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3L 1s (3/2-equivalent): Difference between revisions

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CompactStar (talk | contribs)
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Superpyth is a 5-limit temperament completely different from the 2.3.7 subgroup Archy, I think the 64/63 temperament should be called Napoli-Archy
CompactStar (talk | contribs)
5,020 edits
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Line 2,973: Line 2,973:
   
   
The spectrum looks like this:
The spectrum looks like this:
{| class="wikitable"
{{Scale tree|Comments=3/2:Napoli-Meantone starts here;2/1:Napoli-Meantone ends, Napoli-Pythagorean begins;5/2:Napoli-Neogothic heartland is from here...;8/3:...to here;3/1:Napoli-Pythagorean ends, Napoli-Archy begins;5/1:Napoli-Archy ends}}
! colspan="3" rowspan="2" |Generator
(bright)
! colspan="2" |Cents
! rowspan="2" |L
! rowspan="2" |s
! rowspan="2" |L/s
! rowspan="2" | Comments
|-
!<u>Normalised<ref name=":03">Fractions repeating more than 4 digits written as continued fractions</ref></u>
!''ed7\12<ref name=":04">Fractions repeating more than 4 digits written as continued fractions</ref>''
|-
| 1\4
|
|
|<u>171; 2.{{Overline|3}}</u>
|''175''
|1
|1
|1.000
|Equalised
|-
|6\23
|
|
|<u>180</u>
|''182; 1, 1.{{Overline|5}}''
|6
|5
|1.200
|
|-
|
| 11\42
|
|<u>180; 1.21{{Overline|6}}</u>
|''183.{{Overline|3}}''
|11
|9
|1.222
|
|-
|5\19
|
|
|<u>181.{{Overline|81}}</u>
|''184; 4.75''
|5
|4
|1.250
|
|-
|
|14\53
|
|<u>182; 1, 1.5</u>
|''184; 1, 9.6''
|14
|11
|1.273
|
|-
|
|9\34
|
|<u>183; 19.{{Overline|6}}</u>
|''185; 3.4''
| 9
|7
|1.286
|
|-
|4\15
|
|
|<u>184; 1.625</u>
|''186.{{Overline|6}}''
|4
|3
|1.333
|
|-
|
|11\41
|
|<u>185, 1, 10.8{{Overline|3}}</u>
|''187; 1.{{Overline|24}}''
|11
| 8
|1.375
|
|-
|
|7\26
|
|<u>186.{{Overline|6}}</u>
|''188; 2.1{{Overline|6}}''
|7
|5
|1.400
|
|-
|
|10\37
|
|<u>187.5</u>
|''189.{{Overline|189}}''
|10
| 7
| 1.429
|
|-
|
|13\48
|
|<u>187; 1, 19.75</u>
|''189.58{{Overline|3}}''
|13
|9
|1.444
|
|-
|
|16\59
|
|<u>188; 4.25</u>
|''189; 1, 4.9''
|16
|11
|1.455
|
|-
| 3\11
|
|
|<u>189; 2.{{Overline|1}}</u>
|''190.{{Overline|90}}''
| 3
|2
|1.500
|Napoli-Meantone starts here
|-
|
|17\62
|
|<u>190; 1, 1.{{Overline|12}}</u>
