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) 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.{{Overline|18}} (3/11ed7/5) to [[Tel:538.7755|538.7755]] (2/7ed11/7) cents. 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
! colspan="7" rowspan="2" |Generator
! colspan="2" |Cents<ref name=":0">Fractions which repeat in more than 3 digits in sexagesimal</ref>
! colspan="2" |Cents<ref name=":0">Fractions which repeat in more than 3 digits in sexagesimal</ref>
! 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¢17’9”
| ||514¢17’9”
|514¢17’9”
|514¢17’9”||1||1||1.000||
|''490.{{Overline|90}}''
|''490.{{Overline|90}}''||1||1||1.000||
|-
|-
| || || || || ||17\62
| || || || || ||17\62
| ||510
| ||510
|540
|540||6||5||1.200||
|''493r¢32’54”''
|''522r¢34’50”''||6||5||1.200||
|-
|-
| || || || ||14\51||
| || || || ||14\51||
| ||509.{{Overline|09}}
| ||509.{{Overline|09}}
|545.{{Overline|45}}
|545.{{Overline|45}}||5||4||1.250||
|''494r¢7’4”''
|''529r¢24’42”''||5||4||1.250||
|-
|-
| || || || || ||25\91
| || || || || ||25\91
| ||508¢28’28”
| ||508¢28’28”
|549¢9’9”
|549¢9’9”||9||7||1.286||
|''494r¢30’20”''
|''534r¢3’57”''||9||7||1.286||
|-
|-
| || || ||11\40|| ||
| || || ||11\40|| ||
| ||507¢41’32”
| ||507¢41’32”
|553¢50’46”
|553¢50’46”||4||3||1.333||
|''495''
|''540''||4||3||1.333||
|-
|-
| || || || || ||30\109
| || || || || ||30\109
| ||507¢2’32”
| ||507¢2’32”
|557¢44’47”
|557¢44’47”||11||8||1.375||
|''495r¢24’46”''
|''544r¢57’15”''||11||8||1.375||
|-
|-
| || || || ||19\69||
| || || || ||19\69||
| ||506.{{Overline|6}}
| ||506.{{Overline|6}}
|560
|560||7||5||1.400||
|''495r¢39’8”''
|''547r49’34”''||7||5||1.400||
|-
|-
| || || || || ||27\98
| || || || || ||27\98
| ||506.25
| ||506.25
|562.5
|562.5||10||7||1.428||
|''495r¢55’6”''
|''551r¢1’13”''||10||7||1.428||
|-
|-
| || ||8\29|| || ||
| || ||8\29|| || ||
| ||505¢15’47”
| ||505¢15’47”
|568¢25’16”
|568¢25’16”||3||2||1.500||L/s = 3/2
|''496r¢33’6”''
|''558¢37’14”''||3||2||1.500||L/s = 3/2
|-
|-
| || || || || ||29\105
| || || || || ||29\105
| ||504¢20’52”
| ||504¢20’52”
|573¢54’47”
|573¢54’47”||11||7||1.571||
|''497r¢8’34”''
|''565r¢42’51”''||11||7||1.571||
|-
|-
| || || || ||21\76||
| || || || ||21\76||
| ||504
| ||504
|576
|576||8||5||1.600||
|''497r¢22’6”''
|''568¢25’16”''||8||5||1.600||
|-
|-
| || || || || ||34\123
| || || || || ||34\123
| ||503.{{Overline|703}}
| ||503.{{Overline|703}}
|577.{{Overline|7}}
|577.{{Overline|7}}||13||8||1.625||Unnamed golden tuning
|''497r¢33’40”''
|''570r¢43’54”''||13||8||1.625||Unnamed golden tuning
|-
|-
| || || ||13\47|| ||
| || || ||13\47|| ||
| ||503¢13’33”
| ||503¢13’33”
|580¢38’43”
|580¢38’43”||5||3||1.667||
|''497¢49’47”''
|''574r¢28’5”''||5||3||1.667||
|-
|-
| || || || || ||31\112
| || || || || ||31\112
| ||502.{{Overline|702}}
| ||502.{{Overline|702}}
|583.{{Overline|783}}
|583.{{Overline|783}}||12||7||1.714||
|''498r¢12’51”''
|''578r¢34’17”''||12||7||1.714||
|-
|-
| || || || ||18\65||
| || || || ||18\65||
| ||502¢19’32”
| ||502¢19’32”
|586¢2’47”
|586¢2’47”||7||4||1.750||
|''498r¢27’42”''
|''581r¢32’18”''||7||4||1.750||
|-
|-
| || || || || ||23\83
| || || || || ||23\83
| ||501.{{Overline|81}}
| ||501.{{Overline|81}}
|589.{{Overline|09}}
|589.{{Overline|09}}||9||5||1.800||
|''498r¢47’43”''
