User:Moremajorthanmajor/7L 4s (11/4-equivalent): Difference between revisions

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{{Infobox MOS
{{Infobox MOS
|Periods=1|nLargeSteps=7|nSmallSteps=4|Equalized=3|Paucitonic=2|Pattern=LLsLLsLLsLs|Equave=11/4}}'''7L 4s<11\4>''' has a generator of a narrow wolf to perfect fourth of 477.632 (3/11ed11\4) to 500.377 (2/7ed11\4) cents. Insofar as it may be said to be a Reformed mode, it is an authentic Locrian mode.
|Tuning=7L 4s<11/4>}}{{MOS intro|Scale Signature=7L 4s<11/4>}}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"
{{MOS tuning spectrum|Scale Signature=7L 4s<11/4>}}
! colspan="7" rowspan="2" |Generator
! colspan="2" |Cents<ref name=":0">13ths in dozenal, 17ths in hex</ref>
! colspan="2" |''ed3\2<ref name=":0" />''
! rowspan="2" |L
! rowspan="2" |s
! rowspan="2" |L/s
! rowspan="2" |Comments
|-
!g
!3L
!''g''
!''3L''
|-
|3\11|| || || || ||
| ||514.286
|685.714
|''490.{{Overline|90}}''
|''654.{{Overline|54}}''||1||1||1.000||
|-
| || || || || ||17\62
| ||510
|540
|''493.548''
|''522.581''||6||5||1.200||
|-
| || || || ||14\51||
| ||509.{{Overline|09}}
|545.{{Overline|45}}
|''494.{{Overline|1E}}''
|''529.{{Overline|87}}''||5||4||1.250||
|-
| || || || || ||25\91
| ||508.475
|549.1545
|''494.5055''
|''534.066''||9||7||1.286||
|-
| || || ||11\40|| ||
| ||507.{{Overline|83}}
|553.{{Overline|X1}}
|''495''
|''540''||4||3||1.333||
|-
| || || || || ||30\109
| ||507.042
|557.7465
|''495.413''
|''544.954''||11||8||1.375||
|-
| || || || ||19\69||
| ||506.{{Overline|6}}
|560
|''495.652''
|''547.826''||7||5||1.400||
|-
| || || || || ||27\98
| ||506.25
|562.5
|''495.918''
|''551.02''||10||7||1.428||
|-
| || ||8\29|| || ||
| ||505.263
|568.421
|''496.552''
|''558.621''||3||2||1.500||L/s = 3/2
|-
| || || || || ||29\105
| ||504.348
|573.913
|''497.143''
|''565.714''||11||7||1.571||
|-
| || || || ||21\76||
| ||504
|576
|''497.368''
|''568.421''||8||5||1.600||
|-
| || || || || ||34\123
| ||503.{{Overline|703}}
|577.{{Overline|7}}
|''497.561''
|''570.732''||13||8||1.625||Unnamed golden tuning
|-
| || || ||13\47|| ||
| ||503.226
|580.645
|''497.823''
|''574.468''||5||3||1.667||
|-
| || || || || ||31\112
| ||502.{{Overline|702}}
|583.{{Overline|783}}
|''498.214''
|''578.571''||12||7||1.714||
|-
| || || || ||18\65||
| ||502.326
|586.0465
|''498.{{Overline|56}}''
|''581.{{Overline|65}}''||7||4||1.750||
|-
| || || || || ||23\83
| ||501.{{Overline|81}}
|589.{{Overline|09}}
|''498.795''
|''585.542''||9||5||1.800||
|-
|
|
|
|
|
|
|28\101
|501.4925
|591.045
|''499.01''
|''588.118''
|11
|6
|1.833
|
|-
| ||5\18|| || || ||
| ||500
|600
|''500''
|''600''||2||1||2.000||
|-
|
|
|
|
|
|
|27\97
|498.{{Overline|56}}
|609.{{Overline|29}}
|''501.031''
|''612.371''
|11
|5
|2.200
|
|-
| || || || || ||22\79
| ||498.116
|611.321
|''501.265''
|''615.19''||9||4||2.250||
|-
| || || || ||17\61||
| ||497.561
|614.634
|''501.639''
|''619.672''||7||3||2.333||
|-
| || || || || ||29\104
| ||497.143
|617.143
|''501.{{Overline|E0}}''
|''623.{{Overline|0E}}''||12||5||2.400||
|-
| || || ||12\43|| ||
| ||496.552
|620.69
|''502.326''
|''627.907''||5||2||2.500||
|-
| || || || || ||31\111
| ||496
|624
|''502.{{Overline|702}}''
|''632.{{Overline|432}}''||13||5||2.600||Unnamed golden tuning
|-
| || || || ||19\68||
| ||495.652
|626.087
|''502.{{Overline|F0}}''
|''635.{{Overline|4B}}''||8||3||2.667||
|-
| || || || || ||26\93
| ||495.238
|628.571
|''503.226''
|''638.71''||11||4||2.750||
|-
| || ||7\25|| || ||
| ||494.{{Overline|1E}}
|635.{{Overline|4B}}
|''504''
|''648''||3||1||3.000||L/s = 3/1
|-
|
|
|
|
|
|
|30\107
|493.151
|641.096
|''504.672''
|''656.075''
|13
|4
|3.250
|
|-
| || || || || ||23\82
| ||492.857
|642.857
|''504.878''
|''658.537''||10||3||3.333||
|-
| || || || ||16\57||
| ||492.{{Overline|38}}
|646.{{Overline|1X}}
|''505.263''
|''663.158''||7||2||3.500||
|-
| || || || || ||25\89
| ||491.803
|649.18
|''505.618''
|''667.416''||11||3||3.667||
|-
| || || ||9\32|| ||
| ||490.{{Overline|90}}
|654.{{Overline|54}}
|''506.25''
|''675''||4||1||4.000||
|-
| || || || || ||20\71
| ||489.796
|661.2245
|''507.042''
|''684.507''||9||2||4.500||
|-
| || || || ||11\39||
| ||488.{{Overline|8}}
|666.{{Overline|6}}
|''507.{{Overline|83}}''
|''692.{{Overline|38}}''||5||1||5.000||
|-
| || || || || ||13\46
| ||487.5
|675
|''508.696''
|''704.348''||6||1||6.000||
|-
|2\7|| || || || ||
| ||480
|720
|''720''
|''1080''||1||0||→ inf
|}

