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User:Moremajorthanmajor/3L 2s (minor sixth-equivalent): Difference between revisions

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The generator range is 240 to 342.9 cents, placing it on the [[6/5|diatonic minor third]], usually representing a minor third of some type (like [[6/5]]). The bright (chroma-positive) generator is, however, its minor sixth complement (480 to 514.3 cents).  
The generator range is 240 to 342.9 cents, placing it on the [[6/5|diatonic minor third]], usually representing a minor third of some type (like [[6/5]]). The bright (chroma-positive) generator is, however, its minor sixth complement (480 to 514.3 cents).  


Because this diatonic is a minor sixth-repeating scale, each tone has an 8/5 minor sixth above it. The scale has one major chord, one minor chord and three diminished chords. This diatonic also has two diminished 7th chords, making it a warped melodic minor scale.
Because this diatonic is a minor sixth-repeating scale, each tone has a minor sixth above it. The scale has one major chord, one minor chord and three diminished chords. This diatonic also has two diminished 7th chords, making it a warped melodic minor scale.


[[Basic]] diatonic is in [[8ed8/5]], which is a very good minor sixth-based equal tuning similar to [[12edo]].
[[Basic]] diatonic is in [[8ed8/5]], which is a very good minor sixth-based equal tuning similar to [[12edo]].
Line 9: Line 9:




