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User:Moremajorthanmajor/4L 1s (major sixth-equivalent): Difference between revisions

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[[Basic]] diatonic is in [[9ed5/3]], which is a very good major sixth-based equal tuning similar to [[12edo]].
[[Basic]] diatonic is in [[9ed5/3]], which is a very good major sixth-based equal tuning similar to [[12edo]].
==Notation==
==Notation==
There are 2 main ways to notate the diatonic scale. One method uses a simple sextave (major sixth) repeating notation consisting of 5 naturals (Do, Re, Mi, Fa, Sol or Sol, La, Si, Do, Re). Given that 1-5/4-3/2 is major sixth-equivalent to a tone cluster of 1-10/9-5/4, it may be more convenient to notate these diatonic scales as repeating at the double sextave (augmented eleventh~twelfth), however it does make navigating the [[Generator|genchain]] harder. This way, 3/2 is its own pitch class, distinct from 10\9. Notating this way produces a twelfth which is the Scala Francisci[8L 2s]. 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 (major sixth) repeating notation consisting of 5 naturals (Do, Re, Mi, Fa, Sol or Sol, La, Si, Do, Re). Given that 1-5/4-3/2 is major sixth-equivalent to a tone cluster of 1-10/9-5/4, it may be more convenient to notate these diatonic scales as repeating at the double sextave (augmented eleventh~twelfth), however it does make navigating the [[Generator|genchain]] harder. This way, 3/2 is its own pitch class, distinct from 10\9. Notating this way produces a twelfth which is the Scala Francisci[8L 2s]. Since there are exactly 10 naturals in double sextave notation, Greek numerals 1-10 may be used.
{| class="wikitable"
{| class="wikitable"
Line 518: Line 520:
!34\17
!34\17
1854.{{Overline|54}}
1854.{{Overline|54}}
|}
{| class="wikitable"
|+''ed9\12 (→ed3\4)''
! colspan="2" |Notation
!Supersoft
!Soft
!Semisoft
!Basic
!Semihard
!Hard
!Superhard
|-
!Diatonic
!Scala Francisci
!19eds
!14eds
!23eds
!9eds
!22eds
!13eds
!17eds
|-
|Do#, Sol#
|Α#
|''1\19''
''47.368''
|''1\14''
''64.286''
|''2\23''
''78.261''
| rowspan="2" |''1\9''
''100''
|''3\22''
''122.{{Overline|72}}''
|''2\13''
''138.4615''
|''3\17''
''158.8235''
|-
|Reb, Lab
|Βb
|''3\19''
''142.105''
|''2\14''
''128.571''
|''3\23''
''117.391''
|''2\22''
''81.{{Overline|81}}''
|''1\13''
''69.231''
|''1\17''
''52.941''
|-
|'''Re, La'''
|Β
|'''''4\19'''''
'''''189.474'''''
|'''''3\14'''''
'''''192.857'''''
|'''''5\23'''''
'''''195.652'''''
|'''''2\9'''''
'''''200'''''
|'''''5\22'''''
'''''204.{{Overline|54}}'''''
|'''''3\13'''''
'''''207.692'''''
|'''''4\17'''''
'''''211.765'''''
|-
|Re#, La#
|Β#
|''5\19''
''236.842''
|''4\14''
''257.143''
|''7\23''
''273.913''
| rowspan="2" |''3\9''
''300''
|''8\22''
''327.{{Overline|27}}''
|''5\13''
''346.154''
|''7\17''
''370.588''
|-
|Mib, Sib
|Γb
|''7\19''
''331.579''
|''5\14''
''321.429''
|''8\23''
''313.0345''
|''7\22''
''286.{{Overline|36}}''
|''4\13''
''276.923''
|''5\17''
''264.706''
|-
|Mi, Si
|Γ
|''8\19''
''378.947''
|''6\14''
''385.714''
|''10\23''
