User:Moremajorthanmajor/Greater sephiroid: Difference between revisions

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==Scale tree==
==Scale tree==
{| class="wikitable center-all"
{| class="wikitable center-all"
! colspan="7" |Generator
!Generator
!Cents
!Cents
!Normalized Cents
!Normalized Cents
Line 43: Line 43:
!Comments
!Comments
|-
|-
|3\10|| || || || ||
|3\10||360.000
| ||360.000
|360.000||1||1||1.000||
|360.000||1||1||1.000||
|-
|-
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|19\63
|19\63
|361.905
|361.905
Line 61: Line 54:
|
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|-
|-
| || || || || ||16\53
| 16\53||362.264
| ||362.264
|408.511||6||5||1.200||Submajor
|408.511||6||5||1.200||Submajor
|-
|-
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|29\96
|29\96
|362.500
|362.500
Line 79: Line 65:
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|-
| || || || ||13\43||
| 13\43||362.791
| ||362.791
|410.526||5||4||1.250||
|410.526||5||4||1.250||
|-
|-
| || || || || ||23\76
| 23\76||363.158
| ||363.158
|411.940||9||7||1.286||
|411.940||9||7||1.286||
|-
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|33\109
|33\109
|363.303
|363.303
Line 101: Line 79:
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|-
| || || ||10\33|| ||
| 10\33||363.636
| ||363.636
|413.793||4||3||1.333||
|413.793||4||3||1.333||
|-
|-
| || || || || ||27\89
|37\122
| ||364.045
|363.935
|414.953
|15
|11
|1.455
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|-
| 27\89||364.045
|415.385||11||8||1.375||
|415.385||11||8||1.375||
|-
|-
| || || || ||17\56||
| 17\56||364.286
| ||364.286
|416.327||7||5||1.400||
|416.327||7||5||1.400||
|-
|-
| || || || || ||24\79
| 24\79||364.557
| ||364.557
|417.391||10||7||1.428||
|417.391||10||7||1.428||
|-
|-
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|31\102
|31\102
|364.706
|364.706
Line 131: Line 107:
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|-
|-
| || ||7\23|| || ||
| 7\23||365.217
| ||365.217
|420.000||3||2||1.500||L/s = 3/2
|420.000||3||2||1.500||L/s = 3/2
|-
|-
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|32\105
|32\105
|365.714
|365.714
Line 149: Line 118:
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|-
|-
| || || || || ||25\82
| 25\82||365.854
| ||365.854
|422.535||11||7||1.571||
|422.535||11||7||1.571||
|-
|-
| || || || ||18\59||
| 18\59||366.102
| ||366.102
|423.529||8||5||1.600||
|423.529||8||5||1.600||
|-
|-
| || || || || ||29\95
| 29\95||366.316
| ||366.316
|424.390||13||8||1.625||Unnamed golden tuning
|424.390||13||8||1.625||Unnamed golden tuning
|-
|-
|  ||  ||  ||11\36||  ||
| 11\36 ||366.667
|  ||366.667
|425.806||5||3||1.667||
|425.806||5||3||1.667||
|-
|-
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|37\121
|37\121
|366.942
|366.942
Line 179: Line 138:
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|-
|-
|  ||  ||  ||  ||  ||26\85
| 26\85 ||367.059
|  ||367.059
|427.397||12||7||1.714||
|427.397||12||7||1.714||
|-
|-
|  ||  ||  ||  ||15\49||
| 15\49 ||367.347
|  ||367.347
|428.571||7||4||1.750||
|428.571||7||4||1.750||
|-
|-
|  ||  ||  ||  ||  ||19\62
| 19\62 ||367.742
|  ||367.742
|430.189||9||5||1.800||
|430.189||9||5||1.800||
|-
|-
|23\75
|368.000
|431.250
|11
|6
|1.833
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|-
|27\88
|368.182
|432.000
|13
|7
|1.857
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|-
|31\101
|368.317
|432.558
|15
|8
|1.875
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|-
|35\114
|368.421
|432.990
|17
|9
|1.889
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|-
|39\127
|368.504
|433.333
|19
|10
|1.900
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|-
|43\140
|368.571
|433.614
|21
|11
|1.909
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|-
|47\153
|368.627
|433.846
|23
|12
|1.917
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|-
|51\166
|368.675
|434.042
|25
|13
|1.923
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|55\179
|368.715
|434.210
|27
|14
|1.929
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|59\192
|368.750
|434.356
|29
|15
|1.933
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|23\75
|-
|368.000
|63\205
|431.250
|368.780
|11
|434.483
|6
|31
|1.833
|16
|1.9375
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|-
|67\218
|368.807
|434.595
|33
|17
|1.941
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|-
|71\231
|368.831
|434.694
|35
|18
|1.944
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|-
