User:Moremajorthanmajor/7L 4s (diminished twelfth-equivalent): Difference between revisions

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'''7L 4s<diminished twelfth>''' has a generator of a narrow wolf to wide wolf fourth of 458.{{Overline|18}}¢ (3/11ed7/5) to 538.7755¢ (2/7ed11/7). Insofar as it may be said to be a Reformed mode, it is an authentic Locrian mode.
'''7L 4s<diminished twelfth>''' has a generator of a narrow wolf to wide wolf fourth of 458.182¢ (3/11ed7/5) to 538.776¢ (2/7ed11/7). Insofar as it may be said to be a Reformed mode, it is an authentic Locrian mode.
== Scale tree==
== Scale tree==
{| class="wikitable center-all"
{| class="wikitable center-all"
! colspan="7" rowspan="2" |Generator
! rowspan="2" |Generator
! colspan="2" |Cents<ref name=":0">Fractions which repeat in more than 3 digits in sexagesimal</ref>
! colspan="2" |Cents
! rowspan="2" |L
! rowspan="2" |L
! rowspan="2" |s
! rowspan="2" |s
Line 12: Line 12:
!3L
!3L
|-
|-
|3\11|| || || || ||
|3\11|| 514.286
| || 514.286
|514.286||1||1||1.000||
|514.286||1||1||1.000||
|-
|-
|
|
|
|
|
|
|20\73
|20\73
|510.638
|510.638
Line 30: Line 23:
|
|
|-
|-
|  ||  ||  ||  ||  ||17\62
| 17\62 ||510.000
|  ||510.000
|540.000||6||5||1.200||
|540.000||6||5||1.200||
|-
|-
|
|
|
|
|
|
|31\113
|31\113
|509.589
|509.589
Line 48: Line 34:
|
|
|-
|-
| || || || ||14\51||
| 14\51||509.091
| ||509.{{Overline|09}}
|545.455||5||4||1.250||
|545.{{Overline|45}}||5||4||1.250||
|-
|-
|
|
|
|
|
|
|39\142
|39\142
|508.696
|508.696
Line 66: Line 45:
|
|
|-
|-
|  ||  ||  ||  ||  ||25\91
| 25\91 ||508.475
|  ||508.475
|549.153||9||7||1.286||
|549.153||9||7||1.286||
|-
|-
|
|
|
|
|
|
|36\131
|36\131
|508,235
|508,235
Line 84: Line 56:
|
|
|-
|-
|  ||  ||  ||11\40||  ||
| 11\40 ||507.692
|  ||507.692
|553.846||4||3||1.333||
|553.846||4||3||1.333||
|-
|-
|
|
|
|
|
|
|41\149
|41\149
|507,216
|507,216
Line 102: Line 67:
|
|
|-
|-
|  ||  ||  ||  ||  ||30\109
| 30\109 || 507.042
|  || 507.042
|557.746||11||8||1.375||
|557.746||11||8||1.375||
|-
|-
|
|
|
|
|
|
|49\178
|49\178
|506.897
|506.897
Line 120: Line 78:
|
|
|-
|-
|  ||  ||  ||  ||19\69||
| 19\69 ||506.667
|  ||506.{{Overline|6}}
|560.000||7||5||1.400||
|560.000||7||5||1.400||
|-
|-
|
|
|
|
|
|
|46\167
|46\167
|506.422
|506.422
Line 138: Line 89:
|
|
|-
|-
|  ||  ||  ||  ||  ||27\98
| 27\98 ||506.250
|  ||506.250
|562.500||10||7||1.428||
|562.500||10||7||1.428||
|-
|-
|
|
|
|
|
|
|35\127
|35\127
|506.024
|506.024
Line 156: Line 100:
|
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|-
|-
|  ||  ||8\29||  ||  ||
| 8\29 ||505.263
|  ||505.263
|568.421||3||2||1.500||L/s = 3/2
|568.421||3||2||1.500||L/s = 3/2
|-
|-
|
|
|
|
|
|
|37\134
|37\134
|504.{{Overline|54}}
|504.545
|572.{{Overline|72}}
|572.727
|14
|14
|9
|9
Line 174: Line 111:
|
|
|-
|-
|  ||  ||  ||  ||  ||29\105
| 29\105 || 504.348
|  || 504.348
|573.913||11||7||1.571||
|573.913||11||7||1.571||
|-
|-
|
|
|
|
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|
|50\181
|50\181
|504.202
|504.202
Line 192: Line 122:
|
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|-
|-
|  ||  ||  ||  ||21\76||
| 21\76 ||504.000
|  ||504.000
|576.000||8||5||1.600||
|576.000||8||5||1.600||
|-
|-
| || || || || ||34\123
| 34\123|| 503.704
