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User:Moremajorthanmajor/5L 2s (major sixth-equivalent): Difference between revisions

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|}If we carry this freshman-summing out a little further, new, larger EDSs pop up in our continuum.
|}If we carry this freshman-summing out a little further, new, larger EDSs pop up in our continuum.
{| class="wikitable center-all"
{| class="wikitable center-all"
! colspan="7" |Generator
!Generator
!Cents
!Cents
!Śata
!L
!L
!s
!s
Line 100: Line 99:
!Comments
!Comments
|-
|-
|4\7|| || || || || ||
|4\7
|533.333||711.111||1||1||1.000||
|533.333¢ ||1||1||1.000||
|-
|-
| || || || || || ||27\47
| 27\47
|531.1475|[[Tel:531.1475|531.1475]]||708.196||7||6||1.167||
|531.148¢ ||7||6||1.167||
|-
|-
| || || || || ||23\40||
| 23\40
|530.769||707.692||6||5||1.200||
|530.769¢ ||6||5||1.200||
|-
|-
| || || || || || ||42\73
| 19\33
|530.526||707.368||11||9||1.222||
|530.232¢ ||5||4||1.250||
|-
|-
| || || || ||19\33|| ||
| 15\26
|530.232||706.977||5||4||1.250||
|529.411¢ ||4||3||1.333||
|-
|-
| || || || || || ||53\92
| 11\19
|530.000||706.667||14||11||1.273||
|528.000¢ ||3||2||1.500||L/s = 3/2
|-
|-
| || || || || ||34\59||
| 29\50
|529.870||[[Tel:706.4935|706.4935]]||9||7||1.286||
|527.272¢||8||5||1.600||
|-
|-
| || || || || || ||49\85
| 18\31
|529.730||706.306||13||10||1.300||
|526.829¢||5||3||1.667||3/4 Meantone is in this region
|-
|-
| || || ||15\26|| || ||
| 25\43
|529.411||705.882||4||3||1.333||
|526.316¢||7||4||1.750||
|-
|-
| || || || || || ||56\97
| 32\55
|529.134||705.512||15||11||1.364||
|526.028¢||9||5||1.800||
|-
|-
| || || || || ||41\71||
| 39\67
|529.032||705.376||11||8||1.375||
|525.843¢||11||6||1.833||
|-
|-
| || || || || || ||67\116
| 7\12
|528.947||705.263||18||13||1.385||
|525.000¢||2||1||2.000||Basic 3/4 diatonic
|-
| || || || ||26\45|| ||
|528.814||705.085||7||5||1.400||
|-
| || || || || || ||63\109
|528.617||704.895||17||12||1.417||
|-
| || || || || ||37\64||
|528.571||704.762||10||7||1.429||
|-
| || || || || || ||48\83
|528.440||704.587||13||9||1.444||
|-
| || ||11\19|| || || ||
|528.000||704.000||3||2||1.500||L/s = 3/2
|-
| || || || || || ||51\88
|527.586||703.448||14||9||1.556||
|-
| || || || || ||40\69||
|[[Tel:527.4725|527.4725]]||703.297||11||7||1.571||
|-
| || || || || || ||69\119
|[[Tel:527.3885|527.3885]]||703.185||19||12||1.583||
|-
| || || || ||29\50|| ||
|527.272||703.030||8||5||1.600||
|-
| || || || || || ||76\131
|527.168||702.890||21||13||1.615||Golden 3/4 meantone
|-
| || || || || ||47\81||
|527.103||702.804||13||8||1.625||
|-
| || || || || || ||65\112
|527.027||702.703||18||11||1.636||
|-
| || || ||18\31|| || ||
|526.829||702.409||5||3||1.667||3/4 Meantone is in this region
|-
| || || || || || ||61\105
|526.619||702.158||17||10||1.700||
|-
| || || || || ||43\74||
|526.531||702.041||12||7||1.714||
|-
| || || || || || ||68\117
|526.452||[[Tel:701.9355|701.9355]]||19||11||1.727||The generator closest to 3/4 of a just [[3/2]] for EDSs less than 200
|-
| || || || ||25\43|| ||
|526.316||701.754||7||4||1.750||
|-
| || || || || || ||57\98
|526.154||[[Tel:701.5385|701.5385]]||16||9||1.778||
|-
| || || || || ||32\55||
|526.028||701.370||9||5||1.800||
|-
| || || || || || ||39\67
|525.843||701.124||11||6||1.833||
|-
| ||7\12|| || || || ||
|525.000||700.000||2||1||2.000||Basic 3/4 diatonic
(Generators larger than this are proper)
(Generators larger than this are proper)
|-
|-
| || || || || || ||38\65
| 38\65
|524.138||698.851||11||5||2.200||
|524.138¢||11||5||2.200||