|75\244
|368.852
|434.782
|37
|19
|1.947
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|-
|79\257
|368.872
|434.862
|39
|20
|1.950
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|-
|83\270
|368.889
|434.834
|41
|21
|1.953
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|-
|87\283
|368.905
|435.000
|43
|22
|1.955
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|-
|  ||4\13||  ||  ||  ||
| 4\13 ||369.231
|  ||369.231
|436.364||2||1||2.000||Basic sephiroid<br>(Generators smaller than this are proper)
|436.364||2||1||2.000||Basic sephiroid<br>(Generators smaller than this are proper)
|-
|-
|77\250
|369.600
|437.915
|39
|19
|1.053
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|-
|73\237
|369.620
|438.000
|37
|18
|1.056
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|-
|69\224
|369.643
|438.085
|35
|17
|1.059
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|-
|65\211
|369.668
|438.202
|33
|16
|1.0625
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|-
|61\198
|369.697
|438.323
|31
|15
|2.067
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|-
|57\185
|369.730
|438.462
|29
|14
|2.071
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|53\172
|369.767
|438.621
|27
|13
|2.077
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|-
|49\159
|369.811
|438.806
|25
|12
|2.083
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|45\146
|369.863
|439.024
|23
|11
|2.091
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|41\133
|369.925
|439.286
|21
|10
|2.100
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|37\120
|370.000
|439.604
|19
|9
|2.111
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|-
|33\107
|370.093
|440.000
|17
|8
|2.125
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|-
|29\94
|370.213
|440.506
|15
|7
|2.143
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|-
|25\81
|370.370
|441.176
|13
|6
|2.167
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|-
|21\68
|21\68
|370.588
|370.588
Line 223: Line 406:
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|-
|-
|  ||  ||  ||  ||  ||17\55
| 17\55 ||370.909
|  ||370.909
|443.478||9||4||2.250||
|443.478||9||4||2.250||
|-
|-
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|30\97
|30\97
|371.134
|371.134
Line 241: Line 417:
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|-
|  ||  ||  ||  ||13\42||
| 13\42 ||371.429
|  ||371.429
|445.714||7||3||2.333||
|445.714||7||3||2.333||
|-
|-
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|35\113
|35\113
|371.681
|371.681
Line 259: Line 428:
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|-
|-
|  ||  ||  ||  ||  ||22\71
| 22\71 ||371.831
|  ||371.831
|447.458||12||5||2.400||
|447.458||12||5||2.400||
|-
|-
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|31\100
|31\100
|372.000
|372.000
Line 277: Line 439:
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|-
| ||  ||  ||9\29||  ||
|40\129
|  ||372.414
|372.093
|450.000||5||2||2.500||Sephiroth
|448.598
|22
|9
|2.444
|
|-
|-
|49\158
|372.152
|448.855
|27
|11
|2.455
|
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|-
|58\187
|372.193
|449.032
|32
|13
|2.462
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|-
|
| 9\29 ||372.414
|
|450.000||5||2||2.500||Sephiroth
|
|-
|32\103
|32\103
|372.816
|372.816
Line 295: Line 474:
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|-
|-
|  ||  ||  ||  ||  ||23\74
| 23\74 ||372.973
|  ||372.973
|452.459||13||5||2.600||
|452.459||13||5||2.600||
|-
|-
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|37\119
|37\119
|373.109
|373.109
Line 313: Line 485:
|Golden sephiroth
|Golden sephiroth
|-
|-
|  ||  ||  ||  ||14\45||
| 14\45 ||373.333
|  ||373.333
|454.054||8||3||2.667||
|454.054||8||3||2.667||
|-
|-
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|33\106
|33\106
|373.585
|373.585
Line 331: Line 496:
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|-
|  ||  ||  ||  ||  ||19\61
| 19\61 ||373.770
|  ||373.770
|456.000||11||4||2.750||
|456.000||11||4||2.750||
|-
|-
|24\77
|374.000
|457.143
|14
|5
|2.800
|
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|-
|29\93
|374.194
|457.895
|17
|6
|2.833
|
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|-
|34\109
|374.312
|458.427
|20
|7
|2.857
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|-
|39\125
|374.400
|458.824
|23
|8
|2.875
|
|-
|44\141
|374.468
|459.130
|26
|9
|2.889
|
|-
|49\157
|374.522
|459.375
|29
|10
|2.900
|