|  || 503.{{Overline|703}}
|577.778||13||8||1.625||Unnamed golden tuning
|577.{{Overline|7}}||13||8||1.625||Unnamed golden tuning
|-
|-
|
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|47\170
|47\170
|503.571
|503.571
Line 214: Line 136:
|
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|-
|-
|  ||  ||  ||13\47||  ||
| 13\47 ||503.226
|  ||503.226
|580.645||5||3||1.667||
|580.645||5||3||1.667||
|-
|-
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|44\159
|44\159
|502.857
|502.857
Line 232: Line 147:
|
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|-
|-
| || || || || ||31\112
| 31\112|| 502.703
|  || 502.{{Overline|702}}
|583.784||12||7||1.714||
|583.{{Overline|783}}||12||7||1.714||
|-
|-
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|49\177
|49\177
|502.563
|502.563
Line 250: Line 158:
|
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|-
|-
|  ||  ||  ||  ||18\65||
| 18\65 ||502.326
|  ||502.326
|586.047||7||4||1.750||
|586.047||7||4||1.750||
|-
|-
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|41\148
|41\148
|502.041
|502.041
Line 268: Line 169:
|
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|-
|-
| || || || || ||23\83
| 23\83||501.818
| ||501.{{Overline|81}}
|589.081||9||5||1.800||
|589.{{Overline|09}}||9||5||1.800||
|-
|-
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|
|
|28\101
|28\101
|501.493
|501.493
Line 286: Line 180:
|
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|-
|-
| ||5\18|| || || ||
| 5\18||500.000
| ||500.000
|600.000||2||1||2.000||
|600.000||2||1||2.000||
|-
|-
|42\151
|499.010
|605.941
|17
|8
|2.125
|
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|-
|37\133
|498.876
|606.742
|15
|7
|2.143
|
|
|-
|32\115
|498.701
|607.792
|13
|6
|2.167
|
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|-
|
|
|27\97
|27\97
|498.462
|498.462
Line 304: Line 215:
|
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|-
|-
| || || || || ||22\79
| 22\79||498.113
| ||498.113
|611.321||9||4||2.250||
|611.321||9||4||2.250||
|-
|-
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|39\140
|39\140
|497.872
|497.872
Line 322: Line 226:
|
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|-
|-
|  ||  ||  ||  ||17\61||
| 17\61 ||497.651
|  ||497.651
|614.512||7||3||2.333||
|614.512||7||3||2.333||
|-
|-
|
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|
|46\165
|46\165
|497.{{Overline|297}}
|497.297
|616.{{Overline|216}}
|616.216
|19
|19
|8
|8
Line 340: Line 237:
|
|
|-
|-
|  ||  ||  ||  ||  ||29\104
| 29\104 || 497.143
|  || 497.143
|617.143||12||5||2.400||
|617.143||12||5||2.400||
|-
|-
|
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|
|41\147
|41\147
|496.{{Overline|96}}
|496.970
|618.{{Overline|18}}
|618.182
|17
|17
|7
|7
Line 358: Line 248:
|
|
|-
|-
|  ||  ||  ||12\43||  ||
| 12\43 ||496.552
|  ||496.552
|620.690||5||2||2.500||
|620.690||5||2||2.500||
|-
|-
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|43\154
|43\154
|496.154
|496.154
Line 376: Line 259:
|
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|-
|-
|  ||  ||  ||  ||  ||31\111
| 31\111 || 496.000
|  || 496.000
|624.000||13|| 5||2.600||
|624.000||13|| 5||2.600||
|-
|-
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|
|50\179