''391.304''
|''4\9''
''400''
|''10\22''
''409.{{Overline|09}}''
|''6\13''
''415.385''
|''8\17''
''423.529''
|-
|Mi#, Si#
|Γ#
|''9\19''
''426.316''
| rowspan="2" |''7\14''
''450''
|''12\23''
''469.565''
|''5\9''
''500''
|''13\22''
''531.{{Overline|81}}''
|''8\13''
''553.846''
|''11\17''
''582.353''
|-
|Fab, Dob
|Δb
|''10\19''
''473.684''
|''11\23''
''430.769''
|''4\9''
''400''
|''9\22''
''368.{{Overline|18}}''
|''5\13''
''346.154''
|''6\17''
''317.647''
|-
|Fa, Do
|Δ
|''11\19''
''521.053''
|''8\14''
''514.286''
|''13\23''
''508.696''
|''5\9''
''500''
|''12\22''
''490.{{Overline|90}}''
|''7\13''
''484.615''
|''9\17''
''476.471''
|-
|Fa#, Do#
|Δ#
|''12\19''
''568.421''
|''9\14''
''578.571''
|''15\23''
''578.9655''
| rowspan="2" |''6\9''
''600''
|''15\22''
''613.{{Overline|63}}''
|''9\13''
''623.077''
|''12\17''
''635.293''
|-
|Solb, Reb
|Εb
|''14\19''
''663.158''
|''10\14''
''642.857''
|''16\23''
''626.087''
|''14\22''
''572.{{Overline|72}}''
|''8\13''
''553.846''
|''10\17''
''529.412''
|-
|'''Sol, Re'''
|'''Ε'''
|'''''15\19'''''
'''''710.526'''''
|'''''11\14'''''
'''''707.143'''''
|'''''18\23'''''
'''''704.348'''''
|'''''7\8'''''
'''''700'''''
|'''''17\22'''''
'''''695.{{Overline|45}}'''''
|'''''10\13'''''
'''''692.308'''''
|'''''13\17'''''
'''''688.235'''''
|-
|Sol#, Re#
|Ε#
|''16\19''
''757.895''
|''12\14''
''771.429''
|''20\23''
''782.609''
| rowspan="2" |''8\8''
''800''
|''20\22''
''818.{{Overline|18}}''
|''12\13''
''830.769''
|''16\17''
''847.059''
|-
|Dob, Solb
|Ϛb/Ϝb
|''18\19''
''852.632''
|''13\14''
''835.714''
|''21\23''
''821.739''
|''19\22''
''777.{{Overline|27}}''
|''11\13''
''761.5385''
|''14\17''
''741.1765''
|-
!Do, Sol
!Ϛ/Ϝ
! colspan="7" |''900''
|-
|Do#, Sol#
|Ϛ#/Ϝ#
|''20\19''
''947.368''
|''15\14''
''964.286''
|''25\23''
''978.261''
| rowspan="2" |''10\9''
''1000''
|''25\22''
''1022.{{Overline|72}}''
|''15\13''
''1038.4615''
|''20\17''
''1058.8235''
|-
|Reb, Lab
|Ζb
|''22\19''
''1042.105''
|''16\14''
''1028.571''
|''26\23''
''1017.391''
|''24\22''
''981.{{Overline|81}}''
|''14\13''
''969.231''
|''18\17''
''952.941''
|-
|'''Re, La'''
|'''Ζ'''
|'''''23\19'''''
'''''1089.473'''''
|'''''17\14'''''
'''''1092.857'''''
|'''''28\23'''''
'''''1095.652'''''
|'''''11\9'''''
'''''1100'''''
|'''''27\22'''''
'''''1104.{{Overline|54}}'''''
|'''''16\13'''''
'''''1107.692'''''
|'''''21\17'''''
'''''1111.765'''''
|-
|Re#, La#
|Ζ#
|''24\19''
''1136.842''
|''18\14''
''1157.143''
|''30\23''
''1173.913''
| rowspan="2" |''12\9''
''1200''
|''30\22''
''1227.{{Overline|27}}''
|''18\13''
''1246.154''
|''24\14''
''1270.588''
|-
|Mib, Sib
|Ηb
|''26\19''
''1231.579''
|''19\14''
''1221.429''
|''31\23''
''1213.0345''
|''29\22''
''1186.{{Overline|36}}''
|''17\13''
''1176.923''
|''22\17''
''1164.706''
|-
|Mi, Si
|Η
|''27\19''
''1278.947''
|''20\14''
''1285.714''
|''33\23''
''1291.304''
|''13\9''
''1300''
|''32\22''
''1309.{{Overline|09}}''
|''19\13''
''1315.385''
|''25\17''
''1323.529''
|-
|Mi#, Si#
|Η#
|''28\19''
''1326.316''
| rowspan="2" |''21\14''
''1350''
|''35\23''
''1369.565''
|''14\9''
''1400''
|''35\22''