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|-
|54\173
|374.566
|459.574
|32
|11
|2.909
|
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|-
|59\189
|374.603
|459.740
|35
|12
|2.917
|
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|-
|64\205
|374.634
|459.880
|38
|13
|2.923
|
|
|24\77
|-
|374.000
|69\221
|457.143
|374.660
|460.000
|41
|14
|14
|5
|2.929
|2.800
|
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|-
|-
|  ||  ||5\16||  ||  ||
| 5\16 ||375.000
|  ||375.000
|461.538||3||1||3.000||L/s = 3/1
|461.538||3||1||3.000||L/s = 3/1
|-
|-
|76\243
|375.309
|462.944
|46
|15
|3.067
|
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|-
|71\227
|375.330
|463.043
|43
|14
|3.071
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|-
|66\211
|375.355
|463.158
|40
|13
|3.077
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|-
|61\195
|375.385
|463.291
|37
|12
|3.083
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|-
|56\179
|375.419
|463.448
|34
|11
|3.091
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|-
|51\163
|375.460
|463.636
|31
|10
|3.100
|
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|-
|46\147
|375.510
|463.866
|28
|9
|3.111
|
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|-
|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
|
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|-
|21\67
|21\67
|376.119
|376.119
Line 367: Line 678:
|
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|-
| || || || ||  ||16\51
|37\118
|  ||376.471
|376.271
|457.368
|23
|7
|3.286
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|-
| 16\51 ||376.471
|468.293||10||3||3.333||
|468.293||10||3||3.333||
|-
|-
|
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|27\86
|27\86
|376.744
|376.744
Line 385: Line 697:
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|-
| || || || ||11\35||
|38\121
|  ||377.143
|376.860
|470.103
|24
|7
|3.429
|
|-
| 11\35 ||377.143
|471.429||7||2||3.500||
|471.429||7||2||3.500||
|-
|-
|39\124
|377.419
|472.727
|25
|7
|3,571
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|-
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|28\89
|28\89
|377.528
|377.528
Line 403: Line 724:
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|-
|  ||  ||  ||  ||  ||17\54
| 17\54 ||377.778
|  ||377.778
|474.419||11||3||3.667||Muggles
|474.419||11||3||3.667||Muggles
|-
|-
|23\73
|378.082
|475.862
|15
|4
|3.750
|
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|-
|29\92
|378.261
|476.712
|19
|5
|3.800
|
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|-
|35\111
|378.378
|477.273
|23
|6
|3.833
|
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|-
|41\130
|378.462
|477.670
|27
|7
|3.857
|
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|-
|47\149
|378.523
|477.966
|31
|8
|3.875
|
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|-
|53\168
|378,571
|478.195
|35
|9
|3.889
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|-
|59\187
|378.607
|478.378
|39
|10
|3.900
|
|
|23\73
|-
|378.082
|65\206
|475.862
|378.641
|15
|478.528
|4
|43
|3.750
|11
|3.909
|
|-
|71\225
|378.667
|478.652
|47
|12
|3.917
|
|
|-
|-
| ||  ||  ||6\19||  ||
|77\244
|  ||378.947
|378.689
|480.000||4||1||4.000||Magic/horcrux
|478.756
|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
Line 439: Line 866:
|
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|-
|-
| || || || ||  ||13\41
|32\101
|  ||380.488
|380.198
|486.076
|22
|5
|4.400
|
|-
| 13\41 ||380.488
|487.500||9||2||4.500||Magic/witchcraft
|487.500||9||2||4.500||Magic/witchcraft
|-
|-
|33\104
|380.769
|488.889
|23
|5
|4.600
|
|
|
|-
|
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|
|
|20\63
|20\63
|380.952
|380.952
Line 457: Line 893:
|
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|-
|-
| || || || ||7\22||
|27\85
| ||381.818
|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
|
|-
|62\195
|381.538
|492.715
|44
|9
|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 ||381.818
|494.118||5||1||5.000||Magic/telepathy
|494.118||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
Line 475: Line 1,032:
|
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|-
|-
| || || || ||  ||8\25
|23\72
|  ||384.000
|383.333
|501.818
|17
|3
|5.667
|
|-
| 8\25 ||384.000
|505.263||6||1||6.000||Würschmidt↓
|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
Line 493: Line 1,099:
|
|
|-
|-
|1\3|| || || || ||
|1\3||400.000
| ||400.000
|600.000||1||0||→ inf||
|600.000||1||0||→ inf||
|}
|}