|50\179
|495.868
|495.868
Line 394: Line 270:
|Unnamed golden tuning
|Unnamed golden tuning
|-
|-
|  ||  ||  ||  ||19\68||
| 19\68 ||495.652
|  ||495.652
|626.086||8||3||2.667||
|626.086||8||3||2.667||
|-
|-
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|
|45\161
|45\161
|495.413
|495.413
Line 412: Line 281:
|
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|-
|-
|  ||  ||  ||  ||  ||26\93
| 26\93 ||495.238
|  ||495.238
|628.571||11||4||2.750||
|628.571||11||4||2.750||
|-
|-
|
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|
|33\118
|33\118
|495.000
|495.000
Line 430: Line 292:
|
|
|-
|-
|  ||  ||7\25||  ||  ||
| 7\25 ||494.118
|  ||494.118
|635.294||3||1||3.000||L/s = 3/1
|635.294||3||1||3.000||L/s = 3/1
|-
|-
|
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|
|
|
|
|30\107
|30\107
|493.151
|493.151
Line 448: Line 303:
|
|
|-
|-
|  ||  ||  ||  ||  ||23\82
| 23\82 ||492.857
|  ||492.857
|642.857||10||3||3.333||
|642.857||10||3||3.333||
|-
|-
|
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|
|
|
|
|39\139
|39\139
|492.631
|492.631
Line 466: Line 314:
|
|
|-
|-
|  ||  ||  ||  ||16\57||
| 16\57 ||492.308
|  ||492.308
|646.154||7||2||3.500||
|646.154||7||2||3.500||
|-
|-
|
|
|
|
|
|
|41\146
|41\146
|492.000
|492.000
Line 484: Line 325:
|
|
|-
|-
|  ||  ||  ||  ||  ||25\89
| 25\89 ||491.803
|  ||491.803
|649.180||11||3||3.667||
|649.180||11||3||3.667||
|-
|-
|
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|
|
|
|34\121
|34\121
|491.566
|491.566
Line 502: Line 336:
|
|
|-
|-
| || || ||9\32|| ||
| 9\32|| 490.909
|  || 490.{{Overline|90}}
|654.545||4||1||4.000||
|654.{{Overline|54}}||4||1||4.000||
|-
|-
|
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|
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|
|29\103
|29\103
|490.141
|490.141
Line 520: Line 347:
|
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|-
|-
|  ||  ||  ||  ||  ||20\71
| 20\71 ||489.796
|  ||489.796
|661.224||9||2||4.500||
|661.224||9||2||4.500||
|-
|-
|
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|
|31\110
|31\110
|489.474
|489.474
Line 538: Line 358:
|
|
|-
|-
| || || || ||11\39||
| 11\39||488.889
| ||488.{{Overline|8}}
|666.667||5||1||5.000||
|666.{{Overline|6}}||5||1||5.000||
|-
|-
|
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|
|24\85
|24\85
|488.136
|488.136
Line 556: Line 369:
|
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|-
|-
|  ||  ||  ||  ||  ||13\46
| 13\46 ||487.500
|  ||487.500
|675.000||6||1||6.000||
|675.000||6||1||6.000||
|-
|-
|
|
|
|
|
|
|15\53
|15\53
|486.{{Overline|486}}
|486.486
|681.{{Overline|081}}
|681.081
|7
|7
|1
|1
Line 574: Line 380:
|
|
|-
|-
|2\7||  ||  ||  ||  ||
|2\7|| 480.000
|  || 480.000
|720.000||1||0||→ inf
|720.000||1||0||→ inf
|}
|}
==See also==
==See also==
[[7L 4s (8/3-equivalent)]] - warped Pythagorean tuning
[[7L 4s (343/128-equivalent)]] - 1/2-comma Archytas tuning
[[7L 4s (e-equivalent)|7L 4s ([math]e[/math]-equivalent)]] - natural tuning
[[7L 4s (49/18-equivalent)]] - 1/3-comma Archytas tuning
[[7L 4s (11/4-equivalent)]] - idealized low tuning, low undecimal tuning
[[7L 4s (11/4-equivalent)]] - idealized low tuning, low undecimal tuning
[[7L 4s (224/81-equivalent)]] - 1/6-comma Archytas tuning