|''585r¢33’15”''||9||5||1.800||
|-
|-
|
|
Line 120: Line 85:
|501¢29’35”
|501¢29’35”
|591¢3’23”
|591¢3’23”
|''499r¢36’''
|''588r¢7’8”''
|11
|11
|6
|6
Line 129: Line 92:
| ||5\18|| || || ||
| ||5\18|| || || ||
| ||500
| ||500
|600
|600||2||1||2.000||
|''500''
|''600''||2||1||2.000||
|-
|-
|
|
Line 142: Line 103:
|498¢47’43”
|498¢47’43”
|609¢13’51”
|609¢13’51”
|''501r¢1’51”''
|''612r¢22’16”''
|11
|11
|5
|5
Line 151: Line 110:
| || || || || ||22\79
| || || || || ||22\79
| ||498¢6’48”
| ||498¢6’48”
|611¢19’15”
|611¢19’15”||9||4||2.250||
|''501¢15’57”''
|''615r¢11’24”''||9||4||2.250||
|-
|-
| || || || ||17\61||
| || || || ||17\61||
| ||497¢33’40”
| ||497¢33’40”
|614¢38’3”
|614¢38’3”||7||3||2.333||
|''501r¢38’22”''
|''619r¢40’20”''||7||3||2.333||
|-
|-
| || || || || ||29\104
| || || || || ||29\104
| ||497¢8’34”
| ||497¢8’34”
|617¢8’34”
|617¢8’34”||12||5||2.400||
|''501r¢55’23”''
|''623r¢4’37”''||12||5||2.400||
|-
|-
| || || ||12\43|| ||
| || || ||12\43|| ||
| ||496¢33’6”
| ||496¢33’6”
|620¢41’23”
|620¢41’23”||5||2||2.500||
|''502r¢19’32”''
|''627r¢54’25”''||5||2||2.500||
|-
|-
| || || || || ||31\111
| || || || || ||31\111
| ||496
| ||496
|624
|624||13||5||2.600||Unnamed golden tuning
|''502.{{Overline|702}}''
|''632.{{Overline|432}}''||13||5||2.600||Unnamed golden tuning
|-
|-
| || || || ||19\68||
| || || || ||19\68||
| ||495¢39’8”
| ||495¢39’8”
|626¢5’13”
|626¢5’13”||8||3||2.667||
|''502r¢56’28”''
|''635r¢17’39”''||8||3||2.667||
|-
|-
| || || || || ||26\93
| || || || || ||26\93
| ||495¢14’17”
| ||495¢14’17”
|628¢34’17”
|628¢34’17”||11||4||2.750||
|''503r¢13’33”''
|''638r¢42’35”''||11||4||2.750||
|-
|-
| || ||7\25|| || ||
| || ||7\25|| || ||
| ||494¢7’4”
| ||494¢7’4”
|635¢17’39”
|635¢17’39”||3||1||3.000||L/s = 3/1
|''504''
|''648''||3||1||3.000||L/s = 3/1
|-
|-
|
|
Line 206: Line 149:
|493¢9’2”
|493¢9’2”
|641¢5’45”
|641¢5’45”
|''504r¢40’22”''
|''656r¢1’41”''
|13
|13
|4
|4
Line 215: Line 156:
| || || || || ||23\82
| || || || || ||23\82
| ||492¢51’26”
| ||492¢51’26”
|642¢51’26”
|642¢51’26”||10||3||3.333||
|''504r¢52’41”''
|''658¢32’12”''||10||3||3.333||
|-
|-
| || || || ||16\57||
| || || || ||16\57||
| ||492¢18’28”
| ||492¢18’28”
|646¢50’46”
|646¢50’46”||7||2||3.500||
|''505r¢15’47”''
|''663r¢9’28”''||7||2||3.500||
|-
|-
| || || || || ||25\89
| || || || || ||25\89
| ||491¢48’12”
| ||491¢48’12”
|649¢10’49”
|649¢10’49”||11||3||3.667||
|''505r¢37’5”''
|''667r¢24’57”''||11||3||3.667||
|-
|-
| || || ||9\32|| ||
| || || ||9\32|| ||
| ||490.{{Overline|90}}
| ||490.{{Overline|90}}
|654.{{Overline|54}}
|654.{{Overline|54}}||4||1||4.000||
|''506.25''
|''675''||4||1||4.000||
|-
|-
| || || || || ||20\71
| || || || || ||20\71
| ||489¢47’45”
| ||489¢47’45”
|661¢13’28”
|661¢13’28”||9||2||4.500||
|''507r¢2’32”''
|''684r¢30’25”''||9||2||4.500||
|-
|-
| || || || ||11\39||
| || || || ||11\39||
| ||488.{{Overline|8}}
| ||488.{{Overline|8}}
|666.{{Overline|6}}
|666.{{Overline|6}}||5||1||5.000||
|''507r¢41’32”''
|''692r¢30’25”''||5||1||5.000||
|-
|-
| || || || || ||13\46
| || || || || ||13\46
| ||487.5
| ||487.5
|675
|675||6||1||6.000||
|''508r¢41’44”''
|''704r¢20’52”''||6||1||6.000||
|-
|-
|2\7|| || || || ||
|2\7|| || || || ||
| ||480
| ||480
|720
|720||1||0||→ inf
|''514r¢17’9”''
|''771r¢25’43”''||1||0||→ inf
|}
|}