Revision as of 03:17, 30 July 2023

3L 7s(<5/2>) occupies the spectrum from 10edo (L = s) to 3edo (s = 0).

TAMNAMS calls this MOS pattern sephiroid (named after the abstract temperament sephiroth).

This MOS can represent tempered-flat chains of the 13th harmonic, which approximates phi (~833 cents). In the region of the spectrum around 23edo (L = 3, s = 2) , the 17th and 21st harmonics are tempered toward most accurately, which together are a stable harmony. This is the major chord of the modi sephiratorum. Temperament using phi directly approximates the higher Fibonacci harmonics best.

If L = s, i.e. multiples of 10edo, the 13th harmonic becomes nearly perfect. 121edo seems to be the first to 'accurately' represent the comma (which might as well be represented accurately as it is quite small). Towards the other end, where the large and small steps are more contrasted, the comma 65/64 is liable to be tempered out, equating 8/5 and 13/8. In this category fall 13edo, 16edo, 19edo, 22edo, 29edo, and so on. This ends at s = 0 which gives multiples of 3edo.

Harmonically, the arrangement forming a chord (degrees 0, 1, 4, 7, 10) is symmetrical – not ascending but rather descending, and so reminiscent of ancient Greek practice. These scales, and their truncated heptatonic forms referenced below, are strikingly linear in several ways and so seem suited to a similar outlook as traditional western music (modality, baroque tonality, classical tonality, etc. progressing to today) but with higher harmonics. For more details see Kosmorsky's Tractatum de Modi Sephiratorum (Kosmorsky knows it should be "tractatus", but considers changing it is nothing but a bother.)

There are MODMOS as well, but Kosmorsky has not explored them yet. There's enough undiscovered harmonic resources already in these to last me a while! Taking this approach to the 13th harmonic also yields heptatonic MOS with similar properties: 4s+3L "mish" in the form of modes of ssLsLsL "led".

