Xenharmonic Wiki

User:Moremajorthanmajor/5L 2s (5/3-equivalent): Difference between revisions

← Older editNewer edit →
VisualWikitext
m Fredg999 moved page 5L 2s (5/3-equivalent) to User:Moremajorthanmajor/5L 2s (5/3-equivalent) over redirect: Page not ready for the main namespace
No edit summary
Line 101: Line 101:
|3\5||
|3\5||
|}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"
{{Scale tree|5L 2s<5/3>}}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.
! colspan="7" |Generator
!Cents
!Śata
!L
!s
!L/s
!Comments
|-
|4\7|| || || || || ||
|533.333||711.111||1||1||1.000||
|-
| || || || || || ||27\47
|531.1475||708.196||7||6||1.167||
|-
| || || || || ||23\40||
|530.769||707.692||6||5||1.200||
|-
| || || || || || ||42\73
|530.526||707.368||11||9||1.222||
|-
| || || || ||19\33|| ||
|530.232||706.977||5||4||1.250||
|-
| || || || || || ||53\92
|530.000||706.667||14||11||1.273||
|-
| || || || || ||34\59||
|529.870||706.4935||9||7||1.286||
|-
| || || || || || ||49\85
|529.730||706.306||13||10||1.300||
|-
| || || ||15\26|| || ||
|529.411||705.882||4||3||1.333||
|-
| || || || || || ||56\97
|529.134||705.512||15||11||1.364||
|-
| || || || || ||41\71||
|529.032||705.376||11||8||1.375||
|-
| || || || || || ||67\116
|528.947||705.263||18||13||1.385||
|-
| || || || ||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||
|527.4725||703.297||11||7||1.571||
|-
| || || || || || ||69\119
|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||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||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)
|-
| || || || || || ||38\65
|524.138||698.851||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|| ||
|522.581||696.774||8||3||2.667||3/4 Neogothic is in this region
|-
| || || || || || ||64\109
|522.449||696.599||19||7||2.714||
|-
| || || || || ||37\63||
|522.352||696.4705||11||4||2.750||
|-
| || || || || || ||47\80
|522.222||696.296||14||5||2.800||
|-
| || ||10\17|| || || ||
|521.739||695.652||3||1||3.000||L/s = 3/1
|-
| || || || || || ||43\73
|521.212||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||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
|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 below 7\12 on this chart are called "negative tunings" and they include 3/4 Pythagorean tuning itself (well approximated by 31\53) as well as 3/4 superpyth tunings such as 10\17 and 13\22. As these tunings approach 3\5, the majors become sharper and the minors become flatter. Around 10\17 through 13\22, the thirds fall closer to 5-limit than 7-limit intervals: 6:5 as opposed to 7:6.
Tunings below 7\12 on this chart are called "negative tunings" and they include 3/4 Pythagorean tuning itself (well approximated by 31\53) as well as 3/4 superpyth tunings such as 10\17 and 13\22. As these tunings approach 3\5, the majors become sharper and the minors become flatter. Around 10\17 through 13\22, the thirds fall closer to 5-limit than 7-limit intervals: 6:5 as opposed to 7:6.
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/5L_2s_(5/3-equivalent)"