<references />
<references />

Revision as of 23:24, 5 June 2023

7L 4s<diminished twelfth> has a generator of a narrow wolf to wide wolf fourth of 458.18 (3/11ed7/5) to [[1]] (2/7ed11/7) cents. Insofar as it may be said to be a Reformed mode, it is an authentic Locrian mode.

Scale tree

Generator Cents[1] L s L/s Comments
g 3L
3\11 514¢17’9” 514¢17’9” 1 1 1.000
17\62 510 540 6 5 1.200
14\51 509.09 545.45 5 4 1.250
25\91 508¢28’28” 549¢9’9” 9 7 1.286
11\40 507¢41’32” 553¢50’46” 4 3 1.333
30\109 507¢2’32” 557¢44’47” 11 8 1.375
19\69 506.6 560 7 5 1.400
27\98 506.25 562.5 10 7 1.428
8\29 505¢15’47” 568¢25’16” 3 2 1.500 L/s = 3/2
29\105 504¢20’52” 573¢54’47” 11 7 1.571
21\76 504 576 8 5 1.600
34\123 503.703 577.7 13 8 1.625 Unnamed golden tuning
13\47 503¢13’33” 580¢38’43” 5 3 1.667
31\112 502.702 583.783 12 7 1.714
18\65 502¢19’32” 586¢2’47” 7 4 1.750
23\83 501.81 589.09 9 5 1.800
28\101 501¢29’35” 591¢3’23” 11 6 1.833
5\18 500 600 2 1 2.000
27\97 498¢47’43” 609¢13’51” 11 5 2.200
22\79 498¢6’48” 611¢19’15” 9 4 2.250
17\61 497¢33’40” 614¢38’3” 7 3 2.333
29\104 497¢8’34” 617¢8’34” 12 5 2.400
12\43 496¢33’6” 620¢41’23” 5 2 2.500
31\111 496 624 13 5 2.600 Unnamed golden tuning
19\68 495¢39’8” 626¢5’13” 8 3 2.667
26\93 495¢14’17” 628¢34’17” 11 4 2.750
7\25 494¢7’4” 635¢17’39” 3 1 3.000 L/s = 3/1
30\107 493¢9’2” 641¢5’45” 13 4 3.250
23\82 492¢51’26” 642¢51’26” 10 3 3.333
16\57 492¢18’28” 646¢50’46” 7 2 3.500
25\89 491¢48’12” 649¢10’49” 11 3 3.667
9\32 490.90 654.54 4 1 4.000
20\71 489¢47’45” 661¢13’28” 9 2 4.500
11\39 488.8 666.6 5 1 5.000
13\46 487.5 675 6 1 6.000
2\7 480 720 1 0 → inf
  1. ↑ Fractions which repeat in more than 3 digits in sexagesimal
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