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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
!L
!L
Line 99: Line 99:
!Comments
!Comments
|-
|-
|4\7|| || || || || ||
|4\7
|533.333¢ ||1||1||1.000||
|533.333¢ ||1||1||1.000||
|-
|-
| || || || || || ||27\47
| 27\47
|531.148¢ ||7||6||1.167||
|531.148¢ ||7||6||1.167||
|-
|-
| || || || || ||23\40||
| 23\40
|530.769¢ ||6||5||1.200||
|530.769¢ ||6||5||1.200||
|-
|-
|  ||  ||  ||  ||19\33||  ||
| 19\33
|530.232¢ ||5||4||1.250||
|530.232¢ ||5||4||1.250||
|-
|-
|  ||  ||  ||15\26||  ||  ||
| 15\26
|529.411¢ ||4||3||1.333||
|529.411¢ ||4||3||1.333||
|-
|-
|  ||  ||11\19||  ||  ||  ||
| 11\19
|528.000¢ ||3||2||1.500||L/s = 3/2
|528.000¢ ||3||2||1.500||L/s = 3/2
|-
|-
|  ||  ||  ||  ||  ||  ||51\88
| 29\50
|527.586¢ ||14||9||1.556||
|-
|  ||  ||  ||  ||  ||40\69||
|527.473¢ ||11||7||1.571||
|-
|  ||  ||  ||  ||  ||  ||69\119
|527.389¢||19||12||1.583||
|-
|  ||  ||  ||  ||29\50||  ||
|527.272¢||8||5||1.600||
|527.272¢||8||5||1.600||
|-
|-
|  ||  ||  ||  ||  ||  ||76\131
| 18\31
|527.168¢||21||13||1.615||Golden 3/4 meantone
|-
|  ||  ||  ||  ||  ||47\81||
|527.103¢||13||8||1.625||
|-
|  ||  ||  ||  ||  ||  ||65\112
|527.027¢||18||11||1.636||
|-
|  ||  ||  ||18\31||  ||  ||
|526.829¢||5||3||1.667||3/4 Meantone is in this region
|526.829¢||5||3||1.667||3/4 Meantone is in this region
|-
|-
|  ||  ||  ||  ||  ||  ||61\105
| 25\43
|526.619¢||17||10||1.700||
|-
|  ||  ||  ||  ||  ||43\74||
|526.531¢||12||7||1.714||
|-
|  ||  ||  ||  ||  ||  ||68\117
|526.452¢||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¢||7||4||1.750||
|526.316¢||7||4||1.750||
|-
|-
|  ||  ||  ||  ||  ||  ||57\98
| 32\55
|526.154¢||16||9||1.778||
|-
|  ||  ||  ||  ||  ||32\55||
|526.028¢||9||5||1.800||
|526.028¢||9||5||1.800||
|-
|-
|  ||  ||  ||  ||  ||  ||39\67
| 39\67
|525.843¢||11||6||1.833||
|525.843¢||11||6||1.833||
|-
|-
|  ||7\12||  ||  ||  ||  ||
| 7\12
|525.000¢||2||1||2.000||Basic 3/4 diatonic
|525.000¢||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¢||11||5||2.200||
|524.138¢||11||5||2.200||
|-
|-
|  ||  ||  ||  ||  ||31\53||
| 31\53
|523.944¢||9||4||2.250
|523.944¢||9||4||2.250
|-
|-
|  ||  ||  ||  ||24\41||  ||
| 24\41
|523.636¢||7||3||2.333||
|523.636¢||7||3||2.333||
|-
|-
|  ||  ||  ||17\29||  ||  ||
| 17\29
|523.077¢||5||2||2.500||
|523.077¢||5||2||2.500||
|-
|-
|  ||  ||  ||  ||  ||  ||61\104
| 27\46
|522.857¢||18||7||2.571||
|-
|  ||  ||  ||  ||  ||44\75||
|522.772¢||13||5||2.600||
|-
|  ||  ||  ||  ||  ||  ||71\121
|522.699¢||21||8||2.625||Golden 3/4 neogothic
|-
|  ||  ||  ||  ||27\46||  ||
|522.581¢||8||3||2.667||3/4 Neogothic is in this region
|522.581¢||8||3||2.667||3/4 Neogothic is in this region
|-
|-
|  ||  ||  ||  ||  ||  ||64\109
| 10\17
|522.449¢||19||7||2.714||
|-
|  ||  ||  ||  ||  ||37\63||
|522.352¢||11||4||2.750||
|-
|  ||  ||  ||  ||  ||  ||47\80
|522.222¢||14||5||2.800||
|-
|  ||  ||10\17||  ||  ||  ||
|521.739¢||3||1||3.000||L/s = 3/1
|521.739¢||3||1||3.000||L/s = 3/1
|-
|-
|  ||  ||  ||13\22||  ||  ||
| 13\22
|520.000¢||4||1||4.000||3/4 Archy is in this region
|520.000¢||4||1||4.000||3/4 Archy is in this region
|-
|-
|  ||  ||  ||  ||  ||29\49||
| 29\49
|519.403¢||9||2||4.500||
|519.403¢||9||2||4.500||
|-
|-
|  ||  ||  ||  ||16\27||  ||
| 16\27
|518.919¢||5||1||5.000||
|518.919¢||5||1||5.000||
|-
|-
|  ||  ||  ||  ||  ||19\32||
| 19\32
|518.182¢||6||1||6.000||
|518.182¢||6||1||6.000||
|-
|-
|  ||  ||  ||  ||  ||  ||22\37
| 22\37
|517.647¢||7||1||7.000||
|517.647¢||7||1||7.000||
|-
|-
|3\5||  ||  ||  ||  ||  ||
|3\5
|514.286¢||1||0||→ inf||
|514.286¢||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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