There are 2 main ways to notate the diatonic scale. One method uses a simple sextave (minor sixth) repeating notation consisting of 5 naturals (La, Si, Do, Re, Mi). Given that 1-7/6-3/2 is minor sixth-equivalent to a tone cluster of 1-16/15-7/6, it may be more convenient to notate these diatonic scales as repeating at the double sextave (diminished eleventh~tenth), however it does make navigating the [[Generator|genchain]] harder. This way, 3/2 is its own pitch class, distinct from 16\15. Notating this way produces a tenth which is the Dorian mode of Annapolis[6L 4s] or Oriole[6L 4s]. Since there are exactly 10 naturals in double sextave notation, Greek numerals 1-10 may be used.
There are 2 main ways to notate the diatonic scale. One method uses a simple sextave (minor sixth) repeating notation consisting of 5 naturals (La, Si, Do, Re, Mi; Mi, Fa, Sol, La, Si). Given that 1-7/6-3/2 is minor sixth-equivalent to a tone cluster of 1-16/15-7/6, it may be more convenient to notate these diatonic scales as repeating at the double sextave (diminished eleventh~tenth), however it does make navigating the [[Generator|genchain]] harder. This way, 3/2 is its own pitch class, distinct from 16\15. Notating this way produces a tenth which is the Dorian mode of Annapolis[6L 4s] or Oriole[6L 4s]. Since there are exactly 10 naturals in double sextave notation, Greek numerals 1-10 may be used.
{| class="wikitable"
{| class="wikitable"
|+
|+
Normalized
Normalized
! colspan="2" |Notation
! colspan="3" |Notation
!Supersoft
!Supersoft
!Soft
!Soft
Line 22: Line 22:
!Superhard
!Superhard
|-
|-
!Diatonic
!Aeolian
!Phrygian
!Oriole, Annapolis
!Oriole, Annapolis
!18eds
!18eds
Line 33: Line 34:
|-
|-
|La#
|La#
|Mi#
|Α#
|Α#
|1\18
|1\18, 46.154
46.154
|1\13, 63.158
|1\13
|2\21, 77.419
63.158
| rowspan="2" |1\8, 100
|2\21
|3\19, 124.138
77.419
|2\11, 141.176
| rowspan="2" |1\8
|3\14, 163.636
100
|3\19
124.138
|2\11
141.1765
|3\14
163.{{Overline|63}}
|-
|-
|Sib
|Sib
|Fa
|Βb
|Βb
|3\18
|3\18, 138.462
138.4615
|2\13, 126.316
|2\13
|3\21, 116.129
126.316
|2\19, 82.759
|3\21
|1\11, 70.588
116.129
|1\14, 54.545
|2\19
82.759
|1\11
70.588
|1\14
54.{{Overline|54}}
|-
|-
|Si
|Si
|Fa#
|Β
|Β
|4\18
|4\18, 184.615
184.615
|3\13, 189.474
|3\13
|5\21, 193.548
189.474
|2\8, 200
|5\21
|5\19, 206.897
193.548
|3\11, 211.764
|2\8
|4\14, 218.182
200
|5\19
206.897
|3\11
211.764
|4\14
218.{{Overline|18}}
|-
|-
|Si#
|Si#
|Fax
|Β#
|Β#
|5\18
|5\18, 230.769
230.769
| rowspan="2" |4\13, 252.632
| rowspan="2" |4\13
|7\21, 270.968
252.632
|3\8, 300
|7\21
|8\19, 331.034
270.968
|5\11 352.941
|3\8
|7\14, 381.818
300
|8\19
331.0345
|5\11
352.941
|7\14
381.{{Overline|81}}
|-
|-
|Dob
|Dob
|Solb
|Γb
|Γb
|6\18
|6\18, 276.923
276.923
|6\21, 232.258
|6\21
|2\8, 200
232.258
|4\19, 165.517
|2\8
|2\11, 141.176
200
|2\14, 109.091
|4\19
165.517
|2\11
141.1765
|2\14
109.{{Overline|09}}
|-
|-
|'''Do'''
|'''Do'''
|'''Sol'''
|'''Γ'''
|'''Γ'''
|'''7\18'''
|'''7\18,''' '''323.076'''
'''323.076'''
|'''5\13,''' '''315.789'''
|'''5\13'''
|'''8\21,''' '''309.677'''
'''315.7895'''
|'''3\8,''' '''300'''
|'''8\21'''
|'''7\19,''' '''289.655'''
'''309.677'''
|'''4\11.''' '''282.353'''
|'''3\8'''
|'''5\14,''' '''272.727'''
'''300'''
|'''7\19'''
'''289.655'''
|'''4\11'''
'''282.353'''
|'''5\14'''
'''272.{{Overline|72}}'''
|-
|-
|Do#
|Do#
|Sol#
|Γ#
|Γ#
|8\18
|8\18, 369.231
369.231
|6\13, 378.947
|6\13
|10\21, 387.097
378.947
| rowspan="2" |4\8, 400
|10\21
|10\19, 413.793
387.097
|6\11, 423.529
| rowspan="2" |4\8
|8\14, 436.364
400
|10\19
413.793
|6\11
423.529
|8\14
436.{{Overline|36}}
|-
|-
|Reb
|Reb
|Lab
|Δb
|Δb
|10\18
|10\18, 461.538
461.5385
|7\13, 442.105
|7\13
|11\21, 425.806
442.105
|9\19, 372.413
|11\21
|5\11 352.941
425.8065
|6\14, 327.272
|9\19
372.413
|5\11
352.941
|6\14
327.{{Overline|27}}
|-
|-
|'''Re'''
|'''Re'''
|'''La'''
|'''Δ'''
|'''Δ'''
|'''11\18'''
|'''11\18,''' '''507.692'''
'''507.692'''
|'''8\13,''' '''505.263'''
|'''8\13'''
|'''13\21,''' '''503.226'''
'''505.263'''
|'''5\8,''' '''500'''
|'''13\21'''
|'''12\19,''' '''496.551'''
'''503.226'''
|'''7\11,''' '''494.118'''
|'''5\8'''
|'''9\14,''' '''490.909'''
'''500'''
|'''12\19'''
'''496.551'''
|'''7\11'''
'''494.118'''
|'''9\14'''
'''490.{{Overline|90}}'''
|-
|-
|Re#
|Re#
|La#
|Δ#
|Δ#
|12\18
|12\18, 553.846
553.846
|9\13, 568.421
|9\13
|15\21, 580.645
568.421
| rowspan="2" |6\8, 600
|15\21
|15\19, 620.689
580.645
|9\11, 635.294
| rowspan="2" |6\8
|12\14, 654.545
600
|15\19
620.689
|9\11
635.294
|12\14
654.{{Overline|54}}
|-
|-
|Mib
|Mib
|Sib
|Εb
|Εb
|14\18
|14\18, 646.154
646.154
|10\13, 631.579
|10\13
|16\21, 619.355
631.579
|14\19, 579.310
|16\21
|8\11, 564.706
619.355
|10\14, 545.455
|14\19
579.310
|8\11
564.706
|10\14
545.{{Overline|45}}
|-
|-
|Mi
|Mi
|Si
|Ε
|Ε
|15\18
|15\18, 692.308
692.308
|11\13, 694.737
|11\13
|18\21, 696.774
694.737
|7\8, 700
|18\21
|17\19, 703.448
696.774
|10\11, 705.882
|7\8
|13\14, 709.091
700
|17\19
703.448
|10\11
705.88235
|13\14
709.{{Overline|09}}
|-
|-
|Mi#
|Mi#
|Si#
|Ε#
|Ε#
|16\18
|16\18, 738.462
738.4615
| rowspan="2" |12\13, 757.895
| rowspan="2" |12\13
| 20\21, 774.194
757.895
|8\8, 800
| 20\21
|20\19, 827.586
774.194
|12\11, 847.059
|8\8
|16\14, 872.727
800
|20\19
827.586
|12\11
847.059
|16\14
872.{{Overline|72}}
|-
|-
|Lab
|Lab
|Mib
|Ϛb/Ϝb
|Ϛb/Ϝb
|17\18
|17\18, 784.615
784.615
|19\21, 735.484
|19\21
|7\8, 700
735.484
|16\19, 662.069
|7\8
|9\11, 635.294
700
|11\14, 600
|16\19
662.069
|9\11
635.294
|11\14
600
|-
|-
!La
!La
!Mi
!Ϛ/Ϝ
!Ϛ/Ϝ
!18\18
!18\18, 830.769
830.769
!13\13, 821.053
!13\13
!21\21, 812.903
821.053
!8\8, 800
!21\21
!19\19, 786.207
812.903
!11\11, 776.471
!8\8
!14\14, 763.636
 
