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

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Created page with "'''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) cents. Insofar as it may be sai..."
 
 
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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) cents. 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
! colspan="2" |''ed18\12 (→ed3\2)<ref name=":0" />''
! rowspan="2" |L
! rowspan="2" |L
! rowspan="2" |s
! rowspan="2" |s
Line 12: Line 11:
!g
!g
!3L
!3L
!''g''
!''3L''
|-
|-
|3\11|| || || || ||
|3\11|| 514.286
| ||514¢17’9”
|514.286||1||1||1.000||
|514¢17’9”
|''490.{{Overline|90}}''
|''490.{{Overline|90}}''||1||1||1.000||
|-
|-
| || || || || ||17\62
|20\73
| ||510
|510.638
|540
|536.170
|''493r¢32’54”''
|7
|''522r¢34’50”''||6||5||1.200||
|6
|1.167
|
|-
|-
| || || || ||14\51||
| 17\62 ||510.000
| ||509.{{Overline|09}}
|540.000||6||5||1.200||
|545.{{Overline|45}}
|''494r¢7’4”''
|''529r¢24’42”''||5||4||1.250||
|-
|-
| || || || || ||25\91
|31\113
| ||508¢28’28”
|509.589
|549¢9’9”
|542.466
|''494r¢30’20”''
|11
|''534r¢3’57”''||9||7||1.286||
|9
|1.222
|
|-
|-
| || || ||11\40|| ||
| 14\51||509.091
| ||507¢41’32”
|545.455||5||4||1.250||
|553¢50’46”
|''495''
|''540''||4||3||1.333||
|-
|-
| || || || || ||30\109
|39\142
| ||507¢2’32”
|508.696
|557¢44’47”
|547.825
|''495r¢24’46”''
|14
|''544r¢57’15”''||11||8||1.375||
|11
|1.273
|
|-
|-
| || || || ||19\69||
| 25\91 ||508.475
| ||506.{{Overline|6}}
|549.153||9||7||1.286||
|560
|''495r¢39’8”''
|''547r49’34”''||7||5||1.400||
|-
|-
| || || || || ||27\98
|36\131
| ||506.25
|508,235
|562.5
|550.588
|''495r¢55’6”''
|13
|''551r¢1’13”''||10||7||1.428||
|10
|1.300
|
|-
|-
| || ||8\29|| || ||
| 11\40 ||507.692
| ||505¢15’47”
|553.846||4||3||1.333||
|568¢25’16”
|-
|''496r¢33’6”''
|41\149
|''558¢37’14”''||3||2||1.500||L/s = 3/2
|507,216
|556.701
|15
|11
|1.363
|
|-
|-
| || || || || ||29\105
| 30\109 || 507.042
| ||504¢20’52”
|557.746||11||8||1.375||
|573¢54’47”
|''497r¢8’34”''
|''565r¢42’51”''||11||7||1.571||
|-
|-
| || || || ||21\76||
|49\178
| ||504
|506.897
|576
|558.620
|''497r¢22’6”''
|18
|''568¢25’16”''||8||5||1.600||
|13
|1.385
|
|-
|-
| || || || || ||34\123
| 19\69 ||506.667
| ||503.{{Overline|703}}
|560.000||7||5||1.400||
|577.{{Overline|7}}
|''497r¢33’40”''
|''570r¢43’54”''||13||8||1.625||Unnamed golden tuning
|-
|-
| || || ||13\47|| ||
|46\167
| ||503¢13’33”
|506.422
|580¢38’43”
|561.468
|''497¢49’47”''
|17
|''574r¢28’5”''||5||3||1.667||
|12
|1.416
|
|-
|-
| || || || || ||31\112
| 27\98 ||506.250
| ||502.{{Overline|702}}
|562.500||10||7||1.428||
|583.{{Overline|783}}
|''498r¢12’51”''
|''578r¢34’17”''||12||7||1.714||
|-
|-
| || || || ||18\65||
|35\127
| ||502¢19’32”
|506.024
|586¢2’47”
|563.855
|''498r¢27’42”''
|13
|''581r¢32’18”''||7||4||1.750||
|9
|1.444
|
|-
|-
| || || || || ||23\83
| 8\29 ||505.263
| ||501.{{Overline|81}}
|568.421||3||2||1.500||L/s = 3/2
|589.{{Overline|09}}
|''498r¢47’43”''
|''585r¢33’15”''||9||5||1.800||
|-
|-
|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
|28\101
|501¢29’35”
|501.493
|591¢3’23”
|591.045
|''499r¢36’''
|''588r¢7’8”''
|11
|11
|6
|6