[[7L 4s (14/5-equivalent)]] - low septimal tuning
[[7L 4s (14/5-equivalent)]] - low septimal tuning


[[7L 4s (20/7-equivalent)]] - idealized high tuning, high septimal tuning
[[7L 4s (1024/729-equivalent)]] - Pythagorean tuning
 
[[7L 4s (45/16-equivalent)]] - 1/6-comma meantone tuning
 
[[7L 4s (20/7-equivalent)]] - idealized high tuning, high septimal (meantone) tuning
 
[[7L 4s (72/25-equivalent)]] - 1/3-comma meantone tuning
 
[[7L 4s (32/11-equivalent)]] - high undecimal tuning
 
[[7L 4s (729/250-equivalent)]] - 1/2-comma meantone tuning


[[7L 4s (32/11-equivalent)]] - high undecimal tuning<references />
[[7L 4s (3/1-equivalent)]] - superelectric<references />

Latest revision as of 04:10, 2 November 2024

7L 4s<diminished twelfth> has a generator of a narrow wolf to wide wolf fourth of 458.182¢ (3/11ed7/5) to 538.776¢ (2/7ed11/7). Insofar as it may be said to be a Reformed mode, it is an authentic Locrian mode.

Scale tree

Generator Cents L s L/s Comments
g 3L
3\11 514.286 514.286 1 1 1.000
20\73 510.638 536.170 7 6 1.167
17\62 510.000 540.000 6 5 1.200
31\113 509.589 542.466 11 9 1.222
14\51 509.091 545.455 5 4 1.250
39\142 508.696 547.825 14 11 1.273
25\91 508.475 549.153 9 7 1.286
36\131 508,235 550.588 13 10 1.300
11\40 507.692 553.846 4 3 1.333
41\149 507,216 556.701 15 11 1.363
30\109 507.042 557.746 11 8 1.375
49\178 506.897 558.620 18 13 1.385
19\69 506.667 560.000 7 5 1.400
46\167 506.422 561.468 17 12 1.416
27\98 506.250 562.500 10 7 1.428
35\127 506.024 563.855 13 9 1.444
8\29 505.263 568.421 3 2 1.500 L/s = 3/2
37\134 504.545 572.727 14 9 1.556
29\105 504.348 573.913 11 7 1.571
50\181 504.202 574.790 19 12 1.583
21\76 504.000 576.000 8 5 1.600
34\123 503.704 577.778 13 8 1.625 Unnamed golden tuning
47\170 503.571 578.571 18 11 1.636
13\47 503.226 580.645 5 3 1.667
44\159 502.857 582.857 17 10 1.700
31\112 502.703 583.784 12 7 1.714
49\177 502.563 584.615 19 11 1.727
18\65 502.326 586.047 7 4 1.750
41\148 502.041 587.755 16 9 1.778
23\83 501.818 589.081 9 5 1.800
28\101 501.493 591.045 11 6 1.833
5\18 500.000 600.000 2 1 2.000
42\151 499.010 605.941 17 8 2.125
37\133 498.876 606.742 15 7 2.143
32\115 498.701 607.792 13 6 2.167
27\97 498.462 609.231 11 5 2.200
22\79 498.113 611.321 9 4 2.250
39\140 497.872 612.766 16 7 2.286
17\61 497.651 614.512 7 3 2.333
46\165 497.297 616.216 19 8 2.375
29\104 497.143 617.143 12 5 2.400
41\147 496.970 618.182 17 7 2.429
12\43 496.552 620.690 5 2 2.500
43\154 496.154 623.077 18 7 2.571
31\111 496.000 624.000 13 5 2.600
50\179 495.868 624.793 21 8 2.625 Unnamed golden tuning
19\68 495.652 626.086 8 3 2.667
45\161 495.413 627.523 19 7 2.714
26\93 495.238 628.571 11 4 2.750
33\118 495.000 630.000 14 5 2.800
7\25 494.118 635.294 3 1 3.000 L/s = 3/1
30\107 493.151 641.096 13 4 3.250
23\82 492.857 642.857 10 3 3.333
39\139 492.631 644.211 17 5 3.400
16\57 492.308 646.154 7 2 3.500
41\146 492.000 648.000 18 5 3.600
25\89 491.803 649.180 11 3 3.667
34\121 491.566 650.601 15 4 3.750
9\32 490.909 654.545 4 1 4.000
29\103 490.141 659.155 13 3 4.333
20\71 489.796 661.224 9 2 4.500
31\110 489.474 663.158 14 3 4.667
11\39 488.889 666.667 5 1 5.000
24\85 488.136 671.186 11 2 6.500
13\46 487.500 675.000 6 1 6.000
15\53 486.486 681.081 7 1 7.000
2\7 480.000 720.000 1 0 → inf

See also

7L 4s (8/3-equivalent) - warped Pythagorean tuning

7L 4s (343/128-equivalent) - 1/2-comma Archytas tuning

7L 4s ([math]e[/math]-equivalent) - natural tuning

7L 4s (49/18-equivalent) - 1/3-comma Archytas tuning

7L 4s (11/4-equivalent) - idealized low tuning, low undecimal tuning

7L 4s (224/81-equivalent) - 1/6-comma Archytas tuning

7L 4s (14/5-equivalent) - low septimal tuning

7L 4s (1024/729-equivalent) - Pythagorean tuning

7L 4s (45/16-equivalent) - 1/6-comma meantone tuning

7L 4s (20/7-equivalent) - idealized high tuning, high septimal (meantone) tuning

7L 4s (72/25-equivalent) - 1/3-comma meantone tuning

7L 4s (32/11-equivalent) - high undecimal tuning

7L 4s (729/250-equivalent) - 1/2-comma meantone tuning

7L 4s (3/1-equivalent) - superelectric

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