800
!19\19
786.207
!11\11
776.471
!14\14
 
763.{{Overline|63}}
|-
|-
|La#
|La#
|Mi#
|Ϛ#/Ϝ#
|Ϛ#/Ϝ#
|19\18
|19\18, 876.923
876.923
|14\13, 884.211
|14\13
|23\21, 890.323
884.2105
| rowspan="2" |9\8, 900
|23\21
|22\19, 910.345
890.323
|13\11, 917.647
| rowspan="2" |9\8
|17\14, 927.273
900
|22\19
910.345
|13\11
917.647
|17\14
927.{{Overline|27}}
|-
|-
|Sib
|Sib
|Fa
|Ζb
|Ζb
|21\18
|21\18, 969.231
969.231
|15\13, 947.368
|15\13
|24\21, 929.032
947.368
|21\19, 868.966
|24\21
|12\11, 847.059
929.032
|15\14, 818.182
|21\19
868.9655
|12\11
847.059
|15\14
818.{{Overline|18}}
|-
|-
|Si
|Si
|Fa#
|Ζ
|Ζ
|22\18
|22\18, 1015.385
1015.385
|16\13, 1010.526
|16\13
|26\21, 1006.452
1010.526
|10\8, 1000
|26\21
|24\19, 993.103
1006.452
|14\11, 988.235
|10\8
|18\14, 981.81
1000
|24\19
993.1035
|14\11
988.235
|18\14
981.{{Overline|81}}
|-
|-
|Si#
|Si#
|Fax
|Ζ#
|Ζ#
|23\18
|23\18, 1061.538
1061.5385
| rowspan="2" |17\13, 1071.684
| rowspan="2" |17\13
|28\21, 1083.871
1071.684
|11\8, 1100
|28\21
|27\19, 1117.241
1083.871
|16\11, 1129.412
|11\8
|21\14, 1145.455
1100
|27\19
1117.241
|16\11
1129.412
|21\14
1145.{{Overline|45}}
|-
|-
|Dob
|Dob
|Solb
|Ηb
|Ηb
|24\18
|24\18, 1107.692
1107.692
|27\21, 1045.161
|27\21
|10\8, 1000
1045.161
|23\19, 951.724
|10\8
|13\11, 917.647
1000
|16\14, 872.727
|23\19
951.724
|13\11
917.647
|16\14
872.{{Overline|72}}
|-
|-
|'''Do'''
|'''Do'''
|'''Sol'''
|'''Η'''
|'''Η'''
|'''25\18'''
|'''25\18,''' '''1153.846'''
'''1153.846'''
|'''18\13,''' '''1136.842'''
|'''18\13'''
|'''29\21,''' '''1122.581'''
'''1136.842'''
|'''11\8,''' '''1100'''
|'''29\21'''
|'''26\19,''' '''1075.862'''
'''1122.581'''
|'''15\11,''' '''1058.824'''
|'''11\8'''
|'''19\14,''' '''1036.364'''
'''1100'''
|'''26\19'''
'''1075.862'''
|'''15\11'''
'''1052.8235'''
|'''19\14'''
'''1036.{{Overline|36}}'''
|-
|-
|Do#
|Do#
|Sol#
|Η#
|Η#
|26\18
|26\18, 1200
1200
|19\13, 1200
|19\13
|31\21, 1200
1200
| rowspan="2" |12\8, 1200
|31\21
|29\19, 1200
1200
|17\11, 1200
| rowspan="2" |12\8
|22\14, 1200
1200
|29\19
1200
|17\11
1200
|22\14
1200
|-
|-
|Reb
|Reb
|Lab
|Θb
|Θb
|28\18
|28\18, 1292.308
1292.308
|20\13, 1263.158
|20\13
|32\21, 1238.710
1263.158
|28\19, 1158.621
|32\21
|16\11, 1129.412
1238.710
|20\14, 1090.909
|28\19
1158.621
|16\11
1129.412
|20\14
1090.{{Overline|90}}
|-
|-
|'''Re'''
|'''Re'''
|'''La'''
|'''Θ'''
|'''Θ'''
|'''29\18'''
|'''29\18,''' '''1338.462'''
'''1338.4615'''
|'''21\13,''' '''1326.316'''
|'''21\13'''
|'''34\21,''' '''1316.129'''
'''1326.316'''
|'''13\8,''' '''1300'''
|'''34\21'''
|'''31\19,''' '''1282.759'''
'''1316.129'''
|'''18\11,''' '''1270.588'''
|'''13\8'''
|'''23\14,''' '''1254.545'''
'''1300'''
|'''31\19'''
'''1282.759'''
|'''18\11'''
'''1270.588'''
|'''23\14'''
'''1254.{{Overline|54}}'''
|-
|-
|Re#
|Re#
|La#
|Θ#
|Θ#
|30\18
|30\18, 1384.615
1384.615
|22\13, 1389.474
|22\13
|36\21, 1393.548
1389.474
| rowspan="2" |14\8, 1400
|36\21
|34\19, 1406.897
1393.548
|20\11, 1411.765
| rowspan="2" |14\8
|26\14, 1418.182
1400
|34\19
1406.897
|20\11
1411.765
|26\14
1418.{{Overline|18}}
|-
|-
|Mib
|Mib
|Sib
|Ιb
|Ιb
|32\18
|32\18, 1476.923
1476.923
|23\13, 1452.632
|23\13
|37\21, 1432.258
1452.632
|33\19, 1365.517
|37\21
|19\11, 1341.176
1432.258
|24\14, 1309.091
|33\19
1365.517
|19\11
1341.1765
|24\14
1309.{{Overline|09}}
|-
|-
|Mi
|Mi
|Si
|Ι
|Ι
|33\18
|33\18, 1523.077
1523.077
|24\13, 1515.789
|24\13
|39\21, 1509.677
1515.7895
|15\8, 1500
|39\21
|36\19, 1489.655
1509.677
|21\11, 1482.352
