/witchcraft
|-
|-
|33\104
|380.769
|488.889
|23
|5
|4.600
|
|
|-
|20\63
|380.952
|489.769
|14
|3
|4.667
|
|
|-
|27\85
|381.176
|490.908
|19
|4
|4.750
|
|
|-
|34\107
|381.308
|491.566
|24
|5
|4.800
|
|
|-
|41\129
|381.395
|492.000
|29
|6
|4.833
|
|
|-
|48\151
|381.456
|492.308
|34
|7
|4.857
|
|-
|55\173
|381.503
|492.537
|39
|8
|4.875
|
|
|20\63
|-
|380.952
|62\195
|461.5385
|381.538
|''412.698''
|492.715
|14
|44
|3
|9
|4.667
|4.889
|
|-
|69\217
|381.567
|492.857
|49
|10
|4.900
|
|-
|76\239
|381.590
|492.973
|54
|11
|4.909
|
|-
|83\261
|381.609
|493.069
|59
|12
|4.917
|
|
|-
|-
| || || || ||7\22||
| 7\22 ||381.818
| ||381.818
|494.118||5||1||5.000||Magic/telepathy
|466.667
|''413.636''||5||1||5.000||Magic/telepathy
|-
|-
|50\157
|382.166
|495.868
|36
|7
|5.143
|
|
|-
|43\135
|382.222
|496.153
|31
|6
|5.167
|
|
|-
|36\113
|382.301
|496.551
|26
|5
|5.200
|
|
|-
|29\91
|382.418
|497.143
|21
|4
|5.250
|
|
|-
|22\69
|382.609
|498.113
|16
|3
|5.333
|
|-
|37\116
|382.759
|498.876
|27
|5
|5.400
|
|
|-
|52\163
|382.822
|499.200
|38
|7
|5.429
|
|
|-
|15\47
|15\47
|382.979
|382.979
|473.684
|500.000
|''414.894''
|11
|11
|2
|2
Line 544: Line 1,032:
|
|
|-
|-
| || || || || ||8\25
|23\72
| ||384.000
|383.333
|480.000
|501.818
|''416.000''||6||1||6.000||Würschmidt↓
|17
|3
|5.667
|
|-
| 8\25 ||384.000
|505.263||6||1||6.000||Würschmidt↓
|-
|-
|49\153
|384.314
|506.897
|37
|6
|6.167
|
|
|-
|41\128
|384.375
|507.216
|31
|5
|6.200
|
|
|-
|33\103
|384.466
|507.692
|25
|4
|6.250
|
|
|-
|25\78
|384.615
|508.475
|19
|3
|6.333
|
|
|-
|42\131
|384.733
|509.091
|32
|5
|6.400
|
|
|-
|17\53
|384.906
|510.000
|13
|2
|6.500
|
|
|-
|9\28
|9\28
|385.714
|385.714
|490.909
|514.286
|''417.857''
|7
|7
|1
|1
Line 564: Line 1,099:
|
|
|-
|-
|1\3|| || || || ||
|1\3||400.000
| ||400.000
|600.000||1||0||→ inf||
|600.000
|''433.333''||1||0||→ inf||
|}
|}


Line 574: Line 1,107:
=== Parents of [[User:Moremajorthanmajor/Greater Luachoid|Greater Luachoid]] ===
=== Parents of [[User:Moremajorthanmajor/Greater Luachoid|Greater Luachoid]] ===
[[3L 7s (33/16-equivalent)]] - harmonic subminor ninth tuning
[[3L 7s (33/16-equivalent)]] - harmonic subminor ninth tuning
[[3L 7s (44/21-equivalent)]] - Neogothic minor ninth tuning


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


[[3L 7s (19/9-equivalent)]] - simplest ratio near median edo interval (13\12)
[[3L 7s (19/9-equivalent)]] - simplest ratio near highest tuning (13\12)


=== Upper tunings ===
=== Upper tunings ===
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