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User:Overthink/Perfect fifth ranges: Difference between revisions

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Overthink (talk | contribs)
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Created page with low-to-medium precision
 
Overthink (talk | contribs)
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a few tables
 
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A table of the ranges of the perfect fifth.
A table of the ranges of the perfect fifth. Note that smaller EDOs within a precision may support temperaments corresponding to a range they are not a part of, such as 5edo technically being meantone or 53edo tempering out the garischisma.
{| class="wikitable"
{| class="wikitable"
|+
|+
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! Simple MOS
! Simple MOS
pattern ranges  
pattern ranges  
! Diatonic Range !! colspan="2" | Meantone/Superpyth !! colspan="2" | Near-pyth !! !! Pyth
! Diatonic Range !! colspan="2" | Meantone/Superpyth !! colspan="3" | Near-pyth
|-
|-
| colspan="2" rowspan="2" |Mavila
| colspan="2" rowspan="2" |Mavila
| rowspan="4" |M.
| rowspan="4" |M.
|Sub-flattone
| Sub-flattone<br>(4\7-15\26)
(4\7-15\26)
| rowspan="10" |P.
| rowspan="10" |P.
| rowspan="3" |Pythagorean
| rowspan="4" |Pythagorean<br>(7\12-24\41)
(7\12-24\41)
| Sub-schismic<br>(7\12-38\65)
|-
| Flattone<br>(15\26-11\19)
| Schismic<br>(38\65-31\53)
|-
| colspan="2" | 4\7 (685.714{{C}}) || Lower meantone (meanpop)<br>(11\19-18\31)
| Middle Pythagorean<br>(31\53-55\94)
|-
| rowspan="5" |Diatonic
| Meantone -><br>(4\7-7\12)
| Upper meantone (huygens)<br>(18\31-7\12)
| Garischismic<br>(55\94-24\41)
|-
| colspan="3" |7\12 (700{{C}})
| rowspan="3" |Argent<br>(24\41-17\29)
| rowspan="3" |IDK about subranges<br>here, but many useful<br>edos such as 99edo<br> and 140edo
|-
| colspan="3" | Near-Pythagorean
|-
| colspan="3" |10\17 (705.882{{C}})
|-
| Superpyth -><br>(10\17-3\5)
| rowspan="3" |S.
| Shrub region (quasisupra)<br>(10\17-13\22)
| rowspan="3" |Parapyth/gentle<br>(17\29-10\17)
| Lower gentle<br>(17\29-27\46)
|-
| colspan="2" | 3\5 (720{{C}}) || Superpyth<br>(13\22-16\27)
| Upper gentle<br>(27\46-47\80)
|-
| colspan="2" | Oneiro || Quasiultra/ultrapyth+<br>(16\27-3\5)
| Noble region<br>(47\80-10\17)
|}
{| class="wikitable"
|+Neogothic (loses accuracy beyond ~150)
|261
|278
|
|
|
|
|
|
|
|
|-
|232
|249
|
|
|
|
|
|
|
|
|
|
|-
|-
| Flattone
|203
(15\26-11\19)
|220
| ||
|
|
|
|
|
|
|
|
|-
|-
| colspan="2" | 4\7 (685.714{{C}}) || Lower meantone (meanpop)
|174
(11\19-18\31)
|191
| ||
|208
|
|
|
|
|
|
|
|-
|-
| rowspan="5" |Diatonic
|145
|Meantone ->
|162
|Upper meantone (huygens)
|179
(18\31-7\12)
|196
| rowspan="4" |Argent
|
(24\41-17\29)
|
|
|
|
|
|-
|116
|133
|150
|167
|184
|
|
|
|
|
|-
|87
|104
|121
|138
|155
|172
|
|
|
|
|-
|58
|75
|92
|109
|126
|143
|160
|177
|194b
|211b
|-
|29
|46
|63
|80
|97
|114
|131
|148
|165
|182b
|-
|(0)
|17
|34
|51
|68
|85
|102
|119
|136
|153b
|}
{| class="wikitable"
|+Argent
|205
|234
|263
|292
|
|
|
|
|-
|164
|193
|222
|251
|280
|
|
|
|
|
|-
|-
| colspan="3" |7\12 = 700 C
|123
|152
|181
|210
|239
|268
|
|
|
|
|-
|-
| colspan="3" | Near-Pythagorean || ||
|82
|111
|140
|169
|198
|227
|256
|285
|-
|-
| colspan="3" |10\17 = 705.882 C
|41
|70
|99
|128
|157
|186
|215
|244
|-
|(0)
|29
|58
|87
|116
|145
|174
|203
|}
{| class="wikitable"
|+
|205
|
|
|
|
|
|
|-
|-
|Superpyth ->
|164
| rowspan="3" |S.
|
|Shrub region (quasisupra)
|
(10\17-13\22)
|
| rowspan="3" |Parapyth
|
(17\29-10\17)
|-
|123
|
|
|
|
|
|
|-
|-
| colspan="2" | 3\5 (720{{C}}) || Superpyth
|82
(13\22-16\27)
|
| ||
|
|
|
|-
|-
| colspan="2" | Oneiro || Quasiultra/ultrapyth+
|41
(16\27-3\5)
|53
| ||
|65
|77
|89
|}
|}
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