|15\8
|27\14, 1472.727
1500
|36\19
1489.655
|21\11
1482.352
|27\14
1472.{{Overline|72}}
|-
|-
|Mi#
|Mi#
|Si#
|Ι#
|Ι#
|34\18
|34\18, 1569.231
1569.231
| rowspan="2" |25\13, 1578.947
| rowspan="2" |25\13
|41\21, 1587.097
1578.947
|16\8, 1600
|41\21
|39\19, 1613.793
1587.097
|23\11, 1623.529
|16\8
|30\14, 1636.364
1600
|39\19
1613.793
|23\11
1623.529
|30\14
1636.{{Overline|36}}
|-
|-
|Lab
|Lab
|Αb
|35\18
1615.385
|40\21
1548.387
|15\8
1500
|35\19
1448.286
|20\11
1411.765
|25\14
1363.{{Overline|63}}
|-
!La
!Α
!36\18
1661.5385
!26\13
1642.105
!42\21
1625.8065
!16\8
1600
!38\19
1572.414
!22\11
1552.941
!28\14
1527.{{Overline|27}}
|}
{| class="wikitable"
|+''ed8\12 (→ed2\3)''
! colspan="2" |Notation
!Supersoft
!Soft
!Semisoft
!Basic
!Semihard
!Hard
!Superhard
|-
!Diatonic
!Oriole, Annapolis
!18eds
!13eds
!21eds
!8eds
!19eds
!11eds
!14eds
|-
|La#
|Α#
|''1\18''
''44.{{Overline|4}}''
|''1\13''
''61.5385''
|''2\21''
''76.1905''
| rowspan="2" |''1\8''
''100''
|''3\19''
''126.316''
|''2\11''
''145.{{Overline|45}}''
|''3\14''
''171.429''
|-
|Sib
|Βb
|''3\18''
''133.{{Overline|3}}''
|''2\13''
''123.077''
|''3\21''
''114.286''
|''2\19''
''84.2105''
|''1\11''
''72.{{Overline|72}}''
|''1\14''
''57.143''
|-
|Si
|Β
|''4\18''
''177.{{Overline|7}}''
|''3\13''
''184.615''
|''5\21''
''190.476''
|''2\8''
''200''
|''5\19''
''210.526''
|''3\11''
''218.{{Overline|18}}''
|''4\14''
''228.571''
|-
|Si#
|Β#
|''5\18''
''222.{{Overline|2}}''
| rowspan="2" |''4\13''
''246.154''
|''7\21''
''266.{{Overline|6}}''
|''3\8''
''300''
|''8\19''
''336.842''
|''5\11''
''363.{{Overline|63}}''
|''7\14''
''400''
|-
|Dob
|Γb
|''6\18''
''266.{{Overline|6}}''
|''6\21''
''228.571''
|''2\8''
''200''
|''4\19''
''168.421''
|''2\11''
''145.{{Overline|45}}''
|''2\14''
''114.28''
|-
|'''Do'''
|'''Γ'''
|'''''7\18'''''
'''''311.{{Overline|1}}'''''
|'''''5\13'''''
'''''307.692'''''
|'''''8\21'''''
'''''304.762'''''
|'''''3\8'''''
'''''300'''''
|'''''7\19'''''
'''''294.737'''''
|'''''4\11'''''
'''''290.{{Overline|90}}'''''
|'''''5\14'''''
'''''285.714'''''
|-
|Do#
|Γ#
|''8\18''
''355.{{Overline|5}}''
|''6\13''
''369.231''
|''10\21''
''380.952''
| rowspan="2" |''4\8''
''400''
|''10\19''
''421.053''
|''6\11''
''436.{{Overline|36}}''
|''8\14''
''457.143''
|-
|Reb
|Δb
|''10\18''
''444.{{Overline|4}}''
|''7\13''
''430.769''
|''11\21''
''419.048''
|''9\19''
''378.947''
|''5\11''
''363.{{Overline|63}}''
|''6\14''
''342.857''
|-
|'''Re'''
|'''Δ'''
|'''''11\18'''''
'''''488.{{Overline|8}}'''''
|'''''8\13'''''
'''''492.308'''''
|'''''13\21'''''
'''''495.238'''''
|'''''5\8'''''
'''''500'''''
|'''''12\19'''''
'''''505.263'''''
|'''''7\11'''''
'''''509.{{Overline|09}}'''''
|'''''9\14'''''
'''''514.286'''''
|-
|Re#
|Δ#
|''12\18''
''533.{{Overline|3}}''
|''9\13''
''553.846''
|''15\21''
''571.429''
| rowspan="2" |''6\8''
''600''
|''15\19''
''631.421''
|''9\11''
''654.{{Overline|54}}''
|''12\14''
''685.714''
|-
|Mib
|Mib
|Εb
|''14\18''
''622.{{Overline|2}}''
|''10\13''
''615.385''
|''16\21''
''609.524''
|''14\19''
''589.474''
|''8\11''
''581.{{Overline|81}}''
|''10\14''
''571.424''
|-
|Mi
|Ε
|''15\18''
''666.{{Overline|6}}''
|''11\13''
''676.923''
|''18\21''
''685.714''
|''7\8''
''700''
|''17\19''
''715.7895''
|''10\11''
''727.{{Overline|27}}''
|''13\14''
''742.857''
|-
|Mi#
|Ε#
|''16\18''
''711.{{Overline|1}}''
| rowspan="2" |''12\13''
''738.4615''
|''20\21''
''761.905''
|''8\8''
''800''
|''20\19''
''842.105''
|''12\11''
''872.{{Overline|72}}''