|-
| || || || || ||31\53||
|523.944||[[Tel:698.5915|698.5915]]||9||4||2.250||
|-
| || || || || || ||55\94
|[[Tel:523.8095|523.8095]]||698.413||16||7||2.286||
|-
| || || || ||24\41|| ||
|523.636||698.182||7||3||2.333||
|-
| || || || || || ||65\111
|523.490||697.987||19||8||2.375||
|-
|-
| || || || || ||41\70||
| 31\53
|523.404||697.872||12||5||2.400||
|523.944¢||9||4||2.250
|-
|-
| || || || || || ||58\99
| 24\41
|523.308||697.744||17||7||2.428||
|523.636¢||7||3||2.333||
|-
|-
| || || ||17\29|| || ||
| 17\29
|523.077||697.436||5||2||2.500||
|523.077¢||5||2||2.500||
|-
|-
| || || || || || ||61\104
| 27\46
|522.857||697.142||18||7||2.571||
|522.581¢||8||3||2.667||3/4 Neogothic is in this region
|-
|-
| || || || || ||44\75||
| 10\17
|522.772||697.030||13||5||2.600||
|521.739¢||3||1||3.000||L/s = 3/1
|-
|-
| || || || || || ||71\121
| 13\22
|522.699||[[Tel:696.9325|696.9325]]||21||8||2.625||Golden 3/4 neogothic
|520.000¢||4||1||4.000||3/4 Archy is in this region
|-
|-
| || || || ||27\46|| ||
| 29\49
|522.581||696.774||8||3||2.667||3/4 Neogothic is in this region
|519.403¢||9||2||4.500||
|-
|-
| || || || || || ||64\109
| 16\27
|522.449||696.599||19||7||2.714||
|518.919¢||5||1||5.000||
|-
|-
| || || || || ||37\63||
| 19\32
|522.352||[[Tel:696.4705|696.4705]]||11||4||2.750||
|518.182¢||6||1||6.000||
|-
|-
| || || || || || ||47\80
| 22\37
|522.222||696.296||14||5||2.800||
|517.647¢||7||1||7.000||
|-
|-
| || ||10\17|| || || ||
|3\5
|521.739||695.652||3||1||3.000||L/s = 3/1
|514.286¢||1||0||→ inf||
|-
| || || || || || ||43\73
|521.212||[[Tel:694.9495|694.9495]]||13||4||3.250||
|-
| || || || || ||33\56||
|521.053||694.737||10||3||3.333||
|-
| || || || || || ||56\95
|520.930||694.574||17||5||3.400||
|-
| || || || ||23\39|| ||
|520.755||694.340||7||2||3.500||
|-
| || || || || || ||59\100
|520.588||694.118||18||5||3.600||
|-
| || || || || ||36\61||
|520.482||693.976||11||3||3.667||
|-
| || || || || || ||49\83
|520.354||693.805||15||4||3.750||
|-
| || || ||13\22|| || ||
|520.000||693.333||4||1||4.000||3/4 Archy is in this region
|-
| || || || || || ||42\71
|519.588||[[Tel:692.7835|692.7835]]||13||3||4.333||
|-
| || || || || ||29\49||
|519.403||692.537||9||2||4.500||
|-
| || || || || || ||45\76
|519.231||692.308||14||3||4.667||
|-
| || || || ||16\27|| ||
|518.919||691.892||5||1||5.000||
|-
| || || || || || ||35\59
|[[Tel:518.5185|518.5185]]||691.358||11||2||5.500||
|-
| || || || || ||19\32||
|518.182||690.909||6||1||6.000||
|-
| || || || || || ||22\37
|517.647||690.196||7||1||7.000||
|-
|3\5|| || || || || ||
|514.286||685.714||1||0||→ inf||
|}Tunings above 7\12 on this chart are called "positive tunings" (as they greaten the size of the fifth) and include 3/4 meantone systems such as 1/3-comma (close to 11\19) and 1/4-comma (close to 18\31). As these tunings approach 4\7, the majors become flatter and the minors become sharper.
|}Tunings above 7\12 on this chart are called "positive tunings" (as they greaten the size of the fifth) and include 3/4 meantone systems such as 1/3-comma (close to 11\19) and 1/4-comma (close to 18\31). As these tunings approach 4\7, the majors become flatter and the minors become sharper.


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== See also ==
== See also ==
[[5L 2s (5/3-equivalent)]] - classical tuning
[[5L 2s (5/3-equivalent)]] - classical tuning
[[5L 2s (22\13-equivalent)]] - Neogothic tuning


[[5L 2s (12/7-equivalent)]] - Septimal tuning
[[5L 2s (12/7-equivalent)]] - Septimal tuning
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