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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]].
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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
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!Superhard
!Superhard
|-
|-
!Diatonic
!Aeolian
!Phrygian
!Oriole, Annapolis
!Oriole, Annapolis
!18eds
!18eds
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|-
|-
|La#
|La#
|Mi#
|Α#
|Α#
|1\18, 46.154
|1\18, 46.154
Line 43: Line 45:
|-
|-
|Sib
|Sib
|Fa
|Βb
|Βb
|3\18, 138.462
|3\18, 138.462
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|-
|-
|Si
|Si
|Fa#
|Β
|Β
|4\18, 184.615
|4\18, 184.615
Line 62: Line 66:
|-
|-
|Si#
|Si#
|Fax
|Β#
|Β#
|5\18, 230.769
|5\18, 230.769
Line 72: Line 77:
|-
|-
|Dob
|Dob
|Solb
|Γb
|Γb
|6\18, 276.923
|6\18, 276.923
Line 81: Line 87:
|-
|-
|'''Do'''
|'''Do'''
|'''Sol'''
|'''Γ'''
|'''Γ'''
|'''7\18,''' '''323.076'''
|'''7\18,''' '''323.076'''
Line 91: Line 98:
|-
|-
|Do#
|Do#
|Sol#
|Γ#
|Γ#
|8\18, 369.231
|8\18, 369.231
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|-
|-
|Reb
|Reb
|Lab
|Δb
|Δb
|10\18, 461.538
|10\18, 461.538
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|-
|-
|'''Re'''
|'''Re'''
|'''La'''
|'''Δ'''
|'''Δ'''
|'''11\18,''' '''507.692'''
|'''11\18,''' '''507.692'''
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|-
|-
|Re#
|Re#
|La#
|Δ#
|Δ#
|12\18, 553.846
|12\18, 553.846
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|-
|-
|Mib
|Mib
|Sib
|Εb
|Εb
|14\18, 646.154
|14\18, 646.154
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|-
|-
|Mi
|Mi
|Si
|Ε
|Ε
|15\18, 692.308
|15\18, 692.308
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|-
|-
|Mi#
|Mi#
|Si#
|Ε#
|Ε#
|16\18, 738.462
|16\18, 738.462
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|-
|-
|Lab
|Lab
|Mib
|Ϛb/Ϝb
|Ϛb/Ϝb
|17\18, 784.615
|17\18, 784.615
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|-
|-
!La
!La
!Mi
!Ϛ/Ϝ
!Ϛ/Ϝ
!18\18, 830.769
!18\18, 830.769
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|-
|-
|La#
|La#
|Mi#
|Ϛ#/Ϝ#
|Ϛ#/Ϝ#
|19\18, 876.923
|19\18, 876.923
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|-
|-
|Sib
|Sib
|Fa
|Ζb
|Ζb
|21\18, 969.231
|21\18, 969.231
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|-
|-
|Si
|Si
|Fa#
|Ζ
|Ζ
|22\18, 1015.385
|22\18, 1015.385
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|-
|-
|Si#
|Si#
|Fax
|Ζ#
|Ζ#
|23\18, 1061.538
|23\18, 1061.538
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|-
|-
|Dob
|Dob
|Solb
|Ηb
|Ηb
|24\18, 1107.692
|24\18, 1107.692
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|-
|-
|'''Do'''
|'''Do'''
|'''Sol'''
|'''Η'''
|'''Η'''
|'''25\18,''' '''1153.846'''
|'''25\18,''' '''1153.846'''
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|-
|-
|Do#
|Do#
|Sol#
|Η#
|Η#
|26\18, 1200
|26\18, 1200
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|-
|-
|Reb
|Reb
|Lab
|Θb
|Θb
|28\18, 1292.308
|28\18, 1292.308
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|-
|-
|'''Re'''
|'''Re'''
|'''La'''
|'''Θ'''
|'''Θ'''
|'''29\18,''' '''1338.462'''
|'''29\18,''' '''1338.462'''
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|-
|-
|Re#
|Re#
|La#
|Θ#
|Θ#
|30\18, 1384.615
|30\18, 1384.615
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|-
|-
|Mib
|Mib
|Sib
|Ιb
|Ιb
|32\18, 1476.923
|32\18, 1476.923
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|-
|-
|Mi
|Mi
|Si
|Ι
|Ι
|33\18, 1523.077
|33\18, 1523.077
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|-
|-
|Mi#
|Mi#
|Si#
|Ι#
|Ι#
|34\18, 1569.231
|34\18, 1569.231
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|-
|-
|Lab
|Lab
|Mib
|Αb
|Αb
|35\18, 1615.385
|35\18, 1615.385
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|-
|-
!La
!La
!Mi
!Α
!Α
!36\18, 1661.538
!36\18, 1661.538
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|-
|-
|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
|-
|-
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|-
|-
|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
|}
|}
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{| 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 782: Line 830:


[[3L 2s (11/7-equivalent)]] and [[3L 2s (π/2-equivalent)|3L 2s ([math]π[/math]/2-equivalent)]] - Neogothic 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 (5/2-equivalent)]] - Annapolis Meantone tuning
[[6L 4s (81/32-equivalent)]] - Annapolis Pythagorean tuning


[[6L 4s (28/11-equivalent)]] - Annapolis Neogothic tuning
[[6L 4s (28/11-equivalent)]] - Annapolis Neogothic tuning


[[6L 4s (18/7-equivalent)]] - Annapolis Archytas tuning
[[6L 4s (18/7-equivalent)]] - Annapolis Archytas tuning
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