|''16\14''
''914.286''
|-
|Lab
|Ϛb/Ϝb
|''17\18''
''755.{{Overline|5}}''
|''19\21''
''723.8095''
|''7\8''
''700''
|''16\19''
''673.684''
|''8\11''
''581.{{Overline|81}}''
|''11\14''
''628.571''
|-
!La
!Ϛ/Ϝ
! colspan="7" |''800''
|-
|La#
|Ϛ#/Ϝ#
|''19\18''
''844.{{Overline|4}}''
|''14\13''
''861.5385''
|''23\21''
''876.1905''
| rowspan="2" |''9\8''
''900''
|''22\19''
''926.316''
|''13\11''
''945.{{Overline|45}}''
|''17\14''
''971.429''
|-
|Sib
|Ζb
|''21\18''
''933.{{Overline|3}}''
|''15\13''
''923.077''
|''24\21''
''914.286''
|''21\19''
''884.2105''
|''12\11''
''872.{{Overline|72}}''
|''15\14''
''857.143''
|-
|Si
|Ζ
|''22\18''
''977.{{Overline|7}}''
|''16\13''
''984.615''
|''26\21''
''990.476''
|''10\8''
''1000''
|''24\19''
''1010.526''
|''14\11''
''1018.{{Overline|18}}''
|''18\14''
''1028.571''
|-
|Si#
|Ζ#
|''23\18''
''1022.{{Overline|2}}''
| rowspan="2" |''17\13''
''1046.154''
|''28\21''
''1066.{{Overline|6}}''
|''11\8''
''1100''
|''27\19''
''1136.842''
|''16\11''
''1163.{{Overline|63}}''
|''21\14''
''1200''
|-
|Dob
|Ηb
|''24\18''
''1066.{{Overline|6}}''
|''27\21''
''1028.571''
|''10\8''
''1000''
|''23\19''
''968.421''
|''13\11''
''945.{{Overline|45}}''
|''16\14''
''914.286''
|-
|'''Do'''
|'''Η'''
|'''''25\18'''''
'''''1111.{{Overline|1}}'''''
|'''''18\13'''''
'''''1107.692'''''
|'''''29\21'''''
'''''1104.762'''''
|'''''11\8'''''
'''''1100'''''
|'''''26\19'''''
'''''1094.737'''''
|'''''15\11'''''
'''''1090.{{Overline|90}}'''''
|'''''19\14'''''
'''''1085.714'''''
|-
|Do#
|Η#
|''26\18''
''1155.{{Overline|5}}''
|''19\13''
''1169.237''
|''31\21''
''1180.952''
| rowspan="2" |''12\8''
''1200''
|''29\19''
''1221.053''
|''17\11''
''1236.{{Overline|36}}''
|''22\14''
''1257.143''
|-
|Reb
|Θb
|''28\18''
''1244.{{Overline|4}}''
|''20\13''
''1230.769''
|''32\21''
''1219.048''
|''28\19''
''1178.947''
|''16\11''
''1163.{{Overline|63}}''
|''20\14''
''1142.857''
|-
|'''Re'''
|'''Θ'''
|'''''29\18'''''
'''''1288.{{Overline|8}}'''''
|'''''21\13'''''
'''''1292.308'''''
|'''''34\21'''''
'''''1295.238'''''
|'''''13\8'''''
'''''1300'''''
|'''''31\19'''''
'''''1305.263'''''
|'''''18\11'''''
'''''1309.{{Overline|09}}'''''
|'''''23\14'''''
'''''1314.286'''''
|-
|Re#
|Θ#
|''30\18''
''1333.{{Overline|3}}''
|''22\13''
''1187.924''
|''36\21''
''1371.429''
| rowspan="2" |''14\8''
''1400''
|''34\19''
''1431.421''
|''20\11''
''1454.{{Overline|54}}''
|''26\14''
''1485.714''
|-
|Mib
|Ιb
|''32\18''
''1422.{{Overline|2}}''
|''23\13''
''1415.385''
|''37\21''
''1409.524''
|''33\19''
''1389.474''
|''19\11''
''1381.{{Overline|81}}''
|''24\14''
''1371.429''
|-
|Mi
|Ι
|''33\18''
''1466.{{Overline|6}}''
|''24\13''
''1476.923''
|''39\21''
''1485.714''
|''15\8''
''1500''
|''36\19''
''1515.7895''
|''21\11''
''1527.{{Overline|27}}''
|''27\14''
''1542.857''
|-
|Mi#
|Ι#
|''34\18''
''1511.{{Overline|1}}''
| rowspan="2" |''25\13''
''1538.4615''
|''41\21''
''1561.905''
|''16\8''
''1600''
|''39\19''
''1642.105''
|''23\11''
''1672.{{Overline|72}}''
|''30\14''
''1714.286''
|-
|Lab
|Αb
|Αb
|''35\18''
|35\18, 1615.385
''1555.{{Overline|5}}''
|40\21, 1548.387
|''40\21''
|15\8, 1500
''1523.8095''
|35\19, 1448.286
|''15\8''
|20\11, 1411.765
''1500''
|25\14, 1363.636
|''35\19''
''1473.684''
|''20\11''
''1454.{{Overline|54}}''
|''25\14''
''1428.571''
|-
|-
!La
!La
!Mi
!Α
!Α
! colspan="7" |''1600''
!36\18, 1661.538
!26\13, 1642.105
!42\21, 1625.806
!16\8, 1600
!38\19, 1572.414
!22\11, 1552.941
!28\14, 1527.273
|}
|}