|''191; 1, 14.5''
|17
|11
|1.545
|
|-
|
|14\51
|
|<u>190.{{Overline|90}}</u>
|''192; 8.375''
|14
| 9
| 1.556
|
|-
|
|11\40
|
|<u>191; 3, 2.{{Overline|3}}</u>
|''192.5''
|11
| 7
| 1.571
|
|-
|
|8\29
|
|<u>192</u>
|''193; 9.{{Overline|6}}''
| 8
| 5
|1.600
|
|-
|
|5\18
|
|<u>193; 1, 1, 4.{{Overline|6}}</u>
|''194.{{Overline|4}}''
|5
|3
|1.667
|
|-
|
|
|12\43
|<u>194.{{Overline|594}}</u>
|''195; 2.8{{Overline|6}}''
| 12
| 7
|1.714
|
|-
|
|7\25
|
|<u>195; 2.8{{Overline|6}}</u>
|''196''
|7
|4
|1.750
|
|-
|
|9\32
|
|<u>196.{{Overline|36}}</u>
|''196.875''
|9
|5
|1.800
|
|-
|
|11\39
|
|<u>197; 67</u>
|''197; 2, 3.4''
|11
| 6
|1.833
|
|-
|
|13\46
|
|<u>197; 2.{{Overline|135}}</u>
|''197; 1, 4.75''
| 13
| 7
| 1.857
|
|-
|
|15\53
|
|<u>197; 1, 2, 1, 1.{{Overline|54}}</u>
|''198; 8.8{{Overline|3}}''
|15
|8
|1.875
|
|-
|
| 17\60
|
|<u>198; 17.1{{Overline|6}}</u>
|''198.{{Overline|3}}''
|17
| 9
| 1.889
|
|-
|
|19\67
|
|<u>198: 3, 1, 28</u>
|''198, 1, 1.{{Overline|03}}''
|19
| 10
|1.900
|
|-
|
|21\74
|
|<u>198; 2.3{{Overline|518}}</u>
| ''198.{{Overline |''198.{{Overline|648}}''
|21
| 11
|1.909
|
|-
|
|23\81
|
|<u>198; 1, 3, 1.7</u>
|''198; 1, 3, 3.8''
|23
|12
| 1.917
|
|-
|
| 25\88
|
|<u>198; 1, 2, 12.25</u>
|''198.8{{Overline|63}}''
|25
| 13
|1.923
|
|-
|
|27\95
|
|<u>198; 1, 3.{{Overline|405}}</u>
|''198; 1.0{{Overline|5}}''
|27
|14
|1.929
|
|-
|
|29\102
|
|<u>198; 1, 1.1{{Overline|6}}</u>
|''199; 51''
|29
|15
|1.933
|
|-
|2\7
|
|
|<u>200</u>
|''200''
|2
|1
|2.000
| Napoli-Meantone ends, Napoli-Pythagorean begins
|-
|
|17\59
|
|<u>201.{{Overline|9801}}</u>
|''201; 1, 2.2{{Overline|7}}''
|17
|8
|2.125
|
|-
|
| 15\52
|
|<u>202; 4.0{{Overline|45}}</u>
|''201; 1.08{{Overline|3}}''
|15
|7
|2.143
|
|-
|
|13\45
|
|<u>202; 1, 1, 2.0{{Overline|6}}</u>
|''202.{{Overline|2}}''
|13
|6
|2.167
|
|-
|
|11\38
|
|<u>203; 13</u>
|''202; 1.58{{Overline|3}}''
|11
|5
|2.200
|
|-
|
|9\31
|
|<u>203; 1, 3.41{{Overline|6}}</u>
|''203; 4, 2.{{Overline|3}}''
|9
|4
| 2.250
|
|-
|
|7\24
|
|<u>204; 1. 7.2</u>
|''204.1{{Overline|6}}''
| 7
|3
|2.333
|
|-
|
|
|12\41
|<u>205; 1.4</u>
|''204; 1. 7.2''
|12
|5
|2.400
|
|-
|
|5\17
|
|<u>206; 1, 8.{{Overline|6}}</u>
|''205; 1.1{{Overline|3}}''
|5
|2
|2.500
|Napoli-Neogothic heartland is from here…