Latest revision as of 16:47, 3 March 2025

↖ 6L 3s⟨11/4⟩ ↑ 7L 3s⟨11/4⟩ 8L 3s⟨11/4⟩ ↗
← 6L 4s⟨11/4⟩ 7L 4s (11/4-equivalent) 8L 4s⟨11/4⟩ →
↙ 6L 5s⟨11/4⟩ ↓ 7L 5s⟨11/4⟩ 8L 5s⟨11/4⟩ ↘ 
┌╥╥┬╥╥┬╥╥┬╥┬┐
│║║│║║│║║│║││
│││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLsLLsLLsLs
sLsLLsLLsLL
Equave 11/4 (1751.3 ¢)
Period 11/4 (1751.3 ¢)
Generator size(ed11/4)
Bright 3\11 to 2\7 (477.6 ¢ to 500.4 ¢)
Dark 5\7 to 8\11 (1250.9 ¢ to 1273.7 ¢)
Related MOS scales
Parent 4L 3s⟨11/4⟩
Sister 4L 7s⟨11/4⟩
Daughters 11L 7s⟨11/4⟩, 7L 11s⟨11/4⟩
Neutralized 3L 8s⟨11/4⟩
2-Flought 18L 4s⟨11/4⟩, 7L 15s⟨11/4⟩
Equal tunings(ed11/4)
Equalized (L:s = 1:1) 3\11 (477.6 ¢)
Supersoft (L:s = 4:3) 11\40 (481.6 ¢)
Soft (L:s = 3:2) 8\29 (483.1 ¢)
Semisoft (L:s = 5:3) 13\47 (484.4 ¢)
Basic (L:s = 2:1) 5\18 (486.5 ¢)
Semihard (L:s = 5:2) 12\43 (488.7 ¢)
Hard (L:s = 3:1) 7\25 (490.4 ¢)
Superhard (L:s = 4:1) 9\32 (492.6 ¢)
Collapsed (L:s = 1:0) 2\7 (500.4 ¢)

7L 4s⟨11/4⟩ is a 11/4-equivalent (non-octave) moment of symmetry scale containing 7 large steps and 4 small steps, repeating every interval of 11/4 (1751.3 ¢). Generators that produce this scale range from 477.6 ¢ to 500.4 ¢, or from 1250.9 ¢ to 1273.7 ¢.Insofar as it may be said to be a Reformed mode, it is an authentic Locrian mode.

Scale tree

Scale tree and tuning spectrum of 7L 4s⟨11/4⟩
Generator(ed11/4) Cents Step ratio Comments
Bright Dark L:s Hardness
3\11 477.632 1273.686 1:1 1.000 Equalized 7L 4s⟨11/4⟩
17\62 480.200 1271.118 6:5 1.200
14\51 480.754 1270.564 5:4 1.250
25\91 481.131 1270.187 9:7 1.286
11\40 481.612 1269.706 4:3 1.333 Supersoft 7L 4s⟨11/4⟩
30\109 482.014 1269.304 11:8 1.375
19\69 482.247 1269.071 7:5 1.400
27\98 482.506 1268.812 10:7 1.429
8\29 483.122 1268.196 3:2 1.500 Soft 7L 4s⟨11/4⟩
29\105 483.697 1267.621 11:7 1.571
21\76 483.917 1267.401 8:5 1.600
34\123 484.104 1267.214 13:8 1.625
13\47 484.407 1266.911 5:3 1.667 Semisoft 7L 4s⟨11/4⟩
31\112 484.740 1266.578 12:7 1.714
18\65 484.980 1266.338 7:4 1.750
23\83 485.305 1266.013 9:5 1.800
5\18 486.477 1264.841 2:1 2.000 Basic 7L 4s⟨11/4⟩
Scales with tunings softer than this are proper
22\79 487.709 1263.609 9:4 2.250
17\61 488.072 1263.246 7:3 2.333
29\104 488.348 1262.970 12:5 2.400
12\43 488.740 1262.578 5:2 2.500 Semihard 7L 4s⟨11/4⟩
31\111 489.107 1262.211 13:5 2.600
19\68 489.339 1261.979 8:3 2.667
26\93 489.616 1261.702 11:4 2.750
7\25 490.369 1260.949 3:1 3.000 Hard 7L 4s⟨11/4⟩
23\82 491.223 1260.095 10:3 3.333
16\57 491.598 1259.720 7:2 3.500
25\89 491.943 1259.375 11:3 3.667
9\32 492.558 1258.760 4:1 4.000 Superhard 7L 4s⟨11/4⟩
20\71 493.329 1257.989 9:2 4.500
11\39 493.961 1257.356 5:1 5.000
13\46 494.938 1256.380 6:1 6.000
2\7 500.377 1250.941 1:0 → ∞ Collapsed 7L 4s⟨11/4⟩
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