Line 1,024: Line 367:
|-
|-
|0
|0
|La
|La, Mi
|sextave (minor sixth)
|sextave (minor sixth)
| 0
| 0
|La
|La, Mi
| perfect unison
| perfect unison
|-
|-
|1
|1
|Re
|Re, La
|perfect fourth
|perfect fourth
| -1
| -1
|Do
|Do, Sol
|minor third
|minor third
|-
|-
|2
|2
|Si
|Si, Fa#
|major second
|major second
| -2
| -2
|Mib
|Mib, Sib
|diminished fifth
|diminished fifth
|-
|-
|3
|3
|Mi
|Mi, Si
|perfect fifth
|perfect fifth
| -3
| -3
|Sib
|Sib, Fa
|minor second
|minor second
|-
|-
|4
|4
|Do#
|Do#, Sol#
|major third
|major third
| -4
| -4
|Reb
|Reb, Lb
|diminished fourth
|diminished fourth
|-
|-
Line 1,061: Line 404:
|-
|-
|5
|5
|La#
|La#, Mi#
|augmented unison (chroma)
|augmented unison (chroma)
| -5
| -5
| Lab
| Lab, Mib
|diminished sextave
|diminished sextave
|-
|-
|6
|6
| Re#
| Re#, La#
|augmented fourth
|augmented fourth
| -6
| -6
|Dob
|Dob, Solb
|diminished third
|diminished third
|-
|-
|7
|7
|Si#
|Si#, Fax
|augmented second
|augmented second
| -7
| -7
|Mibb
|Mibb, Sibb
|doubly diminished fifth
|doubly diminished fifth
|}
|}
Line 1,085: Line 428:
{| class="wikitable"
{| class="wikitable"
|Sibb
|Sibb
Fab
|Mibb
|Mibb
Sibb
|Dob
|Dob
Solb
|Lab
|Lab
Mib
|Reb
|Reb
Lab
|Sib
|Sib
Fa
|Mib
|Mib
Sib
|Do
|Do
Sol
|La
|La
Mi
|Re
|Re
La
|Si
|Si
Fa#
|Mi
|Mi
Si
|Do#
|Do#
Sol#
|La#
|La#
Mi#
|Re#
|Re#
La#
|Si#
|Si#
Fax
|Mi#
|Mi#
Si#
|-
|-
|d2
|d2
Line 1,184: Line 544:
[[Comma]] list: [[81/80]]
[[Comma]] list: [[81/80]]