Line 127: Line 180:
|
|
|-
|-
| ||5\18|| || || ||
| 5\18||500.000
| ||500
|600.000||2||1||2.000||
|600
|''500''
|''600''||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
|27\97
|498¢47’43”
|498.462
|609¢13’51”
|609.231
|''501r¢1’51”''
|''612r¢22’16”''
|11
|11
|5
|5
Line 149: Line 215:
|
|
|-
|-
| || || || || ||22\79
| 22\79||498.113
| ||498¢6’48”
|611.321||9||4||2.250||
|611¢19’15”
|-
|''501¢15’57”''
|39\140
|''615r¢11’24”''||9||4||2.250||
|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
|
|-
|-
| || || || ||17\61||
| 29\104 || 497.143
| ||497¢33’40”
|617.143||12||5||2.400||
|614¢38’3”
|''501r¢38’22”''
|''619r¢40’20”''||7||3||2.333||
|-
|-
| || || || || ||29\104
|41\147
| ||497¢8’34”
|496.970
|617¢8’34”
|618.182
|''501r¢55’23”''
|17
|''623r¢4’37”''||12||5||2.400||
|7
|2.429
|
|-
|-
| || || ||12\43|| ||
| 12\43 ||496.552
| ||496¢33’6”
|620.690||5||2||2.500||
|620¢41’23”
|''502r¢19’32”''
|''627r¢54’25”''||5||2||2.500||
|-
|-
| || || || || ||31\111
|43\154
| ||496
|496.154
|624
|623.077
|''502.{{Overline|702}}''
|18
|''632.{{Overline|432}}''||13||5||2.600||Unnamed golden tuning
|7
|2.571
|
|-
|-
| || || || ||19\68||
| 31\111 || 496.000
| ||495¢39’8”
|624.000||13|| 5||2.600||
|626¢5’13”
|''502r¢56’28”''
|''635r¢17’39”''||8||3||2.667||
|-
|-
| || || || || ||26\93
|50\179
| ||495¢14’17”
|495.868
|628¢34’17”
|624.793
|''503r¢13’33”''
|21
|''638r¢42’35”''||11||4||2.750||
|8
|2.625
|Unnamed golden tuning
|-
|-
| || ||7\25|| || ||
| 19\68 ||495.652
| ||494¢7’4”
|626.086||8||3||2.667||
|635¢17’39”
|''504''
|''648''||3||1||3.000||L/s = 3/1
|-
|-
|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
|
|
|30\107
|-
|493¢9’2”
| 9\32|| 490.909
|641¢5’45”
|654.545||4||1||4.000||
|''504r¢40’22”''
|-
|''656r¢1’41”''
|29\103
|490.141
|659.155
|13
|13
|4
|3
|3.250
|4.333
|
|
|-
|-
| || || || || ||23\82
| 20\71 ||489.796
| ||492¢51’26”
|661.224||9||2||4.500||
|642¢51’26”
|''504r¢52’41”''
|''658¢32’12”''||10||3||3.333||
|-
|-
| || || || ||16\57||
|31\110
| ||492¢18’28”
|489.474
|646¢50’46”
|663.158
|''505r¢15’47”''
|14
|''663r¢9’28”''||7||2||3.500||
|3
|4.667
|
|-
|-
| || || || || ||25\89
| 11\39||488.889
| ||491¢48’12”
|666.667||5||1||5.000||
|649¢10’49”
|''505r¢37’5”''
|''667r¢24’57”''||11||3||3.667||
|-
|-
| || || ||9\32|| ||
|24\85
| ||490.{{Overline|90}}
|488.136
|654.{{Overline|54}}
|671.186
|''506.25''
|11
|''675''||4||1||4.000||
|2
|6.500
|
|-
|-
| || || || || ||20\71
| 13\46 ||487.500
| ||489¢47’45”
|675.000||6||1||6.000||
|661¢13’28”
|''507r¢2’32”''
|''684r¢30’25”''||9||2||4.500||
|-
|-
| || || || ||11\39||
|15\53
| ||488.{{Overline|8}}
|486.486
|666.{{Overline|6}}
|681.081
|''507r¢41’32”''
|7
|''692r¢30’25”''||5||1||5.000||
|1
|7.000
|
|-
|-
| || || || || ||13\46
|2\7|| 480.000
| ||487.5
|720.000||1||0||→ inf
|675
|''508r¢41’44”''
|''704r¢20’52”''||6||1||6.000||
|-
|2\7|| || || || ||
| ||480
|720
|''514r¢17’9”''
|''771r¢25’43”''||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 (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 (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


<references />
[[7L 4s (3/1-equivalent)]] - superelectric<references />
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