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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$||1||1||1.000||
|533.333¢ ||1||1||1.000||
|-
|-
| || || || || || ||27\47
| 27\47
|531.1475¢ ||708.196$||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$||5||4||1.250||
|529.411¢ ||4||3||1.333||
|-
|-
| || || || || ||34\59||
| 11\19
|529.870¢ ||706.4935$||9||7||1.286||
|528.000¢ ||3||2||1.500||L/s = 3/2
|-
|-
| || || ||15\26|| || ||
| 29\50
|529.411¢ ||705.882$||4||3||1.333||
|527.272¢||8||5||1.600||
|-
|-
| || ||11\19|| || || ||
| 18\31
|528.000¢ ||704.000$||3||2||1.500||L/s = 3/2
|526.829¢||5||3||1.667||3/4 Meantone is in this region
|-
|-
| || || || || || ||51\88
| 25\43
|527.586¢ ||703.448$||14||9||1.556||
|526.316¢||7||4||1.750||
|-
|-
| || || || || ||40\69||
| 32\55
|527.4725¢ ||703.297$||11||7||1.571||
|526.028¢||9||5||1.800||
|-
|-
| || || || || || ||69\119
| 39\67
|527.3885¢||703.185$||19||12||1.583||
|525.843¢||11||6||1.833||
|-
|-
| || || || ||29\50|| ||
| 7\12
|527.272¢||703.030$||8||5||1.600||
|525.000¢||2||1||2.000||Basic 3/4 diatonic
|-
| || || || || || ||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¢||701.9355$||19||11||1.727||The normalized generator closest to 3/4 of a just [[3/2]] for EDSs less than 200
|-
| || || || ||25\43|| ||
|526.316¢||701.754$||7||4||1.750||
|-
| || || || || || ||57\98
|526.154¢||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$||11||5||2.200||
|524.138¢||11||5||2.200||
|-
| || || || || ||31\53||
|523.944¢||698.5915$||9||4||2.250
|-
| || || || || || ||55\94
|523.8095¢||698.413$||16||7||2.286||
|-
| || || || ||24\41|| ||
|523.636¢||698.182$||7||3||2.333||
|-
| || || || || || ||65\111
|523.490¢||697.987$||19||8||2.375||
|-
| || || || || ||41\70||
|523.404¢||697.872$||12||5||2.400||
|-
| || || || || || ||58\99
|523.308¢||697.744$||17||7||2.428||
|-
| || || ||17\29|| || ||
|523.077¢||697.436$||5||2||2.500||
|-
| || || || || || ||61\104
|522.857¢||697.142$||18||7||2.571||
|-
| || || || || ||44\75||
|522.772¢||697.030$||13||5||2.600||
|-
| || || || || || ||71\121
|522.699¢||696.9325$||21||8||2.625||Golden 3/4 neogothic
|-
|-
| || || || ||27\46|| ||
| 31\53
|522.581¢||696.774$||8||3||2.667||3/4 Neogothic is in this region
|523.944¢||9||4||2.250
|-
|-
| || || || || || ||64\109
| 24\41
|522.449¢||696.599$||19||7||2.714||
|523.636¢||7||3||2.333||
|-
|-
| || || || || ||37\63||
| 17\29
|522.352¢||696.4705$||11||4||2.750||
|523.077¢||5||2||2.500||
|-
|-
| || || || || || ||47\80
| 27\46
|522.222¢||696.296$||14||5||2.800||
|522.581¢||8||3||2.667||3/4 Neogothic is in this region
|-
|-
| || ||10\17|| || || ||
| 10\17
|521.739¢||695.652$||3||1||3.000||L/s = 3/1
|521.739¢||3||1||3.000||L/s = 3/1
|-
|-
| || || || || || ||43\73
| 13\22
|521.212¢||694.9495$||13||4||3.250||
|520.000¢||4||1||4.000||3/4 Archy is in this region
|-
|-
| || || || || ||33\56||
| 29\49
|521.053¢||694.737$||10||3||3.333||
|519.403¢||9||2||4.500||
|-
|-
| || || || || || ||56\95
| 16\27
|520.930¢||694.574$||17||5||3.400||
|518.919¢||5||1||5.000||
|-
|-
| || || || ||23\39|| ||
| 19\32
|520.755¢||694.340$||7||2||3.500||
|518.182¢||6||1||6.000||
|-
|-
| || || || || || ||59\100
| 22\37
|520.588¢||694.118$||18||5||3.600||
|517.647¢||7||1||7.000||
|-
|-
| || || || || ||36\61||
|3\5
|520.482¢||693.976$||11||3||3.667||
|514.286¢||1||0||→ inf||
|-
| || || || || || ||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
|-
| || || || || ||29\49||
|519.403¢||692.537$||9||2||4.500||
|-
| || || || ||16\27|| ||
|518.919¢||691.892$||5||1||5.000||
|-
| || || || || ||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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