[[POL2]] generator: ~6/5 = 308.3057
[[POL2]] generator: ~6/5 = 308.3057¢


[[Mapping]]: [{{val|1 1 2}}, {{val|0 -1 -3}}]
[[Mapping]]: [{{val|1 1 2}}, {{val|0 -1 -3}}]


[[Optimal ET sequence]]: 5ed8/5, 8ed8/5, 13ed8/5
[[Optimal ET sequence]]: [[5ed8/5]], [[8ed8/5]], [[13ed8/5]]
==='''Aeolianic-Superpyth'''===
==='''Aeolianic-Superpyth'''===
[[Subgroup]]: 14/9.4/3.3/2
[[Subgroup]]: 14/9.4/3.3/2
Line 1,194: Line 554:
[[Comma]] list: [[64/63]]
[[Comma]] list: [[64/63]]


[[POL2]] generator: ~7/6 = 276.0795
[[POL2]] generator: ~7/6 = 276.0795¢


[[Mapping]]:  [{{val|1 1 2}}, {{val|0 -1 -3}}]
[[Mapping]]:  [{{val|1 1 2}}, {{val|0 -1 -3}}]


[[Optimal ET sequence]]: 3ed14/9, 11ed14/9, 14ed14/9
[[Optimal ET sequence]]: [[3ed14/9]], [[8ed14/9]], [[11ed14/9]], [[14ed14/9]]