|-
|
|
|18\61
|<u>207; 1.{{Overline|4}}</u>
|''206; 1.{{Overline|259}}''
|18
|7
| 2.571
|
|-
|
|
|13\44
|<u>208</u>
|''206.{{Overline|81}}''
|13
| 5
| 2.600
|
|-
|
|8\27
|
|<u>208; 1.4375</u>
|''207.{{Overline|407}}''
| 8
|3
|2.667
|…to here
|-
|
|11\37
|
|<u>209; 1.{{Overline|90}}</u>
|''208.{{Overline|108}}''
|11
|4
| 2.750
|
|-
|
|14\47
|
|<u>210</u>
|''208; 1.958{{Overline|3}}''
| 14
| 5
|2.800
|
|-
|
|17\57
|
|<u>210; 3.2{{Overline|3}}</u>
|''208; 1.29{{Overline|54}}''
|17
|6
|2.833
|
|-
|
| 20\67
|
|<u>210; 1.9</u>
|''208; 1, 21.{{Overline|3}}''
| 20
|7
|2.857
|
|-
|
| 23\77
|
|<u>210; 1.4{{Overline|5}}</u>
|''209.{{Overline|09}}''
|23
|8
|2.875
|
|-
|3\10
|
|
|<u>211; 1, 3.25</u>
|''210''
|3
| 1
|3.000
|Napoli-Pythagorean ends, Napoli-Archy begins
|-
|
|22\73
|
|<u>212; 1, 9.{{Overline|3}}</u>
|''210; 1, 23.{{Overline|3}}''
|22
|7
|3.143
|
|-
|
|19\63
|
|<u>213; 11.{{Overline|8}}</u>
|''211.{{Overline|1}}''
|19
|6
|3.167
|
|-
|
|16\53
|
|<u>213.{{Overline|3}}</u>
|''211; 3, 8.5''
|16
|5
|3.200
|
|-
|
|13\43
|
|<u>213; 1, 2.3{{Overline|18}}</u>
|''211; 1.{{Overline|592}}''
|13
|4
|3.250
|
|-
|
| 10\33
|
|<u>214; 3.5</u>
|''212.{{Overline|12}}''
|10
|3
|3.333
|
|-
|
|7\23
|
|<u>215; 2.6</u>
|''213; 23''
|7
|2
|3.500
|
|-
|
|11\36
|
|<u>216; 2.541{{Overline|6}}</u>
|''213.{{Overline|3}}''
| 11
|3
|3.667
|
|-
|
|15\49
|
|<u>216; 1.152{{Overline|7}}</u>
|''214; 3.5''
|15
|4
|3.750
|
|-
|
|19\62
|
|<u>217; 7</u>
|''214; 1.9375''
|19
|5
|3.800
|
|-
|4\13
|
|
|<u>218.{{Overline|18}}</u>
|''215; 2.6''
|4
|1
|4.000
|
|-
|
|13\42
|
|<u>219; 1, 2.55</u>
|''216.{{Overline|6}}''
|13
|3
|4.333
|
|-
|
|9\29
|
|<u>220; 2.45</u>
|''217; 4, 7''
|9
|2
|4.500
|
|-
|
|14\45
|
|<u>221; 19</u>
|''217.{{Overline|7}}''
|14
| 3
| 4.667
|
|-
|5\16
|
|
|<u>222.{{Overline|2}}</u>
|''218.75''
|5
| 1
|5.000
|Napoli-Archy ends
|-
|
|16\51
|
|<u>223; 3.{{Overline|90}}</u>
|''219; 1, 1.55''
|16
|3
|5.333
|
|-
|
|11\35
|
|<u>223; 1, 2.6875</u>
|''220''
|11
|2
|5.500
|
|-
|
|17\54
|
|<u>224; 5.7{{Overline|2}}</u>
|''220.{{Overline|370}}''
| 17
| 3
|5.667
|
|-
|6\19
|
|
|<u>225</u>
|''221; 19''
|6
|1
|6.000
|
|-
|1\3
|
|
|<u>240</u>
|''233.{{Overline|3}}''
|1
|0
|→ inf
|Paucitonic
|}
Retrieved from "https://en.xen.wiki/w/3L_1s_(3/2-equivalent)"