''1431.{{Overline|81}}''
|''21\13''
''1453.846''
|''28\17''
''1482.353''
|-
|Fab, Dob
|Θb
|''29\19''
''1373.684''
|''34\23''
''1330.769''
|''13\9''
''1300''
|''31\22''
''1368.{{Overline|18}}''
|''18\13''
''1246.154''
|''23\17''
''1317.647''
|-
|Fa, Do
|Θ
|''30\19''
''1421.053''
|''22\14''
''1414.286''
|''36\23''
''1408.696''
|''14\9''
''1400''
|''34\22''
''1390.{{Overline|90}}''
|''20\13''
''1384.615''
|''26\17''
''1376.471''
|-
|Fa#, Do#
|Θ#
|''31\19''
''1468.421''
|''23\14''
''1478.714''
|''38\23''
''1487.9655''
| rowspan="2" |''15\9''
''1500''
|''37\22''
''1513.{{Overline|63}}''
|''22\13''
''1523.077''
|''29\17''
''1535.294''
|-
|Solb, Reb
|Ιb
|''33\19''
''1563.158''
|''24\14''
''1542.857''
|''39\23''
''1526.087''
|''36\22''
''1472.{{Overline|72}}''
|''21\13''
''1453.846''
|''27\17''
''1429.412''
|-
|'''Sol, Re'''
|'''Ι'''
|'''''34\19'''''
'''''1610.526'''''
|'''''25\14'''''
'''''1607.143'''''
|'''''41\23'''''
'''''1604.348'''''
|'''''16\9'''''
'''''1600'''''
|'''''39\22'''''
'''''1595.{{Overline|45}}'''''
|'''''23\13'''''
'''''1592.308'''''
|'''''30\17'''''
'''''1588.235'''''
|-
|Sol#, Re#
|Ι#
|''35\19''
''1657.895''
|''26\14''
''1671.429''
|''43\23''
''1682.609''
| rowspan="2" |''17\9''
''1700''
|''42\22''
''1718.{{Overline|18}}''
|''25\13''
''1730.769''
|''33\17''
''1747.059''
|-
|Dob, Solb
|Αb
|''37\19''
''1752.632''
|''27\14''
''1735.714''
|''44\23''
''1721.739''
|''41\22''
''1677.{{Overline|27}}''
|''20\13''
''1661.5385''
|''31\17''
''1641.1765''
|-
!Do, Sol
!Α
! colspan="7" |''1800''
|}
|}
==Intervals==
==Intervals==
Line 1,221: Line 738:
(bright)
(bright)
!Normalised
!Normalised
!''ed9\12 (→ed3\4)''
!L
!L
!s
!s
Line 1,231: Line 747:
|
|
|171.429
|171.429
|''180''
|1
|1
|1
|1
Line 1,241: Line 756:
|
|
|180
|180
|''186.207''
|6
|6
|5
|5
Line 1,251: Line 765:
|
|
|181.{{Overline|81}}
|181.{{Overline|81}}
|''187.5''
|5
|5
|4
|4
Line 1,261: Line 774:
|
|
|182.609
|182.609
|''188.06''
|14
|14
|11
|11
Line 1,271: Line 783:
|
|
|183.051
|183.051
|''188.372''
|9
|9
|7
|7
Line 1,281: Line 792:
|
|
|184.615
|184.615
|''189.474''
|4
|4
|3
|3
Line 1,291: Line 801:
|
|
|185.915
|185.915
|''190.385''
|11
|11
|8
|8
Line 1,301: Line 810:
|
|
|186.{{Overline|6}}
|186.{{Overline|6}}
|''190.{{Overline|90}}''
|7
|7
|5
|5
Line 1,311: Line 819:
|
|
|187.5
|187.5
|''191.498''
|10
|10
|7
|7
Line 1,321: Line 828:
|
|
|189.474
|189.474
|''192.857''
|3
|3
|2
|2
Line 1,331: Line 837:
|
|
|190.{{Overline|90}}
|190.{{Overline|90}}
|''193.846''
|14
|14
|9
|9
Line 1,341: Line 846:
|
|
|191.304
|191.304
|''194.118''
|11
|11
|7
|7
Line 1,351: Line 855:
|
|
|192
|192
|''194.{{Overline|594}}''
|8
|8
|5
|5
Line 1,361: Line 864:
|
|
|193.548
|193.548
|''195.652''
|5
|5
|3
|3
Line 1,371: Line 873:
|
|
|195.349
|195.349
|''196.875''
|7
|7
|4
|4
Line 1,381: Line 882:
|
|
|196.{{Overline|36}}
|196.{{Overline|36}}
|''197.561''
|9
|9
|5
|5
Line 1,391: Line 891:
|
|
|197.015
|197.015
|''198''
|11
|11
|6
|6
Line 1,401: Line 900:
|
|
|197.468
|197.468
|''198.305''
|13
|13
|7
|7
Line 1,411: Line 909:
|
|
|197.802
|197.802
|''198.529''