==Scale tree==
==Scale tree==
The spectrum looks like this:
The spectrum looks like this:
{| class="wikitable"
{| class="wikitable"
! colspan="3" |Generator
!Generator
(bright)
(bright)
!Normalised
!Normalised
!''ed8\12 (→ed2\3)''
!L
!L
!s
!s
Line 1,213: Line 572:
|-
|-
|3\5
|3\5
|
|
|514.286
|514.286
|''480''
|1
|1
|1
|1
Line 1,223: Line 579:
|-
|-
|17\28
|17\28
|
|510.000
|
|510
|''485.714''
|6
|6
|5
|5
Line 1,233: Line 586:
|-
|-
|14\23
|14\23
|
|509.091
|
|509.{{Overline|09}}
|''486.9565''
|5
|5
|4
|4
Line 1,242: Line 592:
|
|
|-
|-
|
|25\41
|25\41
|
|508.475
|508.475
|''487.805''
|9
|9
|7
|7
|1.286
|1.286
|
|-
|
|36\59
|
|508.235
|''488.136''
|13
|10
|1.300
|
|
|-
|-
|11\18
|11\18
|
|
|507.692
|507.692
|''488.{{Overline|8}}''
|4
|4
|3
|3
Line 1,272: Line 606:
|
|
|-
|-
|
|30\49
|
|507.062
|''489.796''
|11
|8
|1.375
|
|-
|
|19\31
|
|506.{{Overline|6}}
|''490.323''
|7
|5
|1.400
|
|-
|
|27\44
|
|506.25
|''490.{{Overline|90}}''
|10
|7
|1.429
|
|-
|
|35\57
|35\57
|
|506.024
|506.024
|''491.228''
|13
|13
|9
|9
|1.444
|1.444
|
|-
|
|43\70
|
|505.882
|''491.429''
|16
|11
|1.4545
|
|-
|
|51\83
|
|505.785
|''491.566''
|19
|13
|1.4615
|
|
|-
|-
|8\13
|8\13
|
|
|505.263
|505.263
|''492.308''
|3
|3
|2
|2
Line 1,342: Line 620:
|Aeolianic-Meantone starts here
|Aeolianic-Meantone starts here
|-
|-
|
|45\73
|
|504.673
|''493.151''
|17
|11
|1.5455
|
|-
|
|37\60
|
|504.{{Overline|54}}
|''493.{{Overline|3}}''
|14
|9
|1.556
|
|-
|
|29\47
|
|504.348
|''493.617''
|11
|7
|1.571
|
|-
|
|21\34
|21\34
|
|504.000
|504
|''494.118''
|8
|8
|5
|5
Line 1,382: Line 627:
|
|
|-
|-
|
|
|47\76
|503.571
|''494.737''
|18
|11
|1.636
|
|-
|
|13\21
|13\21
|
|503.226
|503.226
|''495.238''
|5
|5
|3
|3
Line 1,402: Line 634:
|
|
|-
|-
|
|
|49\79
|502.564
|''496.2025''
|19
|11
|1.727
|
|-
|
|18\29
|18\29
|
|502.326
|502.326
|''496.552''
|7
|7
|4
|4
Line 1,422: Line 641:
|
|
|-
|-
|
|23\37
|23\37
|
|501.818
|501.{{Overline|81}}
|''497.{{Overline|297}}''
|9
|9
|5
|5
Line 1,432: Line 648:
|
|
|-
|-
|
|28\45
|28\45
|
|501.492
|501.492
|''497.{{Overline|7}}''
|11
|11
|6
|6
Line 1,442: Line 655:
|
|
|-
|-
|
|33\53
|33\53
|
|501.265
|501.265
|''498.113''
|13
|13
|7
|7
Line 1,452: Line 662:
|
|
|-
|-
|
|38\61
|38\61
|
|501.09
|501.09
|''498.361''
|15
|15
|8
|8
Line 1,462: Line 669:
|
|
|-
|-
|
|43\69
|43\69
|
|500.971
|500.971
|''498.551''
|17
|17
|9
|9
Line 1,473: Line 677:
|-
|-
|5\8
|5\8
|
|500.000
|
|500
|''500''
|2
|2
|1
|1
Line 1,482: Line 683:
|Aeolianic-Meantone ends, Aeolianic-Pythagorean begins
|Aeolianic-Meantone ends, Aeolianic-Pythagorean begins
|-
|-
|
|42\67
|42\67
|
|499.010
|499.01
|''501.4925''
|17
|17
|8
|8
Line 1,492: Line 690:
|
|
|-
|-
|
|37\59
|37\59
|
|498.876
|498.876
|''501.695''
|15
|15
|7
|7
Line 1,502: Line 697:
|
|
|-
|-
|
|32\51
|32\51
|
|498.701
|498.701
|''501.961''
|13
|13
|6
|6
Line 1,512: Line 704:
|
|
|-
|-
|
|27\43
|27\43
|
|498.461
|498.461
|''502.326''
|11
|11
|5
|5
Line 1,522: Line 711:
|
|
|-
|-
|
|22\35
|22\35
|
|498.113
|498.113
|''502.857''
|9
|9
|4
|4
Line 1,532: Line 718:
|
|
|-
|-
|
|17\27
|17\27
|
|497.561
|497.561
|''503.{{Overline|703}}''
|7
|7
|3
|3
Line 1,542: Line 725:
|
|
|-
|-
|
|
|41\65
|496.{{Overline|96}}
|''504.615''
|17
|7
|2.429
|
|-
|
|12\19
|12\19
|
|496.552
|496.552
|''505.263''
|5
|5
|2
|2
Line 1,562: Line 732:
|
|
|-
|-
|
|19\30
|19\30
|
|495.652
|495.652
|''506.{{Overline|6}}''
|8
|8
|3
|3
Line 1,572: Line 739:
|
|
|-
|-
|
|26\41
|26\41
|
|495.238
|495.238
|''507.317''
|11
|11
|4
|4
Line 1,582: Line 746:
|
|
|-
|-
|
|33\52
|33\52
|
|495.000
|495
|''507.692''
|14
|14
|5
|5
|2.800
|2.800
|
|-
|
|40\63
|
|494.536
|''507.9365''
|17
|6
|2.833
|
|-
|
|47\74
|
|494.737
|''508.{{Overline|108}}''
|20
|7
|2.857
|
|-
|
|54\85
|
|494.6565
|''508.235''
|23
|8
|2.875
|
|-
|
|61\96
|
|494.{{Overline|594}}
|''508.{{Overline|3}}''
|26
|9
|2.889
|
|
|-
|-
|7\11
|7\11
|
|
|494.118
|494.118
|''509.{{Overline|09}}''
|3
|3
|1
|1
Line 1,642: Line 760:
|Aeolianic-Pythagorean ends, Aeolianic-Superpyth begins
|Aeolianic-Pythagorean ends, Aeolianic-Superpyth begins
|-
|-
|
|65\102
|
|493.671
|''509.804''
|28
|9
|3.111
|
|-
|
|58\91
|
|493.617
|''509.89''
|25
|8
|3.125
|
|-
|
|51\80
|
|493.548
|''510''
|22
|7
|3.143
|
|-
|
|44\69
|
|493.458
|''510.145''
|19
|6
|3.167
|
|-
|
|37\58
|
|493.{{Overline|3}}
|''510.345''
|16
|5
|3.200
|
|-
|
|30\47
|30\47
|
|493.151
|493.151
|''510.638''
|13
|13
|4
|4
Line 1,702: Line 767:
|
|
|-
|-
|
|23\36
|23\36
|
|492.857
|492.857
|''511.{{Overline|1}}''
|10
|10
|3
|3
Line 1,712: Line 774:
|
|
|-
|-
|
|16\25
|16\25
|
|492.308
|492.308
|''512''
|7
|7
|2
|2
Line 1,722: Line 781:
|
|
|-
|-
|
|25\39
|25\39
|
|491.803
|491.803
|''512.8205''
|11
|11
|3
|3
|3.667
|3.667
|
|-
|
|34\53
|
|491.566
|''513.2075''
|15
|4
|3.750
|
|-
|
|43\67
|
|491.429
|''513.433''
|19
|5
|3.800
|
|-
|
|52\81
|
|491.339
|''513.58''
|23
|6
|3.833
|
|-
|
|61\95
|
|491.275
|''513.684''
|27
|7
|3.857
|
|
|-
|-
|9\14
|9\14
|
|490.909
|
|490.{{Overline|90}}
|''514.286''
|4
|4
|1
|1
Line 1,782: Line 795:
|
|
|-
|-
|
|47\73
|
|490.435
|''515.0685''
|21
|5
|4.200
|
|-
|
|38\59
|
|490.323
|''515.254''
|17
|4
|4.250
|
|-
|
|29\45
|
|490.141
|''515.{{Overline|5}}''
|13
|3
|4.333
|
|-
|
|20\31
|20\31
|
|489.795
|489.795
|''516.129''
|9
|9
|2
|2
|4.500
|4.500
|
|-
|
|31\48
|
|489.474
|''516.{{Overline|6}}''
|14
|3
|4.667
|
|-
|
|42\65
|
|489.32
|''516.923''
|19
|4
|4.750
|
|
|-
|-
|11\17
|11\17
|
|488.889
|
|488.{{Overline|8}}
|''517.647''
|5
|5
|1
|1
|5.000
|5.000
|Aeolianic-Superpyth ends
|Aeolianic-Superpyth ends
|-
|
|35\54
|
|488.372
|''518.{{Overline|518}}''
|16
|3
|5.333
|
|-
|
|24\37
|
|488.136
|''518.{{Overline|918}}''
|11
|2
|5.500
|
|-
|
|37\57
|
|487.912
|''519.298''
|17
|3
|5.667
|
|-
|-
|13\20
|13\20
|
|487.500
|
|487.5
|''520''
|6
|6
|1
|1
Line 1,893: Line 817:
|-
|-
|2\3
|2\3
|
|480.000
|
|480
|''533.{{Overline|3}}''
|1
|1
|0
|0
Line 1,902: Line 823:
|Paucitonic
|Paucitonic
|}
|}
==See also==
==See also==
[[3L 2s (13/8-equivalent)]] and [[3L 2s (φ-equivalent)|3L 2s ([math]φ[/math]-equivalent)]] - Harmonic and Golden tuning
[[3L 2s (14/9-equivalent)]] - idealized Archytas tuning
[[3L 2s (14/9-equivalent)]] - idealized Archytas tuning
[[3L 2s (11/7-equivalent)]] and [[3L 2s (π/2-equivalent)|3L 2s ([math]π[/math]/2-equivalent)]] - Neogothic tuning
[[3L 2s (128/81-equivalent)]] - Pythagorean tuning


[[3L 2s (8/5-equivalent)]] - idealized Meantone tuning
[[3L 2s (8/5-equivalent)]] - idealized Meantone tuning
[[6L 4s (5/2-equivalent)]] - Annapolis Meantone tuning
[[6L 4s (81/32-equivalent)]] - Annapolis Pythagorean tuning
[[6L 4s (28/11-equivalent)]] - Annapolis Neogothic tuning
[[6L 4s (18/7-equivalent)]] - Annapolis Archytas tuning
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