Modes

s s s L s s L s s L - Keter

s s L s s L s s L s - Chesed

s L s s L s s L s s - Netzach

L s s L s s L s s s - Malkuth

s s L s s L s s s L - Binah

s L s s L s s s L s - Tiferet

L s s L s s s L s s - Yesod

s s L s s s L s s L - Chokmah

s L s s s L s s L s - Gevurah

L s s s L s s L s s - Hod

Scale tree

Generator Cents Normalized Cents L s L/s Comments
3\10 360.000 360.000 1 1 1.000
19\63 361.905 407.143 7 6 1.167
16\53 362.264 408.511 6 5 1.200 Submajor
29\96 362.500 409.412 11 9 1.222
13\43 362.791 410.526 5 4 1.250
23\76 363.158 411.940 9 7 1.286
33\109 363.303 412.500 13 10 1.300
10\33 363.636 413.793 4 3 1.333
37\122 363.935 414.953 15 11 1.455
27\89 364.045 415.385 11 8 1.375
17\56 364.286 416.327 7 5 1.400
24\79 364.557 417.391 10 7 1.428
31\102 364.706 417.978 13 9 1.444
7\23 365.217 420.000 3 2 1.500 L/s = 3/2
32\105 365.714 421.978 14 9 1.556
25\82 365.854 422.535 11 7 1.571
18\59 366.102 423.529 8 5 1.600
29\95 366.316 424.390 13 8 1.625 Unnamed golden tuning
11\36 366.667 425.806 5 3 1.667
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
43\140 368.571 433.614 21 11 1.909
47\153 368.627 433.846 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
75\244 368.852 434.782 37 19 1.947
79\257 368.872 434.862 39 20 1.950
83\270 368.889 434.834 41 21 1.953
87\283 368.905 435.000 43 22 1.955
4\13 369.231 436.364 2 1 2.000 Basic sephiroid
(Generators smaller than this are proper)
77\250 369.600 437.915 39 19 1.053
73\237 369.620 438.000 37 18 1.056
69\224 369.643 438.085 35 17 1.059
65\211 369.668 438.202 33 16 1.0625
61\198 369.697 438.323 31 15 2.067
57\185 369.730 438.462 29 14 2.071
53\172 369.767 438.621 27 13 2.077
49\159 369.811 438.806 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\68 370.588 442.105 11 5 2.200
17\55 370.909 443.478 9 4 2.250
30\97 371.134 444.444 16 7 2.286
13\42 371.429 445.714 7 3 2.333
35\113 371.681 446.809 19 8 2.375
22\71 371.831 447.458 12 5 2.400
31\100 372.000 448.193 17 7 2.429
40\129 372.093 448.598 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\103 372.816 451.765 18 7 2.571
23\74 372.973 452.459 13 5 2.600
37\119 373.109 453.061 21 8 2.625 Golden sephiroth
14\45 373.333 454.054 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
49\157 374.522 459.375 29 10 2.900
54\173 374.566 459.574 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
61\195 375.385 463.291 37 12 3.083
56\179 375.419 463.448 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\67 376.119 466.667 13 4 3.250
37\118 376.271 457.368 23 7 3.286
16\51 376.471 468.293 10 3 3.333
27\86 376.744 469.565 17 5 3.400
38\121 376.860 470.103 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\89 377.528 473.239 18 5 3.600
17\54 377.778 474.419 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
65\206 378.641 478.528 43 11 3.909
71\225 378.667 478.652 47 12 3.917
77\244 378.689 478.756 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\60 380.000 485.105 13 3 4.333
32\101 380.198 486.076 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
62\195 381.538 492.715 44 9 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\22 381.818 494.118 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\47 382.979 500.000 11 2 5.500
23\72 383.333 501.818 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\28 385.714 514.286 7 1 7.000
1\3 400.000 600.000 1 0 → inf

See also

Parents of Greater Luachoid

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 (19/9-equivalent) - simplest ratio near highest tuning (13\12)

Upper tunings

3L 7s (15/7-equivalent) - septimal diatonic minor ninth tuning

3L 7s (11/5-equivalent) - undecimal neutral ninth tuning

3L 7s (9/4-equivalent) - major ninth tuning

3L 7s (7/3-equivalent) - septimal minor tenth tuning

3L 7s (5/2-equivalent) - major tenth tuning

3L 7s (8/3-equivalent) - Anti-Choralic

3L 7s (11/4-equivalent) - undecimal augmented eleventh/diminished twelfth tuning

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