|15
|15
|8
|8
Line 1,421: Line 918:
|
|
|198.058
|198.058
|''198.701''
|17
|17
|9
|9
Line 1,431: Line 927:
|
|
|198.261
|198.261
|''198.837''
|19
|19
|10
|10
Line 1,441: Line 936:
|
|
|198.425
|198.425
|''198.947''
|21
|21
|11
|11
Line 1,451: Line 945:
|
|
|198.561
|198.561
|''199.039''
|23
|23
|12
|12
Line 1,461: Line 954:
|
|
|200
|200
|''200''
|2
|2
|1
|1
Line 1,471: Line 963:
|
|
|201.6
|201.6
|''201.064''
|21
|21
|10
|10
Line 1,481: Line 972:
|
|
|201.77
|201.77
|''201.1765''
|19
|19
|9
|9
Line 1,491: Line 981:
|
|
|201.98
|201.98
|''201.316''
|17
|17
|8
|8
Line 1,501: Line 990:
|
|
|202.247
|202.247
|''201.4925''
|15
|15
|7
|7
Line 1,511: Line 999:
|
|
|202.597
|202.597
|''201.724''
|13
|13
|6
|6
Line 1,521: Line 1,008:
|
|
|203.076
|203.076
|''202.041''
|11
|11
|5
|5
Line 1,531: Line 1,017:
|
|
|203.774
|203.774
|''202.5''
|9
|9
|4
|4
Line 1,541: Line 1,026:
|
|
|204.838
|204.838
|''203.226''
|7
|7
|3
|3
Line 1,551: Line 1,035:
|12\53
|12\53
|205.714
|205.714
|''203.774''
|12
|12
|5
|5
Line 1,561: Line 1,044:
|
|
|206.897
|206.897
|''204.{{Overline|54}}''
|5
|5
|2
|2
Line 1,571: Line 1,053:
|18\79
|18\79
|207.692
|207.692
|''205.063''
|18
|18
|7
|7
Line 1,581: Line 1,062:
|
|
|208.696
|208.696
|''205.714''
|8
|8
|3
|3
Line 1,591: Line 1,071:
|
|
|209.524
|209.524
|''206.25''
|11
|11
|4
|4
Line 1,601: Line 1,080:
|
|
|210
|210
|''206.557''
|14
|14
|5
|5
Line 1,611: Line 1,089:
|
|
|211.765
|211.765
|''207.692''
|3
|3
|1
|1
Line 1,621: Line 1,098:
|
|
|212.903
|212.903
|''208.421''
|22
|22
|7
|7
Line 1,631: Line 1,107:
|
|
|213.084
|213.084
|''208.5365''
|19
|19
|6
|6
Line 1,641: Line 1,116:
|
|
|213.{{Overline|3}}
|213.{{Overline|3}}
|''208.696''
|16
|16
|5
|5
Line 1,651: Line 1,125:
|
|
|213.699
|213.699
|''208.929''
|13
|13
|4
|4
Line 1,661: Line 1,134:
|
|
|214.286
|214.286
|''209.322''
|10
|10
|3
|3
Line 1,671: Line 1,143:
|
|
|215.385
|215.385
|''210''
|7
|7
|2
|2
Line 1,681: Line 1,152:
|
|
|216.393
|216.393
|''210.638''
|11
|11
|3
|3
Line 1,691: Line 1,161:
|
|
|216.867
|216.867
|''210.9375''
|15
|15
|4
|4
Line 1,701: Line 1,170:
|
|
|217.143
|217.143
|''211.{{Overline|1}}''
|19
|19
|5
|5
Line 1,711: Line 1,179:
|
|
|218.{{Overline|18}}
|218.{{Overline|18}}
|''211.765''
|4
|4
|1
|1
Line 1,721: Line 1,188:
|
|
|219.13
|219.13
|''212.36''
|21
|21
|5
|5
Line 1,731: Line 1,197:
|
|
|219.355
|219.355
|''212.5''
|17
|17
|4
|4
Line 1,741: Line 1,206:
|
|
|219.718
|219.718
|''212.{{Overline|72}}''
|13
|13
|3
|3
Line 1,751: Line 1,215:
|
|
|220.408
|220.408
|''213.158''
|9
|9
|2
|2
Line 1,761: Line 1,224:
|
|
|221.053
|221.053
|''213.559''
|14
|14
|3
|3
Line 1,771: Line 1,233:
|
|
|222.{{Overline|2}}
|222.{{Overline|2}}
|''214.286''
|5
|5
|1
|1
Line 1,781: Line 1,242:
|
|
|223.729
|223.729
|''215.217''
|11
|11
|2
|2
Line 1,791: Line 1,251:
|
|
|224.176
|224.176
|''215.492''
|17
|17
|3
|3
Line 1,801: Line 1,260:
|
|
|225
|225
|''216''
|6
|6
|1
|1
Line 1,811: Line 1,269:
|
|
|240
|240
|''225''
|1
|1
|0
|0
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/4L_1s_(major_sixth-equivalent)"